HALLEY'S COMET. 



183 



It is difficult to convey to one who is not conversant with such investiga- 

 tions, an adequate notion of the labor which such an inquiry involved, 'ihe 

 calculation of the influence of any one planet of the system upon any other, is 

 itself a problem of some complexity and difficulty ; but still, one general com- 

 putation, depending upon the calculation of the terms of a certain series, is 

 sufficient for its solution. This comparative simplicity arises entirely from two 

 circumstances which characterize the planetary orbits. These are, that though 

 they are ellipses, they differ very slightly from circles ; and though the plan- 

 ets do not move in the plane of the ecliptic, yet none of them deviate consider- 

 ably from that plane. But these characters do not, as we have already stated, 

 belong to the orbits of comets, which, on the contrary, are highly eccentric, 

 and depart from the ecliptic at all possible angles. The consequence of this 

 is, that the calculation of the disturbances produced in the cometary orbit by 

 the action of the planets, must be conducted, not like the planets, in one gen- 

 eral calculation applicable to the whole orbit, but in a vast number of separate 

 calculations, in which the oifeit is considered, as it were, bit by bit, each bit 

 requiring a calculation similar to that of the whole orbit of the planet. In 

 fact, for a very small part of its course, we treat the comet as we would a 

 planet ; making our calculations, and completing them, nearly in the same 

 manner ; but for the next part we are obliged to enter upon a new calculation, 

 starting with a different set of numbers, but performing over again similar 

 arithmetical operations upon them. When it i-s considered that the period of 

 Halh-y's cornet is about seventy-five years, and that every portion of its course, 

 for two successive periods, was necessary to be calculated separately in this 

 way, some notion may be formed of the labor encountered by Lalande and 

 Madame Lepaute. " During six months," says Lalande, " we calculated from 

 morr.ing till night, sometimes even at meals, the consequence of which was, 

 that I contracted an illness which changed my constitution for the remainder 

 of my life. The assistance rendered by Madame Lepaute was such, that with- 

 out her we never could have dared to undertake this enormous labor, in which 

 it was necessary to calculate the distance of each of the two planets, Jupiter 

 and Saturn, from the comet, and their attraction upon that body, separately, for 

 every successive degree, and for 150 years."* 



These elaborate calculations having been completed, Clairaut, fearing that the 

 comet would anticipate his announcement, presented his first memoir to the 

 Academy on the 14th of November, 1758. In this memoir he was compelled to 

 adopt the path of the comet upon its former appearance, as determined by the 

 observations of Appian. These, however, were made at a time when little at- 

 tention was paid to comets ; and were made, moreover, without that conscious- 

 ness on the part of the observer of their future importance, which would doubt- 

 less have produced greater accuracy. In calculating the effect of the attrac- 

 tion of Jupiter and Saturn upon the comet, in its two periods between 1707 

 and 1682, and between the latter period and the expected return, Clairaut pro- 

 ceeded upon the supposition that the masses of these planets were each what 

 they were ther. supposed to be. It has, Eowever, since appeared, that the es- 

 timates cf these masses were incorrect, more especially that of Saturn. The 

 planet Hcrschel being then unknown, its influence upon the comet was, of 



* The name of Madame Lepante does not appear in Clairaut' s memoir ; a suppression which La- 

 lande attributes to the influence exercised by another lady to whom Clairaut was attached. La- 

 lande, however, quotes letters of Clairaut, in which he speaks in terms of high admiration of " la 

 savante calculatrice." The labors of this lady in the work of calculation (for she also assisted La- 

 lande in constructing his Ephemeridcs) at length so weakened her sight, that she was compelled to 

 desist. She died in 1788, while attending on her husband, who had become insane. See the arti- 

 cles on comets, written with considerable ability, in the Companion to the British Almanac for the 

 rear 1833. They are understood to be the production of Mr. De Morgan, secretary of the Astro- 

 aomical Society. 



