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History of the inductive sciences, from the earliest to the present time Flashcards

William Whewell · Public domain edition · 443 cards · 117 chapters

William Whewell’s History of the Inductive Sciences traces the development of scientific disciplines and argues that science arises from the union of observed facts with governing ideas. This deck covers his organizing plan, definitions of induction, treatment of logic, and index conventions for figures such as Bacon, Galileo, and the Bernoullis.

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Chapter 1 · Question

What plan does Whewell say the work follows for organizing each science's history?

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Section 14 cards

What plan does Whewell say the work follows for organizing each science's history?
Whewell says the history of each science is thrown into EPOCHS at which some great and cardinal discovery was made, with subordinate events arranged as PRELUDES and SEQUELS of those Epochs. He argues this plan conveniently and fairly exhibits the progress of scientific truth and makes the reader's view clearer and more comprehensive.
Chapter 1
What does Whewell say his work aims to be, beyond narrating facts?
Whewell states the work aimed at being not merely a narration of the facts in the history of Science, but a basis for the Philosophy of Science. He argues that study of the modes of discovering truth ought to be based on a survey of the truths already discovered, a maxim he says is self-evident yet rarely acted on.
Chapter 1
According to Whewell, what is wrong with most existing treatises on Logic?
Whewell argues that those who discourse on the nature of Truth and its discovery commonly make for themselves examples of truths that are for the most part utterly frivolous and unsubstantial, as in most Treatises on Logic. Alternatively they dig up the narrow and special field of mathematical truth, which cannot by itself exemplify the general mode of discovery.
Chapter 1
Where does Whewell reserve discussions of Ideas such as Matter, Force, and Atoms?
Whewell says discussions concerning the nature and necessary attributes of Matter, of Force, of Atoms, of Mediums, of Kinds, and of Organization have an important place in the history of Natural Science. Yet he reserves their account and consequent controversies for the other work, the Philosophy of the Inductive Sciences, since that history naturally belongs to the Philosophy of Science.
Chapter 1

Section 24 cards

What does the index entry for Francis Bacon list?
The entry for Francis Bacon lists page references under two markers: _a._ 278, 383, 412, and _b._ 25, 32, 165. The chapter is an index of names, so it records where Bacon is mentioned rather than describing his work. The two sets of numbers, marked _a._ and _b._, appear to distinguish different volumes or sections of the work.
Chapter 2
How does the index distinguish the two Bernoulli brothers named John?
The index lists John Bernoulli with references _a._ 359, 361, 363, 366, 375, 393, 430 and _b._ 32. A separate entry, John Bernoulli the younger, carries only _b._ 32. The same pattern distinguishes James Bernoulli (_a._ 358) from James Bernoulli the younger (_b._ 42). The qualifier "the younger" separates the generations.
Chapter 2
What page references does the index give for Galileo?
The Galileo entry reads _a._ 276, 319, 322, 324, &c., 336, 342, 345. The "&c." signals that the list continues beyond the pages shown. All references fall under the _a._ marker, with none under _b._ The entry thus points to a run of pages rather than a few scattered mentions.
Chapter 2
How are entries for the Herschels and Babbage presented?
Sir John Herschel appears with _a._ 467 and _b._ 67, 81, 254, 333, 555, 559. Sir William Herschel has _a._ 446 and _b._ 80. Babbage, Mr. is listed with _b._ 254, 555. Each entry pairs a name with page numbers under the _a._ and _b._ markers, following the index's uniform format.
Chapter 2

Section 34 cards

According to Whewell, what two elements are required to form science?
Whewell states that two things are requisite to the formation of science: Facts and Ideas—observation of things without, and an inward effort of thought, or Sense and Reason. Neither element by itself, he argues, can constitute substantial general knowledge.
Chapter 3
How does Whewell define Induction in this introduction?
Whewell defines Induction as the process of collecting general truths from the examination of particular facts, and says it is by this process that the physical sciences have been formed. He defers a fuller explanation of how inductive science differs from other knowledge to his separate work on the philosophy of inductive sciences.
Chapter 3
What does Whewell say the completeness of a historical view consists in?
The author argues that completeness in a historical view does not consist in accumulating all the details of each science's cultivation, but in marking the larger features of its formation. The historian should point out how important advances were made, and when and by whom each valuable truth was obtained.
Chapter 3
What does Whewell say a history of inductive science should provide for the future?
Whewell argues such a history should offer a philosophical distribution of existing knowledge and indicate the most promising mode of directing future efforts to extend it. He says this aim is not abandoned but reserved for a separate treatise, On the Philosophy of the Inductive Sciences.
Chapter 3

Section 44 cards

What does Whewell compare an Inductive Table of a science to?
Whewell compares it to a map of a river: waters from separate sources unite into rivulets, which join other rivulets and form trunks of higher and higher order. Each general truth contains the particular truths from which it was derived, so the table exhibits all principal doctrines and gives the most advanced generalization its proper place and evidence of validity.
Chapter 4
What is deduction, and when does Whewell say it has no value?
Deduction is drawing conclusions from principles by rigorous, unimpeachable trains of demonstration. Whewell says it is a highly important part of every science in its due place, but has no value when the fundamental principles have not first been obtained by induction of facts. Without such materials, demonstrations resemble physical science only as a shadow resembles a real object.
Chapter 4
How do scientific Ideas differ from common Notions, according to Whewell?
Whewell says both are acquired by the mind connecting external impressions and both may be used in reasoning, but scientific Ideas are precise and stable, held with clear insight and used in a rigorously limited, identical sense. Common Notions are vague and variable, grown from many dim suggestions whose obscurity hangs about all their applications. Reasoning by definitions from common Notions leads to empty forms or confusion.
Chapter 4
What is a School Philosophy, and which two periods does Whewell name?
A School Philosophy arises when thinkers attend not to external objects but to speculations previously delivered, seeking to interpret man's mind rather than nature; the Masters' opinions are the facts disciples reduce to unity or follow into consequences. Whewell names the Greeks and the Middle Ages as the two great periods, calling them the first waking of science and its midday slumber.
Chapter 4

Section 54 cards

How did Herodotus explain the Nile's summer flooding?
Herodotus claimed the sun draws water to itself; in summer it traverses upper Libya and draws up the Nile's water, which winds disperse as moisture. In winter the sun returns north and still draws the Nile, but its supplies are shut up, so the Nile alone is lower in winter than summer. Whewell notes this ascribes the inequality to the sun's influence on springs alone.
Chapter 5
What fundamental mistake does Whewell attribute to Greek physical philosophy?
The author argues the Greeks made abstractions vague and then refined them by reflection on language alone rather than by observation of facts. They analyzed and expanded common conceptions instead of reforming and fixing them through observation, selecting notions arbitrarily. Whewell says they should have derived clear ideas inductively from things, but instead deduced results from familiar conceptions.
Chapter 5
What example shows Aristotle starting from common language?
Discussing whether a void exists, Aristotle first asks in how many senses we say one thing is in another: the part in the whole, the species in the genus, the government of Greece in the king, and a thing in a vessel, which he calls most proper. He concludes a body is in place if another body includes it, then defines void as place without matter.
Chapter 5
What was the Greek doctrine of contrarieties?
Whewell describes it as assuming that adjectives or substantives opposed in common language, or in some abstract conception, must point to a fundamental antithesis in nature worth studying. He cites Aristotle reporting that the Pythagoreans drew contraries from this principle. It was one of the widely applied modes of reasoning in Greek physical philosophy.
Chapter 5

Section 64 cards

Which four elementary qualities does Aristotle retain, and why reject the others?
Aristotle considers only contrarieties of quality relating to touch, rejecting black/white and sweet/bitter as non-tangible. Of the tangible pairs—hot/cold, dry/wet, heavy/light, hard/soft, and others—he rejects heavy/light because they are not active and passive qualities, and the rest because they are combinations of the first four, which he infers to be the four elementary qualities.
Chapter 6
How does Aristotle combine the four qualities into the four elements?
Of the six possible pairings of four qualities, pairings of opposites like hot and cold are rejected, leaving four elementary combinations matching the four apparently elementary bodies: fire is hot and dry, air is hot and wet (since steam is air), water is cold and wet, and earth is cold and dry.
Chapter 6
What error does Whewell say underlies Aristotle's doctrine of absolute light and heavy?
Whewell argues the errors have a verbal origin: treating light as the opposite of heavy, and treating levity as a quality of a body rather than the effect of surrounding bodies. Things that rise by lightness do so only because heavier surrounding bodies press them upward, so the assumption of absolute levity is gratuitous or merely nominal and vitiates the reasoning.
Chapter 6
How does Aristotle explain a thrown stone continuing to move before stopping?
Aristotle holds that a motion is communicated to the air, whose successive parts urge the stone onward; each part of the medium keeps acting for a while after being acted on, and the motion ceases when it reaches a particle that cannot act after it has ceased to be acted on. Whewell notes the difficulty arises from ascribing retardation to the body rather than surrounding resistances.
Chapter 6

Section 74 cards

What was Anaxagoras's Homoiomeria, opposed to atomism?
Anaxagoras held that material things consist of particles homogeneous within each kind of body but various across different kinds—for example, since food increases flesh, blood, and bone, he held that food contains particles of flesh, blood, and bone. Whewell says this tenet may be considered a dim glimpse of the idea of chemical analysis, while atomism points toward modern corpuscular theories.
Chapter 7
What did the Stoics mean by λόγοι σπερματικοί?
The Stoics, inclined especially at a later period toward materialist views, asserted that matter contains in itself tendencies or dispositions to certain forms. These dispositions they called λόγοι σπερματικοί, rendered as seminal proportions or seminal reasons. Whewell groups this among the technical modes of speaking the Stoics used on such physical subjects.
Chapter 7
Why did Whewell say Greek physical philosophy failed?
Whewell argues the failure was not neglect of facts: the Greeks recognized experience, collected particulars, and sought general principles by induction. Rather, sound notions were quenched and overlaid by trifling, barren speculations and by love of subtilizing and commenting on earlier writers instead of interpreting nature. Technical terms gave fixity to sect dogmas but led to no progress.
Chapter 7
How does Whewell assess Aristotle's physical Problems?
Whewell says that in scarcely any instance are Aristotle's answers to his physical questions of any value; he propounds them with hesitation or vacillation showing absence of scientific distinctness, and they involve no settled general principle. Examples include the lever, the wedge, and the sling. Whewell concludes Aristotelian physics was a complete failure, collecting no general laws from facts.
Chapter 7

Section 83 cards

How does Whewell explain the round image formed by sunlight through a hole?
Whewell explains it by conceiving light as straight rays from every point of the sun's disk passing through every point of the hole. Each point of the hole becomes the vertex of a double cone of rays with the sun's disk as base. The image is determined by a series of equal bright circles along the hole's boundary; these circles grow larger with distance while the central image of the hole stays the original size, so at a considerable distance the hole's form is nearly obliterated and the image is nearly a perfect circle.
Chapter 8
Why does Whewell say Aristotle failed to create a science of mechanics?
Whewell argues Aristotle failed because he did not refer mechanical facts to the appropriate Idea, namely Force, the cause of motion. Instead he used relations of space, properties of circles, proportions of velocities, and notions of natural and unnatural motion. In his Mechanical Problems he even claims the circle contains the principle of the cause. Whewell says such loose notions made a true perception of mechanical properties impossible, though he notes this example shows indistinct rather than inappropriate ideas.
Chapter 8
What does Whewell mean by an 'appropriate Idea,' and why does it matter?
Whewell uses 'appropriate' as a technical term for the Idea, drawn from a series such as Space, Time, Number, Cause, Likeness, and Substance, that suits a given class of facts and brings their laws into view. He argues the Idea must be distinctly possessed and homogeneous with the facts. He states that an error in the Ideas is as fatal to discovering truth as an error in the Facts, and may equally impede the progress of knowledge.
Chapter 8

Section 93 cards

What did Archimedes contribute to hydrostatics according to Whewell?
Whewell states Archimedes solved the principal problem of hydrostatics: the conditions of floating bodies. His principles went unpursued until the revival of modern science, and the main proposition was later called the hydrostatic paradox because it was not obvious. The doctrine rests on the Idea of Pressure plus a distinct Idea of a Fluid.
Chapter 9
How does Whewell define the Idea of Fluidity?
Whewell defines a fluid as a body whose parts are perfectly movable among each other by the slightest partial pressure, and in which all pressure exerted on one part is transferred to all other parts. From this idea necessarily follows the multiplication of pressure constituting the hydrostatic paradox. This notion is expressed in the postulate heading Archimedes' Treatise on Floating Bodies.
Chapter 9
What was Euclid's and the Platonists' error about vision?
Whewell reports that Euclid and the Platonists maintained vision is exercised by rays proceeding from the eye, not to it, so we learn objects' forms as a blind man feels with his staff. Whewell notes Montucla speaks severely of this mistake, but argues it was neither very discreditable nor very injurious, since the mathematical conclusions are necessarily the same on either supposition.
Chapter 9

Section 104 cards

Why did Plato's Timaeus fail as a theory of the universe, according to the chapter?
The author argues the Timaeus failed because it assumed that the reason why everything is as it is must be that so it is best, according to some human view of better or worse. Socrates in the Phaedo says he turned from Anaxagoras for lacking such reasons, and the Timaeus attempts to supply them. The author calls it a noble and instructive failure.
Chapter 10
Why could early astronomy become a science before other fields?
The chapter gives two reasons. First, the familiar act of thought that unifies impressions into notions like Month, Year, or Sky is itself an inductive act, sharing the nature of all scientific processes. Second, the ideas appropriate to this induction—Space and Figure, Time and Number, Motion and Recurrence—are very clear and definite even in the least cultivated minds.
Chapter 10
Why is the notion of a Year harder to form than that of a Day?
The chapter states that the recurrence of similar circumstances at equal intervals is less manifest for the year, and the longer intervals require some exertion of memory for the recurrence to be perceived. A child might be persuaded that successive years were unequal, or even that one year was two, whereas such deception about the day would require artifice beyond mere words.
Chapter 10
What did nations need before they could fix the year at 365 days?
The chapter says fixing the year at a set number of days requires a system of numeral terms and practical methods of numeration. Peoples like the South American Indians, Koussa Caffres, Hottentots, and New Holland natives, said to reckon no further than fingers and toes, could not include 365 days in their notion of a year.
Chapter 10

Section 114 cards

Why did the Greeks consider a correct system of intercalation a religious duty?
The Greeks adopted a calendar of alternating 29- and 30-day months and treated its days as representing the moon's changes. Their festivals and sacrifices were thought necessarily tied to the sun's and moon's cycles; Geminus says laws and oracles required observing months, days, and years in sacrifices. Under this persuasion, correct intercalation became a religious obligation.
Chapter 11
What was the Octaëteris, and how did it fall short?
The Octaëteris was an 8-year cycle: 8 years of 354 days plus 3 intercalary months of 30 days, totaling 2922 days in 99 lunations, matching 8 years of 365¼ days. Custom added a thirteenth month in the 3rd, 5th, and 8th years. It was imperfect: 99 lunations are nearer 2923½ days, so 16 years fell 3 days short of the moon.
Chapter 11
What was Meton's 19-year cycle and why is it significant?
Meton introduced, in 432 B.C., a 19-year cycle in which 19 years and 235 lunations are nearly equal (6940 days). It required 125 full months of 30 days and 110 hollow months of 29, with seven years of 13 months. The author notes it is so exact it is still used to calculate the new moon for Easter, and its Golden Number names the cycle's year.
Chapter 11
How did Calippus correct Meton's cycle?
Calippus corrected Meton's cycle about a hundred years later, in 330 B.C., after detecting its error by observing a lunar eclipse six years before Alexander's death. His period took four 19-year cycles (76 years) and dropped one day at the end, allowing for the hours by which 6940 days exceed both 19 years and 235 lunations. Ptolemy's Almagest uses it for eclipse observations.
Chapter 11

Section 123 cards

According to the chapter, what is the basis of astronomy regarding the sun's motion?
The chapter states that the notion that the sun moves round among the stars in a year is the basis of astronomy, and that a considerable part of the science is only the development and particularization of this general conception. It explains that the sun's brightness hides the stars on his side of the heavens, so as he moves through the circuit of stars in a year, every part of the starry sphere is presented in succession as the nocturnal sky.
Chapter 12
Who does Pliny credit with first pointing out the obliquity of the sun's path?
Pliny states that Anaximander, a scholar of Thales, was the first person who pointed out the obliquity of the circle of the signs relative to the circles in which the stars move about the poles, and thus, as Pliny says, 'opened the gate of nature.' The chapter notes, however, that Plutarch attributes this discovery to Pythagoras, and that it is difficult to conceive the Egyptians and Chaldeans had not already advanced so far.
Chapter 12
How did Aristotle argue for the earth's spherical form from lunar eclipses?
Aristotle argued that in the configurations during the month the moon's deficient part takes various shapes—straight, concave, and convex—but in eclipses the line of division is always convex. Since the moon is eclipsed by the interposition of the earth, the earth's periphery must cause this by having a spherical form. He also cited the changed horizon and stars visible in Egypt versus northern regions as evidence the earth is round and not large.
Chapter 12

Section 134 cards

What astronomical theory marks the inductive epoch of Hipparchus?
The Theory of Epicycles and Eccentrics. Whewell presents it as the next great discovery making an epoch in astronomy, and notes that before its establishment there were conjectures and a growing acquaintance with facts that made such an explanation felt to be needed.
Chapter 13
How did the Greeks explain a planet's retrograde and stationary motion?
By supposing the planet sits in the rim of a wheel turned edgeways to us, whose centre moves from west to east while the wheel rotates about its own centre. The wheel's rotation can counterbalance the general motion, making the planet appear retrograde, then stationary, while overall westerly motion prevails. Such wheels were called epicycles.
Chapter 13
What lunar period did the Chaldeans use for eclipses, and what does it contain?
A period of about eighteen years, or 6585⅓ days, containing 223 lunations, 239 revolutions of anomaly, and 241 revolutions with regard to one of the Nodes. This brings about a succession of the same lunar eclipses. Whewell notes Delambre probably rightly attributes measurement of the moon's variation to the Greeks.
Chapter 13
What problem did Plato pose to astronomers, and why did it cause trouble?
To reconcile the celestial phenomena by the combination of equable circular motions. Whewell argues that requiring equable as well as circular motion was inconsistent with nature, and that adherence to it introduced endless complexity. He calls this a marked instance of the love of simplicity and symmetry that sources general truths yet often perpetuates error.
Chapter 13

Section 144 cards

How did Hipparchus represent the moon's anomaly in longitude?
Hipparchus determined the moon's mean equable motions in longitude and latitude more accurately than earlier astronomers, then represented the anomaly of the motion in longitude by means of an eccentric, in the same manner as he had done for the sun. Ptolemy later used an epicycle for the moon's first inequality, but Hipparchus employed an eccentric.
Chapter 14
What did the moon's moving apogee require astronomers to determine?
The moon's apogee was found to move among the stars, unlike the sun's. Since 6585⅓ days contain 241 revolutions relative to the stars but only 239 relative to the anomaly, the eccentric itself was supposed to have angular motion carrying its apogee in the moon's direction. Tables then required the eccentricity, the apogee's place at a given time, and its rate of motion.
Chapter 14
What data did Hipparchus use to derive his lunar conclusions?
Hipparchus deduced all his conclusions from six eclipses of the moon. Three, recorded at Babylon in the 366th and 367th years from the era of Nabonassar, let him determine the eccentricity and apogee of the moon's orbit at that time. Three observed at Alexandria in the 547th year gave another position 180 years later, revealing the orbit's motion as well as its form.
Chapter 14
Why were Hipparchus's lunar tables fairly accurate for eclipses?
The moon's motions are affected by several other considerable inequalities beyond those Hipparchus considered, but his lunar paths were still considerably correct, especially for calculating eclipses. The greatest of the additional irregularities disappear at new and full moon, which are the only times when eclipses take place, so the tables' main application was largely unaffected by the omitted terms.
Chapter 14

Section 153 cards

What two major discoveries does Whewell credit to Hipparchus's inductive epoch?
Whewell identifies the construction of Solar and Lunar Tables and the discovery of Precession as the two great advances. The first revealed constant law and order amid apparent disorder; the second showed perpetual mutation where all had seemed fixed. Together they prompted new, more exact methods of observation and led, as Whewell says such epochs must, to a period of development, verification, application, and extension.
Chapter 15
Why did Hipparchus construct a catalogue of 1080 stars?
After discovering precession, the question arose whether the so-called fixed stars really keep constant relative positions. Hipparchus therefore made a star map, recording positions by alineations—three or more stars touchable by an apparent straight line. Ptolemy later quoted these configurations to show the stars had not moved. Pliny attributes the undertaking to the appearance of a new star, though Ptolemy does not mention this story.
Chapter 15
How did Hipparchus and later astronomers treat the equality of days?
The equality of days was harder to establish than that of years, since days could only be subdivided by artificial means and ancient instruments lacked precision. Astronomers assumed the apparent revolution of the stars was accurately uniform, and from this it followed that solar days would be unequal because of the sun's unequal motion—giving rise to the Equation of Time. Thus they effectively assumed the equality of sidereal days.
Chapter 15

Section 162 cards

How did Eratosthenes estimate the earth's circumference?
Syene lay on the tropic, where at the solstice noon objects cast no shadow and a well was fully lit. At Alexandria the same day the sun was a fiftieth of the circumference from the zenith. The cities were north-south, 5000 stadia apart by royal road-measure, giving a circumference of 250,000 stadia and a radius of about 40,000.
Chapter 16
What did the Arabian astronomers under Caliph Almamon measure?
On the plain of Singiar in Mesopotamia they split into two bands, one going north under Chalid ben Abdolmalic, one south under Alis ben Isa, measuring distance by rods on the ground until each was one degree from the start. The degrees came out as 56 and 56 two-thirds miles, the mile being 4000 black cubits of 27 inches.
Chapter 16

