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THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



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the comet of 1082 would re-appear; lie marked out the constellations 

 and stars which it would meet in its career. It was not one of those 

 long-winded predictions which astrologers and other fortune-tellers 

 formerly very cl^-verly combined with the tables of mortality, in such 

 way as not to be put to the lie in their own lifetime ; the event was 

 to happen, and it concerned nothing less than to create a new era in 

 cometary astronomy, or to cast on science a discredit from which it 

 would for a long while suffer. 



Clairaut found by very long and learned calculation that the action 

 of Jupiter and Saturn ought to retard the movement of the comet; 

 and that the duration of its entire revolution, compared with the pre- 

 ceding, would be augmented 518 days by the attraction of Jupiter and 

 100 by the attraction of Saturn, being a total of (518 days, or more than 

 a year and eight months. Never did any astronomical question create 

 a more lively or more natural interest; every class of society awaited 

 the re-appearance foretold with equal anxiety. A Saxon labourer, 

 Palitszch, was the first to see it. From that moment, from one end of 

 Europe to the other, a thousand telescopes nightly marked the points 

 of the path of this star among the constellations. The path was 

 always within the limits of calculation, that which Clairaut had laid 

 down beforehand. The prediction of the illustrious mathematician 

 w as accomplished both in time and space ; astronomy had made a 

 great and important gain, and with the same blow beat down, as often 

 happens, a vile and inveterate prejudice. From the time when it was 

 laid down that the return of a comet may be foretold and calculated, 

 these bodies finally lost their former prestige. The most timid men 

 felt as little trouble about them as about the equally calculable eclipses 

 of the sun and moon. The labours of Clairaut had therefore in the 

 end, and with the public, yet more good fortune than the learned, in- 

 genious, and witty arguments of Bayle. 



The firmament offers to reflecting minds nothing stranger or more 

 remarkable than the equality of the mean angular movements of revo- 

 lution and rotation of our satellite. On account of this perfect equality 

 the moon presents always the same side to the earth. The hemi- 

 sphere which we now view is precisely that which our forefathers 

 viewed at the most distant epochs, and the same which our children's 

 latest offspring will observe. The final causes used with so little re- 

 serve by certain philosophers to account for a great many natural phe- 

 nomena were in that particular case without possible application. 

 How could we in fact pn'tend that men could have any interest what- 

 ever in incessantly looking at the same halfspherc of the moon, and 

 never looking at the other halfsphere? On the other hand a perfect 

 mathematical equality between elements without necessary connection, 

 such as the movement of translation or rotation of a given heavenly 

 body did not less shock the idea of probability. There were besides 

 two other numerical coincidences quite as extraordinary ; an identical 

 orientation, relatively to the stars, of the equator and orbit of the 

 moon, and movements of precession of these two planes exactly equal. 

 '1 his aggregate of singular phenomena, discovered by J. D. Cassini, 

 constituted the mathematical code of what was called the libration of 

 the moon. The libration was yet a vast and very melancholy lacun.i 

 in physical astronomy, when Lagrange made it depend on a circum- 

 stance in the figure of our satellite not observable from the earth, 

 when he completely combined it with the universal principles of gra- 

 vitation. At the time when the moon solidified, she took under the 

 influence of the e.irth, a form less regular and less simple than if any 

 foreign attractive body had been in proximity. This action did not 

 prevent the lunary equator from being everywhere swelled out, but 

 prominence of the equatorial diameter turned toward the earth, be- 

 came four times more considerable than that of the diameter, which 

 we see perpendicularly. The moon would then exhibit to an observer 

 situated in space and who could examine it transversely, a body elon- 

 gated towards the earth, like a pendulum without a point of suspen- 

 sion. When a pendulum is moved from verticality, the action of 

 gravity brings it back, and when the great axis of the moon departs 

 from its habitual direction, the earth equally compels it to return. 

 Here then is that strange phenomenon thoroughly explained without 

 referring to an equality in some kind miraculous, between two move- 

 ments of rotation and translation entirely independent. Men will 

 never see more than one side of the moon. Observation had taught 

 ui this, now we know moreover that it is owing to a physical course, 

 calculable and visible only by the eye of the mind; that it is owing to 

 the lengthening experienced by the diameter of the moon, when that 

 star passed from the liquid to the solid state under the attractive in- 

 fluence of the earth. If originally a little difference had existed be- 

 tween the rotary and revolving movements of the moon, the attraction 

 of the earth would have brought these movements to a rigorous 

 equality. This attraction would in like manner have sufficed to get 

 rid of little want of coincidence between the lines resulting from the 

 intersections of the lunary equator and orbit with the plane of the 



ecliptic. The work in which Lagrange connected with so much good 

 fortime, the laws of libration to the principles of universal gravity, so 

 capital in its matter, is not less remarkable in its form. After having 

 read it, every one will comprehend that the term "elegance" may be 

 applied to a mathematical treatise. 



