Royal Society. 55 



in consort with a philosopher distinguished by the sagacity 

 which enabled him to seize the clues leading to all the recesses 

 of modern chemistry, by the indefatigable industry and acumen 

 exerted in exploring every chamber of the labyrinth, and by 

 the unfortunate period in which his lot was cast: a period 

 devoted to an unrestrained action of the worst passions of the 

 human heart, — which could have alone arrested, by a violent 

 death, the progress of Lavoisier. Deprived of his friend and 

 associate in chemical pursuits, La Place appears to have de- 

 voted the whole energies of his powerful mind to a science the 

 most abstruse and difficult, but the most sublime of all that are 

 placed within the reach of human intellect. Astronomy, so 

 far as two bodies were alone concerned, had attained absolute 

 perfection by the discoveries of Kepler and by the demon- 

 strations of Newton. 



The elliptic orbits, areas proportional to the times, and the 

 squares of the periods, as the distances cubed, left nothing to 

 be desired. But when the regular motion of a heavenly body 

 round its primary is disturbed by a third, the circumstances 

 are widely different. Sir Isaac Newton had indeed sufficiently 

 shown that the principles of gravity and inertia were adequate 

 to solving the problems of three bodies : but in a field so 

 vast, the exertions of no one man, not even those of Newton, 

 were sufficient for its entire cultivation. The labour of others, 

 — of Bernouilli, of Clairaut, of Euler, of Mayer, of La Place, 

 were required in aid ; but still pursuing the system and plan 

 dictated by their great master. 



To describe the first important discovery of La Place, it 

 will be necessary to premise some particulars. The problem 

 of three bodies requires, From the momentary direction and 

 intensity of the disturbing force, expressed in the generality 

 applicable to all parts of the orbits, to infer the effects pro- 

 duced (through the medium of integration) in any finite time. 

 It is probable that no effort of the human intellect could 

 ever have attained this object, but for the expedient of im- 

 puting to the orbit a physical existence, and consequently a 

 liability to variation in all its parts. The larger axis equal to 

 twice the mean distance, the lesser axis indicative of the ex- 

 centricity, the line of the apsides, and the inclination of the 

 orbit and the nodes in respect to the orbit of the disturbing 

 body. All these variations are expressed by expansions the 

 most elaborate and complicated. But La Place has the glory of 

 discovering, that after including every term of the expansion 

 which involves the second powers of the excentricities, the 

 larger axes, and consequently the mean distances, remain un- 

 changed. All the larger terms in expanded series indicative of 



perturbations 