Section 174 cards

How did Ptolemy account for planetary motions, and what role did the equant play?
Ptolemy treated planetary motions as independent of the sun and referred them to the earth alone, so the apparent eccentricities he explained combined the earth's orbital eccentricity with each planet's own. He used an eccentric deferent carrying an epicycle, with motion in the deferent uniform not about the circle's centre but about another point, the equant. Using his own and older observations, he determined the orbits' dimensions and positions.
Chapter 17
What did Albategnius discover about the sun's apogee, and why did Delambre doubt him?
Albategnius found the sun's apogee at longitude 82 degrees, whereas Ptolemy had placed it at 65 degrees. The 17-degree difference exceeded probable calculation error, making motion of the apogee the obvious inference. Delambre doubted or downplayed his claim because Albategnius never expressly stated the discovery, but Whewell argues we cannot agree with that doubt.
Chapter 17
What was the Trepidation of the fixed stars, and who proposed it?
Arzachel, in the 11th century, found the sun's apogee less advanced than Albategnius had, and inferred it had receded. In fact Albategnius's less trustworthy method had erred. From this, Arzachel conceived two circles of about eight degrees radius around the equinoctial points, whose first points of Aries and Libra traverse them in about 800 years, producing alternating progression and regression and changing star latitudes. Whewell calls it entirely visionary; it was adopted in the first Alphonsine Tables, then rejected.
Chapter 17
Who discovered the moon's third inequality, the Variation, and what is it?
Whewell reports that M. Sedillot recently pointed out that Mohammed-Aboul Wefa-al-Bouzdjani, a tenth-century Arabian astronomer at Cairo who observed at Bagdad in 975, discovered a third lunar inequality beyond Ptolemy's Equation of the Centre and Evection. The Variation, usually credited to Tycho Brahe six centuries later, makes the moon quickest at new or full and slowest at the quarters, with greatest effect in the octants.
Chapter 17

Section 183 cards

Why does Whewell consider collections of philosophers' opinions harmful to science?
The author argues that mere collections of opinions, such as Plutarch's or Diogenes Laërtius's, indicate a loose and inadequate grasp of physical philosophy. Physical doctrines are proved only by applying general theory to particular cases, not by the authority of great men, and technical terms are poorly understood by ordinary readers. Dwelling on verbal statements of what has been said, he says, is fatal to firm and clear thought.
Chapter 18
Why did Pappus fail to solve the inclined plane problem?
Whewell says Pappus's problem was wrongly posed, lacking a clear measure of powers and ignoring speed and surface. Pappus assumed a sphere on the plane acted like a weight on a horizontal lever with the fulcrum at the contact point. This showed no distinct ideas of force and pressure; he merely tried a geometrical conjecture that matched the limiting cases.
Chapter 18
Why did Pliny's remora fish story reveal unclear mechanical ideas?
Whewell says anyone with a distinct idea of mechanical action would reject the tale that a small fish could stop a large ship by adhering to it. Pliny relates it gravely and moralizes on human vanity. Whewell notes that a little clear thinking would show the ship and rowers pull the fish through the oars' hold on the water, so the fish could not resist without an equally strong hold on something external.
Chapter 18

Section 194 cards

How did Cosmas Indicopleustes describe the earth and heavens?
Cosmas described the earth as an oblong floor surrounded by upright walls and covered by a vault, below which the heavenly bodies revolve around a high northern mountain that intercepts the sun's light to make night. Whewell says the distinctness of his pictures only shows his lack of clear conception of what suppositions would explain the phenomena.
Chapter 19
Why did Augustine deny inhabitants on the opposite side of the earth?
Augustine did not deny the globular form of the earth, but asserted there are no inhabitants on the opposite side because Scripture records no such race among the descendants of Adam. Whewell notes similar reasoning operated in the case of Virgil, Bishop of Salzburg, though the story of his deposition is false.
Chapter 19
What did Boethius, Bede, and Gerbert contribute regarding the earth's figure?
Boethius in the sixth century urged the smallness of the globe compared with the heavens as a reason to repress love of glory; Bede assented to this doctrine and knew Ptolemy and his commentators. Gerbert, in the tenth century, studied astronomy with the Arabians in Spain, surpassed his masters, reportedly made clocks and an astrolabe, and became Pope Sylvester II.
Chapter 19
What does Montucla say about monks preserving ancient science?
Montucla says it is impossible not to reflect that all those men who at least transmitted the sciences were monks or had been such; convents were the asylum of sciences and letters in stormy ages. Without them, transcribing and studying ancient works, those works would have perished and the thread connecting us with Greeks and Romans would have snapped.
Chapter 19

Section 204 cards

How does Whewell characterize Alexander Aphrodisiensis as a commentator?
The author reports that a recent editor of Aristotle called Alexander "sometimes useful," but criticized his prolixity, his perverse itch to discuss the argument himself, defend his own opinions, and refute or reconcile others—so that he rather obscures than enlightens. Alexander lived at the end of the second century and belonged to the more servile class of commentators who followed Aristotle step by step.
Chapter 20
What futile task does Whewell attribute to Simplicius and many Alexandrian philosophers?
The author states that Simplicius, Alexander, Ammonius, and a great number of Alexandrian philosophers employed themselves in the futile task of reconciling the doctrines of the Pythagoreans, the Eleatics, Plato, and the Stoics with those of Aristotle. Boethius planned a similar project—translating all of Aristotle's and Plato's works into Latin and showing their agreement—a gigantic plan he never executed.
Chapter 20
Why does Whewell argue the Arabians produced no great scientific names or discoveries?
The author argues the Arabians were not prepared to use the Greek treasures: their imagination was awakened by indigenous poetry but their rational powers remained torpid, and they lacked the gradations of curiosity and research, plus the political freedom and mental activity of a small city, that had educated the Greeks. Thus they merely translated Greek philosophy, became Aristotelians, and swelled the herd of commentators.
Chapter 20
Why was Averroes called "the Commentator" and how did the schoolmen regard him?
Averroes of Cordova, the most illustrious Spanish Aristotelian, became the guide of the schoolmen, who placed him on a level with Aristotle or above him. The author says he deserves the title "the Commentator" by the servility with which he maintained that Aristotle carried the sciences to the highest possible degree and fixed their permanent boundaries. He translated Aristotle from a Syriac version, not reading Greek.
Chapter 20

Section 214 cards

What did Plotinus give as his reason for denying that distance makes objects appear smaller?
Plotinus denied that smaller visual angles explain why distant objects look smaller. He argued that if this were so, the heaven could not appear smaller than it is, since it occupies the whole visual angle. Saint-Hilaire cites this extract to show that the Alexandrian school was incapable of treating scientific questions properly.
Chapter 21
What was Mystical Arithmetic, and why did number tempt such speculation?
Mystical Arithmetic tried to link external objects through vague notions of goodness, perfection, and relation to the divine, instead of distinct, verifiable ideas. Number tempted men most because it applies to moral and emotional matters as well as material things, and the discovery of musical concords suggested numerical relations might underlie the whole universe of matter and thought.
Chapter 21
Which regular solids did Plato assign to the four elements, and why?
Plato gave each element a regular solid: fire got pyramids because they are sharp and tend upward; earth got cubes because they are stable and fill space; air got octahedra as most resembling fire; water got the icositetrahedron as most nearly spherical. The dodecahedron was the figure of the heavenly element, shown in the twelve zodiac signs.
Chapter 21
What arguments did Cicero and Pliny use against astrology?
Cicero argued that people born at the same time have different fortunes and characters, that predictions for Pompey, Crassus, and Caesar failed, and that the planets are so remote compared with the moon that no contagion could reach us. Pliny cited Homer's Hector and Polydamus, born the same night with different fortunes, and noted lords and slaves born every hour.
Chapter 21

Section 224 cards

What powers did alchemists attribute to the philosophers' stone beyond transmuting metals?
The same preparation believed to turn base metals into gold was also imagined as a universal medicine: able to cure or prevent diseases, prolong life, and produce bodily strength and beauty. The philosophers' stone was thus invested with every desirable efficacy the fancy of the 'philosophers' could devise, an exaggeration of the vague notion of perfection and power in the object of the alchemist's search.
Chapter 22
What claim does Whewell examine about Alchemy being the mother of Chemistry?
It has been usual to say Alchemy was the mother of Chemistry, since men might never have made the experiments founding real science without the hopes the delusive art inspired. Whewell questions this: since Alchemy's fall, real Chemistry has attracted a larger and no less zealous body, and Astronomy was long cultivated without the bribe of Astrology. He suggests instead that in the stationary period men's minds were so enfeebled that pure speculative truth had not its full effect.
Chapter 22
Why did people of the stationary period attribute magic to eminent scholars?
The author argues that in dark and degraded periods, superior knowledge becomes an object of hatred and fear rather than admiration. The crowd, ignorant and spiritless, lacks sympathy with the learned man, seeing him raised above them without knowing how; he becomes an object of aversion, envy, and vague terror, and these emotions are confirmed by superstition. Thus superior knowledge was considered Magic, and Magic a detestable employment.
Chapter 22
How does Whewell define Mysticism's opposition to the habits science requires?
Whewell states science requires clear Ideas, distinctly employed to connect well-ascertained Facts. Mysticism's ideas were vague and unstable, and the temper in which it contemplated them was an urgent, aspiring enthusiasm that could not submit to a calm conference with experience upon even terms. Fervor of thought partly supplied the place of reason in producing belief, but opinions so obtained had no enduring value, being neither a permanent record of old truths nor a firm foundation for new.
Chapter 22

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Why did scholastic disputes continue without progress, according to Whewell?
The author argues that because schoolmen pursued questions through abstract terms, verbal distinctions, and logical rules alone, their activity had no tendency to end since there was no progress. The same questions, answers, difficulties, and subtleties recurred without limit. John of Salisbury found Parisian teachers not a step advanced after years away, still urging and parrying the same arguments—a condition Hallam says lasted for centuries.
Chapter 23
How did Aristotle's authority fluctuate at the University of Paris?
Aristotle's works were explained at Paris early in the thirteenth century, then prohibited by a council in 1209 as occasioning the heresy of Almeric and possibly "other heresies not yet invented." His Logic was publicly taught again by 1215, but Gregory the Ninth prohibited Natural Philosophy and Metaphysics in 1231. Aquinas and Albertus Magnus later wrote commentaries with profound deference, and in 1452 Cardinal Totaril required knowledge of Aristotle for a degree.
Chapter 23

Section 244 cards

How does Whewell rate Arabian scientific achievements compared to many writers?
The author argues the Arabians' scientific merits are much less exalted than many writers, including some of his own time, have claimed. He insists on using terms of science strictly and precisely, and says that by that standard little in their particular discoveries or general processes is important in the history of the Inductive Sciences.
Chapter 24
What two astronomical advances does Whewell credit to the Arabians?
He names two great instances: the discovery of the Motion of the Sun's Apogee by Albategnius, and the recently brought-to-light existence of the Moon's Second Inequality by Aboul Wefa. But he notes they treated these differently from Hipparchus or Ptolemy: the Variation of the Moon was allowed to fall into neglect and oblivion rather than incorporated into the system.
Chapter 24
Why does Whewell reject the claim that Arabians had a superior 'experimental intellect'?
He says their minds were devoured by Mysticism and Commentation, following Greek leaders with abject servility, and choosing Aristotle's Physical Books, which never promoted science. Though experiments occurred in any commercial age, he finds no evidence they understood the real principles of Mechanics, Hydrostatics, and Harmonics; Europe had to restart where it stopped, with no Arabian name between Archimedes and Stevinus.
Chapter 24
What does Whewell say Gothic architecture contributed to the progress of science?
He argues Gothic builders revived the idea of true mechanical relations in an edifice, making support and stability conspicuous in decorative construction, with ornamental parts entering apparent construction and almost every moulding a sustainer of weight. This practical possession of the idea of mechanical pressure and support prepared the way for Mechanics, though the speculative development came centuries later, between Salisbury, Amiens, and Cologne and the treatises of Stevinus.
Chapter 24

Section 254 cards

What two aspects of the Copernican theory did Whewell distinguish?
Whewell distinguishes the formal aspect, concerning the relations of space and time and the apparent motions of the universe, from the physical aspect, concerning the relations of force and matter. He says these were not clearly separated at first, but the physical side was gradually extricated. Copernicus rested mainly on the formal condition, while Kepler, Galileo, and others gave increasing attention to physical relations, leading toward Newton.
Chapter 25
Why does Whewell say pre-Copernican heliocentric views were not clearly superior?
Whewell argues the two hypotheses share the same relative motions, so simplicity favors heliocentrism while the testimony of the senses favors geocentrism, and both arguments are vague and indecisive. He notes the Copernican system itself retained eccentrics and epicycles, and no published heliocentric theory before Copernicus could match the Ptolemaic account of inequalities.
Chapter 25
Which ancient figures does the chapter associate with the heliocentric doctrine?
The chapter names Pythagoras as the most ancient Greek to whom the doctrine is ascribed, though Diogenes Laertius credits Philolaus. Archimedes reports Aristarchus of Samos held that the fixed stars and sun rest while the earth circles the sun, and Plutarch says Seleucus claimed to prove it. Aristotle and Ptolemy argued against the doctrine. Aryabatta and other Indian astronomers are said to have advocated the earth's axial revolution.
Chapter 25
How does Whewell judge the idea that Greeks borrowed heliocentrism from orientals?
Whewell gives this opinion little weight. He argues the ancient heliocentric hypothesis was too obvious to require teaching, gained no strength from oriental sources, and each astronomer adopted or rejected it based on love of geometrical simplicity or prejudices of sense. Real science, depending on clear views of phenomena and general ideas, cannot be communicated through secret traditions.
Chapter 25

Section 264 cards

What two axioms did Copernicus retain in his theory of planetary motions?
Copernicus held that celestial motions must be circular and uniform, and fashioned his theory of planetary inequalities on this axiom. He desired to apply it more rigidly than Ptolemy had. The axiom was not rejected until Tycho Brahe's observations and Kepler's calculations were made.
Chapter 26
What did Copernicus retain from the old system, and how did he modify it?
Copernicus retained epicycles and eccentrics but altered their centres of motion, translating what was true in the old system into his own. He combined epicycles to replace the equant and make all motions equable about the centres of motion. Kepler's elliptic theory later expelled this device along with all epicycles.
Chapter 26
Why did Copernicus propose a new theory of the moon?
He proposed a new theory of the moon because the ratio of the moon's distances from the earth at different times was inconsistent with the circular hypothesis. This was the very reason that eventually overturned the doctrine of epicycles. He also made complex suppositions for Mercury's more eccentric orbit, showing awareness of the common theory's imperfections.
Chapter 26
Why did Copernicus delay publishing De Revolutionibus, and when did it appear?
Copernicus, an ecclesiastic, foresaw that the new interpretation of scriptural expressions would disquiet many, and this plus other causes long withheld publication. He kept the book about four times Horace's nine years. It was published in 1543, the year he died; he received the only copy he ever saw on his death day and never opened it.
Chapter 26

Section 274 cards

What did Gilbert conclude about the Earth's motion in De Magnete?
In De Magnete (1600), Gilbert gives the principal arguments for the Copernican system and decides that the earth revolves on its axis. He connects this with his magnetic doctrines, especially to account for the precession of the equinoxes. However, he was not equally confident of the annual motion; in a posthumous work of 1661 he hesitates between the systems of Tycho and Copernicus.
Chapter 27
How did Galileo's discovery of Jupiter's satellites affect reception of the Copernican system?
The discovery, announced in the Nuncius Sidereus (1610), had an immediately considerable effect. It showed the real universe differed from ancient philosophers' imaginings and offered the bodily eye a model of the solar system under Copernicus's views, supporting belief by an analogy all but irresistible. A modern writer, Sir J. Herschel, said it gave the 'holding turn' to opinions on the system.
Chapter 27
How did Venus's phases answer objections to the Copernican theory?
Venus was found to assume the same succession of phases as the moon, showing decisively that she moves about the sun. This met the long-standing objection that such phases had not been observed; Copernicus had supposed the sun's rays passed freely through the planet. It also explained why Venus does not appear four times larger when nearer: her bright part is not four times as large, though her visible diameter is.
Chapter 27
Why did the heliocentric theory face theological opposition in Galileo's time but not Copernicus's?
Copernicus's doctrine, promulgated soon after 1500, excited no visible alarm among contemporary theologians; intelligent ecclesiastics received it with favor, and lectures supporting it were delivered in ecclesiastical colleges. But Galileo's assertion and confirmation about a century later provoked a storm of controversy and severe condemnation. The author argues this change was largely due to controversies and alarms arising from the Reformation, which made the Romish Church more jealous of innovations.
Chapter 27

Section 284 cards

What sentence did Galileo receive, and how was it actually carried out?
Galileo was formally condemned to imprisonment and to recite the seven penitential psalms once a week for three years. In practice the confinement was reduced to slight restrictions: he stayed first at the house of Nicolini, his sovereign's ambassador, and later at the country seat of Archbishop Piccolomini, a warm friend. The author stresses that he was treated with courtesy and indulgence throughout.
Chapter 28
Did Galileo's 'rigorosum examen' imply he was tortured, and who argued each side?
Libri and Quinet argued that the term rigorosum examen necessarily implies bodily torture. Biot called the procedure incredible, and Delambre rejected it as inconsistent with the authorities' general conduct, with accounts by Galileo and a servant who never left him, and with the sentence's phrase that his error not remain 'omnino impunitus.' The author endorses Biot and Delambre.
Chapter 28
How did editors of Galileo and Newton handle the earth's motion after the condemnation?
The 1744 Padua edition of Galileo's works printed the Dialogue with license but still declared the earth's motion admissible only as a mathematical hypothesis. The 1760 Le Sueur and Jacquier edition of Newton's Principia prefixed a Declaratio saying they assumed a character not their own and professed obedience to the pontifical decrees against the earth's motion.
Chapter 28
What two reflections does the author draw from the Galileo affair about Scripture and science?
First, the meaning a generation puts on Scripture's phrases depends on the received philosophy of the time, so men defending Revelation are often defending their own interpretation. Second, those who cling to the traditional reading of physical passages are condemned by later generations with contempt or pity. The author argues the See of Rome made an unwise stretch of authority.
Chapter 28

Section 294 cards

What did Kepler's Mysterium Cosmographicum (1596) claim explained the number of planets?
Kepler proposed that the five regular solids, nested between the planetary spheres, gave the true relation of the orbits. He described a dodecahedron around Earth's orbit yielding Mars, a tetrahedron giving Jupiter, a cube giving Saturn, an icosahedron inscribed giving Venus, and an octahedron giving Mercury. The author notes this doctrine was a failure and is now entirely abandoned, though Kepler propounded it with great triumph.
Chapter 29
How is Kepler's third law stated, and what example does he give?
Kepler states that the squares of the periodic times are in the same proportion as the cubes of the mean distances (the sesquiplicate proportion of the radii). His example: Earth's period is one year, Saturn's thirty; taking the cube root of 30 (greater than 3) and squaring it gives more than 9, matching Saturn's mean distance of a little more than nine times Earth's. The author says it greatly aided Newton's law of the sun's attractive force.
Chapter 29
Why does the author reject the charge that Kepler was blind not to see the third law sooner?
The author argues the ex-post-facto obviousness of discoveries is a delusion. Connecting two quantities by comparing their powers is obvious only to those familiar with general algebraic views, and in Kepler's time algebra had not replaced geometry as the usual vehicle of mathematical reasoning. The author adds that Kepler always sought formal laws through physical reasonings, which, though vague or erroneous, determined the mathematical connection he assumed.
Chapter 29
What are Kepler's First and Second Laws, and what discovery prompted them?
The First Law: the orbits of the planets are elliptical. The Second: areas swept by lines from the sun to the planet are proportional to the times. The occasion was the attempt to reconcile the theory of Mars to eccentrics and epicycles; the result was the complete overthrow of that theory and establishment of the Elliptical Theory. Kepler published these researches in 1609 in On the Motions of Mars.
Chapter 29

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Which tables did Kepler publish in 1627, and what were they based on?
Kepler published the Rudolphine Tables in 1627, the result and application of his own theory. They were founded on Tycho's observations, as Kepler's discoveries had been. The Rudolphine Tables were for a long time those universally used, succeeding the Prutenic Tables, which were founded on Copernicus's doctrines, by seventy-six years.
Chapter 30
How did Horrox's view of Lansberg change, and who warned him?
Horrox had been seduced by Lansberg's magnificent promises and the praises prefixed to his work, believing the preference for Tycho and Kepler was prejudice. In 1636 Crabtree, a young Lancashire astronomer, warned him that Lansberg was not to be depended on, his hypotheses vicious and observations falsified or forced to fit his theories. Horrox then read and adopted Kepler's works.
Chapter 30
What lunar inequalities did Tycho Brahe establish?
Beyond the Equation of the Centre and the Evection, Tycho proved the Variation, depending on the moon's position relative to the sun, at maximum forty minutes and a half, about a quarter of the evection. He also perceived, though not distinctly, the need for the Annual Equation depending on the sun's longitude. On latitude, he found the inclination varied by twenty minutes and the nodes sometimes moved forward.
Chapter 30
What did Horrox argue about errors in astronomical tables?
Horrox argued against Kepler's opinion that such errors were casual. He noted the errors alternate between excess and defect, and the alternation is fastest in the Moon, slowest in Jupiter and Saturn, where errors last years. If tables are right in mean motions but wrong in equations, this must happen, since Saturn's inequalities have long periods while the Moon's are numerous and rapidly changing.
Chapter 30

