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THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[SeptembbR 



Five geometricians, Clairaut, Euler, D'Alembert, Lagrange, and 

 Laplace, divided among them tlie world which Nevtton had brought 

 to light. They explored it in every quarter, penetrated into regions 

 which might have been thought inaccessible, and pointed out nun^ber- 

 less phenomena which had escaped observation ; in fine, nnd that is 

 their immortal glory, they bound up in one principle, one single law, 

 the most mysterious and most subtile of the heavenly movements. 

 Geometry moreover had the boldness to provide for the future, and 

 ages as they go on scrupulously ratify the judgments of science. 



We shall not have to take account of the magnificent labours of 

 Euler, on the contrary, we shall draw here a rapid analysis of the dis- 

 coveries of his four rivals, our fellow countrymen.' If a star, the 

 moon for example, only gravitates toward the centre of the earth, it 

 would mathematically describe an ellipse, and would strictly follow 

 the law of Kepler, or what is the same thing, the mechanical princi- 

 ples laid down by Newton in the early chapters of his immortal work. 

 Now let us put in action a second power ; let us take into account the 

 attraction of the sun upon the moon ; instead of two bodies, in fine, we 

 may take three, and the Keplerian ellipse will only give a rough idea 

 of the movement of our satellite. Here the attraction of the sun will 

 tend to augment the dimension of the former orbit, and will really 

 augment them ; there, on the other hand, it will diminish them. At 

 certain points the solar power will act in the direction where the star 

 is displaced, and the movement will become more rapid, elsewhere 

 the effect will be inverse. In a word, by bringing in a third attractive 

 body, the utmost complication and every appearance of disorder will 

 succeed a simple and regular course on which the mind had compla- 

 cently relied. If Newton gave a complete solution of the question of 

 heavenly movements in the case of two stars attracting each oilier, be 

 did not even analytically enter upon the infinitely more dilBcult pro- 

 blem of three bodies. The problem of three bodies, the name under 

 which he became celebrated, the problem of determining the course 

 of a star affected by the attractive action of two other stars was first 

 determined by our fellow countryman Clairant. From that solution 

 may be dated the important progress already made in the last century 

 toward perfecting lunar tables. 



The most beautiful astronomical discovery of antiquity is that of the 

 succession of the equinoxes. Hipparclius, to whom the honour of it 

 belongs, pointed out all the results of that movement with perfect 

 clearness. Among these results, two have had more particularly the 

 privilege of drawing public attention. On account of the succession 

 of the equinoxes the same starry groups and constellations are not 

 perceived in the firmament on every night in each season. In the 

 course of time, the actual winter constellations will become summer 

 constellations, and reciprocally. On account of the succession of the 

 equinoxes the pole does not constantly occupy the same place in the 

 starry sphere. That star, brilliant enough, now very properly named 

 the polar, was very far off from the pole in the time of Hipparclius, and 

 it will again occur in some centuries hereafter. The name of polar 

 has been, and will be successively given to stars very far off from each 

 other. When we have the ill fortune in seeking an exphination of 

 natural phenomena to get into a false path, every certain observation 

 throws the theorist into new complications. Seven spheres cased in 

 crystal would no longer do for the delineation of phenomena, when the 

 illustrious astronomer of Rhodes had found out the procession. An 

 eighth sphere was then wanted to account for the movement in which 

 all the stars participate together. After having torn the earth from 

 its pretended immobility, Copernik, on the contrary, provided in a 

 very simple manner for the most minute particulars of the procession. 

 He supposed that the axis of rotation of the earlh does not lie 

 exactly parallel to ilself, but that after every thorough revolution of 

 our globe around the sun, that axis deviates by a minute quaitity ; in 

 a word, instead of making the whole of the circumpolar stars move in 

 a certain manner on meeting with the pole, he made the pole move to 

 meet the stars. This hypothesis cleared the mechanism of the world 

 from the greatest complication which the spirit of system had found 

 out. A new Alpbonso would then have wanted a plea for addressing 

 to his astronomical conclave the profound, but badly interpreted words 

 attributed by history to the king of Castile. - 



If the conception of Copernik, improved by Kepler, had, as we have 

 now seen, greatly perfected the mechanism of the heavens, there yet 



1 We may be asked, perhaps, why we reckon Lagrange among French geometricians. 

 In two words we Kive our answer; — he who was named Lagrange Tovirnier, two of the 

 most truly French names capable of being conceived, who had for maternal graiuifalher 

 AI. Gros, and for paternal great grandfather a Fiench officer born in Paris, who never 

 wrote but in French, and held in our country the highest dignities for nearly thirty years, 

 It seems, although burn at Turin, must be consiilered as a Frenchman. 



