CHAPTER II

FRENCH GEODESY

Every one understands our interest in knowing the form and dimensions of our earth; but some persons will perhaps be surprised at the exactitude sought after. Is this a useless luxury? What good are the efforts so expended by the geodesist?

Should this question be put to a congressman, I suppose he would say: "I am led to believe that geodesy is one of the most useful of the sciences; because it is one of those costing us most dear." I shall try to give you an answer a little more precise.

The great works of art, those of peace as well as those of war, are not to be undertaken without long studies which save much groping, miscalculation and useless expense. These studies can only be based upon a good map. But a map will be only a valueless phantasy if constructed without basing it upon a solid framework. As well make stand a human body minus the skeleton.

Now, this framework is given us by geodesic measurements; so, without geodesy, no good map; without a good map, no great public works.

These reasons will doubtless suffice to justify much expense; but these are arguments for practical men. It is not upon these that it is proper to insist here; there are others higher and, everything considered, more important.

So we shall put the question otherwise; can geodesy aid us the better to know nature? Does it make us understand its unity and harmony? In reality an isolated fact is of slight value, and the conquests of science are precious only if they prepare for new conquests.

If therefore a little hump were discovered on the terrestrial ellipsoid, this discovery would be by itself of no great interest. On the other hand, it would become precious if, in seeking the cause of this hump, we hoped to penetrate new secrets.

Well, when, in the eighteenth century, Maupertuis and La Condamine braved such opposite climates, it was not solely to learn the shape of our planet, it was a question of the whole world-system.

If the earth was flattened, Newton triumphed and with him the doctrine of gravitation and the whole modern celestial mechanics.

And to-day, a century and a half after the victory of the Newtonians, think you geodesy has nothing more to teach us?

We know not what is within our globe. The shafts of mines and borings have let us know a layer of 1 or 2 kilometers thickness, that is to say, the millionth part of the total mass; but what is beneath?

Of all the extraordinary journeys dreamed by Jules Verne, perhaps that to the center of the earth took us to regions least explored.

But these deep-lying rocks we can not reach, exercise from afar their attraction which operates upon the pendulum and deforms the terrestrial spheroid. Geodesy can therefore weigh them from afar, so to speak, and tell us of their distribution. Thus will it make us really see those mysterious regions which Jules Verne only showed us in imagination.

This is not an empty illusion. M. Faye, comparing all the measurements, has reached a result well calculated to surprise us. Under the oceans, in the depths, are rocks of very great density; under the continents, on the contrary, are empty spaces.

New observations will modify perhaps the details of these conclusions.

In any case, our venerated dean has shown us where to search and what the geodesist may teach the geologist, desirous of knowing the interior constitution of the earth, and even the thinker wishing to speculate upon the past and the origin of this planet.

And now, why have I entitled this chapter _French Geodesy_? It is because, in each country, this science has taken, more than all others, perhaps, a national character. It is easy to see why.

There must be rivalry. The scientific rivalries are always courteous, or at least almost always; in any case, they are necessary, because they are always fruitful. Well, in those enterprises which require such long efforts and so many collaborators, the individual is effaced, in spite of himself, of course; no one has the right to say: this is my work. Therefore it is not between men, but between nations that rivalries go on.

So we are led to seek what has been the part of France. Her part I believe we are right to be proud of.

At the beginning of the eighteenth century, long discussions arose between the Newtonians who believed the earth flattened, as the theory of gravitation requires, and Cassini, who, deceived by inexact measurements, believed our globe elongated. Only direct observation could settle the question. It was our Academy of Sciences that undertook this task, gigantic for the epoch.

While Maupertuis and Clairaut measured a degree of meridian under the polar circle, Bouguer and La Condamine went toward the Andes Mountains, in regions then under Spain which to-day are the Republic of Ecuador.

Our envoys were exposed to great hardships. Traveling was not as easy as at present.

Truly, the country where Maupertuis operated was not a desert and he even enjoyed, it is said, among the Laplanders those sweet satisfactions of the heart that real arctic voyagers never know. It was almost the region where, in our days, comfortable steamers carry, each summer, hosts of tourists and young English people. But in those days Cook's agency did not exist and Maupertuis really believed he had made a polar expedition.

Perhaps he was not altogether wrong. The Russians and the Swedes carry out to-day analogous measurements at Spitzbergen, in a country where there is real ice-cap. But they have quite other resources, and the difference of time makes up for that of latitude.