Section 314 cards

What did Stevinus's loop-of-chain argument establish about the inclined plane?
Stevinus supposed a loop of string loaded with fourteen equal balls hanging over a triangular support made of two inclined planes with a horizontal base, whose sides were in the proportion of two to one and supported four and two balls. He argued any motion would only restore the same condition, so the loop must rest; removing the festoon of eight balls left four balls balancing two, meaning weights are as the lengths of the planes intercepted by the horizontal line.
Chapter 31
How does Whewell distinguish Kepler's forces from Newton's forces?
The author argues Kepler's forces were imaginary qualities appearing in actual motion, urging bodies forward, so that if destroyed the body would instantly stop; Newton's forces were causes appearing by change of motion, deflecting bodies from straight progress, so that if annihilated the body would continue uniformly in a straight line. Whewell says Kepler's essays may anticipate Descartes's vortices but not Newton's dynamical theory.
Chapter 31
What did Stevinus state about the triangle of forces?
Whewell notes that Stevin distinctly states the triangle of forces: three forces acting on a point are in equilibrium when they are parallel and proportional to the three sides of any plane triangle. This includes the principle of the composition of statical forces. Stevin also applied his equilibrium principle to cordage, pulleys, funicular polygons, and especially bridle bits, a branch he called Chalinothlipsis.
Chapter 31
What did Leonardo da Vinci contribute to the equilibrium of oblique forces?
From manuscripts published by Venturi in 1797 and Libri in 1839, and examined by Whewell in Paris, Leonardo as early as 1499 gave a correct statement of the proportion of forces exerted by a cord acting obliquely and supporting a weight on a lever, distinguishing the real lever from the potential levers, the perpendiculars from the centre upon the directions of the forces. Whewell says Leonardo also anticipated Galileo's inclined-plane time assertion, but considers it a guess without proof.
Chapter 31

Section 324 cards

What law of falling bodies did Galileo assume, and what did he deduce from it?
Galileo assumed that natural motion is the simplest, so falling bodies receive equal additions of velocity in equal times. From this he deduced that spaces described from the start of motion are as the squares of the times, and he verified this by experiments with balls rolling down inclined planes, assuming their descent follows the same law as free fall.
Chapter 32
What false law of velocity did Galileo first hold, and who else defended it?
Galileo initially supposed velocity proportional to the space described rather than to time. The author notes this false law was also asserted by M. Varro in 1584 and by Baliani of Genoa in 1638, and later defended by Casraeus, one of Galileo's opponents. Galileo soon rejected it; the author adds it is at variance with fact and mathematically self-contradictory.
Chapter 32
How did Galileo define a uniform force, and how did Descartes disagree?
Galileo held that a uniform force generates equal velocities in equal successive times, so forces are compared by the velocities they generate in equal times. Descartes rejected this, saying a stone already moving quickly is not equally disposed to receive new motion. The author notes gravity adds the same velocity each second regardless of prior downward motion.
Chapter 32
What is the Second Law of Motion, and how did Galileo apply it to projectiles?
The Second Law states that the motion a force produces is compounded with the motion the body already has. Galileo applied it to a horizontally projected body: uniform horizontal motion combined with uniformly accelerated downward motion, producing a parabola. Cardan had denied this, claiming a body moved by two motions arrives slower than by either alone.
Chapter 32

Section 334 cards

What did Aristotle's falling-body doctrine confuse, according to Whewell?
Whewell says Aristotle's claim that a body ten times heavier falls ten times faster confuses Statical and Dynamical Forces. The heavier body's force at rest is ten times greater, but the force measured by velocity produced is equal in both bodies. The two would fall with the same rapidity except for accidental causes such as air resistance.
Chapter 33
Who besides Galileo experimentally refuted Aristotle's falling-body rule?
Whewell notes Galileo's experiment from the leaning tower of Pisa around 1590 is usually credited with refuting the Aristotelian dogma. But F. Piccolomini in 1597 wrote that Aristotle's rules on quickness and slowness are palpably false, since a stone twice as great does not move twice as fast. Stevinus also described making the experiment and correctly noted deviations from air resistance.
Chapter 33
What principle did Galileo assume about bodies falling down inclined planes?
In his Dialogues on Motion, Galileo assumed as a postulate that when the same body falls down different planes of the same height, the velocities acquired are equal. He illustrated this with a pendulum experiment showing the weight swings to the same height whatever path it follows. Whewell says Galileo later discovered a proof, reportedly during a sleepless night, and added it to later editions.
Chapter 33
How does Whewell judge Descartes's contribution to mechanics?
Whewell argues it is saying far too much to call Descartes's Laws of Motion an important event in mechanics. He says the Principia did little for physical science, that Descartes's Third Law is false in substance, and that Descartes claimed discoveries of Galileo and others he did not understand or apply. Whewell concludes Galileo grasped as many attainable mechanical truths as possible, Descartes as few.
Chapter 33

Section 344 cards

Who first rediscovered the laws of fluid equilibrium, and when was his work published?
Stevinus is considered the earliest author of the rediscovery; his Principles of Statik and Hydrostatik was published in Dutch about 1585. In it he restates Archimedes' doctrines and shows that a fluid's pressure on a vessel's bottom may greatly exceed the fluid's own weight, proving this by imagining upper portions filled with fixed solids that do not alter the base pressure.
Chapter 34
How did Galileo argue against the Aristotelians on floating bodies?
In his 1612 Discourse on Floating Bodies, Galileo asserted that ice is rarefied water, not condensed water, as shown by its floating, and proved by experiments that floating does not depend on form. The author notes the controversy was complicated by capillary phenomena, such as an ebony ball sinking while a flat slip of the same material floats.
Chapter 34
What did Pascal's Treatise of the Equilibrium of Fluids demonstrate?
Written in 1653, it shows that a fluid enclosed in a vessel presses equally in all directions, illustrated by two pistons whose surfaces differ a hundredfold: one man at the small piston balances a hundred men at the large one. Pascal called a vessel full of water a new principle of mechanics and a machine multiplying force at will, and referred fluid equilibrium to virtual velocities.
Chapter 34
How did Pascal's Puy de Dôme experiment confirm the cause of mercury suspension?
Pascal had mercury heights compared on a Paris steeple and, via his brother-in-law Perrier, on Puy de Dôme. Perrier found the mercury three inches lower at the summit, which Pascal argued proved the weight and pressure of the air alone cause the suspension, not horror of a vacuum, since more air weighs at the bottom than the top.
Chapter 34

Section 354 cards

What did Hooke's 1666 paper explain about motion, and what did Halley do in 1684?
Hooke's 1666 paper explained "the inflexion of a direct motion into a curve by a supervening attractive principle." In 1684 Halley went to Cambridge expressly to consult Newton about producing the planets' elliptical motion by a central force, and on 10 December announced to the Royal Society that he had seen Newton's De Motu Corporum.
Chapter 35
How does Whewell assess the Principia as a work on dynamics?
The author argues the Principia contains hardly any new inductive discovery in mechanics: Newton's Axioms or Laws of Motion are clearer and more general than earlier statements but involve no doctrines not previously stated or taken for granted by other mathematicians. Its merit lies in refined mathematical artifices applied to general problems, and in exhibiting a clear conception of dynamics' new character.
Chapter 35
What principle did Huyghens assume to solve the centre of oscillation?
Huyghens assumed that if weights are put in motion by gravity, they cannot move so that their common centre of gravity rises higher than the place from which it descended. From this it follows that the centre of gravity rises as high as its original position, which determines the oscillation of a compound pendulum. He published this in the fourth part of his Horologium Oscillatorium (1673).
Chapter 35
What error did Newton make about rotatory motion in the Principia, and who corrected Bernoulli's related mistake?
Newton assumed that when a part communicates rotatory movement to a whole, the quantity of "motus" is unaltered; but he considered velocity only, making motion identical with momentum, instead of moment of inertia. The error was retained in later editions. Separately, James Bernoulli wrongly estimated action and reaction by velocity acquired rather than the increment of velocity; the Marquis de l'Hôpital corrected him.
Chapter 35

Section 364 cards

What method did Newton predominantly use in the first two books of the Principia?
The method is predominantly geometrical: space is not represented symbolically or by number, and numbers measuring time and force are represented by spaces, with laws of change indicated by properties of curve lines. Newton preferred such methods in exposition even when he had discovered theorems by analytical calculation, since the intuitions of space seemed a clearer road to knowledge.
Chapter 36
How did Euler describe his purpose in his 1736 Mechanics?
In the preface, Euler says that although Newton's and Hermann's solutions of problems were quite satisfactory, he found difficulty applying them to new problems differing little from theirs. He therefore thought it useful to extract an analysis out of their synthesis. The work was published at St. Petersburg as a supplement to the Imperial Academy's Transactions.
Chapter 36
What does D'Alembert's Principle state, and what does it accomplish?
The motion impressed on each particle by the acting forces may be resolved into effective motion and motion gained or lost; the effective motions are the real motions, and the gained and lost motions are such as would keep the system at rest. The principle reduces every dynamical question to a statical one, though determining equilibrium laws in complex cases can be as difficult as direct methods.
Chapter 36
What error of Newton's did John Bernoulli correct, and how did Newton respond?
Bernoulli pointed out a material error in Newton's determination of the path of a body in a resisting medium. This correction reached Newton in London in October 1712, when the second edition of the Principia was nearly finished under Cotes at Cambridge; Newton immediately cancelled the leaf and corrected the error.
Chapter 36

Section 374 cards

What did Gauss contribute in 1818 to physical astronomy's secular equations?
Gauss pointed out that secular equations may be conceived to result from the disturbing body being distributed along its orbit so as to form a ring, making the result more distinctly conceivable than as a mere result of calculation. The author notes this addressed Lagrange's late-life complaint that approximation methods rested on arbitrary processes rather than insight into mechanical action.
Chapter 37
How did Lubbock and Pontécoulant change the treatment of the lunar theory?
They made the moon's mean longitude, that is the time, the independent variable, expressing the moon's co-ordinates in sines and cosines of angles increasing proportionally to the time, rather than expressing co-ordinates as functions of true longitude and reverting series. They also made the lunar and planetary theories agree instead of following two different paths. Poisson adopted this method.
Chapter 37
What did Euler's 1765 work on rigid bodies accomplish, and what simplified its formulas?
Euler's Theory of the Motion of Solid and Rigid Bodies, written about 1760 and published in 1765, gave final form to solutions of rotary motion under forces and applied them to many problems. Its formulas were much simplified by Segner's discovery that every body has three Principal Axes about which alone it would permanently revolve.
Chapter 37
What did Lagrange establish about the functions in the vibrating string controversy?
Lagrange established, to the satisfaction of the mathematical world, that the functions introduced in such cases are not necessarily continuous but are arbitrary to the same degree that the motion is practically, though capable of expression by a series of circular functions. This followed D'Alembert's 1747 claim of infinitely many curves and Euler's further generalization.
Chapter 37

Section 384 cards

According to the chapter, what did Lagrange call Mechanics?
The chapter's note states that Lagrange termed Mechanics "An Analytical Geometry of four dimensions," because besides the three co-ordinates determining a body's place in space, time enters as a fourth co-ordinate. The note is attributed to Littrow.
Chapter 38
Why do recent analytical treatises deduce all mechanical doctrines from the Law of Inertia alone?
The chapter explains that the symbolic language of mathematics is more general than words, so truths translated into symbols suggest their own generalizations. The same formula expresses the general condition of both Statics and Dynamics. This tendency makes mathematicians unwilling to acknowledge a plurality of mechanical principles, so they reduce all doctrines to the single Law of Inertia, though the author does not decide whether this is a real advance.
Chapter 38
What physical theory did Kepler propose to explain planetary motion, and what did it resemble?
Kepler held that a force or virtue resides in the sun, carrying bodies round it, compared to light and magnetism. The chapter argues his phrases are best interpreted as a fluid vortex whirling round the sun, kept moving by the sun's rotation, carrying planets like a whirlpool carries straws. Kepler called this an immaterial species, leaving the theory confused.
Chapter 38
Why does the chapter criticize Descartes for proposing the Theory of Vortices?
The chapter argues that Kepler might be excused for vortices before mechanics developed, but Descartes proposed them in 1644 after the laws of motion were known, while mathematicians like Borelli, Hooke, Wallis and Huyghens worked on the mechanical problem. The author says this shows conceit and shallowness, and that systems deduced from assumed principles without verification by facts hardly contain truth.
Chapter 38

Section 392 cards

What did Borelli propose about planets and their central bodies in 1666?
Borelli proposed that planets and satellites revolve around a principal globe as a 'fountain of virtue' that draws and holds them. He suggested planets have a natural appetite to unite with the central body, while circular motion gives a tendency to recede; when these opposing forces are equal, the planet stays balanced at a fixed distance. The author notes Borelli lacked a clear account of how the direction of motion changes from instant to instant.
Chapter 39
What did Gilbert state about the moon and earth's magnetic virtue?
In his posthumous work of 1651, Gilbert stated that the force emanating from the moon reaches the earth, and the earth's magnetic virtue pervades the moon's region, both conspiring by joint action according to a proportion of motions. The earth has more effect due to superior mass; it attracts and repels the moon, and the moon within limits the earth, not so they come together but so they continue in a continuous course.
Chapter 39

Section 403 cards

What error explained Newton's early moon-gravity discrepancy, and what corrected it?
Newton had used the common estimate of sixty English miles to one degree of latitude, which made the earth's size, and hence the moon's distance, incorrect. Picard's more accurate meridian measurement in France in 1670 supplied amended data; repeating the calculation with these, Newton found his conjecture agreed with the phenomena to remarkable precision.
Chapter 40
How does Whewell distinguish Newton's claim from earlier uses of 'gravity' for celestial forces?
Whewell argues that before Newton, philosophers generally did not suppose terrestrial gravity itself produced the moon's motion. Earlier thinkers used 'gravity' only by analogy to describe what kind of forces celestial ones were, as others compared them to magnetism. Huyghens's language about Borelli may mislead; the notion of terrestrial gravity as an actual cosmical force is foreign to Borelli's speculations.
Chapter 40
What did Hooke and Borelli contribute to the idea of mutual attraction among celestial bodies?
Hooke, in his Attempt to prove the Motion of the Earth (1674), conjectured that the sun and moon act on the earth and that Mercury, Venus, Mars, Jupiter, and Saturn also influence its motion, with the earth affecting them in turn. Borelli dimly saw that the sun would disturb Jupiter's satellites, acting on them alongside their revolution about Jupiter.
Chapter 40

Section 414 cards

What experiment did Bacon propose to test whether gravity is mutual attraction or a tendency to Earth's center?
Bacon proposed comparing the rate of a clock in a deep mine with one on a high place, to decide whether the gravity of bodies arises from attraction of the parts of matter toward each other or from a tendency toward the center of the earth. Whewell notes this experiment remains one of the best that can be devised to exhibit the universal gravitation of matter.
Chapter 41
What did Newton have to prove about the inverse-square law for particles versus spherical masses?
Whewell explains that if every finite mass exerts forces from its infinitely numerous particles acting in different directions, it is not obvious the law relating force to distance is the same for particles as for masses — and in fact it is not, except in special cases. Newton therefore solved new problems showing the inverse-square law for particles yields the same law for spherical masses.
Chapter 41
Which phenomena did Newton's reasoning about mutual attraction of particles address, and where did he err?
Whewell lists the Figure of the Earth, the Tides, the Precession of the Equinoxes, the Regression of the Nodes of a ring like Saturn's, and effects not yet observed such as difference of gravity in different latitudes and nutation of the earth's axis. Whewell says Newton's process was mostly a rude approximation, and in the Precession he committed an error.
Chapter 41
How does Whewell describe the relationship between one generation's theories and the next generation's facts?
Whewell argues that what Newton used as facts were the laws his predecessors had established: what Kepler and Horrox put forth as theories became established truths fit for constructing new theories. He states that in this manner one theory is built upon another, rising from particulars to generals through successive steps of induction.
Chapter 41

Section 424 cards

How was Newton's work received in England, according to Whewell?
The author argues the popular belief that great discoveries meet prejudiced opposition was reversed in Newton's case in England. Halley proclaimed the work's transcendent value before publication, and Royal Society leaders like Wren embraced it immediately. Literary figures such as Evelyn, Locke, and Pepys adopted high estimates of the Principia on the credit of mathematical friends. Within five years, Bentley referenced its principles from the pulpit as incontestably proved.
Chapter 42
What honors did Newton receive in his later life?
In 1695 Newton became Warden of the Mint through Montague, and in 1699 Master of the Mint, worth £1200 or £1500 yearly, which he held for life. He became President of the Royal Society in 1703, re-elected annually for twenty-five years. Queen Anne knighted him in 1705 at Trinity College. On his death in 1727 his body lay in state and was buried in Westminster Abbey.
Chapter 42
How does Whewell describe the reception of Newtonianism at Oxford and Cambridge?
Whewell disputes writers like Playfair who portray universities as bigoted resisters of new truths. He argues that in Cambridge and Oxford there are no traces even of a struggle over Newtonian opinions, since Cartesianism had never struck deep roots in England. Cartesian texts like Rohault's were used because they contained the best physical science treatises, but the Vortices were never dwelt upon as important.
Chapter 42
What evidence does Whewell give of Cambridge's early adoption of Newton?
Samuel Clarke defended a Newtonian thesis in the public schools as early as 1694. Bentley became Master of Trinity in 1699, and Whiston, a Newtonian disciple, was appointed deputy professor of mathematics that year. In 1709-10 Laughton became moderator of disputations to promote the new mathematical doctrines. Cotes supervised the 1713 second edition of the Principia, urged by Bentley.
Chapter 42

Section 433 cards

How did the French Academy sometimes handle prize questions dividing Cartesians and Newtonians?
The Academy not unfrequently divided the prize between the two camps, as if desirous to show its impartiality. In 1734, on the cause of the inclination of planetary orbits, the prize was shared between John Bernoulli, whose memoir was founded on vortices, and his son Daniel, a Newtonian. The last such homage came in 1740 on the tides.
Chapter 43
What did Voltaire's 1727 visit to England lead him to observe about French and English philosophy?
Voltaire noticed a national difference in physical creed: a Frenchman arriving in London finds the world empty rather than full, no vortices, the sea gravitating toward the moon rather than the moon pressing the sea, the sun contributing to tides, and the earth flattened at the poles rather than melon-shaped. The author credits Voltaire as mainly instrumental in giving Newtonian doctrines currency in France.
Chapter 43
What role did comets play in undermining the Cartesian vortex system?
Comets were a kind of artillery the Cartesian plenum could not resist. When it appeared that their paths traversed the vortices in all directions, it was impossible to maintain that these imaginary currents governed the movements of bodies immersed in them, and the mechanism ceased to have real efficacy. The author argues the controversy still encouraged observation and calculation.
Chapter 43

Section 444 cards

What did Laplace identify as the cause of the moon's acceleration?
In 1787 Laplace announced that the moon's acceleration arose from the action of the sun upon the moon, combined with the secular variation of the eccentricity of the earth's orbit. This combination was found to account exactly for the observed changes. Laplace noted the inequality is periodical but requires millions of years to re-establish itself, after which the acceleration becomes a retardation.
Chapter 44
What did Airy detect in 1827 regarding Venus and Earth?
Comparing Delambre's tables with 2000 Greenwich observations, Airy suspected an unnoticed inequality. Weeks later he announced to the Royal Society an inequality arising from the mutual attraction of Venus and the Earth, with a period of about 240 years and an effect on Earth's longitude of nearly three seconds. He said it fully accounted for differences in secular motions between the epochs compared.
Chapter 44
Why did Jupiter's fourth satellite's nodes advance rather than retrograde?
Newtonian theory seemed to require the nodes to go backwards, but observation showed them advancing on Jupiter's orbit. The theory actually requires retrogression relative to the orbit of the perturbing body, here the third satellite. Lalande showed that by the necessary relations of space, the latter motion may be retrograde even though the former is direct.
Chapter 44
How did Bradley and Wargentin contribute to tables of Jupiter's satellites?
Bradley observed that the three interior satellites are affected by errors recurring in a cycle of 437 days, matching their return to the same relative position with regard to each other and Jupiter's shadow axis. Wargentin noticed the same circumstance independently and applied it diligently to improve the tables in 1746. Laplace later established the theorem behind this cycle, called the libration of Jupiter's satellites.
Chapter 44

Section 454 cards

How did Olbers locate Vesta, and what did he later claim about his sky surveys?
Olbers reasoned that fragments of a shattered planet must pass through one of two opposite constellations, the Virgin or the Whale, so he surveyed all the small stars there three times a year. This succeeded on 29 March 1807 with the discovery of Vesta. He later published a notification that he had examined those same regions so regularly he was certain no new planet had passed that way between 1808 and 1816.
Chapter 45
How did Halley establish that certain comets were periodic, and what did he conclude?
In 1705 Halley explained how to determine a parabolic orbit from three observations and calculated the positions and orbits of twenty-four comets. He found the comets of 1607 and 1531 shared the orbit of 1682, with intervals near seventy-five years, and traced records back to 1456, 1380 and 1305. He concluded they were one revolving body: a planet on a long ellipse, not a parabola.
Chapter 45
What did Clairaut predict about Halley's comet, and how did the comet's arrival compare?
Halley had proposed but not solved the question of how planetary perturbations affect a comet's return. Clairaut undertook the immense labor, assisted by Lalande and Madame Lepaute, and predicted the comet would reach perihelion on 13 April 1759, claiming a month's license for inevitable inaccuracy. The comet arrived at perihelion on 13 March, justifying both his calculation and his caution.
Chapter 45
What did the double appearance of Biela's comet in 1846 demonstrate about comets?
Biela's comet appeared double, but the two bodies did not perceptibly affect each other's motions, as Professor Challis of Cambridge reported from observing both from 23 January to 25 March 1846. This proved the quantity of matter in each body was exceedingly small. Similarly, Lexell's comet was supposed to have passed twice through Jupiter's satellites without disturbing their motions, though its own orbit was entirely altered.
Chapter 45

Section 462 cards

Who produced the accurate Liverpool Tide-tables and from what observations?
A clergyman named Holden deduced the Liverpool Tide-tables from observations made at that port by harbor-master Hutchinson, who observed the tides carefully day and night for above twenty years out of love for such pursuits. Holden's tables, founded on four years of these observations, were remarkably accurate.
Chapter 46
What did comparison with the equilibrium theory show about tides?
Lubbock compared results with Daniel Bernoulli's equilibrium theory and found it represented the facts precisely with certain modified elements, especially the semi-mensual inequality. Whewell showed similar agreement at Liverpool for times and heights. The general result was that facts agreed with equilibrium at a certain anterior time, but that time differed for different phenomena, and the moon's mass had to be supposed different at different places.
Chapter 46

