MEMOIR OF LEGENDRE 139 



M. Legeiidre propounds the equation of the movement of the projectile on the 

 supposition that the resistance of the air is proportional to the square of the velocity. 

 He integrates this equation with elegance, and the reduction into series fonns moi'e 

 especially the remarkable part of the memoir. Althoug-h the hypotheses which 

 he advances on the variation of the density of the air have been modified, his 

 calcalations have remained the type of those that have been made more in 

 detail on the supposition of a resistance proportional to the square of the velocity. 

 M. FrauQais, professor at the schools of artillery, and General Didion have only 

 supplied improvements to his method.* But this solution of the balistic ques- 

 tion is simply a monument, so to speak, in the history of the science, since the 

 necessity has been recognized of introducing, in the expression of the resistance 

 of the air, a tenn proportional to the cube of the velocity. It is not the less cer- 

 tain, however, that by his memoir Legendre, young as he yet was, has earned 

 for himself a distinguished place in the series of mathematicians to wliom is due 

 the superiority of the European artillery ; a series which commences with New- 

 ton, in which M. Poisson occupies au eminent rank, and which is continued 

 with so much eclat by the learned officers to whom we owe the actual precision 

 of our artillery and the employment of rifled cannon. 



But, however seductive this first success might appear, M. Legendre did not 

 continue to occupy himself with the application of science to military art, and we 

 read at this early stage on the title page of the Dissertation on Balistics, printed 

 in 1782, the announcement that it is "by A. M. Legendre, late professor of 

 mathematics in the military school at Paris." The youthful veteran, to whom 

 perhaps the military discipline had never been particularly congenial, had decided 

 to reserve his whole time for the study of departments of mathematics which, 

 while not more difficult, pertain to an order of ideas generally considered as more 

 elevated. 



He had beeri occupied for some time with researches on the mutual attractions 

 and forms of the planetary spheroids, and read at the Academy of Sciences of 

 Paris, January 22, 1783, a memoir on the attraction of spheroids, for the exami- 

 nation of which, MM. d'Alembert and de Laplace were named commissioners. 

 It was at this same sitting, as we learn from the invaluable journals of the 

 Academy, that MM. Daubenton and Bezout made a favorable report on a 

 memoir of the Abbe Haiiy, relative to the stmcture of fluor spars ; for it was the 

 epoch when M. Haiiy was submitting to the Academy, in a series of memoirs, the 

 ideas which have become the basis of crystallography. 



M. Legendre finished the reading of his memoir in the sitting of the 19th of 

 February, and in that of the 15th of March, MM. d'Alembcrt, Bezout and de 

 Laplace read the following report : 



The Academy having charged us with the exarnination of two memoirs of M. Legendre on 

 the attraction of spheroids, we proceed to render an account of them. Geometers well know 

 the admirable synthetic theory of M. Maclaiirin ou the attractions of spheroids, of which all the 

 sections are elliptical, «fec., &c. M. de Lagrange subsequently arrived at the same results 

 by analogy alone in the Memoirs of Berlin for 1771, but all these researches suppose the 

 point attracted at the surface, or in the interior of the spheroids. * * « » 



I regret the impossibility of reading the whole of this report, written with 

 a masterly hand and inimitable clearness by M. de Laplace, who had him- 

 self the 3'ear before communicated to the Academy a learned theory of tiie 

 attractions of spheroids and of the figure of planets,t a circumstance which 

 renders still more honorable, both for himself and M. Legendre, the justice wdiicli 

 he so cheerfully and explicitly accords to his competitor, as yet almost unknown. 

 I will content myself with saying that after having analyzed the two memoirs of 

 M. Legendre, who arrives at the conclusion that, in order to determine the 



* See Traits de balistique, by General Didion, second edition, revised and enlarged, 18G0 ; 

 pp. 246-251. 

 t Memoires dc V Academic royaledes Sciences for the year 1782. 