The name of Maupertuis has reached us much scratched by the claws of Doctor Akakia; the scientist had the misfortune to displease Voltaire, who was then the king of mind. He was first praised beyond measure; but the flatteries of kings are as much to be dreaded as their displeasure, because the days after are terrible. Voltaire himself knew something of this.

Voltaire called Maupertuis, my amiable master in thinking, marquis of the polar circle, dear flattener out of the world and Cassini, and even, flattery supreme, Sir Isaac Maupertuis; he wrote him: "Only the king of Prussia do I put on a level with you; he only lacks being a geometer." But soon the scene changes, he no longer speaks of deifying him, as in days of yore the Argonauts, or of calling down from Olympus the council of the gods to contemplate his works, but of chaining him up in a madhouse. He speaks no longer of his sublime mind, but of his despotic pride, plated with very little science and much absurdity.

I care not to relate these comico-heroic combats; but permit me some reflections on two of Voltaire's verses. In his 'Discourse on Moderation' (no question of moderation in praise and criticism), the poet has written:

You have confirmed in regions drear What Newton discerned without going abroad.

These two verses (which replace the hyperbolic praises of the first period) are very unjust, and doubtless Voltaire was too enlightened not to know it.

Then, only those discoveries were esteemed which could be made without leaving one's house.

To-day, it would rather be theory that one would make light of.

This is to misunderstand the aim of science.

Is nature governed by caprice, or does harmony rule there? That is the question. It is when it discloses to us this harmony that science is beautiful and so worthy to be cultivated. But whence can come to us this revelation, if not from the accord of a theory with experiment? To seek whether this accord exists or if it fails, this therefore is our aim. Consequently these two terms, which we must compare, are as indispensable the one as the other. To neglect one for the other would be nonsense. Isolated, theory would be empty, experiment would be blind; each would be useless and without interest.

Maupertuis therefore deserves his share of glory. Truly, it will not equal that of Newton, who had received the spark divine; nor even that of his collaborator Clairaut. Yet it is not to be despised, because his work was necessary, and if France, outstripped by England in the seventeenth century, has so well taken her revenge in the century following, it is not alone to the genius of Clairauts, d'Alemberts, Laplaces that she owes it; it is also to the long patience of the Maupertuis and the La Condamines.

We reach what may be called the second heroic period of geodesy. France is torn within. All Europe is armed against her; it would seem that these gigantic combats might absorb all her forces. Far from it; she still has them for the service of science. The men of that time recoiled before no enterprise, they were men of faith.

Delambre and Méchain were commissioned to measure an arc going from Dunkerque to Barcelona. This time there was no going to Lapland or to Peru; the hostile squadrons had closed to us the ways thither. But, though the expeditions are less distant, the epoch is so troubled that the obstacles, the perils even, are just as great.

In France, Delambre had to fight against the ill-will of suspicious municipalities. One knows that the steeples, which are visible from so far, and can be aimed at with precision, often serve as signal points to geodesists. But in the region Delambre traversed there were no longer any steeples. A certain proconsul had passed there, and boasted of knocking down all the steeples rising proudly above the humble abode of the sans-culottes. Pyramids then were built of planks and covered with white cloth to make them more visible. That was quite another thing: with white cloth! What was this rash person who, upon our heights so recently set free, dared to raise the hateful standard of the counter-revolution? It was necessary to border the white cloth with blue and red bands.

Méchain operated in Spain; the difficulties were other; but they were not less. The Spanish peasants were hostile. There steeples were not lacking: but to install oneself in them with mysterious and perhaps diabolic instruments, was it not sacrilege? The revolutionists were allies of Spain, but allies smelling a little of the stake.

"Without cease," writes Méchain, "they threaten to butcher us." Fortunately, thanks to the exhortations of the priests, to the pastoral letters of the bishops, these ferocious Spaniards contented themselves with threatening.

Some years after Méchain made a second expedition into Spain: he proposed to prolong the meridian from Barcelona to the Balearics. This was the first time it had been attempted to make the triangulations overpass a large arm of the sea by observing signals installed upon some high mountain of a far-away isle. The enterprise was well conceived and well prepared; it failed however.

The French scientist encountered all sorts of difficulties of which he complains bitterly in his correspondence. "Hell," he writes, perhaps with some exaggeration--"hell and all the scourges it vomits upon the earth, tempests, war, the plague and black intrigues are therefore unchained against me!"