Section 473 cards

Why is calculating orbits of double stars especially difficult?
The plane of the orbit is unknown and probably oblique to the visual ray, so even an elliptical orbit described about the focus by planetary laws will appear otherwise; the true orbit must be deduced from the apparent one. The chapter adds that the two stars revolving about their common centre of gravity adds little difficulty, since Newton showed the relation in the problem of two bodies.
Chapter 47
What evidence did Whewell cite for elliptical motion in double stars?
Whewell reports that since Sir W. Herschel's first measures in 1781, one star of γ Virginis described over 305 degrees about the other, with annual angular motion varying from about 20 minutes to 80 degrees. Yet the observed and computed curves, with a total ordinate of 305 parts, never deviated by as much as two parts. He says this should give astronomers strong conviction of the law.
Chapter 47
How did Huyghens' pendulum clock change astronomical observation?
Huyghens applied the pendulum to clocks in 1656, connecting it to machinery that kept its motion from languishing and recorded its swings, giving a measure of time more accurate than the sun. Astronomers then obtained a star's right ascension indirectly by observing the moment of its transit rather than measuring a distance in the heavens, with transits noted to a tenth of a second of time.
Chapter 47

Section 484 cards

Which observatories outside Europe does the chapter mention, and who founded them?
The chapter notes an observatory at Bagdad erected in 1786 by M. de Beauchamp at Louis the Sixteenth's expense; a British government observatory at the Cape of Good Hope completed in 1828, where Lacaille had observed in 1750; an observatory in New South Wales formed by Sir T. M. Brisbane in 1822 and presented to the government; and East India Company observatories at Madras, Bombay, and St. Helena.
Chapter 48
How does the chapter describe the Royal Societies of London and Paris relative to the observatories?
The author states the Royal Societies of London and Paris were founded nearly at the same time as the metropolitan observatories of the two countries. He argues such associations benefit science by testing a speculator's ideas against other minds, and that astronomy especially requires division of labor and sympathy because of its vast extent.
Chapter 48
Which astronomers did Louis the Fourteenth and other rulers draw to their capitals?
Louis the Fourteenth brought Dominic Cassini to Paris in 1669, initially for six years, then fixed him there with honors; the French government also drew Römer from Denmark and Huyghens from Holland, and pensioned Hevelius. Peter the Great took Delisle to Petersburg in 1725; Frederick the Great drew Voltaire, Maupertuis, Euler, and Lagrange to Berlin; Catharine obtained Euler and two Bernoullis.
Chapter 48
What does the chapter say about the dispute over annual parallax of fixed stars?
The author reports Brinkley asserted an annual parallax of the fixed stars and Pond denied it, calling it a dispute between two of the best modern observers proving the quantity, if real, is of the same order as unsurmounted instrumental errors. A second-edition note adds that belief gains ground, citing Bessel's parallax of 61 Cygni (0"·34) and Maclear's of α Centauri (0"·9).
Chapter 48

Section 493 cards

What did the Earl of Rosse's telescope show about nebulae, and how did it affect the Nebular Hypothesis?
Whewell reports that the most powerful telescope, recently erected by the Earl of Rosse, resolved diffused nebulous masses into separate stars in all cases yet examined. He notes that no observed changes in nebulae tend to confirm Laplace's Nebular Hypothesis, and that Rosse's results actually militate against it. Whewell also classifies such speculations as Cosmogony or Palætiological Science rather than Astronomy proper.
Chapter 49
According to Whewell, why is the Parmenides probably not a genuine Platonic dialogue?
Whewell argues the Parmenides differs in substance, manner, and tendency from characteristic Platonic dialogues. In typical dialogues Socrates refutes his adversaries and sums up in his own way; in the Parmenides, Parmenides and Zeno reply with solid arguments Socrates does not answer, and Socrates becomes a passive respondent saying yes or no. Whewell concludes it should be regarded as an Eleatic dialogue composed to confute, not assert, the Platonic doctrine of Ideas.
Chapter 49
What did Socrates argue against Anaxagoras's claim that the Sun is fire or hot stone?
Per Xenophon's Memorabilia, Socrates said Anaxagoras held the Sun to be Fire, but men can look at fire and cannot look at the Sun; they grow dark from the Sun but not from fire. Plants grow well only with sunshine, yet are spoiled by fire. Against the Sun-as-red-hot-stone view, Socrates noted a heated stone is not luminous and soon cools, while the Sun is always luminous and always hot. Whewell adds a disciple could reply that a large enough hot mass might behave as described.
Chapter 49

Section 504 cards

How does Whewell characterize Plato's mathematical doctrines about the universe?
Whewell says Plato puts these forward not as physical assertions to be tested against nature, but as examples of a higher truth, revelations of principles in the Creator's mind, or contemplations raising the mind above sense toward the Divine Mind. In the Timaeus they appear as an exposition of the necessary scheme of creation; in Republic Book VII, more as a mental discipline for the true philosopher.
Chapter 50
What musical problem does Whewell use to illustrate Plato's error about harmony?
Whewell notes that ascending from A1 to C3 by two octaves and a third, versus by four repeated fifths, yields notes that differ by a small interval the Greeks called a Comma, ratio 80 to 81. The ear detects this, confirming the mathematical principles of harmony. Whewell argues Plato wrongly treats seeking such sensory confirmation as leaning unphilosophically on the senses.
Chapter 50
What did Hero of Alexandria contribute to mechanics, according to the chapter?
Hero described pumps and hydraulic machines, and an instrument some moderns called a steam-engine, though it was merely a toy whirled round by steam from holes in its arms. He wrote Mechanics and Barulcos (Weight-lifter), listing the Five Mechanical Powers — lever, wheel and axle, pulley, wedge, screw — and in Mechanics reduced all machines to the lever. In Barulcos he solved moving any object by any small power.
Chapter 50
How does Whewell distinguish Hero's Dioptra from modern Dioptrics?
Whewell warns the two must be carefully distinguished. Modern Dioptrics treats properties of refracted light, on which the ancients had little exact knowledge until later. Hero's Dioptra was an instrument for taking angles, to measure position and determine the distance of inaccessible objects — like the modern theodolite. Hero also wrote Catoptrics, with proofs of properties of reflected rays.
Chapter 50

Section 514 cards

What date did Airy assign to the Eclipse of Thales, and on what assumption?
Airy assumed the eclipse must have been decidedly total, since the difference between a total and a nearly total eclipse is very marked, and only a total eclipse was likely to produce so strong an effect on the combatants. From his calculations he concluded the eclipse predicted by Thales took place B.C. 585.
Chapter 51
Why are ancient eclipses valuable to modern astronomy, according to the chapter?
If ancient eclipses can be identified, they are of great value because over the long interval of two to three thousand years the inequalities—accelerations or retardations of the Moon's motion—accumulate to a large amount. The actual time and circumstances of the eclipse therefore let astronomers determine the rate of these accelerations or retardations.
Chapter 51
What date did Airy determine for the Eclipse of Agathocles, and why did he rank it above Thales'?
Airy discussed the eclipse Diodorus relates during an expedition of Agathocles, ruler of Sicily, and determined it occurred B.C. 310. He treated it as even more important than the eclipse of Thales for determining the rate of the Moon's accelerations or retardations.
Chapter 51
What doubts does M. H. Martin raise about Thales' prediction?
Martin does not cordially believe Thales delivered the prediction before the event. Even if he predicted an eclipse by the Chaldean period of 18 years or 223 lunations, he could only guess whether it would be visible in Greece; no author says he or his successors tried again; and Anaximander's earthquake and Anaxagoras' aërolites are fabulous stories as well attested.
Chapter 51

Section 524 cards

What three prerogatives does Bacon attribute to experimental science?
Roger Bacon says experimental science, the sole mistress of speculative sciences, has three prerogatives: first, it tests by experiment the noblest conclusions of other sciences; second, it discovers magnificent truths about notions other sciences cannot reach; third, by its own power it investigates the secrets of nature.
Chapter 52
How does Bacon investigate the rainbow's cause?
Bacon collects instances where the same colors appear: hexagonal crystals from Ireland and India, other transparent stones, furrowed surfaces, drops from oars, mill-wheel spray, dew on grass, water sprayed into sunbeams, and oil-lamp reflections. Whewell calls this a most happy example of experimental inquiry, approaching the true explanation.
Chapter 52
What did Bacon say about the state of learning in his time?
Bacon says there was never so great an appearance of wisdom nor so much study in so many faculties and regions as in the last forty years, with doctors dispersed everywhere, yet never so much ignorance and error. He blames neglect of mathematics and the adoption of Aristotelian philosophy by the Dominican and Franciscan Orders.
Chapter 52
Why does Whewell argue rotation should be referred to absolute space?
Whewell says choosing a centre of rotation is arbitrary in a multi-body system: the Moon turns all faces to the Sun, so it rotates relative to the Sun while also revolving around it. A cup of water carried in a circle leaves a floating straw parallel to itself, showing no rotation; yet the Moon does rotate. Simplicity and physical reasons favor absolute space.
Chapter 52

Section 534 cards

What did Thomas Digges's 1573 work say about Copernicus?
In his "Alæ sive Scalæ Mathematicæ" (1573), Thomas Digges bestows high praise upon Copernicus and his system. According to the chapter, Digges appears to have been a believer in the real motion of the Earth, not merely an admirer of Copernicus's system as an explanatory hypothesis. The chapter also notes that Digges was a clear and decided Copernican by other writings.
Chapter 53
What did Bacon mean by "Instantia Crucis"?
The chapter explains that Bacon's meaning is "Guide-Post Instances": the Crux alluded to is not a Cross but a Guide-Post at Cross-roads. Bacon applies such instances to the diurnal motion of the heavens and the special motions of heavenly bodies, suggesting tests that would decide between competing explanations, such as whether any comet failed to share the diurnal revolution.
Chapter 53
Did Francis Bacon reject the Copernican system, according to the chapter?
The chapter argues that Bacon's Novum Organon passage shows an inclination toward belief in the Earth's diurnal motion, since the conditions he sets for denying it are not satisfied. The author says Bacon did not fully see the value of Formal Astronomy, but agrees with De Morgan that Bacon's remarks do not justify Hume's assertion that he rejected the Copernican system "with the most positive disdain."
Chapter 53
What did the 1818 repeal of edicts against Copernicanism actually amount to?
The chapter says inquiry could not confirm the story that Pius VII repealed the edicts against the Copernican system in 1818. The only foundation found is that in 1818, on the revisal of the Index Expurgatorius, Galileo's writings were, after some opposition, expunged from that Catalogue. The author could not learn of any further basis for the repeal statements.
Chapter 53

Section 544 cards

What is the modulus of elasticity, and what are its values for air and steel?
The modulus of elasticity is a measure whose height is the same for the same substance regardless of its breadth and thickness. For atmospheric air it is about five miles, and for steel nearly 1500 miles. Whewell notes its advantage is that it applies equally to the flexure of a substance and to the minute vibrations that propagate sound.
Chapter 54
How do wrought iron and cast iron differ in resisting tension versus compression?
Whewell states that wrought iron yields to compressive force somewhat more easily than to tensile force, while cast iron yields far more easily to tensile than to compressive strains. Because a beam's resistance to fracture resides mainly in its upper and under sides, iron beams were made with broad flanges connected by a vertical web, a form Hodgkinson tested extensively.
Chapter 54
What was novel about Stephenson's tubular bridge across the Menai Strait?
The bridge is a quadrangular tube whose upper and under surfaces are the beam's flanges and whose sides are the webs. Its upper surface was built of a series of iron-plate cells to resist compression. Whewell argues its principle was invented for this purpose, experimentally verified, and applied with exact calculation, unlike arches and vaults whose principles had long been tried on smaller scales.
Chapter 54
What role does friction play in the stability of a stone arch?
Each vaulting stone of an arch is a truncated wedge. Whewell explains that although such stones might be proportioned to balance exactly, that balance would be a tottering equilibrium that the slightest shock would throw down. Friction between the vaulting stones prevents this instability, making an equilibrated arch strong for practical purposes.
Chapter 54

Section 554 cards

What did Bessel's experiments on gravitating intensity versus inertia conclude?
Bessel presented a laborious series of experiments to the Berlin Academy in 1832 that completely disproved the conjecture of a specific difference in gravitating intensity among substances. Every substance examined gave exactly the same coefficient of gravitating intensity compared with inertia, including metallic and stony meteoric masses, which might be supposed to come from other parts of the solar system.
Chapter 55
Why did the French Academy offer a prize for a purely theoretical lunar determination?
Lunar tables were still as much as thirty seconds wrong in single observations. This, plus Laplace's expressed wish, induced the French Academy to offer a prize for a complete and purely theoretical determination of the lunar path, rather than determinations resting partly on theory and partly on observations. In 1820 prize essays appeared by Damoiseau and by Plana and Carlini.
Chapter 55
What did Hansen discover from the remaining lunar discrepancies?
Hansen devised new mathematical methods and found two previously unknown lunar inequalities, of 273 and 239 years, with coefficients of 27 and 23 seconds, both originating in the attraction of Venus. He later found two more new equations, one in latitude and one in longitude, agreeing with ones Airy found from observations, plus a theoretical correction for the Moon's node motion.
Chapter 55
Who is credited with first publishing the prediction that led to Neptune's discovery?
The author states there can be no doubt that to M. Le Verrier belongs the glory of having first published a prediction of the place and appearance of the new planet, thus occasioning its discovery by observers. Galle saw it at Berlin on September 23, 1846; Challis had seen it earlier but not recognized it. The author also records Adams's contemporaneous unpublished calculations.
Chapter 55

Section 564 cards

What did Bessel hypothesize to explain irregularities in Sirius's proper motion?
Bessel proposed that Sirius has a dark, invisible companion star; the two revolve around their common center of mass as the system moves, so Sirius's motion appears sometimes quicker and sometimes slower. M. Peters reportedly confirmed the hypothesis through recent researches, as cited by the author.
Chapter 56
What did Airy's 1854 Harton mine pendulum experiment yield for Earth's density?
Airy compared pendulums at the surface and 1260 feet deep in the Harton coal mine, transmitting time between stations by galvanism rather than portable watches. The result was a density of 6.56, much larger than earlier torsion-balance results, though Airy held it deserved to compete on equal terms.
Chapter 56
How did Herschel conclude Newtonian gravitation governs double stars, and who objected?
From gamma Virginis, whose components revolve in 182 years, Herschel found the calculated orbit matched recorded observations across nearly nine-tenths of a circuit, so he held no doubt the Newtonian law prevailed there. Villarceau objected that the observations amount to only seven or eight distinct data, insufficient to prove an ellipse under that law.
Chapter 56
What did the 1835 tide observations cover, and what did the author conclude about cotidal lines?
Through the Admiralty and the Duke of Wellington, tide observations ran for a fortnight at coastguard stations in 1834 and were repeated in 1835 across Europe from the North Cape to Gibraltar and America from the St. Lawrence to the Mississippi. The author argues cotidal lines suit littoral tides but are precarious across oceans, where tides are more like stationary undulations.
Chapter 56

Section 574 cards

What does Whewell call sciences that reduce secondary qualities like sound, light, and heat to mechanical laws via a medium?
Whewell names them the Secondary Mechanical Sciences. Their phenomena do not appear to the senses as position and motion, but as secondary qualities derived from those primary attributes, and they are reduced to mechanical laws only in a secondary manner, by treating them as the operation of a medium interposed between the object and the organ of sense. The three he lists are Acoustics, Optics, and Thermotics.
Chapter 57
According to Whewell, what is the stated purpose of his history of each science?
Whewell says his object is not to give a full statement of all additions to knowledge or a complete list of contributors, but to present the progress of each branch as a theoretical science: to point out the Epochs of discovery of general principles that reduce many facts to one theory, and to note what is most characteristic and instructive in the circumstances and persons bearing on those Epochs.
Chapter 57
Why does Whewell begin the Secondary Mechanical Sciences with Acoustics rather than Optics or Thermotics?
Whewell gives two reasons. First, progress toward right theoretical views was in fact made much earlier in the science of Sound than in Light or Heat. Second, a clear comprehension of the theory reached in Acoustics is the best preparation for the difficulties, by no means inconsiderable, of the reasonings of theorists on the other subjects.
Chapter 57
What does Whewell say about early speculators and the true theory of sound?
Whewell states that in some measure the true theory of sound was guessed by very early speculators on the subject, though undoubtedly conceived in a very vague and wavering manner. He thus credits early thinkers with partial insight while denying them a clear or stable grasp of the theory.
Chapter 57

Section 584 cards

How did Sauveur calculate the vibration rate of a harpsichord string?
Sauveur treated a horizontally stretched string's flat curve (festoon) as analogous to pendulum swingings. Observing the middle C string hung 1/323rd of an inch, he calculated by pendulum laws an oscillation time of 1/122nd of a second, giving 122 vibrations per second for his fixed note. Whewell notes the process, though seemingly arbitrary, can be justified mechanically.
Chapter 58
What did Brook Taylor contribute to the vibrating string problem in 1715?
In his Methodus Incrementorum, Taylor first attacked and mastered the problem, showing the string might move in a curve like the companion to the cycloid, confirming the established laws relating tone to length, tension, and bulk. Whewell calls it the most important step, though Taylor showed only a possible mode of vibration, not the necessary one.
Chapter 58
What did Newton's Principia establish about how sound propagates?
Newton explained that a vibrating body propagates pulses through an elastic medium: air parts move forward and back, successively affecting more distant parts. Forward motion condenses, return allows extension, and elasticities from these changes supply the propagating forces. Whewell notes Newton showed a possible oscillation type, not the necessary one, and his velocity estimate (968 feet) fell short of later measurements.
Chapter 58
How did early experimenters measure the velocity of sound, and what did they find?
Gassendi used fire-arms and found 1473 Paris feet per second, and was surprised that loud and gentle sounds travel at the same speed. Roberval's small figure of 560 feet threw uncertainty on results and affected Newton's reasoning. Cassini, Huyghens, Picard, and Römer found 1172 Paris feet, more accurate than Gassendi's. Newton's Principia later gave the theoretical explanation.
Chapter 58

Section 594 cards

How did Lagrange and Bernoulli differ in modeling air vibration in flutes?
Lagrange treated the vibration of open flutes as oscillations of a fibre of air, with elasticity at both ends equal to the surrounding atmosphere throughout. Bernoulli supposed the whole inertia of the air in the flute collected into one particle, moved by the whole elasticity from its displacement. The author notes both come near Newton's theory and that Bernoulli perhaps laid down a hypothesis more special than necessary.
Chapter 59
What did experimental research show about mathematicians' assumed nodal positions in pipes?
Early mathematicians supposed that when a pipe's air vibrates with several nodes dividing it into equal parts, the part adjacent to the open end is half the other parts. Savart and later Mr. Hopkins of Cambridge traced nodes experimentally and found the outermost node is displaced from that assigned position by a quantity depending on several collateral circumstances.
Chapter 59
What did Chladni contribute to the study of nodal lines?
Chladni discovered the vast variety of symmetrical figures of nodal lines shown on regularly shaped plates when made to sound. His first investigations, Entdeckungen über die Theorie des Klangs, appeared in 1787, with further discoveries in 1802 and 1817. He traced square-plate vibrations to forms with nodal lines parallel to the sides and established a notation such as 5-2 for five lines parallel to one side and two to another.
Chapter 59
How did Poisson and Cauchy advance the mathematical theory of vibrating elastic bodies?
Poisson demonstrated the fundamental equation in an 1814 memoir and determined the relation of notes from longitudinal and transverse vibrations of a rod, plus circular plates with concentric nodal lines. Cauchy calculated transverse, longitudinal, and rotatory vibrations of elastic rods, agreeing closely with experiment. The author concludes mathematics has handled simpler cases, but most complex cases remain unsubdued.
Chapter 59

Section 603 cards

How does Whewell divide optics, and why is the division harder to keep than in astronomy?
Whewell divides optics into Formal Optics (laws of phenomena) and Physical Optics (their causes), just as astronomy is divided. He argues the distinction is clear but hard to maintain in narrative, because once theory advanced, many laws of phenomena were studied in direct reference to the theoretical cause. In astronomy, Formal Astronomy was nearly complete before Physical Astronomy began, since mechanics had to be built first.
Chapter 60
What did Alhazen contribute to the understanding of refraction?
Alhazen, an Arabian mathematician, argued refraction occurs toward the perpendicular and cited experiment for this. He stated that the quantities of refraction differ with the magnitudes of the angles the incident rays make with the perpendicular, and decisively asserted that angles of refraction do not follow the proportion of angles of incidence. Whewell calls his work the most considerable monument of Arabian scientific genius, largely not borrowed from Greek sources.
Chapter 60
How did Descartes explain the rainbow's narrow bright circle and secondary bow?
Earlier writers, including Fleischer, Kepler, and Antonio de Dominis, had ascribed the rainbow to sunlight refracted into raindrops, reflected at the inner surface, and refracted out again. But none explained why there is a narrow bright circle of definite diameter. Descartes showed that rays emerging after two refractions and a reflection at about forty-one degrees from their original direction are far denser than elsewhere, and similarly accounted for the secondary bow.
Chapter 60

Section 614 cards

What did Hooke and Huyghens object to in Newton's optics, and what did each propose?
They objected less to the laws of refraction of different colors than to Newton's expressions about the composition and nature of light. Hooke maintained all natural colors arise from combinations of two primaries, red and violet; Huyghens held a similar doctrine using yellow and blue. Both also held light consisted in vibrations and objected that Newton's language implied light was a body.
Chapter 61
Why did Newton believe achromatic refraction was impossible, and what did he pursue instead?
Newton held the false opinion that dispersion must be the same when refraction is the same, so he concluded the chromatic imperfection of lenses was insurmountable and achromatic refraction could not be obtained. This led him to turn to reflecting rather than refracting telescopes. The later correction of this error further confirmed his general principles, and his law of refraction was hardly questioned afterward.
Chapter 61
How did Dollond's 1757 experiment overturn Newton's rule about colorless refracted light?
Newton had claimed light is white after refraction only when emergent rays are parallel to incident ones. Dollond repeated the experiment and found that an object seen through two prisms, one glass and one water, at angles producing no apparent displacement, was still colored. Hence rays could be refracted without being colored, making an achromatic telescope possible. Euler had already argued from the human eye that such a combination must exist.
Chapter 61
What was Goethe's theory of color, and how does Whewell explain Goethe's rejection of Newton?
Goethe held colors arise when light or darkness is seen through a dim medium: light through dimness appears yellow, deepening to ruby-red; darkness through an illuminated dim medium appears blue, becoming violet. He also invoked accessory images in refraction. The author argues Goethe lacked geometrical habits of thought and conceived 'composition' of colors differently, so he never grasped Newton's doctrine.
Chapter 61