We have been content in this analysis to glance over the astronomi- 

 cal discoveries of Clairaut, D'Alembert, and Lagrange ; we shall be 

 rather less concise in speaking of the works of Laplace. After having 

 enumerated the multiplied powers, which must result from the mutual 

 action of the planets and setellitcs of our solar system, Newton, the 

 Great Newton, dared not to undertake to grasp their whole effects. 

 Amid the labyrinth of augmentations and diminutions of speed, of 

 variations of form in the orbit, of changes of distances and inclinations 

 which these powers would evidently produce, the most learned geo- 

 metry itself would not have found out a firm and faithful guiding clue. 

 This extreme complication gave birth to a discouraging thought. 

 Powers or forces so numerous, so variable in position, so different in 

 intensity, did not seem able to maintain their balance but by a kind of 

 miracle. Newton went so far as to suppose that the planetary system 

 did not contain in itself elements of indefinite conservation ; he be- 

 lieved that a powerful hand must intervene from time to time to repair 

 the disorder. Eular, although more advanced than Newton in the 

 knowledge of planetary perturbations, did not any more admit that the 

 solar system was so constructed as to last eternally. Never did a 

 greater philosophical question present itself to the curiosity of men. 

 iLaplace attacked it with boldness, constancy and good fortune. The 

 profound and long continued labours of that illustrious mathematician, 

 established on firm evidence, that the planetary ellipses are perpe- 

 tually varying; that the extremities of their great diameter traverse 

 the heavens, and that independently of an oscillatory movement, the 

 planes of the orbits sustain a displacement, by the effect of which 

 their traces on the plane of the terrestrial orbit are every year directed 

 toward different stars. Amid this apparent chaos there is one thing 

 which remains constant, or which is only subject to small periodical 

 changes, and that is the great axis of each orbit, and consequently the 

 period of revolution of each planet; and that is the quantity which 

 should most have varied according to the learned preconceptions of 

 Newton and Euler. 



The universal gravitation suffices for the preservation of the solar 

 system ; it maintains the forms and inclinations of the orbits in a mean 

 state around which the variations are slight; the variety does not 

 produce disorder, and the world exhibits harmonies and perfections 

 which Newton never conceived. That depends on circumstances 

 which calculation disclosed to Laplace, and which on cursory inspec- 

 tion would not appear to exert so great an influence. For planets 

 moving themselves in the same direction, in orbits of slight ellipticity, 

 and in planes little inclined to each other, substitute dirterent condi- 

 tions, and the stability of the world will be put in question anew, and 

 in all probability a fearful chaos would ensue. 



Although since the labours to which we have referred, the indura- 

 bility of the great axes of that planetary orbits may have been better 

 demonstrated, that is to say, by means of more extension in analytical 

 approximations,^ it does not the less remain one of the admirable dis- 

 coveries of the author of the Mecanique Celeste. Dates on such sub- 

 jects are not a luxury of erudition: the paper in which Laplace com- 

 municated his results on the invariability of the mean movements or 

 of great axes is of 1773; it was in 1784 only, that he deduced the 

 stability of the other elements of the system, of the small mass of the 

 planets, the slight ellipticity of their orbits, and the similitude of 

 direction in the circulatory movement of these stars around the sun. 



The discovery of which I have just given an account, no longer 

 allowed us, at least in our solar systenj, to consider the Newtonian 

 attraction as a cause of disorder ; but was it impossible that other 

 powers might combine with that and produce the gradually increasing 

 perturbations which Newton and Euler feared? Positive facts seeiu 

 to authorize such fear. Old observations as compared with the modern 

 revealed a continual acceleration in the movements of the moon and 

 of Jupiter ; a diminution not less manifest in the movement of Saturn. 

 From these variations resulted the strangest conclusions. From the 

 presumed causes of these perturbations to say of a star that its velo- 

 city increased from age to age, was to declare in equivalent terms that 

 it came nearer to the centre of movement. The star on the contrary 

 would depart from that same centre, when its velocity slackened. 

 Thus, singularly, our planetary system seemed destined to lose Saturn," 

 its most mysterious ornament ; to see that planet accompanied by the 

 ring and seven satellites, gradually buried in the unknown regions, 

 where the eye armed with the most powerful telescopes has never 



3 On this subject may be consulted two beautiful papers by Lsgrange and Poisson. 

 ■' Then regarded as Its outermost member,— Translator. 



2b* 