The fact is that he encountered among his collaborators more of proud obstinacy than of good will and that a thousand accidents retarded his work. The plague was nothing, the fear of the plague was much more redoubtable; all these isles were on their guard against the neighboring isles and feared lest they should receive the scourge from them. Méchain obtained permission to disembark only after long weeks upon the condition of covering all his papers with vinegar; this was the antisepsis of that time.

Disgusted and sick, he had just asked to be recalled, when he died.

Arago and Biot it was who had the honor of taking up the unfinished work and carrying it on to completion.

Thanks to the support of the Spanish government, to the protection of several bishops and, above all, to that of a famous brigand chief, the operations went rapidly forward. They were successfully completed, and Biot had returned to France when the storm burst.

It was the moment when all Spain took up arms to defend her independence against France. Why did this stranger climb the mountains to make signals? It was evidently to call the French army. Arago was able to escape the populace only by becoming a prisoner. In his prison, his only distraction was reading in the Spanish papers the account of his own execution. The papers of that time sometimes gave out news prematurely. He had at least the consolation of learning that he died with courage and like a Christian.

Even the prison was no longer safe; he had to escape and reach Algiers. There, he embarked for Marseilles on an Algerian vessel. This ship was captured by a Spanish corsair, and behold Arago carried back to Spain and dragged from dungeon to dungeon, in the midst of vermin and in the most shocking wretchedness.

If it had only been a question of his subjects and his guests, the dey would have said nothing. But there were on board two lions, a present from the African sovereign to Napoleon. The dey threatened war.

The vessel and the prisoners were released. The port should have been properly reached, since they had on board an astronomer; but the astronomer was seasick, and the Algerian seamen, who wished to make Marseilles, came out at Bougie. Thence Arago went to Algiers, traversing Kabylia on foot in the midst of a thousand perils. He was long detained in Africa and threatened with the convict prison. Finally he was able to get back to France; his observations, which he had preserved and safeguarded under his shirt, and, what is still more remarkable, his instruments had traversed unhurt these terrible adventures. Up to this point, not only did France hold the foremost place, but she occupied the stage almost alone.

In the years which follow, she has not been inactive and our staff-office map is a model. However, the new methods of observation and calculation have come to us above all from Germany and England. It is only in the last forty years that France has regained her rank. She owes it to a scientific officer, General Perrier, who has successfully executed an enterprise truly audacious, the junction of Spain and Africa. Stations were installed on four peaks upon the two sides of the Mediterranean. For long months they awaited a calm and limpid atmosphere. At last was seen the little thread of light which had traversed 300 kilometers over the sea. The undertaking had succeeded.

To-day have been conceived projects still more bold. From a mountain near Nice will be sent signals to Corsica, not now for geodesic determinations, but to measure the velocity of light. The distance is only 200 kilometers; but the ray of light is to make the journey there and return, after reflection by a mirror installed in Corsica. And it should not wander on the way, for it must return exactly to the point of departure.

Ever since, the activity of French geodesy has never slackened. We have no more such astonishing adventures to tell; but the scientific work accomplished is immense. The territory of France beyond the sea, like that of the mother country, is covered by triangles measured with precision.

We have become more and more exacting and what our fathers admired does not satisfy us to-day. But in proportion as we seek more exactitude, the difficulties greatly increase; we are surrounded by snares and must be on our guard against a thousand unsuspected causes of error. It is needful, therefore, to create instruments more and more faultless.

Here again France has not let herself be distanced. Our appliances for the measurement of bases and angles leave nothing to desire, and, I may also mention the pendulum of Colonel Defforges, which enables us to determine gravity with a precision hitherto unknown.

The future of French geodesy is at present in the hands of the Geographic Service of the army, successively directed by General Bassot and General Berthaut. We can not sufficiently congratulate ourselves upon it. For success in geodesy, scientific aptitudes are not enough; it is necessary to be capable of standing long fatigues in all sorts of climates; the chief must be able to win obedience from his collaborators and to make obedient his native auxiliaries. These are military qualities. Besides, one knows that, in our army, science has always marched shoulder to shoulder with courage.

I add that a military organization assures the indispensable unity of action. It would be more difficult to reconcile the rival pretensions of scientists jealous of their independence, solicitous of what they call their fame, and who yet must work in concert, though separated by great distances. Among the geodesists of former times there were often discussions, of which some aroused long echoes. The Academy long resounded with the quarrel of Bouguer and La Condamine. I do not mean to say that soldiers are exempt from passion, but discipline imposes silence upon a too sensitive self-esteem.