Section 624 cards

What did Huyghens discover about two Iceland spar crystals in parallel positions?
Huyghens found that when two rhombohedrons of Iceland spar are in parallel positions, a ray doubly refracted by the first is not further divided by the second: the ordinarily refracted ray is only ordinarily refracted, and the extraordinary ray only extraordinarily refracted. If the second crystal's principal plane is perpendicular to the first's, the reverse occurs; in other positions, four rays result.
Chapter 62
How did Newton explain polarization phenomena in the 1717 Opticks?
Newton proposed that rays of light have "sides," undergoing ordinary or extraordinary refraction according as these sides are parallel to the crystal's principal plane or at right angles to it (Query 26). Whewell notes this view captures some leading features but leaves considerable difficulties, and it was not until Malus, about a hundred years later, that the subject materially advanced.
Chapter 62
What did Malus discover about polarization in 1808-1811?
Malus accidentally observed in 1808 that light from the setting sun reflected off the Luxembourg windows varied in intensity through Iceland spar. He found complete polarization by reflection occurs at a definite angle for each substance, that double-refracting crystals polarize the two rays oppositely, and that polarization by reflection, water, or double refraction is identical. The term "polarization" was introduced in 1811.
Chapter 62
What is Brewster's rule for the polarizing angle?
In 1815 Sir D. Brewster stated that the index of refraction is the tangent of the angle of polarization. It follows that polarization occurs when the reflected and refracted rays are at right angles. Whewell calls this simple rule fully confirmed by later observations and one of the happiest and most important discoveries of the laws of phenomena in optics.
Chapter 62

Section 634 cards

What did Arago observe in quartz in 1811, and how did Herschel connect it to crystal form?
Arago observed that quartz plates cut perpendicular to the axis twist the plane of polarization to the right or left, with the amount differing by color—later called circular polarization. Herschel discovered this polarization corresponded to the plagihedral faces of the crystal, the right- or left-handed character of the polarization matching that of the crystal in all cases.
Chapter 63
What did Biot discover in 1815 about circular polarization in fluids?
Biot found that circular polarization, which seemed to require crystalline structure, also belonged to several fluids, with different rotation directions: oil of turpentine and an essential oil of laurel rotated the plane to the left, while oil of citron, syrup of sugar, and a solution of camphor rotated it to the right. Seebeck independently made a similar discovery soon after.
Chapter 63
Why does Whewell not credit Huygens as the epoch-maker of the undulatory theory?
Whewell argues Huygens found only strong presumptions for the theory, not establishment. It was not established until later, when the fringes of shadows, rightly understood, made the waves visible, and when the hypothesis assumed for double refraction was found also to explain polarization. Whewell still calls Huygens the leading figure of the prelude.
Chapter 63
What role did Newton play in the reception of the undulatory theory?
Newton adopted the emission hypothesis and gave it currency among his followers, keeping the sounder undulatory theory down for over a century. Yet he was not wholly averse to an ether: in 1672 he said the vibrations of the ether were as useful and necessary as Hooke's hypothesis, and he treated ether vibrations as probable to the last, though he developed emission mathematically while leaving the ether as queries.
Chapter 63

Section 643 cards

What did Young's 1801 paper on thin plates conclude about the undulatory theory?
In a paper read before the Royal Society on November 12, 1801, Young states that further consideration of the colors of thin plates converted his earlier prepossession for the undulatory theory into a very strong conviction of its truth and efficiency. He says this conviction was later most strikingly confirmed by an analysis of the colors of striated surfaces.
Chapter 64
How did Young explain the periodical colors of thin plates and Coventry's micrometers?
Young explained the colors observed in Coventry's micrometers, where lines were drawn on glass at 1/500th of an inch apart, by the interference of undulations of rays reflected from the two sides of these fine lines. Similarly, he accounted for the colors of thin plates by interference of light partially reflected from the two surfaces of the plates, a suggestion Hooke had made earlier.
Chapter 64
What difficulty and what inaccuracy did Young's early views contain, according to the chapter?
The difficulty was that Young found it necessary to suppose light reflected at a rarer medium is retarded by half an undulation, an assumption later justified by mechanical principles. The inaccuracy was his considering the external fringe of shadows as interference of a ray reflected from the object's edge with a ray passing clear of it, rather than all parts of the wave interfering.
Chapter 64

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What did Fresnel's 1821 theory predict about refraction in biaxal crystals?
Fresnel's solution, presented to the French Institute in November 1821 and extended in 1822 memoirs, showed that the wave surface in biaxal crystals is a complex symmetrical double envelope. From it he concluded that in biaxal crystals both rays suffer extraordinary refraction according to determinate laws, unlike uniaxal crystals where a sphere and spheroid govern the rays.
Chapter 65
How did Fresnel's predicted polarization directions compare with Biot's empirical law?
Fresnel's theory gave polarization directions for the two rays that were not exactly accordant with Biot's experimental law but deviated so little that there could be small doubt the empirical formula was wrong and the theoretical one right. The theory thus corrected while it explained the best prior observations.
Chapter 65
What did Arago and Fresnel establish in 1816 about interference of polarized light?
They proved by direct experiment that pencils of light with a common origin and polarized in parallel planes interfere completely, while those polarized in opposite, that is perpendicular, planes do not interfere at all. Fresnel then used these principles to explain the colors produced by crystallized plates, including the need for initial polarization and the analyzing plate.
Chapter 65
What did Fresnel predict about internal reflection and Fresnel's rhomb?
Fresnel extended his formulae to internal reflection at the surface of a transparent body, a case where the formulae became imaginary. Interpreting these impossible operations, he concluded that reflection through a rhomb of glass of a certain form, since called Fresnel's rhomb, would produce circular polarization, a kind altogether different from those previously considered. Trial completely confirmed this unexpected result.
Chapter 65

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Who reviewed Young's 1803 Bakerian Lecture on light, and what was the verdict?
Mr. (later Lord) Brougham wrote the critique in the Edinburgh Review, published January 1803. It was, per Whewell, an uninterrupted strain of blame and rebuke: Brougham said the paper contained nothing deserving the name of experiment or discovery, charged Young with dangerous relaxations of physical logic, called his ideas a mere hypothesis of fancy, and urged the Royal Society to stop admitting hasty papers.
Chapter 66
Why did Young's own style of presentation fail to win converts?
Whewell says Young's mathematical reasonings put his work out of reach of popular readers, while his want of symmetry and system in symbolical calculations made it unattractive to mathematicians. Young himself admitted that, from dislike of algebraical formality seen in foreign authors, he fell into an affectation of simplicity equally inconvenient to scientific readers.
Chapter 66
How did Fresnel's undulatory theory fare in France, and who opposed it?
It was little noticed until Fresnel revived it; even then older mathematicians opposed it. Laplace and other leading Institute members were so vehemently opposed they would not tolerate arguments for it, and Arago, as a member, bore the brunt of the debates. Fresnel's key memoirs were delayed in publication, though his diffraction memoir was crowned in 1819 and a commission of Ampère, Fourier, and Arago reported on his double-refraction work in 1822.
Chapter 66
What was the outcome of the controversy between undulation and Biot's moveable polarization?
Whewell calls it the last struggle in favor of the emission theory among eminent mathematicians. Biot conceded that the undulatory theory took phenomena at a higher point and carried them further, but Fresnel could surrender no part of his all-of-one-piece hypothesis. After this crisis, moveable polarization lost ground, and explanations published in the Annales de Chimie et de Physique, with Arago as a conductor, spread the undulatory theory over Europe.
Chapter 66

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How did Fresnel test his predicted law of retardation using a glass rhomb?
Fresnel calculated the proper angles for a circularly-polarizing glass rhomb assuming four internal reflections rather than two, with two occurring when the surface was dry and two when wet. When made, the light was not circularly polarized with all points dry, was circularly polarized with two points wet, and was not circularly polarized with all four wet—verifying the prediction.
Chapter 67
What hypothesis did Airy propose to explain the colored rings around quartz's central spot?
Airy hypothesized that rays oblique to the axis of a quartz crystal are elliptically polarized, with ellipticity depending in some unknown manner on obliquity, and that each ray is split by double refraction into two elliptically polarized rays, one right-handed and one left-handed. He argued this supposition represented the phenomena, including minute deviations from symmetry, with extreme accuracy.
Chapter 67
How did Mac Cullagh modify the equations of motion to account for circular and elliptical polarization?
Mac Cullagh added to the two equations of motion, expressed by second differentials, two other terms involving third differentials in a simple symmetrical manner. This introduces a coefficient whose magnitude determines both the rotation of polarization along the axis (as measured by Biot) and the ellipticity of oblique rays (per Airy's theory), with the two sets of measures agreeing strikingly.
Chapter 67
What did Hamilton predict about conical refraction, and who verified it?
Hamilton deduced from the Fresnelian doctrine of double refraction that in one particular crystal direction a single ray would be refracted into a conical pencil. Because the wave surface has a cusp, a tangent plane can touch it in an entire circle, so the ray travels to every point of that circle. His friend Professor Lloyd verified this experimentally and found the conical light polarized by an unusual law consistent with theory.
Chapter 67

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What two sciences does Whewell use to illustrate the same type of scientific progress?
Whewell compares Physical Astronomy and Physical Optics, arguing both follow the same pattern: Laws of Phenomena accumulated by acute and inventive men, then Preludial guesses touching the true theory but remaining imperfect and unconfirmed, then an Epoch when the true theory is clearly apprehended and confirmed by explaining what it was not meant to explain.
Chapter 68
Whom does Whewell pair to make up 'the Newton of optical science'?
Whewell says Young and Fresnel combined make up the Newton of optical science. He pairs Huyghens and Hooke as standing in the place of Copernicus, since they announced the true theory but left its development and mechanical confirmation to a future age, and groups Malus and Brewster as corresponding to Tycho Brahe and Kepler.
Chapter 68
What did Sir John Herschel discover about quartz crystals and circular polarization?
Herschel discovered that circular polarization is right-handed or left-handed according as the plagihedral form of the quartz crystal is so. Whewell notes such crystals resemble right- or left-handed screws, and that in Tovey's hypothetical investigation it does not appear on what part of the hypothesis this difference of right and left-handed depends.
Chapter 68
What does Whewell mean by Atmology, and how does it relate to Meteorology?
Whewell borrows Atmology from the Greek word for vapor to cover laws and principles concerning the relations of heat and moisture. He says Meteorology in its collective form is composed of parts of many different sciences, and that it is useful to consider separately those portions referring to the laws of aqueous vapor, which he includes under Atmology.
Chapter 68

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How did Leslie measure underground temperature, and what did he find?
Leslie sank thermometer bulbs to depths of one, two, four, and eight feet at Abbotshall in Fifeshire, observing in 1813, 1816, and 1817. He found the annual oscillation diminished with depth: a range of twenty-five degrees Fahrenheit at one foot, twenty at two, fifteen at four, and only nine and a half at eight feet. The time of maximum heat also came later at greater depths, while the mean temperature of all thermometers was nearly the same.
Chapter 69
What did Fourier conclude about the Earth's internal heat and its surface effects?
Fourier concluded that the observed increase of temperature in descending can arise only from remaining primitive heat. Solar heat alone, in its permanent state, would be uniform below the superficial oscillations, and would decrease rather than increase with depth. He calculated that an increase of one degree per forty yards is consistent with the surface being less than a quarter degree hotter than it would otherwise be.
Chapter 69
What did Fourier propose about the heat of planetary spaces, and who agreed?
In his 1827 memoir, Fourier argued that planetary spaces are not absolutely cold but possess a proper heat independent of the sun and planets; without it, polar cold would be more intense and solar alternations more extreme. He assigned the radiation of the innumerable stars as its cause. Svanberg reached the same temperature, fifty degrees centigrade below zero, by different reasoning about the atmosphere.
Chapter 69
How did Dulong and Petit correct Newton's law of cooling?
Experimenting in 1817 through a range up to two hundred and forty degrees centigrade, and in a vacuum to remove the medium's effect, they found Newton's law inaccurate mainly at high temperatures. They concluded that for a constant excess of temperature, the quickness of cooling increases geometrically as the surrounding space's temperature rises arithmetically; and that, depending on the hot body's excess, quickness follows a geometric progression diminished by a constant.
Chapter 69

Section 704 cards

What did Powell conclude about the polarization of simple radiant heat in 1830?
Powell repeated Berard's experiments with a similar apparatus and found that although heat conveyed along with light is polarizable, "simple radiant heat" showed no difference between the two rectangular azimuths of the second glass, and thus no trace of polarization. With old thermometers the point remained doubtful.
Chapter 70
How did Forbes first demonstrate a decided polarizing effect on heat?
In 1834 Forbes used mica and found a decided polarizing effect, first when heat was transmitted through several films of mica at a certain angle, then when reflected from them. With non-luminous heat, even water below boiling, the difference between parallel and crossed positions was manifest. He also detected tourmaline's polarizing effect, soon confirmed by Melloni.
Chapter 70
How does diathermancy differ from diaphaneity, and what examples does Whewell give?
Diaphaneity is a body's power to transmit light; diathermancy, Melloni's term, is its power to transmit heat. A plate of alum and a plate of rock-salt both transmit nearly all light, but alum stops nearly all heat while rock-salt stops very little; opaque quartz, nearly impenetrable by light, lets much heat pass. Thus heat can be sifted from accompanying light.
Chapter 70
What law of gaseous expansion did Dalton and Gay-Lussac discover, and what later doubts were raised?
For equal increments of temperature, gases expand by the same fraction of their own bulk — three-eighths from freezing to boiling water. Dalton and Gay-Lussac found it independently. Later Magnus and Regnault argued gases expand unequally, but Whewell notes their differences were no larger than those between observers and does not treat the law as disproved.
Chapter 70

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What did Wallerius Ericsen establish about water evaporation, and what did he conclude from it?
By various experiments Wallerius Ericsen established the important fact that water evaporates in a vacuum. From this he inferred the falsity of the common explanation of evaporation by the solution of water in air. He also judged there are two causes: one producing the first ascent of vapors (mutual repulsion of particles), the other supporting them afterwards, and concluded permanently-elastic air is different from vapor.
Chapter 71
What did Le Roi's solution theory explain, and what was its fatal defect?
Le Roi's theory held that air, like other solvents, could be saturated, with excess water appearing visibly; the saturating quantity depended mainly on warmth and wind. It explained transparency of vapor, precipitation by cooling, disappearance of visible moisture by warming, and increased evaporation by rain and wind. Its fatal defect: it does not apply to facts that occur when air is excluded.
Chapter 71
What two arguments against independent vapor did Robison give, and how were they answered?
Robison argued that when moist air is suddenly rarefied, water precipitates, which the new doctrine should not predict, and that if vapor and air were merely mixed, the heavier fluid would settle below the lighter. The first was answered by noting rarefaction changes specific heat and lowers temperature below the vapor's constituent temperature; the second by reference to Dalton's law of the mixture of gases.
Chapter 71
What did Pictet's 1786 experiment and 1791 Essay on Fire demonstrate?
Pictet's Essay on Fire in 1791 demonstrated that all the train of hygrometrical phenomena takes place just as well, indeed rather quicker, in a vacuum than in air, provided the same quantity of moisture is present. Together with De Luc's 1792 paper in the Philosophical Transactions, this gave the death-blow to the theory of the solution of water in air.
Chapter 71

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What did Dalton conclude about steam elasticity at equidistant temperatures in 1801?
Dalton told the Manchester Philosophical Society that his elasticities for equidistant temperatures resembled a geometrical progression, but with a ratio constantly diminishing. He also noted that while forces at high temperatures matter most for steam as a mechanical agent, philosophy is more immediately interested in accurate observations at low temperatures.
Chapter 72
What did the French and American government steam experiments find about the law of elastic force?
The French experiments (1823, directed by Prony, Arago, Girard, and Dulong) reached 435°F, corresponding to 24 atmospheres, and indicated increase of elastic force according to the fifth power of a binominal 1 + mt. The American Franklin Institute experiments (1830, Bache and others) reached 346°F, over 9 atmospheres, and led to a sixth power of a like binominal.
Chapter 72
According to Wells's Essay on Dew, what causes dew formation?
Wells recounts that in 1784 he first thought dew formation produced cold, but later suspected he, Wilson, and Six had erred in treating the cold as an effect. He came to regard the cold as the cause, supposing bodies on which dew is deposited are cooled by radiation into the clear night-sky to the proper temperature. Davy applied the same principle to mists over streams and lakes.
Chapter 72
How did Daniell's hygrometer improve on earlier hygrometers?
Earlier hygrometers measured moisture by expansion or contraction of organic substances — De Saussure's hair, De Luc's whalebone, Dalton's whipcord — but were variable and their readings hard to interpret physically. The dew-point is constant and definite. Le Roi and Dalton (1802) used it with cold water condensation; Daniell (1812) built an instrument producing the condensing temperature by evaporation of ether, enabling determination of vapor quantity in a given air mass.
Chapter 72

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What evidence did Forbes and others offer for an undulatory theory of heat?
Biot and Melloni found quartz impresses circular polarization on heat; Forbes found mica of certain thickness produces effects like circular polarization of supposed transversal vibrations of radiant heat; a rock-salt rhomb shaped like Fresnel's glass rhomb verified expected polarization of heat. Forbes also tried to calculate heat's undulation length from polarized heat through mica. Whewell says these analogies strongly dispose one toward an undulatory theory, but it lacks full confirmation.
Chapter 73
Why does Whewell say the undulatory theory of heat is not yet fully confirmed?
It rests on analogy with the theory of light and would have little weight without it. The separation of rays in double refraction and periodical intensity phenomena—the two fact classes from which the undulatory theory of optics grew—have not been detected in thermotical experiments. Forbes assumed alternations of heat for increasing mica thicknesses, but his experiments show only one maximum; alternate maxima and minima would exhibit visible waves of heat.
Chapter 73
What is Laplace's atmological hypothesis of heat, and what laws does it explain?
Laplace proposed bodies consist of particles each attracting a quantity of caloric; particles attract each other and caloric, and caloric particles repel each other. In gases, particle attraction is insensible and caloric's mutual repulsion tends to expand matter; internal radiation density is temperature. It explains Boyle-Mariotte, Gay-Lussac-Dalton expansion, heat from compression, Dalton's mixtures, expansion of solids and fluids, and changes of consistence.
Chapter 73
Why does Whewell judge Laplace's theory unfavorably, and how does it conflict with vibratory heat?
Whewell says a true theory shows consilience of inductions—hypotheses assumed for one class of facts explaining another class. Laplace's theory shows none of this unexpected confirmation; his assumptions bear a large proportion to laws explained, and latent heat requires a new quantity that produces no effect on his calculations. Ampère notes that if heat consists in vibrations, attributing a repulsive force to caloric particles is a contradiction.
Chapter 73

Section 744 cards

Who first received the electric shock from a water-filled vessel, and when?
Cunæus, a native of Leyden, received a sudden shock in his arms and breast in 1746 while handling a vessel of water connected to an electrical machine and bringing its inside and outside into connexion; the apparatus was named the Leyden phial after him. The chapter notes, however, that Von Kleist, a German prelate at Camin in Pomerania, had received a shock under nearly the same circumstances in 1746.
Chapter 74
How did Franklin explain the action of the Leyden phial?
Franklin showed in 1747 that the inside of the bottle is electrized positively and the outside negatively, and that the shock is produced by the restoration of equilibrium when the two are suddenly connected. He held that the whole force of the bottle is in the glass itself, and that non-electrics in contact with the glass served only to unite the force of the several parts. The author notes Franklin was less successful in tracing how the electric matter acts upon itself.
Chapter 74
What did Canton, Wilcke, and Æpinus contribute to electrical theory?
Canton's experiments, communicated to the Royal Society in 1753, showed that the electricity on one body acts on another at a distance with repulsive energy. Wilcke showed that parts of non-electrics plunged in electric atmospheres acquire electricity opposite to that of the atmospheres. Æpinus devised a method of examining the electricity at any part of a body's surface, ascertained its distribution, and found it agreed with a law of self-repulsion; his attempt at mathematical precision was an important step toward electrical theory.
Chapter 74
How was the analogy between lightning and electricity verified, and at what cost?
In 1752 D'Alibard and other French philosophers erected a pointed iron rod forty feet high at Marli, which gave out electrical sparks when a thunder-cloud passed over. Franklin suggested a kite for communicating with the clouds. The essays led to a fatal accident: Richman at Petersburg was struck dead on Aug. 6th, 1753, while observing electricity from an approaching thunder-cloud by means of a rod he called an electrical gnomon.
Chapter 74

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Why was the electric fluid accepted as a physical reality rather than a mere hypothesis?
The author states that the light, sound, and mechanical effects produced by the electric discharge caused the electric fluid to be universally accepted as a physical reality, not merely a mathematical hypothesis useful for reducing phenomena to formulae. By contrast, the magnetic fluid had long been treated only as a mathematical hypothesis. The fluid's existence was thus learned through the common use of the senses.
Chapter 75
Who established the inverse-square law for electric force, and with what instrument?
The author credits Coulomb with the clear and satisfactory establishment of the inverse-square law, in papers in the Academy Memoirs for 1785. Robison had already proved it in 1769, and Meyer discovered but did not publish the same result. Coulomb's invention of the torsion-balance, which measures very small forces with certainty and exactness, enabled him to settle the question for ever.
Chapter 75
What did Coulomb conclude about where electricity resides on conductors?
Using a small disk he called his tangent plane, applied to bodies and then removed as an electric taster, Coulomb found that the electricity is entirely collected at the surface of conductors. The author notes Beccaria had before shown this to be the case. Coulomb also recorded electric intensity at the surfaces of globes, cylinders, and other conducting bodies placed within each other's influence in various ways.
Chapter 75
Why did the Coulombian theory not receive the general reception one might expect?
The author argues this was partly owing to the extreme abstruseness of the mathematical reasoning it employs, which put it out of reach of most experimenters and writers of general works. He adds that English compilations still state the one-fluid and two-fluid theories as nearly on a par in experimental evidence. He also notes the theory lacked the fuller, more varied confirming experiments that other permanent sciences had.
Chapter 75

