XXX1L 



THE PROGRESS OF 



starvations of Lacaille, lie determined very 

 nearly the masses of the principal planets, ami 

 showed that the greatest erfect of their accumu- 

 lated influence in deranging the earth's motion 

 onn amount only to about a minute. His esti- 

 mate of the attraction of Venus has been con- 

 firmed by later and more elaborate calculation. 



In 171!> 1)'. Uembcrt investigated rigorously 

 the effects arising from the moon's attracting the 

 spheroidal prominence of the earth. By the 

 ransformation of this general expression ho 

 found the precestion or conical motions of the 

 terrestrial axis about the poles of the ecliptic to 

 be 50" annually, and the nutation, or alternate 

 vibration on the same plane to be only 18'' during 

 the period of the revolution of the lunar nodes. 

 Comparing this quantity with observation, he 

 (included, that at the surface of the earth the 

 attraction of the sun is to that of the moon as 3 

 to 7 ; which makes the satellite to have only the 

 70th part of the mass of our planet 



Astronomers now turned their attention to the 

 motions of the comets. These bodies describe 

 elliptic orbits with very different inclinations, 

 and so extremely elongated as to resemble para- 

 bolas, through a considerable part of their course. 

 Being very small, they are seen for a short space 

 only in the vicinity of the sun, and become quite 

 invisible when they approach the other extremity 

 of their orbit, which is probably beyond the 

 boundaries of our planetary system. The peri- 

 odic time of comets depending upon the trans- 

 verse axis of the ellipsis can seldom be deter- 

 mined with accuracy. The few observations 

 which can be made while it is near the perihe- 

 lium are scarcely sufficient to assign its mean 

 motion, and the places of its nodes and peri- 

 helium. 



Halley applied the formulas of Newton to the 

 computation of twenty-four remarkable comets. 

 But his attention was particularly fixed on the 

 nearest of them, which had been observed in 1531 , 

 1607, and 1682, and seemed to be the same with 

 one noticed in old chronicles in 1080, 1155, 1230, 

 1305, 1381, and 1456. Hence it performed its 

 revolutions in about 75 years. He therefore 

 ventured to predict its return about the end of 

 1753 or beginning of 1759. The time of the 

 expected return approaching excited intense 

 curiosity in the scientific world. Clairaut ap- 

 plied his formulas to the investigation of the 

 progress of this comet. He found that the last 

 revolution would be retarded 618 days longer 

 than the preceding, from the attractions ot Jupi- 

 ter and Saturn. He fixed the time of its appear- 

 ance to the 4th April. This exceeded that of ob- 

 servation by twelve days only. The discrepancy 

 was probably owing to the influence of Uranus, 

 which was not yet discovered. The comet was first 



seen by a peasant in Saxony on Christmas day ; 

 but soon became the admiration of Paris, and 

 procured for Clairaut the enthusiasm of popular 

 applause. 



Clairaut, eager to complete a work in which 

 he had gathered so many laurels, proceeded to 

 calculate the disturbing influence of Jupiter and 

 Saturn on the place of the nodes of the comet of 

 1682 and 1759, which lias an inverted motion. 

 Newton had shown that the perturbations in the 

 planetary system always advance the perihclium 

 and retract the nodes. But the case here was 

 just reversed, and the quantity of recession thence 

 determined agreed most exactly with observation. 



But the comets in traversing our system often 

 suffer such derangements that the most select 

 observations are insufficient to determine, with 

 any sort of precision, their elliptical orbits. The 

 famous comet of 1759 was calculated by Kuler 

 and Lexell to perform its revolution in a period 

 between 449 and 519 years, while Pingre as- 

 signed it a period of 1231 years. In some cases 

 the observations have indicated an hyperbolic 

 orbit Conti, following the method of Gauss, 

 found the comet of 1811 to revolve in 30.5(5 .') 

 years ; but by a second computation, he reduced 

 the time to 2301 years. Bessel gave the comet 

 of 1807 a period of 1953-2 years; but afterwards 

 brought it down to 1483-3 years. 



Though the comets suffer such great derange- 

 ment from the large planets, they have no sen- 

 sible effect on our system. They must therefore 

 be exceedingly small. They consist of a dark 

 nucleus, invested with a cloudy or hazy ex- 

 crescence, and usually provided with a very long 

 taiL They have never disturbed our tides, 

 though having sometimes approached within the 

 third part of the distance of the moon, they 

 would, with the same mass, exert twenty-seven 

 times greater deranging force. But their passage 

 was so rapid that time was not given to produce 

 the requisite effect on the ocean. 



In 1764, Lagrange, who, at the early age of 23, 

 had invented the calculus of variations, gained 

 the prize offered by the Academy of Sciences, 

 for his memoir on the libration of the moon. He 

 explained in the most satisfactory manner, from 

 the theory of attraction, the cause why the moon 

 always presents nearly the same face towards the 

 earth. He again resumed the subject in 1780. 



The theory of Jupiter's satellites is of great 

 importance for finding the longitude. In 1766, 

 Lagrange embraced the subject in its fullest ex- 

 tent, by introducing into his equations, not only 

 the attractive force of the sun, but the mutual 

 attractions of the satellites themselves. His in 

 vestigation was a model of analytical research ; 

 yet it did not descend into all the practical de- 

 tails. 