Several foreign governments have called upon our officers to organize their geodesic service: this is proof that the scientific influence of France abroad has not declined.

Our hydrographic engineers contribute also to the common achievement a glorious contingent. The survey of our coasts, of our colonies, the study of the tides, offer them a vast domain of research. Finally I may mention the general leveling of France which is carried out by the ingenious and precise methods of M. Lallemand.

With such men we are sure of the future. Moreover, work for them will not be lacking; our colonial empire opens for them immense expanses illy explored. That is not all: the International Geodetic Association has recognized the necessity of a new measurement of the arc of Quito, determined in days of yore by La Condamine. It is France that has been charged with this operation; she had every right to it, since our ancestors had made, so to speak, the scientific conquest of the Cordilleras. Besides, these rights have not been contested and our government has undertaken to exercise them.

Captains Maurain and Lacombe completed a first reconnaissance, and the rapidity with which they accomplished their mission, crossing the roughest regions and climbing the most precipitous summits, is worthy of all praise. It won the admiration of General Alfaro, President of the Republic of Ecuador, who called them 'los hombres de hierro,' the men of iron.

The final commission then set out under the command of Lieutenant-Colonel (then Major) Bourgeois. The results obtained have justified the hopes entertained. But our officers have encountered unforeseen difficulties due to the climate. More than once, one of them has been forced to remain several months at an altitude of 4,000 meters, in the clouds and the snow, without seeing anything of the signals he had to aim at and which refused to unmask themselves. But thanks to their perseverance and courage, there resulted from this only a delay and an increase of expense, without the exactitude of the measurements suffering therefrom.

GENERAL CONCLUSIONS

What I have sought to explain in the preceding pages is how the scientist should guide himself in choosing among the innumerable facts offered to his curiosity, since indeed the natural limitations of his mind compel him to make a choice, even though a choice be always a sacrifice. I have expounded it first by general considerations, recalling on the one hand the nature of the problem to be solved and on the other hand seeking to better comprehend that of the human mind, which is the principal instrument of the solution. I then have explained it by examples; I have not multiplied them indefinitely; I also have had to make a choice, and I have chosen naturally the questions I had studied most. Others would doubtless have made a different choice; but what difference, because I believe they would have reached the same conclusions.

There is a hierarchy of facts; some have no reach; they teach us nothing but themselves. The scientist who has ascertained them has learned nothing but a fact, and has not become more capable of foreseeing new facts. Such facts, it seems, come once, but are not destined to reappear.

There are, on the other hand, facts of great yield; each of them teaches us a new law. And since a choice must be made, it is to these that the scientist should devote himself.

Doubtless this classification is relative and depends upon the weakness of our mind. The facts of slight outcome are the complex facts, upon which various circumstances may exercise a sensible influence, circumstances too numerous and too diverse for us to discern them all. But I should rather say that these are the facts we think complex, since the intricacy of these circumstances surpasses the range of our mind. Doubtless a mind vaster and finer than ours would think differently of them. But what matter; we can not use that superior mind, but only our own.

The facts of great outcome are those we think simple; may be they really are so, because they are influenced only by a small number of well-defined circumstances, may be they take on an appearance of simplicity because the various circumstances upon which they depend obey the laws of chance and so come to mutually compensate. And this is what happens most often. And so we have been obliged to examine somewhat more closely what chance is.

Facts where the laws of chance apply become easy of access to the scientist who would be discouraged before the extraordinary complication of the problems where these laws are not applicable. We have seen that these considerations apply not only to the physical sciences, but to the mathematical sciences. The method of demonstration is not the same for the physicist and the mathematician. But the methods of invention are very much alike. In both cases they consist in passing up from the fact to the law, and in finding the facts capable of leading to a law.

To bring out this point, I have shown the mind of the mathematician at work, and under three forms: the mind of the mathematical inventor and creator; that of the unconscious geometer who among our far distant ancestors, or in the misty years of our infancy, has constructed for us our instinctive notion of space; that of the adolescent to whom the teachers of secondary education unveil the first principles of the science, seeking to give understanding of the fundamental definitions. Everywhere we have seen the rôle of intuition and of the spirit of generalization without which these three stages of mathematicians, if I may so express myself, would be reduced to an equal impotence.