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What fundamental magnetic facts did Gilbert establish in De Magnete?
Gilbert's work contains all the fundamental facts of magnetism, so fully examined that little has been added since. His first Book covers that the magnet has poles, that these may be called north and south poles, and that in two magnets the north pole of each attracts the south pole and repels the north pole of the other. The author calls this the cardinal fact on which generalizations rest.
Chapter 76
Who discovered the dip of magnetic iron, and when?
Robert Norman, described by Gilbert as a good seaman and ingenious artificer, first discovered the dip of magnetic iron. This important discovery was made in 1576. Gilbert lists Norman among Englishmen who observed magnetic variations and invented instruments, citing his work the New Attractive.
Chapter 76
What did Gellibrand discover about magnetic variation in 1633?
Gellibrand discovered that the variation is not constant, as Gilbert had imagined, but that at London it had diminished from eleven degrees east in 1580 to four degrees in 1633. Since then the variation became more westerly, reaching about twenty-five degrees west, and the needle is supposed to have begun traveling eastward again.
Chapter 76
What did Coulomb establish about magnetic force and the earth's directive force?
Coulomb first clearly confirmed by torsion-balance that magnetic force follows the inverse square law, as Mayer in 1760 and Lambert had asserted against Newton's inverse-cube guess. He also established that the directive magnetic force the earth exerts on a needle is a constant quantity, parallel to the magnetic meridian, passing through the same point of the needle whatever its position.
Chapter 76

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What did Humboldt's magnetic storms turn out to be, and how was this detected?
Small, irregular disturbances in the needle's position, termed magnetic storms by M. de Humboldt, were found to rage simultaneously over large tracts of the globe. This was detected about 1825 by comparing M. Arago's observations at Paris with simultaneous observations by M. Kupffer at Kasan in Russia, more than 47 degrees of longitude apart.
Chapter 77
What did Gauss assume about terrestrial magnetism, and what function did he derive?
Gauss rejected the arbitrary assumption of definite magnetic poles, two, four, or more, and instead assumed magnetism is distributed throughout the earth's mass in an unknown manner. From this he obtained a function V whose differentials express the magnetic force elements at any point; it was proposed to call it the 'integral proximity' of the attracting mass.
Chapter 77
How many magnetic poles does the earth have under Gauss's simplest meaning of 'pole'?
According to the most simple meaning of the term 'pole' — points where the magnetic force is vertical — the earth has only two magnetic poles. The isogonal curves are deformations of Euler's two-pole curves, and Hansteen's Siberian 'pole' is really a region of convergence that never comes to a point.
Chapter 77
What did the British government and others establish after Humboldt's 1836 appeal?
Humboldt wrote to the Duke of Sussex, then President of the Royal Society, asking for British co-operation. The Royal Society and the British Association, at Newcastle in 1838, promoted the cause, and the British government established four complete magnetical observatories at Toronto, St. Helena, the Cape of Good Hope, and Van Diemen's Land; the East India Company founded four more in India and Sincapore.
Chapter 77

Section 784 cards

What did Volta identify as the essential conditions of Galvani's new action?
Volta concluded (about 1794) that the essential conditions depended on the metals: the action is brought into play most decidedly when two different metals touch each other and are connected by any moist body. The animal parts used served as both moist bodies and sensitive electrometers. He suggested Galvani's "animal electricity" be called "metallic electricity."
Chapter 78
What did Volta's pile of 1800 consist of, and how did Cruickshanks modify it?
The voltaic pile, described in the Philosophical Transactions for 1800, repeated the triple combination of two metals and a fluid in contact, forming a circuit returning into itself. Cruickshanks introduced the most important modification, substituting a trough for a pile. The principle stayed the same in all versions. Whewell calls the pile a more important step than the Leyden jar.
Chapter 78
How did the political revolutions of Italy affect Galvani and Volta differently?
Galvani refused to swear allegiance to the Cisalpine republic the French established, was stripped of his offices, and sank into poverty and melancholy. The republic later decreed his restoration, but he died in 1798 without profiting. Volta was called to Paris by Bonaparte and received honors, emoluments, and titles.
Chapter 78
What did Oersted announce in 1820 about a voltaic wire and a magnetic needle?
Oersted of Copenhagen announced that the conducting wire of a voltaic circuit acts upon a magnetic needle, reviving the effort to connect magnetism with electricity. He found the needle tends to place itself at right angles to the wire, an action altogether different from any previously suspected. Whewell says the observation was of vast importance.
Chapter 78

Section 794 cards

How did Ampère avoid fully integrating the electrodynamic force equations?
Ampère noted that if his integrals could be shown to vanish over the whole under certain conditions, this would correspond to apparatus arrangements preserving equilibrium even when some parts changed form. He found two such cases of great importance to the theory, one proving the force of any voltaic wire element could be resolved into other forces by a theorem resembling the parallelogram of forces.
Chapter 79
What did Ampère's first equilibrium case prove about a straight wire?
It proved that the force exerted by any element of the voltaic wire might be resolved into other forces by a theorem resembling the parallelogram of forces. This was shown by demonstrating that the action of a straight wire is the same as that of another wire joining the same extremities but bent and contorted in any way whatever.
Chapter 79
What two fundamental quantities remained to be determined in Ampère's theory?
One expressed the power of the distance according to which the force varied; the other, the degree in which the force is affected by the obliquity of the elements. One of the general causes of equilibrium gave a relation between these two quantities; and since the power was conjectured, and later appeared rightly, to be the inverse square, the other quantity was also determined and the problem fully solved.
Chapter 79
How did Ampère's theory fare on publication, and why?
Whewell notes it was hailed with far less enthusiasm than so remarkable a triumph of generalizing power might appear to deserve, because clear mathematical conceptions and familiarity with mathematical operations were needed to appreciate the evidence. For some time much of the public was held in suspense by the opposing weight of rival names, and the theory advanced amid contention and competition.
Chapter 79

Section 804 cards

What did the doctrine of the three principles hold, and what was its real value?
It held that the first principles of things are three—salt, sulphur, and mercury—not four, and that all things are compounded of these. The author argues it contained no valuable truth, since the extracted substances were named salt, sulphur, and mercury to save the hypothesis rather than because they truly were those substances, as Boyle urged. Its only real advance was acknowledging that chemical operations involve union and separation of substantial elements.
Chapter 80
What does the term Spagiric art denote, and why does Whewell treat it as a real step?
The Spagiric art (often misspelt Spagyric) comes from Greek words meaning to separate parts and to unite them—that is, analysis and synthesis, which constitute the whole business of the chemist. The author argues that recognizing this object marks a genuine step in chemistry's progress, so he is not making a fanciful arrangement when he singles it out.
Chapter 80
What did Sylvius contribute to chemistry, and how did Boyle respond?
Francis de la Boé Sylvius, born 1614, framed a system treating acid and alkaline bodies as eminently acrid yet opposite, and applied this to the human frame—lymph containing an acid, bile an alkaline salt—which neutralize each other into a milder substance. Boyle doubted the view, arguing that supposing acid and alkaline parts in all bodies was precarious and the notion unsettled.
Chapter 80
What proposition did Geoffroy state about elective attractions, and how did he qualify it?
Geoffroy stated that when two substances disposed to combine are united, and a third approaches with more affinity for one of them, that one unites with the third and lets go the other. He presented affinities as a table, allowing separation is not always complete. He could not enunciate the proposition as universal, not having examined all possible combinations.
Chapter 80

Section 814 cards

What did Black discover about caustic lime versus common limestone?
Black found that common limestone consists of caustic lime combined with a certain air fixed in the solid body, which he called fixed air (carbonic acid gas). He also found that magnesia, caustic potash, and caustic soda would combine with the same air with similar results. He announced this discovery in his inaugural dissertation at Edinburgh in 1755.
Chapter 81
What did Cavendish conclude from burning inflammable air in common air?
Cavendish found that when inflammable air is used in phlogistication (burning), the diminution of common air is accompanied by the formation of a dew in the apparatus. He inferred that almost all the inflammable air and one-fifth of the common air are turned into pure water. This discovery of water's composition was published in the Philosophical Transactions for 1784.
Chapter 81
Who is credited with the first great step in pneumatic chemistry, and why?
The author states the credit is justly assigned to Dr. Black, who was twenty-four when he made his discovery. Black found that the difference between caustic lime and common limestone arose from the latter consisting of the former combined with fixed air. The author notes that despite earlier preludes by Newton, Boyle, Rey, Hooke, and Mayow, Black deserves credit for this first great step.
Chapter 81
How did the phlogiston theory shape chemical nomenclature?
The phlogiston theory, established from Berlin and diffused across Europe, shaped naming: Priestley's oxygen was called dephlogisticated air, Scheele's chlorine dephlogisticated marine acid, and azotic acid gas, having no disposition to combustion, was called phlogisticated air. This phraseology persisted until expelled by the antiphlogistic, or oxygen, theory, and Cavendish's papers were expressed in its terms.
Chapter 81

Section 824 cards

Why was Lavoisier imprisoned and executed despite his scientific fame?
Lavoisier was imprisoned on a charge of adulterating tobacco while in public office, though the text says the real motive was confiscating his property. He asked the tribunal for a few days' respite to complete researches important to humanity; he was told the republic wanted no savants and was guillotined on May 8, 1794, in his fifty-second year.
Chapter 82
What was the purpose and structure of the new chemical nomenclature of 1787?
Lavoisier, De Morveau, Berthollet and Fourcroy built a nomenclature matching the new theory, published in 1787. It selected simple radical words and used systematic terminations to express relations: sulphurous and sulphuric acids, sulphides and sulphates, sulphurets, and oxide for a lower oxygen combination. The text notes the old names were fantastical, arbitrary, and multiplied beyond measure.
Chapter 82
How was Lavoisier's claim that acidification always involves oxygen corrected?
The dispute centered on oxymuriatic and muriatic acids. In 1809 Gay-Lussac and Thenard in France, and Davy in England, argued oxymuriatic acid was a simple substance, chlorine, and muriatic acid was chlorine combined with hydrogen, hence hydrochloric acid. Davy's 1812 Edinburgh test of dry muriatic acid with ammonia produced too little water to support the old theory.
Chapter 82
What three parts make up Dalton's law of chemical combination, per Whewell?
Whewell says the law consists of three parts: elements combine in definite proportions; these determining proportions operate reciprocally; and when several combining proportions occur between the same elements, they are related as multiples. He stresses the law of phenomena is the important, certain part, while the atomic view of matter is neither so important nor so certain.
Chapter 82

Section 834 cards

What did Gay-Lussac and Humboldt discover about combining gases?
They found the theory of volumes: gases unite by volume in very simple and definite proportions, such as 1 to 1, 1 to 2, or 1 to 3. For example, water is composed of 100 measures of oxygen and 200 measures of hydrogen. This law includes Dalton's rule as far as it goes but extends only to combinations of gases.
Chapter 83
What did Nicholson and Carlisle discover in 1800 about the voltaic pile?
They found that water was decomposed by Volta's pile: when the wires were placed near each other in the fluid, bubbles arose from each wire, and these were found to be oxygen and hydrogen, already known as water's constituents. Davy called this the true origin of electro-chemical science.
Chapter 83
What conclusion did Davy draw about chemical and electrical attractions?
Davy concluded that combinations and decompositions by electricity were referrible to the law of electrical attractions and repulsions. He advanced the hypothesis that chemical and electrical attractions were produced by the same cause, acting on particles in one case and on masses in the other, and that the same property caused all voltaic phenomena.
Chapter 83
What did Davy achieve after decomposing potassa?
Davy decomposed potassa into a metallic base and oxygen, which he called 'a capital experiment.' This was soon followed by the decomposition of soda and then other similar bodies, turning the intense interest and activity of the whole chemical world to the subject.
Chapter 83

Section 844 cards

What did Faraday's researches establish about electrical and chemical action?
Faraday established the identity of electrical and chemical action, confirming Davy's 1806 view that chemical and electrical attractions arise from the same cause. The author argues Davy's version was only a sagacious conjecture until Faraday supplied interpretation, measure, and proof, comparing this to Newton confirming Borelli and Hooke on gravity, or Young confirming Huygens's undulatory theory.
Chapter 84
How did Faraday describe the role of the conducting wire in the voltaic circuit?
Faraday held that the forces at the point of chemical composition and at the point of decomposition are of the same kind and oppose each other through the conducting wire. He spoke of the wire as conducting chemical affinity, allowing two like forces to oppose one another, and said the pile's circumstances could be expressed using only chemical affinity, though the term electricity is convenient.
Chapter 84
What did Faraday's volta-electrometer allow him to measure?
Combined with his method for comparing voltaic and common electricity, the volta-electrometer let Faraday measure the actual quantity of electricity exhibited as chemical affinity in given cases. He found one grain of water requires for decomposition as much electricity as a powerful lightning flash—not less than 800,000 charges of his Leyden battery, the quantity naturally associated with the elements' mutual affinity.
Chapter 84
What law limits which bodies can undergo electrical decomposition, per Faraday?
Faraday rendered highly probable a remarkable law: only binary compounds consisting of single proportionals of their elementary principles are capable of electrical decomposition. The author declines to speculate on its import but notes it closely connects the Atomic with the Electro-chemical Theory, holding out prospects of wider and more profound generalizations in chemistry.
Chapter 84

Section 854 cards

According to Whewell, what is the object of the classificatory sciences?
The author argues the object of the classificatory sciences is to obtain fixed characters of the kinds of things, and that the criterion of the fitness of names is that they make general propositions possible. Classification must be made consistent and systematic, based on marks and characters that are constant in their occurrence and relations.
Chapter 85
What did Steno and Gulielmini establish about crystal angles?
Nicolas Steno, in a 1669 dissertation, said that though the sides of the hexagonal crystal may vary, the angles are not changed. Dominic Gulielmini, in a 1707 dissertation on salts, held that the inclination of planes and angles is always constant, and that figures must be determined by experiments and observations, not proved a priori.
Chapter 85
Why did Buffon reject crystalline form as a mineral character?
Buffon asserted that the form of crystallization is not a constant character but is more equivocal and variable than any other mineral character, and he made no use of it in his mineral history. Whewell suggests this perverseness may be ascribed to Buffon's reputed dislike of Linnaeus, who had made crystalline form a leading mineral character.
Chapter 85
How did Linnaeus contribute to crystallographic mineralogy?
Linnaeus was the first to attempt arranging minerals by mathematical forms, seeing crystalline form as a definite and important character. Whewell says he failed by not employing geometry, instead using arbitrarily selected and often delusive resemblances, such as deriving pyrites from vitriol and grouping alum with diamond for their common octahedral form. Yet he animated Romé de Lisle to the study.
Chapter 85

Section 864 cards

What did Haüy's use of cleavage lead Romé de Lisle to call innovators in crystallography?
Romé de Lisle referred to innovators in crystallography, in connection with Haüy's use of cleavage, as "crystalloclasts." Yet the chapter notes that Romé himself largely adopted the same views of crystal formation by laminae that Haüy illustrated through the destructive cleavage process he mocked. The author attributes Romé's irritation partly to being overshadowed in his later years by his more brilliant successor.
Chapter 86
What did Wollaston invent that improved the accuracy of measuring crystalline angles?
Wollaston invented the Reflecting Goniometer, which measured the angle of two faces using reflected images of bright objects seen in them, so the measure became more accurate as the faces grew more minute. This placed a new degree of accuracy within reach of crystallographers. William Phillips was especially laborious and successful in using it, and Wollaston said Phillips had "a geometrical sense."
Chapter 86
According to Weiss, what governs crystalline form instead of the atomistic view?
Weiss says that, seeking a dynamical ground instead of the untenable atomistic view, he found that the fundamental relations of the Dimensions gradually unfolded to him — the Axes of Symmetry. These are lines in reference to which every face is accompanied by other faces with like positions and properties. Weiss held that a multiplicity of internal oppositions, each with its own polarity, are developed in the mass, so the crystalline character is co-extensive with these polarities.
Chapter 86
What did the chapter conclude about who introduced Systems of Crystallization, Weiss or Mohs?
The chapter says the introduction of reference to Systems of Crystallization was controversial, with some ascribing it to Weiss and some to Mohs. The author concludes that Weiss first published works employing the method, but Mohs earned the merit of making it the basis of real crystallography by applying it to all known species of minerals. Weiss published his Dissertation in 1809.
Chapter 86

Section 874 cards

What did Haüy assume about chemical composition and crystalline form?
Haüy assumed that the same chemical elements combined in the same proportions always exhibit the same crystalline form, and reciprocally that the same form and angles imply the same chemical constitution (except in the tessular system). Whewell notes this dogma could only be an approximate conjecture, since many glaring and unexplained exceptions existed.
Chapter 87
What did Mitscherlich discover in 1822, and what examples did he give?
Mitscherlich discovered isomorphism: elements that can replace one another without altering crystalline form. He found the carbonates of lime, magnesia, protoxide of iron and protoxide of manganese agree in form with angles varying only one or two degrees; similarly carbonates of baryta, strontia, lead and lime, the felspars, and phosphates with arseniates.
Chapter 87
How did Fuchs anticipate Mitscherlich's law of isomorphism?
Fuchs, as early as 1815, suggested oxide of iron was not essential to Gehlenite but a 'vicarious' element replacing lime. In an 1820 lecture he again used the term vicarious. Whewell stresses this was only a conjectural prelude; Mitscherlich's experimental discovery gave it substance, and Fuchs later retracted his opinions.
Chapter 87
What is dimorphism, and how does it relate to isomorphism?
Dimorphism is when the same definite chemical compound appears in two different crystalline forms, as carbonate of lime occurs as calcspar and arragonite, belonging to different crystallization systems. Whewell argues dimorphism does not interfere with isomorphism; both stand at the same stage of inductive generalization, awaiting a higher truth including both.
Chapter 87

Section 884 cards

What did Mohs attempt to construct for mineralogy, and what did he reject?
Mohs attempted to construct a Natural System of mineralogy that borrowed nothing from chemistry, rejecting all divisions of chemical import. He turned to botany for guidance, and also produced an Artificial System, his Characteristic of the Mineral Kingdom (Dresden, 1820), by which classes are recognized rather than formed.
Chapter 88
How did Mohs answer Whewell's objection that his book alone should yield the natural system?
Whewell asked whether, from Mohs's descriptions alone and without seeing minerals, one could construct the same natural system. Mohs pondered and replied, "It is true; but what an enormous imagination a man must have for such a work!" Vivid conception of sensible properties and steady intuition of objects were held essential by him and the Wernerian school.
Chapter 88
Why did Berzelius's first chemical mineral system collapse?
Berzelius's 1816 system arranged minerals by their electro-positive element, ranked electro-chemically. In 1820 Mitscherlich discovered isomorphism, showing that bodies with very different electro-positive elements could not be distinguished, so they could not be placed in distant parts of the classification. The first system crumbled.
Chapter 88
What did Whewell consider the test of success for mineral systems, and did either succeed?
Whewell argues success requires the chemical and natural-history systems to coincide: a chemical arrangement matching external properties, and a natural-history arrangement matching chemical constitution. Their agreement would be verification. Since the two systems, though tending toward each other, remain far apart, he concludes neither method succeeded.
Chapter 88

Section 894 cards

What vague plant classification persisted in botany until Linnaeus?
The unscientific distinction of vegetables into trees, shrubs, and herbs kept its ground until the time of Linnaeus. Whewell notes that loose terms from common life remained in botany long after their defects were felt, because men did not suspect that a science of classification was the proper remedy.
Chapter 89
What kinds of lore made up the earliest plant knowledge, according to Whewell?
The earliest lore about plants consisted of mythological legends, marvellous relations, and extraordinary medicinal qualities. Whewell explains that early man acquired opinions through fancy, emotions, love of the marvellous, hopes, and fears rather than observation subordinated to reason, so Greek myths like Narcissus and Hyacinthus attached to plants.
Chapter 89
How does Theophrastus describe the root-cutters' rules for gathering plants?
Theophrastus says drug-sellers and rhizotomists tell some things that may be true but others that are mere solemn quackery. He notes rules like drawing a sword three times around the mandragora, cutting it facing west, dancing around it with obscene language, and avoiding an eagle lest the cutter die within a year.
Chapter 89
What error in Pliny's Natural History arose from his hurried reading habits?
Whewell notes that Pliny appears to have had books read to him and heard them amiss. Theophrastus said the plane-tree is rare in Italy, but Pliny, misled by the similarity of the Greek word for rare, spanian, says the tree occurs in Italy and Spain. Pliny's work has been called the Encyclopaedia of Antiquity.
Chapter 89

Section 903 cards

Which botanist does Whewell credit with first establishing plant genera?
Whewell assigns most of the merit for establishing genera to Conrad Gessner of Zurich, who died of plague in 1565 while preparing a History of Plants. Gessner stressed that flower and fruit are the key characters for detecting plant affinities, and Whewell notes that the best botanists, including Linnaeus and Haller, declare Gessner the inventor of genera.
Chapter 90
How did Hieronymus Tragus (Jerom Bock) advance plant arrangement in 1551?
Whewell says Tragus, a laborious German botanist, published a herbal in 1551 in which several natural families, such as the Labiatæ, Cruciferæ, and Compositæ, are for the most part brought together. Though many mistakes remained about such connections, Whewell treats this as introducing a new principle of order based on natural resemblances rather than use or alphabet.
Chapter 90
What did Cæsalpinus say about the need to arrange plants?
Cæsalpinus compared the plant kingdom to an unordered crowd that must be arranged into brigades like an army, or all is tumult. He held that all science consists in collecting similar and distinguishing dissimilar things, producing genera and species as natural classes governed by real differences. His De Plantis libri xvi appeared at Florence in 1583.
Chapter 90

