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182 



HALLEY'S COMET. 



amount of attraction depending on the greatness of the attracting body, the in- 

 tensity of the solar attraction of each of the planets must predominate enormously 

 over the comparatively feeble influence of their diminutive masses on each other. 

 The tendency of the solar attraction to impress the elliptic form on the paths 

 of those planets, must therefore prevail in the main ; a4id although their mutual 

 attraction, however feeble, cannot be wholly ineffective, their orbits will, in 

 obedience to the solar mandate, preserve a general elliptic form, subject to 

 those very slight deviations, or disturbances, due to their reciprocal attraction. 

 The problem to discover the nature and amount of these disturbances is one of 

 paramount importance in astronomy, and has been called the " problem of 

 three bodies ;'' and its extension embraces the effects of the mutual gravitation 

 of all the planets of the system upon each other. This celebrated problem 

 presented enormous mathematical difficulties. A particular case of it, which, 

 from the comparative smallness of the third body considered, was attended 

 with greater facility, was solved by Euler, D'Alembert, and Clairaut. This 

 was the case in which the single planet, revolving round the sun, was the 

 earth, and the third body the moon. 



Clairaut undertook the difficult application of this problem to the case of the 

 comet of 1682, with a view to calculate the effects which would be produced 

 upon it by the attraction of the different planets of the system; and by such 

 means to convert the conjecture of Halley into a distinct astronomical predic- 

 tion, attended with all the circumstances of time and place. The exact verifi- 

 cation of the prediction would, it was obvious, furnish the most complete dem- 

 onstration of the principle of universal gravitation ; which, though generally re- 

 ceived, was not yet considered so completely demonstrated as to be independ- 

 ent of so remarkable a body of evidence as the fulfilment of such a calculation 

 would afford. 



To attain completely the end proposed, it was necessary to solve two very 

 different classes of problems, requiring different powers of mind, and different 

 habits of thought and application. The mathematical part of the inquiry, 

 strictly speaking, consisted in the discovery of certain general analytical for- 

 mulae, applicable to the case in question ; which, when translated into ordinary 

 language, would become a set of rules expressing certain arithmetical proces- 

 ses, to be effected upon certain give* numbers ; and when so effected would 

 give as the final results, numbers wnich would determine the place of the 

 comet, under all the circumstances influencing it from hour to hour. The ac- 

 tual place of the body being thus determined, it became a simple question of 

 practical astronomy to ascertain its apparent place in the firmament, at corre- 

 sponding times. A table exhibiting its apparent place thus determined in the 

 firmament for stated intervals of time, is called its Ephemeris ; it is the final 

 result to which the whole investigation must tend, and is that whose verifica- 

 tion by observation would ultimately decide the validity of the reasoning, and 

 the accuracy of the computations. Clairaut, a mathematician and natural phi- 

 losopher, was eminently qualified to conduct such an investigation, as far as 

 the attainment of those general analytical forntulae which embodied the rules 

 by which the practical astronomer and arithmetician might woxk out the final 

 results ; but beyond this point neither his habits nor his powers would conduct { 

 aim. Lalande, a practical astronomer, no less eminent in his own department, 

 and who, indeed, first urged Clairaut to this inquiry, accordingly undertook the 

 management of the astronomical and arithmetical part of the calculation. In 

 this prodigious labor (for it was one of most appalling magnitude) he was as- 

 sisted by the -wile of an eminent watchmaker in Paris, named Lepaute, whose 

 exertions on this occasion have deservedly registered her name in astronom- 

 ical history. 