And in the demonstration itself, the logic is not all; the true mathematical reasoning is a veritable induction, different in many regards from the induction of physics, but proceeding like it from the particular to the general. All the efforts that have been made to reverse this order and to carry back mathematical induction to the rules of logic have eventuated only in failures, illy concealed by the employment of a language inaccessible to the uninitiated. The examples I have taken from the physical sciences have shown us very different cases of facts of great outcome. An experiment of Kaufmann on radium rays revolutionizes at the same time mechanics, optics and astronomy. Why? Because in proportion as these sciences have developed, we have the better recognized the bonds uniting them, and then we have perceived a species of general design of the chart of universal science. There are facts common to several sciences, which seem the common source of streams diverging in all directions and which are comparable to that knoll of Saint Gothard whence spring waters which fertilize four different valleys.

And then we can make choice of facts with more discernment than our predecessors who regarded these valleys as distinct and separated by impassable barriers.

It is always simple facts which must be chosen, but among these simple facts we must prefer those which are situated upon these sorts of knolls of Saint Gothard of which I have just spoken.

And when sciences have no direct bond, they still mutually throw light upon one another by analogy. When we studied the laws obeyed by gases we knew we had attacked a fact of great outcome; and yet this outcome was still estimated beneath its value, since gases are, from a certain point of view, the image of the milky way, and those facts which seemed of interest only for the physicist, ere long opened new vistas to astronomy quite unexpected.

And finally when the geodesist sees it is necessary to move his telescope some seconds to see a signal he has set up with great pains, this is a very small fact; but this is a fact of great outcome, not only because this reveals to him the existence of a small protuberance upon the terrestrial globe, that little hump would be by itself of no great interest, but because this protuberance gives him information about the distribution of matter in the interior of the globe, and through that about the past of our planet, about its future, about the laws of its development.

* * * * *

INDEX

aberration of light, 315, 496

Abraham, 311, 490-1, 505-7, 509, 515-6

absolute motion, 107 orientation, 83 space, 85, 93, 246, 257, 353

acceleration, 94, 98, 486, 509

accidental constant, 112 errors, 171, 402

accommodation of the eyes, 67-8

action at a distance, 137

addition, 34

aim of mathematics, 280

alchemists, 11

Alfaro, 543

algebra, 379

analogy, 220

analysis, 218-9, 279

analysis situs, 53, 239, 381

analyst, 210, 221

ancestral experience, 91

Andrade, 93, 104, 228

Andrews, 153

angle sum of triangle, 58

Anglo-Saxons, 3

antinomies, 449, 457, 477

Arago, 540-1

Aristotle, 205, 292, 460

arithmetic, 34, 379, 441, 463

associativity, 35

assumptions, 451, 453

astronomy, 81, 289, 315, 512

Atwood, 446

axiom, 60, 63, 65, 215

Bacon, 128

Bartholi, 503

Bassot, 542

beauty, 349, 368

Becquerel, 312

Beltrami, 56, 58

Bergson, 321

Berkeley, 4

Berthaut, 542

Bertrand, 156, 190, 211, 395

Betti, 239

Biot, 540

bodies, solid, 72

Boltzmann, 304

Bolyai, 56, 201, 203

Borel, 482

Bouguer, 537, 542

Bourgeois, 543

Boutroux, 390, 464

Bradley, 496

Briot, 298

Brownian movement, 152, 410

Bucherer, 507

Burali-Forti, 457-9, 477, 481-2

Caen, 387-8

Calinon, 228

canal rays, 491-2

canals, semicircular, 276

Cantor, 11, 448-9, 457, 459, 477

Cantorism, 381, 382, 480, 484

capillarity, 298

Carlyle, 128

Carnot's principle, 143, 151, 300, 303-5, 399

Cassini, 537

cathode rays, 487-92

cells, 217

center of gravity, 103

central forces, 297

Chaldeans, 290

chance, 395, 408

change of position, 70 state, 70

chemistry of the stars, 295

circle-squarers, 11

Clairaut, 537-8

Clausius, 119, 123, 143

color sensation, 252

Columbus, 228

commutativity, 35-6

compensation, 72

complete induction, 40

Comte, 294

Condorcet, 411

contingence, 340

continuity, 173

continuum, 43 amorphous, 238 mathematical, 46 physical, 46, 240 tridimensional, 240