Section 913 cards

Why did Cæsalpinus's method fail to gain wide adoption at first?
The author explains that Cæsalpinus omitted the smaller groups, Genera, which were obvious to common botanists and convenient for describing plants. He also neglected to give synonyms of other authors, an appendage now indispensable. Thus a work forming a great epoch was probably little read and soon treated as forgotten.
Chapter 91
What problem did botanical nomenclature face before a true system was established?
The chapter states nomenclature was in such disorder that thirty or forty botanists had given the same plant almost as many names, and it was impossible to determine which plants earlier writers meant. Gaspard Bauhin's Pinax attempted a synonymy in 1623, but lacking genuine order, it could not be of great permanent utility.
Chapter 91
Why did scientific progress become languid after this period?
The author argues that wars and troubles across almost all of Europe left men neither leisure nor disposition for science. He lists England's civil wars, France's wars of the League and Fronde, the Thirty Years' War in Germany, and Spain's wars, saying amid such storms intellectual powers could not work with due calmness.
Chapter 91

Section 924 cards

Why did Tournefort's botanical work dominate for over half a century after 1700?
The chapter states Tournefort's success was much promoted by including a figure of a flower and fruit for each genus, drawn by Aubriet with great merit. Botany was thus rendered easy, learnable by turning over the leaves of a book. Despite various defects, these advantages gave him an ascendancy lasting from 1700 for more than half a century, even though Linnaeus began publishing in 1735.
Chapter 92
Why does the chapter say Linnaeus should be admired as a reformer rather than a discoverer?
The chapter says the most intelligent botanists always speak of Linnaeus not as a great discoverer but as a judicious and strenuous reformer; he even placed himself among the "Reformatores." The doctrine of plant sexes, even if he first established it, was botanical physiology, and his system on that basis was no higher an improvement than those of Ray and Tournefort.
Chapter 92
What was the problem with pre-Linnaean species names, and what remedy did Linnaeus introduce?
Species were designated by the genus name plus a descriptive Latin phrase, producing long, inconvenient designations that varied by author and contained insufficient, confused distinctions. Haller's numbering proposal failed because memory could not handle arbitrary abstractions. Linnaeus's remedy was trivial names: each species designated by the genus name plus a single conventional word imposed without general rule, now universally adopted.
Chapter 92
What distinction does the chapter draw between terminology and nomenclature, and why does terminology matter?
Terminology is the system of terms used in describing natural history objects; nomenclature is the collection of species names. The chapter argues that without technical terms and fixed rules there can be no certain or progressive knowledge, since common language cannot hold objects steadily. Linnaeus's Fundamenta Botanica gave botany a fixed, complete terminology of about a thousand explained terms.
Chapter 92

Section 934 cards

How did Linnaeus view the relationship between artificial and natural methods?
The author argues Linnaeus always held that an artificial method is instrumental to investigating a natural one. Linnaeus's followers, especially the English, often opposed his Sexual System to the Natural Method, but Linnaeus himself taught that artificial methods are a means of arriving at a natural method, and this distinct presentation of their relations was one of his great improvements to botany.
Chapter 93
What did Linnaeus say about naming natural orders in his conversation with Giseke?
Linnaeus told Giseke it matters little what you call an order if you take a proper series of plants and give it a clearly understood name, borrowing a name a potiori from the principal member. He insisted the transition from order to order is one thing and the character of an order another, and that a character of a natural order is impossible.
Chapter 93
What maxims did Linnaeus give for forming natural orders?
Linnaeus held that natural orders must be formed by attention to all parts of plants, not one or two; that the same organs matter greatly in one part of the system and little in another; that the character does not constitute the genus but the genus the character; and that the character is necessary not to make the genus but to recognize it.
Chapter 93
Why did the Linnaean system spread widely, according to de Candolle?
De Candolle assigns the system's success to its specific names, the characteristic phrase, the fixation of descriptive language, the distinction of varieties and species, the extension of the method to all kingdoms of nature, and the practice of introducing newly discovered species. Linnaeus constantly added new species, making his works valuable in matter and convenient in form.
Chapter 93

Section 944 cards

What did Antoine Laurent de Jussieu contribute to the natural method of plants?
The author argues credit belongs to both Jussieus, not just the uncle. Bernard left only unexplained catalogues of the Trianon garden. Antoine Laurent examined the Ranunculaceae himself in 1773, which he said made him a botanist, and in that memoir explained the relative importance and subordination of plant characters—a consideration Adanson's scheme had failed to address.
Chapter 94
How was Jussieu's Genera Plantarum (1789) written and received?
After nineteen years of botanical work, Jussieu published Genera Plantarum in 1789, composing it so fully in his head that printing began before writing and the manuscript never exceeded two pages ahead of the type. It met no enthusiasm: the French Revolution absorbed Europe's attention, the author was drawn into public affairs, and the method spread slowly in France, England, and Germany.
Chapter 94
What is the monocotyledon/dicotyledon distinction and why does it matter?
Plants with embryos of two little leaves are dicotyledonous; those with one are monocotyledonous. Monocotyledon flowers and fruit generally follow the number three, dicotyledons usually five. Whewell says this cotyledon division ranks higher than number-based divisions and reflects general organization. Desfontaines found the ligneous fibre develops inward in monocotyledons and outward in dicotyledons, hence endogenous and exogenous.
Chapter 94
Why does Whewell insist no single character can be absolute in a natural method?
Even at this high point of generalization, Whewell warns no one character can be imperative in a natural method. Lamarck held no single plant part, however essential, can be an absolute classification rule, and blamed the Jussieuian method for over-weighting cotyledons. Roscoe noted Orchis morio and Limodorum verecundum have no visible cotyledons; Cuscuta also lacks them.
Chapter 94

Section 954 cards

What does Whewell say Aristotle was unconscious of regarding classification?
The author argues Aristotle was quite unconscious of the classification ascribed to him; if he had adopted that or any system, this was precisely the place he must have referred to and employed it. Whewell denies Aristotle credit for a system he never dreamt of, which could not possibly be constructed at that period, while still praising his perception of the need for groups and group names.
Chapter 95
How does Whewell characterize Aristotle's place in zoological classification?
Whewell places Aristotle at the head of the naturalists to whom the first views of the necessity of a zoological system are due, calling him the great figure in the Prelude to the Formation of Systems. He notes Aristotle shows a perception of the need of groups and names of groups in studying the animal kingdom, as far as could be done at his time.
Chapter 95
What does Aristotle regret about genera of viviparous quadrupeds?
Aristotle says viviparous quadrupeds have many genera, but these are without names except specific names such as man, lion, stag, horse, dog. He notes some animals have names, like the horse, ass, oreus, ginnus, innus, and heminus (mule), called mules from resemblance only, not being mules since they breed their own kind. Therefore, lacking recognized genera and generic names, we must take species separately and study each nature.
Chapter 95
How does Whewell contrast botany and zoology in developing natural systems?
Whewell says reference to physiological principles influenced natural systems of vegetables in a latent and obscure manner, with botanists guided by its light but hardly aware. In zoology it affected systematic study more directly and evidently, since men can neither overlook general physiological features of animals nor avoid being swayed by them in judging affinities. Thus zoological classifications tended more and more toward union with comparative anatomy.
Chapter 95

Section 964 cards

What distinction became clearer in classification during this period?
The chapter states that in the course of various essays, the distinction between artificial and natural methods of classification came more clearly into view than before. Whewell calls this point so important to the philosophy of the subject that he devotes a few words to it, noting that all artificial methods must be natural as to their narrowest members, while proposed natural methods remain artificial as to their characteristic marks until modified.
Chapter 96
What classification principle did Bloch adopt in his general fish system?
Bloch followed Linnaeus's method in his great work, but toward the end of his life prepared a general system founded on one single numerical principle: the number of fins, just as Linnaeus's sexual system rests on the number of stamina. He subdivided according to the position of the ventral and pectoral fins. Cuvier said he could not have done better to turn artificial methods into ridicule.
Chapter 96
How did Cuvier divide fishes in his Règne Animal?
Cuvier divides fishes into two series: chondropterygians (cartilaginous fish), whose palatine bones replace the upper jaw bones, and ordinary fishes. The first contains Cyclostomes, Selacians, and Sturoniians. Ordinary fishes divide into Pectognaths, Lophobranchs, then Malacopterygians and Acanthopterygians, the former subdivided by ventral fins into Abdominal, Subbrachians, and Apodes. He admits the Acanthopterygian subdivision remained insoluble.
Chapter 96
Why does Whewell judge Agassiz's fish method artificial?
Whewell argues Agassiz's method, based entirely on the scaly covering and even a single scale, is artificial. It does not conform to the bony-versus-cartilaginous distinction almost all ichthyologists considered permanent, since each order contains both. Yet Whewell grants it great advantages for fossil fish, where scales remain when the skeleton is gone, and values it because it enables general propositions about geological eras.
Chapter 96

Section 974 cards

What were the Dogmatic and Empiric medical schools, and what did they oppose?
The Dogmatic school, successors of Hippocrates, framed general systems of abstract principles to give their tenets an appearance of connexion and profundity. The Empiric sect arose in opposition, professing to deduce modes of cure from experience rather than theoretical dogmas. Both prevailed mainly in Asia Minor and Egypt during the time of Alexander's successors—a period the chapter calls rich in names but poor in discoveries.
Chapter 97
According to Galen, why did anatomical books become necessary for students?
Galen says the ancients did not need anatomical manuals because from childhood they were exercised by their parents in dissecting as familiarly as in writing and reading, so they could no more forget anatomy than the alphabet. But when grown men as well as children were taught, this thorough discipline fell off; the art left the family of the Asclepiads and declined by repeated transmission, making books necessary.
Chapter 97
How did Galen argue the seat of the soul is in the brain, not the heart?
Galen notes it is allowed by all, both physicians and philosophers, that where the origin of the nerve is, there the seat of the soul must be. He adds that this origin is in the brain, not the heart. He supported the necessity of the nerve experimentally by cutting through bundles of nerves and thus preventing the corresponding motions.
Chapter 97
What did Galen think of Asclepiades' denial of purpose in the body?
Asclepiades, whom the chapter calls an impudent pretender, adopted the Epicurean dogma that the eye was not made for seeing nor the ear for hearing. Galen says it is easy for people like Asclepiades, when they meet a difficulty, to say Nature has worked to no purpose. Galen instead calls his own work a religious hymn in honor of the Creator.
Chapter 97

Section 984 cards

What did Harvey tell Boyle induced him to imagine the circulation of the blood?
Harvey told Boyle that the valves in the veins of many body parts gave free passage to blood toward the heart but opposed flow the other way. He was incited to imagine that so provident a cause as Nature had not placed so many valves without design, and no design seemed more probable than that blood should be sent through the arteries and return through the veins.
Chapter 98
What did Harvey insist was necessary for natural knowledge, according to his preface?
Harvey insisted that in every science diligent observation is requisite and sense itself must be frequently consulted. He held that we must not rely on other men's experience but our own, without which no man is a proper disciple of any part of natural knowledge. By publishing his experiments, he trusted he had enabled his reader to be an equitable umpire between Aristotle and Galen.
Chapter 98
What does the author argue about vital forces in physiology?
The author argues that physiological truths necessarily involve some peculiar agency belonging to living things, something vital and not merely physical. Life is not a collection of forces, polarities, or affinities such as physical or chemical sciences contemplate; it has powers of its own. The author compares this to Kepler's laws awaiting Newton, and cites Cuvier asking why Natural History may not one day have its Newton.
Chapter 98
Who discovered the lacteals and what was notable about his treatise?
Aselli discovered the lacteals in 1622, vessels that absorb the white liquid chyle from the bowels and pour it into the blood. Eristratus had found them in the ancient world, but Aselli was the first modern to attend to them. His treatise De Venis Lacteis, printed at Milan in 1627 after his death, was the first work to exhibit colored anatomical figures.
Chapter 98

Section 993 cards

How did Tournefort and Reaumur misread the stamina?
Tournefort, misled by insufficient experiments, maintained that the stamina are excretory organs, and Reaumur at the beginning of the eighteenth century inclined to the same doctrine. Geoffroy, an apothecary at Paris, then re-scrutinized the sexual organs, examined pollen forms already observed by Grew and Malpighi, and pointed out the excretory canal through the style and the micropyle, though he made some mistakes about the pollen's nature.
Chapter 99
What was the pre-existence doctrine of the embryo, and its difficulty?
A widely received opinion held that the embryo pre-existed in the mother before any union of the sexes. The difficulty is that if the mother contains embryos of all future children, those embryos must contain their own children, and so on indefinitely, so each female of each species contains the germs of infinite future generations. This perplexity drove inquirers to other suppositions, such as Leeuwenhoek's animalcules in the male seed.
Chapter 99
What did Willis contribute to the anatomy of the nerves?
Willis's Cerebri Anatome, with a description of the nerves, appeared in London in 1664. He first distinctly described the nervous centre, the pyramidal eminences communicating brain and spinal marrow, and proved the rete mirabile found in ruminants does not exist in man. He described the pairs of nerves more carefully, called the olfactory nerves the First Pair, added the Sixth and Ninth Pairs, and his numbering is still used.
Chapter 99

Section 1004 cards

What does Whewell conclude about physiological speculation before recent principles?
Whewell argues that physiological research has largely been a story of failures: it begins with exact examination of organization and function but ends in wide conjectures and arbitrary hypotheses. He compares this knowledge to a stream that starts clear but spreads into sands and deserts rather than reaching the ocean of general scientific truth.
Chapter 100
What is the morphological view of flower parts according to Göthe's principle?
The morphological view holds that the members of each whorl—calyx sepals, corolla petals, stamens, and ovaries—are in nature identical, essentially whorls of ordinary leaves shortened on a common axis and modified by successive elaboration of nutriment. All plant parts represent successive metamorphoses of the same elementary member, from root-leaves through bracts, sepals, petals, stamens, and ovaries to fruit and seed.
Chapter 100
What evidence does Whewell cite for the identity of plant organs?
Whewell cites transformations caused by accidents of nutriment or exposure, considered monstrosities when remarkable. Examples include the wild-rose transforming stamens into petals to become the double garden-rose, petals becoming leaves, branches growing from flower centers, and the snap-dragon's Peloria variety, where an irregular personate corolla becomes strictly symmetrical with five equal spurs and five equal stamens.
Chapter 100
What was Göthe's merit regarding metamorphosis, and who preceded him?
Whewell notes the idea was not absolutely new: Linnæus spoke of prolepsis when leaves changed into bracts, calyx, corolla, stamens, or pistil, and Caspar Wolf held that the whole plant is nothing but leaves and stalk. Göthe's merit, per Sprengel, was applying metamorphosis to the regular formation of the flower, not merely to double and monstrous flowers as Jussieu had done.
Chapter 100

Section 1014 cards

What four great branches did Cuvier divide the animal kingdom into?
Cuvier divided the animal world into four plans or branches: vertebrata (backbone and skull), mollusca (soft animals without bony skeleton, often with shells), articulata (crustacea, insects, spiders, annulose worms with jointed segments), and radiata (zoophytes, with parts radiating circularly from an axis). He held that further divisions are only slight modifications of these plans.
Chapter 101
How did Cuvier's fourfold division differ from earlier classification?
Before Cuvier, naturalists followed Linnaeus and divided non-vertebrate animals into just two classes, insects and worms. Cuvier began attacking this view in a 1795 memoir, distinguished annelides in 1801, distributed classes into three branches coordinate with vertebrata in 1812, and published the Règne Animal in 1817, after which the division was commonly accepted.
Chapter 101
What did Geoffroy Saint-Hilaire argue about the unity of animal types?
Geoffroy Saint-Hilaire, having argued all vertebrates share one osteological plan, extended this unity by claiming the hard parts of crustaceans and insects are modifications of the higher skeleton, so articulata belong to the vertebrate type: their segments are analogous to vertebrae, and they live within their vertebral column as vertebrates live without it. Attempts were also made to unite molluscs and vertebrates.
Chapter 101
Why did Cuvier reject the unity of composition and embryonic recapitulation views?
Cuvier never assented to referring his divisions to a common type. His biographer reports he could not admit that vertebrate lungs or gills correspond to mollusc and crustacean branchiae, nor that vertebrate skeleton matches articulate skin, nor that taenia and sepia, bird and echinus, whale and snail share a plan. He also rejected the view that the higher embryo passes through lower animal forms, which critics said lacked precision.
Chapter 101

Section 1024 cards

What did Cuvier argue against Geoffroy's unity-of-composition hypothesis for the Sepia?
Cuvier argued that if the Sepia's assumed posture were correct, the brain relative to the beak and the œsophagus relative to the liver should match vertebrate positions, but they are exactly contrary. He therefore asked how one can claim identity or unity of composition between cephalopods and vertebrates without using those words in a sense entirely different from their common meaning.
Chapter 102
How did the theorist reply to Cuvier's objection about organ positions?
The theorist admitted the facts but denied they implied a different sort of composition. He argued molluscous animals were placed too high in the scale and may be embryos of lower stages, where fewer organs come into play. If development stops and organ B is never produced, organ A can sit in an unusual relation to organ C, producing different apparent arrangements.
Chapter 102
Why does Whewell reject the theorist's concession as destroying the theory?
Whewell argues that if unity of composition admits unusual, varied arrangements of some organs accompanied by the total absence of others, then it excludes no arrangement at all. He says this differs from Cuvier's statement only by adding arbitrary hypotheses of development and stoppage, making the principle vacuous rather than explanatory.
Chapter 102
What does Whewell argue about final causes in physiology, citing Kant?
Whewell argues final causes are an irremovable principle of zoological philosophy, since assuming every organ has some use guided discoveries like the circulation of the blood and comparative anatomy. He notes Kant, though denying physical proof of God, defined an organized being as one where all parts are mutually ends and means, and called the teleological maxim indispensable.
Chapter 102

Section 1034 cards

According to Whewell, what bond unites geology with antiquarian studies?
Whewell argues that both endeavor to ascend to a past state of things by the aid of the evidence of the present. He cites Cuvier's claim that the geologist is an antiquary of a new order, treating this as a real philosophical connexion rather than a fanciful resemblance, since fossils and medals are studied in a similar spirit and for a similar purpose.
Chapter 103
What three portions does Whewell say every aetiological science consists of?
Whewell states that all aetiological sciences consist of three portions: the Description of the facts and phenomena; the general Theory of the causes of change appropriate to the case; and the Application of the theory to the facts. For geology he names these Descriptive or Phenomenal Geology, Geological Dynamics, and Physical Geology, noting the three are often combined in writers' works.
Chapter 103
Why does Whewell avoid calling palaetiological sciences 'historical'?
Whewell explains that the term would be insufficiently precise, because Natural History has accustomed us to a use of 'history' in which time plays no part. Citing Mohs, he notes that Natural History when systematically treated rigorously excludes all that is historical, classifying objects by permanent and universal properties rather than narrating particular and casual facts.
Chapter 103
What does Whewell call the hypothetical science of past changes of the whole universe?
Whewell notes that geology irresistibly impels its students toward inquiries about the origin of our planet and solar system, and that some have traced systems like ours forming from condensing nebulous matter. He declines to judge whether the Nebular Hypothesis is tenable, but says such a science of past cosmic changes would properly be called Cosmical Palaetiology.
Chapter 103

Section 1044 cards

What did Woodward conclude from collecting geological information from many countries?
Woodward concluded by patient induction that stone and other terrestrial matter in France, Flanders, Holland, Spain, Italy, Germany, Denmark, and Sweden was distinguished into strata or layers, as in England; that these strata were divided by parallel fissures; and that great numbers of sea shells were enclosed in the denser terrestrial matter, as in England.
Chapter 104
What did Michell contribute to understanding stratified structure?
Michell, appointed Woodwardian Professor at Cambridge in 1762, described the stratified structure of the earth more distinctly than his predecessors. He pointed out that the same kinds of earths, stones, and minerals appear at the surface in long parallel slips, parallel to the long ridges of mountains, and that this is in fact what we find.
Chapter 104
How did Werner's system treat organic fossils as geological characters?
Werner's classifications were drawn mostly from mineralogical constitution. Though he welcomed Schlottheim's work on fossils and strata in 1792, Werner and his school never used organic remains as boldly as others did. Humboldt doubted whether all formations are characterized by particular species. The author argues that a descriptive geology neglecting this evidence was a retrograde step.
Chapter 104
What did William Smith accomplish and how?
William Smith, a civil engineer, noticed the continuity and constant order of strata near Bath as discriminated by their fossils. About 1793 he drew up a Tabular View of that district. Finding the same strata and associations in the north of England, he named and mapped them across England; his maps appeared in 1815. The author credits his own sagacity and perseverance.
Chapter 104

Section 1054 cards

Who does Whewell name as the three main authors of geological classification?
Whewell identifies Werner, Smith, and Cuvier as the three persons who must be looked upon as the main authors of geological classification. He notes they were of very different mental constitution, and compares them in reference to clearness of ideas, possession of numerous facts, and the power of bringing these two elements into contact.
Chapter 105
How does Whewell characterize Werner's approach to geology?
Whewell argues that in Werner the ideal element predominated: his love of system, fostered by mineralogical studies, was too strong for the facts he had to deal with. He promulgated as representing the world a scheme collected from a province, gathered too hastily. Yet his intense spirit of method gave a scientific character to what had been miscellaneous phenomena.
Chapter 105
What did William Smith discover that let him identify strata?
Whewell reports that Smith dated his attempts to discriminate and connect strata from 1790, when he was twenty. In 1792 he had considered how best to represent the order of superposition, continuity of course, and general eastern declination of the strata. Soon after, doubts were removed by the discovery of a mode of identifying strata by the organized fossils respectively imbedded therein.
Chapter 105
Why did the Geological Society of London focus on descriptive geology at its founding?
Whewell states the Society was established in 1807 to multiply and record observations and patiently await the result of some future period. Its founders resolved to apply themselves to Descriptive Geology, thinking the time not come for the theoretical geology which had long fired the controversial ardor of Neptunists and Plutonists. Its first Transactions volume appeared in 1811.
Chapter 105