- Yielding to just presentiments on the majestic simplicity which, sooner or later, was 

 10 become tlie attribute of the heavenly movements, Alpbonso cried out—" If I had been 

 called to the council of Hod when he created the world things would have been better or- 

 dsred," 



remained to be discovered the motive power, which yearly modifying 

 the axis of the earth, made it describe, in 2(>,000yRars an entire circle 

 of about 50 degrees in diametej. 



Newton divined that that power emanated from the action of the 

 sun and the moon on matter, which in the equatorial regions arose 

 above a sphere of which the centre would agree with that of the earth, 

 and would have for a radius a line brought from that centre to one of 

 the poles; thus he made the precession of the equinoxes depend on 

 the flattening of the globe, and declared that on a spherical planet no 

 precession would occur. That was true, but Newton did not arrive at 

 the mathematical proof. Now that great man had introduced into 

 philosophy the just and severe rule — "do not believe anything for true 

 until it is demonstrated." The demonstration of the Newtonian ideas 

 on the precession of the equinoxes was therefore a great discovery, 

 and to D'Alembert belongs the glory. That illustrious inatheraatician 

 has given a complete explanation of the general movement, in virtue 

 of which the axis of the terrestrial globi; returns to the same stars in 

 2t5,000 years. He has connected to witli attraction the perturbation 

 of procession found out by Bradley, and the remarkable oscillation in- 

 cessantly undergone by the axis of the earth during its progressive 

 movement, and of which the period, about eighteen years, is exactly 

 equal to the time that the intersection of the orbit of the moon and the 

 ecliptic, employs to go through the 360 degrees of the entire circum- 

 ference. 



Mathematicians and astronomers have been quite as ftiUy occupied, 

 and with reason, with the form and physical structure that the terres- 

 trial globe may have had at the earliest epoch, as with the form and 

 structure of the actual globe. When our fellow-countrymen Richer 

 had discovered that a body, whatever its nature, weighs the less as it 

 is further transported to the equinoctical regions, every one perceived 

 that the earth, if it were originally fluid, must be puffed out at the 

 equator. Huygens and Newton did more ; they calculated the differ- 

 ence of the great and little axis, and the excess of equatorial diameter 

 over that of the polar. Huygens founded his calculation on the hvpo- 

 thetical and totally inadmissible properties of attractive force ; New- 

 ton on a theorem which required to be proved. The theory of New- 

 ton had a graver defect; it held the primitive and fluid earth to be in 

 a state of complete homogeneity.- When, in endeavouring to solve 

 great problems, we give way to such simplifications, when to avoid 

 difficulty in calculating we wander so essentially from natural and 

 physical conditions, the results belong to an ideal world, and are 

 nothing more than frolics of the mind. To apply analysis in a profit- 

 able manner to determine the figure of the earth every idea of homo- 

 geneity had to be got rid of, and every obligatory likeness between the 

 forms of the superimposed and unequally dense layers ; the case of a 

 central kernel had also to be examined. This generalization made 

 the difficulty tenfold, but did not however impede Clairaut and D'Alem- 

 bert. Thanks to the endeavours of these two powerful mathemati- 

 cians, thanks to a few essential developements due to their imme- 

 diate successors, and particularly to the illustrious Legendre, the the- 

 oretical determination of the figure of the earth has acquired the 

 desired perfection ; and complete accord prevails between the calcu- 

 lated results and those of direct measurement. The earth has there- 

 fore been originally fluid, and analysis has enabled us to go up to the 

 infancy of our planet. 



In the time of Alexander, comets were with the greater part of the 

 Greek philosophers simple meteors, engendered in our atmosphere. 

 The middle age, without taking any trouble about their nature, made 

 prognostics from ihem, and signs forerunning sinister events. Regio- 

 mentarius and Tycho Brahe placed them by their observations beyond 

 the moon; Hevelius,Doerfel,&c.,made them go round the sun; Newton 

 laid down that they move under the immediate protective influence 

 of that body, that they do not describe right lines but obey the Kep- 

 lerian law. It required to be proved that the orbits were closed curves 

 or that the earth sees the same comet on many occasions. This dis- 

 covery remained for Halley. By carefully collecting in the recitals of 

 historians and chroniclers, and in astronoinical annals, the circum- 

 stances of the a[jpearances of all the more brilliant comets, this inge- 

 nious savant pointed out by subtile and profound discussion that the 

 comets of lliSi!, I(i(l7, and 1531 were in truth successive appearances 

 of one and tlie same star. This identity led to a result from which 

 more than one astronomer drew back — that the time of an entire 

 cometary revolution varied much, and that the variation might go 

 from two years to seventy-six. Were such great differences attribut- 

 able to perturbations caused by planetary action? The reply to this 

 question would bring comets into the category of ordinary planets, or 

 lor ever keep them out. It was difficult to be calculated, but Clairaut 

 found out the means of eftecting it. Success might seem doubtful, 

 but Clairaut gave proof of the greatest boldness, for in the course of 

 175S be undertook to determine the period in the following year when 