convention, 50, 93, 106, 125, 173, 208, 317, 440, 451

convergence, 67-8

coordinates, 244

Copernicus, 109, 291, 354

Coulomb, 143, 516

Couturat, 450, 453, 456, 460, 462-3, 467, 472-6

creation, mathematical, 383

creed, 1

Crémieu, 168-9, 490

crisis, 303

Crookes, 195, 488, 527-8

crude fact, 326, 330

Curie, 312-3, 318

current, 186

curvature, 58-9

curve, 213, 346

curves without tangents, 51

cut, 52, 256

cyclones, 353

d'Alembert, 538

Darwin, 518-9

De Cyon, 276, 427

Dedekind, 44-5

Defforges, 542

definitions, 430, 453

deformation, 73, 415

Delage, 277

Delambre, 539

Delbeuf, 414

Descartes, 127

determinism, 123, 340

dictionary, 59

didymium, 333

dilatation, 76

dimensions, 53, 68, 78, 241, 256, 426

direction, 69

Dirichlet, 213

dispersion, 141

displacement, 73, 77, 247, 256

distance, 59, 292

distributivity, 36

Du Bois-Reymond, 50

earth, rotation of, 326, 353

eclipse, 326

electricity, 174

electrified bodies, 117

electrodynamic attraction, 308 induction, 188 mass, 311

electrodynamics, 184, 282

electromagnetic theory of light, 301

electrons, 316, 492-4, 505-8, 510, 512-4

elephant, 217, 436

ellipse, 215

Emerson, 203

empiricism, 86, 271

Epimenides, 478-9

equation of Laplace, 283

Erdély, 203

errors, accidental, 171, 402 law of, 119 systematic, 171, 402 theory of, 402, 406

ether, 145, 351

ethics, 205

Euclid, 62, 86, 202-3, 213

Euclidean geometry, 65, 235-6, 337

Euclid's postulate, 83, 91, 124, 353, 443, 453, 468, 470-1

experience, 90-1

experiment, 127, 317, 336, 446

fact, crude, 326, 330 in the rough, 327 scientific, 326

facts, 362, 371

Fahrenheit, 238

Faraday, 150, 192

Faye, 536

Fechner, 46, 52

Fehr, 383

finite, 57

Fitzgerald, 415-6, 500-1, 505

Fizeau, 146, 149, 309, 498, 504

Flammarion, 400, 406-7

flattening of the earth, 353

force, 72, 98, 444 direction of, 445 -flow, 284

forces, central, 297 equivalence of, 445 magnitude of, 445

Foucault's pendulum, 85, 109, 353

four dimensions, 78

Fourier, 298-9

Fourier's problem, 317 series, 286

Franklin, 513-4

Fresnel, 132, 140, 153, 174, 176, 181, 351, 498

Fuchsian, 387-8

function, 213 continuous, 218, 288

Galileo, 97, 331, 353-4

gaseous pressure, 141

gases, theory of, 400, 405, 523

Gauss, 384-5, 406

Gay-Lussac, 157

generalize, 342

geodesy, 535

geometer, 83, 210, 438

geometric space, 66

geometry, 72, 81, 125, 207, 380, 428, 442, 467 Euclidean, 65, 93 fourth, 62 non-Euclidean, 55 projective, 201 qualitative, 238 rational, 5, 467 Riemann's, 57 spheric, 59

Gibbs, 304

Goldstein, 492

Gouy, 152, 305, 410

gravitation, 512

Greeks, 93, 368

Hadamard, 459

Halsted, 3, 203, 464, 467

Hamilton, 115

helium, 294

Helmholtz, 56, 115, 118, 141, 190, 196

Hercules, 449

Hermite, 211, 220, 222, 285

Herschel, 528

Hertz, 102, 145, 194-5, 427, 488, 498, 502, 504, 510

Hertzian oscillator, 309, 317

Hilbert, 5, 11, 203, 433, 450-1, 464-8, 471, 475-7, 484

Himstedt, 195

Hipparchus, 291

homogeneity, 74, 423

homogeneous, 67

hydrodynamics, 284

hyperbola, 215

hypotheses, 6, 15, 127, 133

hysteresis, 151

identity of spaces, 268 of two points, 259

illusions, optical, 202

incommensurable numbers, 44

induction, complete, 40, 452-3, 467-8 electromagnetic, 188 mathematical, 40, 220 principle of, 481