Section 1064 cards

Why did Murchison choose the name 'Silurian' for the strata of South Wales?
Murchison selected 'Silurian' from the former inhabitants of the country where his type specimens were found, because the group needed a name not necessarily leading to assumption or controversy. Whewell calls it excellent in many respects, but notes it will probably not quite supersede 'Transition,' since transition rocks occur elsewhere corresponding to none of the Silurian members.
Chapter 106
What naming mistake does Whewell attribute to Brongniart's new geological nomenclature?
Whewell says Brongniart, acting on the sound principle that mineralogical-signification terms cause inconvenience, coined an entirely new list: terrains agalysiens, hemilysiens, yzemiens, clysmiens, with subdivisions like clastiques and tritoniens. Whewell argues these terms labor under great inconveniences: they are descriptive in derivation yet not generally intelligible, and refer to theoretical views without systematic connexion.
Chapter 106
Why is geological synonymy more important than botanical synonymy, according to Whewell?
In plants the species are really fixed and easily known when seen, so ambiguity comes only from imperfect communication or confused observers. In geology, the identity of a stratum in different places may be very doubtful even to one who has examined it, and assigning a stratum's right place largely establishes the whole geological history of a country.
Chapter 106
How did Buckland's 1820 work change views of the Alpine strata?
Under the Wernerian theory, the dark marbles and schists of the Alps were referred to the transition class. Buckland pointed out that these masses, by their fossils, approach the Oolitic Series of England, so the equivalents of that series occur in rocks with altogether different mineralogical characters. Later work confirmed the correspondence, including Red Marl at the bottom and Green Sand and Chalk at the top.
Chapter 106

Section 1074 cards

What did Agassiz conclude about fish orders below the lias?
Agassiz held that below the lias, two of his four orders of fish—the Cycloïdean and Ctenoïdean—vanish entirely, while the Ganoïdean and Placoïdean, rare in modern times, suddenly appear in great numbers alongside large sauroid and carnivorous fishes. Cuvier had transferred the whole subject of fossil fishes to Agassiz, esteeming his talents highly.
Chapter 107
How does Whewell distinguish Geological Dynamics from theoretical Geology?
Whewell argues Geological Dynamics, if perfected, would be a demonstrative science dealing with general cases, resembling Mechanics, determining what must always be under given conditions. Theoretical Geology, by contrast, is an ætiological view of special facts, satisfied with knowing what is and has been and why—more like philosophical Archæology. He credits Lyell's Principles with giving Dynamics its prominent position.
Chapter 107
What analogy does Whewell use to justify Geological Dynamics?
Whewell compares geology to astronomy: Kepler and others conjectured causes of planetary motion before knowing what motions bodies could produce, and progress stalled for nearly a century until Galileo and successors formed Mechanics. Only then could philosophers pass securely from Phenomenal to Physical Astronomy. Likewise, a science of Geological Dynamics must precede the transition from Phenomenal to Physical Geology.
Chapter 107
What does the second edition say about the succession of organic forms?
Going downward through formations, one class of organic forms after another disappears: Tertiary rocks hold all present classes; Secondary rocks lack mammals except the minute marsupial amphitherium and phascolotherium in the Stonesfield slate; Carboniferous and Devonian have no large reptiles; lower Silurian rocks lose fishes, leaving only mollusks, crustaceans and zoophytes. Geologists disagree whether these changes came by determinate steps or insensible gradations.
Chapter 107

Section 1082 cards

How does Lyell explain large geological changes from ordinary operations?
Mr. Lyell urged the consequences that would follow in a long course of time from the constant repetition of operations in themselves of no extraordinary amount. A lava-stream many miles long and wide, several yards deep, or a subsidence or elevation of a few feet, are not extraordinary facts. Let these operations be repeated thousands of times, and we have results of the same order as the changes geology discloses.
Chapter 108
What did Edward Forbes discover about marine life in the Aegean?
Prof. Edward Forbes observed the marine animals of the Aegean Sea and found that mollusks and zoophytes are already distributed into strata even in their living state. Dividing depth into eight regions from 2 to 230 fathoms, he found each region had peculiar inhabitants that disappeared quickly when ascending or descending. The zero of animal life appeared at about 300 fathoms. He used this to determine the depth of the Neokaimeni eruption of 1707.
Chapter 108

Section 1094 cards

What did Sir James Hall's experiments demonstrate about rocks?
Hall heated powdered chalk under pressure and converted it into crystalline calcspar, illustrating Hutton's theory that subterraneous heat or crystalline forces can alter rocks after deposition—making sedimentary rock crystalline, obliterating fossils, or producing slaty cleavage.
Chapter 109
What does Lyell's term 'metamorphic' refer to?
Lyell applied 'metamorphic' to rocks that have undergone changes since deposition. Whewell notes the great extent of heat-altered metamorphic rock is now uncontested, and Sedgwick made important speculations on internal changes produced by crystalline forces in mountain masses.
Chapter 109
Why was the idea of a formerly perpendicular earth's axis rejected?
The hypothesis held the axis was once perpendicular, giving perpetual spring, but such a shift would subvert the equilibrium of the surface in a way not observed, and physical astronomers generally declared the change impossible. Herschel instead calculated effects of changing orbital eccentricity.
Chapter 109
How does Lyell's land-and-water distribution theory explain climate change?
Lyell argued that if land clustered at the poles it would breed constant ice and snow, lowering global temperature; if polar regions were water and the tropics a land belt, frost could gain no hold and the torrid zone would heat the whole. Whewell calls the theory ingenious but hard to calculate.
Chapter 109

Section 1104 cards

Why does Whewell reject species transmutation via embryo development?
Whewell reports that the hypothesis of progressive species development was linked to the claim that higher embryos pass through forms permanent in lower animals. He argues that all the best physiologists declare such extraordinary embryo development physiologically impossible, and that any correspondence between embryo progression and animal order is an incomplete mark of universal analogy, not causality.
Chapter 110
What does Whewell say paletiological sciences can and cannot achieve?
Whewell argues that sciences tracing the past by causation can go far back, determine remote circumstances, and exclude many suppositions about origins. But they cannot reach a beginning homogeneous with known events; the origins of language, civilization, law, and species resist physiological and geological investigation, so he suggests other grounds of truth may be needed.
Chapter 110
How should theology and geology relate, according to Whewell?
The author argues that theology and geology may both point to a mysterious origin but must not share parts: supernatural dynamics must not be added to natural geological dynamics. Extraneous evidence must not influence physics or geology; each science stays within its own limits, and their consistency is real though not fully comprehensible to us.
Chapter 110
What does Whewell conclude about geology and the mystery of creation?
Whewell concludes that geology and astronomy cannot give a distinct account of the universe's origin. Geology can show extinct and living species were profoundly adapted to their conditions, but when we ask whence they came, geology is silent. The mystery of creation lies outside her legitimate territory: she says nothing, but points upwards.
Chapter 110

Section 1114 cards

What two problems must be solved to judge hypotheses of species extinction?
Whewell states that judging the sufficiency of any extinction hypothesis requires solving two difficult problems: estimating the effect on the organic world even if physical circumstances were given, and determining the physical conditions to which a given state of the earth would give rise. He adds that for how new species replace extinct ones, physiology sanctions no hypothesis.
Chapter 111
What did Vitaliano Donati find in the Adriatic in 1750?
During the Italian controversy over Sub-Apennine fossils, Vitaliano Donati examined the Adriatic in 1750 and found deposits containing shells and corals, extremely resembling the strata of the hills, in the act of formation. Whewell cites this as evidence that fossil-bearing deposits were then forming.
Chapter 111
How does Whewell distinguish Geology from Mineralogy?
Whewell argues Geology connects with Mineralogy only insofar as Mineralogy classifies many objects Geology uses as evidence. Confounding them is like treating philosophical history as identical with knowledge of medals. The geologist seeks the earth's past history, drawing evidence from minerals or seas, inorganic or organic bodies, ground or skies.
Chapter 111
Why does Whewell reject ancient cosmogonies as physical doctrines?
Whewell argues ancient traditions of cyclic creations and destructions were mythological, not physical: they aimed to impress the mind with marvels and infinite times, not to explain terrestrial facts. He notes Ovid's Pythagoras passage mixes verified land-sea changes with fables like the Ammon fountain and Salmacis waters, serving metempsychosis and vegetarian doctrine.
Chapter 111

Section 1124 cards

What two classes of facts confirmed the catastrophist view of Earth history?
Whewell states the catastrophist opinion was confirmed by two great classes of facts: symptoms of mechanical violence on a very large scale, and complete changes in the forms of animal and vegetable life between formations. Species in successive epochs were said to be entirely different, suggesting a new creation had intervened, and such an out-of-the-ordinary transition was readily believed to bring paroxysms of mechanical energy.
Chapter 112
What did Hutton's doctrine of uniformity rest on, according to Whewell?
Whewell says Hutton denied evidence of a beginning of the present state of things and referred many processes of strata formation to existing causes, but did not assert that elevatory forces raising continents were of the same order as present volcanoes and earthquakes. His uniformity rested rather on supposed analogy with other lines of speculation than on examining the amount of change now occurring.
Chapter 112
What did Lyell observe in Italy that weakened the catastrophist doctrine?
In 1828 Lyell toured France and Italy, finding that the number of extinct fossil species decreased southward. He explored Ischia and found shells 2000 feet above sea level all of species now living in the Mediterranean, and made similar collections on Etna's flanks and in the Val di Noto. In the Val di Noto he saw thick limestone filled with recent shells, dissolving his belief in high antiquity for such strata.
Chapter 112
Why does Whewell criticize Lyell's rule of rejecting past causes more intense than present ones?
Whewell grants we must not arbitrarily assume catastrophes and should derive uniformity from facts. But he argues Lyell errs in treating it as a merit to reject any difference in intensity between past and present causes. Effects must teach us the nature and intensity of causes; invoking time with ten thousand earthquakes to explain a sudden mountain-chain uplift is ill excused by appealing to known causes.
Chapter 112

Section 1134 cards

Why does Whewell feel uneasy about judging the eminent philosophers in his history?
He says he reverences them as his Teachers in the very sciences he must judge, and calls even the name Pupil perhaps too presumptuous. He trusts such men are as full of candor and tolerance as of knowledge, and will accept that estimating the advances was the historian's duty, viewing inevitable imperfections with indulgence.
Chapter 113
What does Whewell hope the history of physical science ultimately leads to?
He trusts the survey is not barren: at various points researches lead from matter to mind and from the external to the internal world. The thread snapped only because he confined himself to material sciences. He argues the method of obtaining speculative truth is not confined to the least worthy subjects but has unity across all employments of mind.
Chapter 113
How did Wertheim determine the velocity of sound in water, and what value did he find?
He made an organ-pipe sound by the passage of water through it, noting that a poorly constructed mouthpiece produces its own sounds and that the note depends slightly on pipe breadth and mouthpiece size. He found vibration travels 1157 mètres per second along the pipe in sea-water; applying the √3 to √2 ratio gives 1454 mètres per second in an unlimited expanse.
Chapter 113
What did Stokes conclude about fluorescence, and how does it differ from phosphorescence?
Stokes was led to the conviction that certain bodies change the color and refrangibility of rays falling on them, always making rays less refrangible; this was called degradation or dependent emission. It differs from phosphorescence because the emitted light depends on active rays and lasts only while the body is under their influence. He named it fluorescence, and rejected analysis of light by absorption as subjective contrast.
Chapter 113

Section 1144 cards

What does the dynamical theory of heat assert about motion and heat?
The author describes the hypothesis that Motion may be converted into Heat and Heat into Motion, each exactly measuring the other, as seen in rarefaction and condensation of air and in steam-engines. He credits Mr. Joule of Manchester with laying its foundation in 1844, and notes it was pursued by Joule and Professor Thomson through experiments, though he says such experiments are difficult to make fully satisfactory.
Chapter 114
How does Thomson explain the heat of the sun?
The author reports Thomson's speculation that solar heat is sustained by meteoric matter perpetually falling toward the sun, its motion converted into heat. Thomson inclines to think the meteors storing energy for future sunlight lie principally within the earth's orbit, visible as the Zodiacal Light, an illuminated tornado of stones whose inner parts get caught in the sun's atmosphere and drawn in by gravitation.
Chapter 114
How does Faraday's view of electric induction differ from Coulomb's?
Coulomb and Æpinus held that electric particles exert attractive and repulsive forces in straight lines at a distance, so induction rearranges fluids in the conductor by complex calculation. Faraday instead conceived induction as action between the electrified body and conductor through contiguous particles of an intermediate body, the Dielectric, leading him to conclude induction takes place in curved lines. The author argues this curved-line view is itself vague and not forced by the complex mathematics.
Chapter 114
What ten-year period did Sabine find in magnetic elements, and what coincided with it?
Examining declination, dip, and intensity at Toronto, Hobart Town, and St Helena, Sabine found the inequalities increased steadily from 1843 to 1848, becoming over twice as large. Lamont had already noted indications of a decennial period, about five years from minimum to maximum. Schwabe's 24 years of solar observation showed sunspots also had a period, with maximum years 1828, 1838, 1848; Sabine pointed out the coincidence in 1852.
Chapter 114

Section 1153 cards

What did Faraday discover in November 1846 about magnets and light?
Faraday announced the "action of magnets on light," but the effect appeared not on light directly, only on light passing through certain glasses, such as silicated borate of lead, flint glass, rock salt, and water. When polarized light passed through the glass parallel to the magnetic line of force, the plane of polarization was rotated by an angle increasing with magnetic force and glass thickness.
Chapter 115
How does Faraday's magneto-optic rotation differ from natural rotation by quartz or oil of turpentine?
In oil of turpentine, polarized rays are rotated in the same direction regardless of their direction of passage. In Faraday's heavy glass, the rotation exists only in a plane perpendicular to the magnetic line, and its right- or left-handed direction is reversed by reversing the magnetic polarity. Faraday himself remarked on this great difference between the two cases.
Chapter 115
What did Plücker find in 1847 about crystals and magnetic lines of force?
Using a powerful magnetic apparatus like Faraday's, Plücker found crystals generally tend to assume a certain position relative to magnetic lines of force. A crystal with a single optic axis tends to place that axis transverse to the magnetic line, as if repelled by each pole; crystals with two axes act as if each axis were repelled. The force is independent of magnetic or diamagnetic character and is directive rather than attractive or repulsive.
Chapter 115

Section 1164 cards

What botanical relationship did Hooker say exists among New Zealand, Australia, and extra-tropical South America?
Hooker states that upwards of 100 genera or other well-marked plant groups are entirely or nearly confined to New Zealand, Australia, and extra-tropical South America. Each is represented by one or more species in two or more of these countries, creating a botanical affinity between them that every botanist appreciates.
Chapter 116
How did Ray divide plants in his natural system?
Ray divided plants first into Flowerless and Flowering, then divided the Flowering into Monocotyledonous and Dicotyledonous. He defined Dicotyledons by seeds emerging with two seed-leaves or splitting into two lobes, and Monocotyledons as lacking two seed-leaves or lobes. Hooker notes this division can extend to trees, since palms differ from other trees as Monocotyledons differ from other herbs.
Chapter 116
How do monocot and dicot wood bundles differ in course and growth?
In Monocotyledons the wood fibres form bundles that curve inward toward the axis then outward to the circumference, making the stem harder outside than inside. Because these arcs are short, the trunk does not increase in girth and grows only at the apex; the bundles are definite. In Dicotyledonous trunks, wood layers run parallel from base to top, each outside the last formed, so the trunk grows in both height and girth; bundles are indefinite.
Chapter 116
What physiological distinction separates Phænogams from Cryptogams?
Hooker calls this the highest physiological generalization in the vegetable kingdom. In Phænogams, fertilization occurs when a pollen-tube touches the nucleus of an ovule; in Cryptogams, it occurs when a sperm-cell, usually ciliated and called an antherozoid, contacts a germ-cell. Hooker adds that Phænogam reproductive organs are all modified leaves, while Cryptogam organs are not homologous.
Chapter 116

Section 1174 cards

According to Whewell, what are the two elements in speculations about animal structure?
Whewell says such speculations contain two elements: one given, the other worked out from examining the case. He calls them the datum and the problem, or homology and teleology. Homology is the unity of plan or correspondence of parts, while teleology is the adaptation of means to ends. He credits Mr. Owen with advancing the former while remaining alive to the latter.
Chapter 117
How does Whewell respond to Bacon's comparison of Final Causes to barren Vestal Virgins?
Whewell says he has repeatedly shown that in physiology almost all great discoveries were made by assuming a purpose in animal structures. He suggests Bacon, had he developed the simile, would say barrenness is no reproach to Final Causes, since they ought to be daughters rather than mothers of natural sciences, kept pure. He adds that in physiology, if not mothers, they are admirable nurses.
Chapter 117
What did fossil discoveries after Cuvier's death show about monkeys and man?
Whewell, following Owen, notes that at Cuvier's death in 1832 no fossil Quadrumana were known. Later finds included a Macacus in eocene Suffolk deposits, a Semnopithecus in Himalayan tertiaries, a large extinct platyrhine monkey in Brazil, and a jaw fragment of Hylobates in southern France. No fossil human remains were found in regularly deposited tertiary layers, which Whewell takes as evidence man was placed on earth last.
Chapter 117
What does Whewell say about the state of geology's great questions?
Whewell states that no important new light has been thrown on the general doctrines of geology. Surveys and studies of special phenomena continued actively, and zoologists reconstructed animals from strata remains, as in the Palæontological Society's publications. But the great questions of how animal and vegetable species were created and succeeded on earth remain, he thinks, where they stood at the last edition of the History.
Chapter 117

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All questions and answers

What plan does Whewell say the work follows for organizing each science's history?

What does Whewell say his work aims to be, beyond narrating facts?

According to Whewell, what is wrong with most existing treatises on Logic?

Where does Whewell reserve discussions of Ideas such as Matter, Force, and Atoms?

What does the index entry for Francis Bacon list?

How does the index distinguish the two Bernoulli brothers named John?

What page references does the index give for Galileo?

How are entries for the Herschels and Babbage presented?

According to Whewell, what two elements are required to form science?

How does Whewell define Induction in this introduction?

What does Whewell say the completeness of a historical view consists in?

What does Whewell say a history of inductive science should provide for the future?

What does Whewell compare an Inductive Table of a science to?

What is deduction, and when does Whewell say it has no value?

How do scientific Ideas differ from common Notions, according to Whewell?

What is a School Philosophy, and which two periods does Whewell name?

How did Herodotus explain the Nile's summer flooding?

What fundamental mistake does Whewell attribute to Greek physical philosophy?

What example shows Aristotle starting from common language?

What was the Greek doctrine of contrarieties?

Which four elementary qualities does Aristotle retain, and why reject the others?

How does Aristotle combine the four qualities into the four elements?

What error does Whewell say underlies Aristotle's doctrine of absolute light and heavy?

How does Aristotle explain a thrown stone continuing to move before stopping?

What was Anaxagoras's Homoiomeria, opposed to atomism?

What did the Stoics mean by λόγοι σπερματικοί?

Why did Whewell say Greek physical philosophy failed?

How does Whewell assess Aristotle's physical Problems?

How does Whewell explain the round image formed by sunlight through a hole?

Why does Whewell say Aristotle failed to create a science of mechanics?

What does Whewell mean by an 'appropriate Idea,' and why does it matter?

What did Archimedes contribute to hydrostatics according to Whewell?

How does Whewell define the Idea of Fluidity?

What was Euclid's and the Platonists' error about vision?

Why did Plato's Timaeus fail as a theory of the universe, according to the chapter?

Why could early astronomy become a science before other fields?

Why is the notion of a Year harder to form than that of a Day?

What did nations need before they could fix the year at 365 days?

Why did the Greeks consider a correct system of intercalation a religious duty?

What was the Octaëteris, and how did it fall short?

What was Meton's 19-year cycle and why is it significant?

How did Calippus correct Meton's cycle?

According to the chapter, what is the basis of astronomy regarding the sun's motion?

Who does Pliny credit with first pointing out the obliquity of the sun's path?

How did Aristotle argue for the earth's spherical form from lunar eclipses?

What astronomical theory marks the inductive epoch of Hipparchus?

How did the Greeks explain a planet's retrograde and stationary motion?

What lunar period did the Chaldeans use for eclipses, and what does it contain?

What problem did Plato pose to astronomers, and why did it cause trouble?

How did Hipparchus represent the moon's anomaly in longitude?

What did the moon's moving apogee require astronomers to determine?

What data did Hipparchus use to derive his lunar conclusions?

Why were Hipparchus's lunar tables fairly accurate for eclipses?

What two major discoveries does Whewell credit to Hipparchus's inductive epoch?

Why did Hipparchus construct a catalogue of 1080 stars?

How did Hipparchus and later astronomers treat the equality of days?

How did Eratosthenes estimate the earth's circumference?

What did the Arabian astronomers under Caliph Almamon measure?

How did Ptolemy account for planetary motions, and what role did the equant play?

What did Albategnius discover about the sun's apogee, and why did Delambre doubt him?

What was the Trepidation of the fixed stars, and who proposed it?

Who discovered the moon's third inequality, the Variation, and what is it?

Why does Whewell consider collections of philosophers' opinions harmful to science?

Why did Pappus fail to solve the inclined plane problem?

Why did Pliny's remora fish story reveal unclear mechanical ideas?

How did Cosmas Indicopleustes describe the earth and heavens?

Why did Augustine deny inhabitants on the opposite side of the earth?

What did Boethius, Bede, and Gerbert contribute regarding the earth's figure?

What does Montucla say about monks preserving ancient science?

How does Whewell characterize Alexander Aphrodisiensis as a commentator?

What futile task does Whewell attribute to Simplicius and many Alexandrian philosophers?

Why does Whewell argue the Arabians produced no great scientific names or discoveries?

Why was Averroes called "the Commentator" and how did the schoolmen regard him?

What did Plotinus give as his reason for denying that distance makes objects appear smaller?

What was Mystical Arithmetic, and why did number tempt such speculation?

Which regular solids did Plato assign to the four elements, and why?

What arguments did Cicero and Pliny use against astrology?

What powers did alchemists attribute to the philosophers' stone beyond transmuting metals?

What claim does Whewell examine about Alchemy being the mother of Chemistry?