inertia, 93, 486, 489, 507

infinite, 448

infinitesimals, 50

inquisitor, 331

integration, 139

interpolation, 131

intuition, 210, 213, 215

invariant, 333

Ionians, 127

ions, 152

irrational number, 44

irreversible phenomena, 151

isotropic, 67

Japanese mice, 277, 427

Jevons, 451

John Lackland, 128

Jules Verne, 111, 536

Jupiter, 131, 157, 231, 289

Kant, 16, 64, 202-3, 450-1, 471

Kauffman, 311, 490-1, 495, 506-7, 522, 545

Kazan, 203

Kelvin, 145, 523-4, 526-7

Kepler, 120, 133, 153, 282, 291-2

Kepler's laws, 136, 516

kinematics, 337

kinetic energy, 116 theory of gases, 141

Kirchhoff, 98-9, 103-5

Klein, 60, 211, 287

knowledge, 201

König, 144, 477

Kovalevski, 212, 286

Kronecker, 44

Lacombe, 543

La Condamine, 535, 537-8, 542-3

Lagrange, 98, 151, 179

Laisant, 383

Lallamand, 543

Langevin, 509

Laplace, 298, 398, 514-5, 518, 522, 538

Laplace's equation, 283, 287

Larmor, 145, 150

Lavoisier's principle, 301, 310, 312

law, 207, 291, 395

Leibnitz, 32, 450, 471

Le Roy, 28, 321-6, 332, 335, 337, 347-8, 354, 468

Lesage, 517-21

Liard, 440

Lie, 62-3, 212

light sensations, 252 theory of, 351 velocity of, 232, 312

Lindemann, 508

line, 203, 243

linkages, 144

Lippmann, 196

Lobachevski, 29, 56, 60, 62, 83, 86, 203

Lobachevski's space, 239

local time, 306-7, 499

logic, 214, 435, 448, 460-2, 464

logistic, 457, 472-4

logisticians, 472

Lorentz, 147, 149, 196-7, 306, 308, 311, 315, 415-6, 492, 498-502, 504-9, 512, 514-6, 521

Lotze, 264

luck, 399

Lumen, 407-8

MacCullagh, 150

Mach, 375

Mach-Delage, 276

magnetism, 149

magnitude, 49

Mariotte's law, 120, 132, 157, 342, 524

Maros, 203

mass, 98, 312, 446, 486, 489, 494, 515

mathematical analysis, 218 continuum, 46 creation, 383 induction, 40, 220 physics, 136, 297, 319

mathematics, 369, 448

matter, 492

Maupertuis, 535, 537-8

Maurain, 543

Maxwell, 140, 152, 175, 177, 181, 193, 282-3, 298, 301, 304-5, 351, 503, 524-5

Maxwell-Bartholi, 309, 503-4, 519, 521

Mayer, 119, 123, 300, 312, 318

measurement, 49

Méchain, 539-40

mechanical explanation, 177 mass, 312

mechanics, 92, 444, 486, 496, 512 anthropomorphic, 103 celestial, 279 statistical, 304

Méray, 211

metaphysician, 221

meteorology, 398

mice, 277

Michelson, 306, 309, 311, 316, 498, 500-1

milky way, 523-30

Mill, Stuart, 60-1, 453-4

Monist, 4, 89, 464

moons of Jupiter, 233

Morley, 309

motion of liquids, 283 of moon, 28 of planets, 341 relative, 107, 487 without deformation, 236

multiplication, 36

muscular sensations, 69

Nagaoka, 317

nature, 127

navigation, 289

neodymium, 333

neomonics, 283

Neumann, 181

Newton, 85, 96, 98, 109, 153, 291, 370, 486, 516, 536, 538

Newton's argument, 108, 334, 343 law, 111, 118, 132, 136, 149, 157, 233, 282, 292, 512, 514-5, 518, 525 principle, 146, 300, 308-9, 312

no-class theory, 478

nominalism, 28, 125, 321, 333, 335

non-Euclidean geometry, 55, 59, 388 language, 127 space, 55, 235, 237 straight, 236, 470 world, 75

number, 31 big, 88 imaginary, 283 incommensurable, 44 transfinite, 448-9 whole, 44, 469

objectivity, 209, 347, 349, 408

optical illusions, 202

optics, 174, 496

orbit of Saturn, 341

order, 385

orientation, 83

osmotic, 141

Padoa, 463

Panthéon, 414

parallax, 470

parallels, 56, 443

Paris time, 233

parry, 419-22, 427

partition, 45

pasigraphy, 456-7

Pasteur, 128

Peano, 450, 456-9, 463, 472

Pender, 490

pendulum, 224

Perrier, 541

Perrin, 195

phosphorus, 333, 468, 470-1

physical continuum, 46

physics, 127, 140, 144, 279, 297

physics of central forces, 297 of the principles, 299

Pieri, 11, 203

Plato, 292

Poincaré, 473

point, 89, 244

Poncelet, 215

postulates, 382

potential energy, 116

praseodymium, 333

principle, 125, 299 Carnot's, 143, 151, 300, 303-5, 399 Clausius', 119, 123, 143 Hamilton's, 115 Lavoisier's, 300, 310 Mayer's, 119, 121, 123, 300, 312, 318 Newton's, 146, 300, 308-9, 312 of action and reaction, 300, 487, 502 of conservation of energy, 300 of degradation of energy, 300 of inertia, 93, 486, 507 of least action, 118, 300 of relativity, 300, 305, 498, 505

Prony, 445

psychologist, 383

Ptolemy, 110, 291, 353-4

Pythagoras, 292

quadrature of the circle, 161

qualitative geometry, 238 space, 207 time, 224

quaternions, 282

radiometer, 503

radium, 312, 318, 486-7

Rados, 201

Ramsay, 313

rational geometry, 5, 467

reaction, 502

reality, 217, 340, 349

Réaumur, 238

recurrence, 37

Regnault, 170

relativity, 83, 305, 417, 423, 498, 505

Richard, 477-8, 480-1

Riemann, 56, 62, 145, 212, 239, 243, 381, 432 surface, 211, 287

Roemer, 233

Röntgen, 511, 520

rotation of earth, 225, 331, 353

roulette, 403

Rowland, 194-7, 305, 489

Royce, 202

Russell, 201, 450, 460-2, 464-7, 471-4, 477-82, 484-5

St. Louis exposition, 208, 320

Sarcey, 442

Saturn, 231, 317

Schiller, 202

Schliemann, 19

science, 205, 321, 323, 340, 354

Science and Hypothesis, 205-7, 220, 240, 246-7, 319, 353, 452

semicircular canals, 276

series, development in, 287 Fourier's, 286

Sirius, 226, 229

solid bodies, 72

space, 55, 66, 89, 235, 256 absolute, 85, 93 amorphous, 417 Bolyai, 56 Euclidean, 65 geometric, 66 Lobachevski's, 239 motor, 69 non-Euclidean, 55, 235, 237 of four dimensions, 78 perceptual, 66, 69 tactile, 68, 264 visual, 67, 252

spectra, 316

spectroscope, 294

Spencer, 9

sponge, 219

Stallo, 10

stars, 292

statistical mechanics, 304

straight, 62, 82, 236, 433, 450, 470

Stratonoff, 531

surfaces, 58

systematic errors, 171

tactile space, 68, 264

Tait, 98

tangent, 51

Tannery, 43

teaching, 430, 437

thermodynamics, 115, 119

Thomson, 98, 488

thread, 104

time, 223 equality, 225 local, 306, 307 measure of, 223-4

Tisserand, 515-6

Tolstoi, 354, 362, 368

Tommasina, 519

Transylvania, 203

triangle, 58 angle sum of, 58

truth, 205

Tycho Brahe, 133, 153, 228

unity of nature, 130

universal invariant, 333

Uriel, 203

van der Waals, 153

Vauban, 210

Veblen, 203

velocity of light, 232, 312

Venus of Milo, 201

verification, 33

Virchow, 21

visual impressions, 252 space, 67, 252

Volga, 203

Voltaire, 537-8

Weber, 117, 515-6

Weierstrass, 11, 212, 432

Whitehead, 472, 481-2

whole numbers, 44

Wiechert, 145, 488

x-rays, 152, 511, 520

Zeeman effect, 152, 196, 317, 494

Zeno, 382

Zermelo, 477, 482-3

zigzag theory, 478

zodiac, 398, 404

* * * * *

Transcriber's Note: The Greek alphabets are represented within square brackets. For example, [alpha] stands for first Greek alphabet alpha. Square root of a number is represented using the symbol (sqrt). That is to say, sqrt(25) stands for square root of 25. The superscript is shown with carat (^) symbol, example, 10^{5} stands for 5th power of 10. Similarly, subscript is represented by underscore (_) symbol. For instance, n_{3} stands for letter n with subscript 3.