2 Prof. J. Le Coiite on the Discrepancy between the Computed 



proposition, he compares calculation with observation, and vainly 

 endeavours to explain the glaring discrepancy by assumptions 

 which are both gratuitous and untenable. 



The logical incompleteness of Newton's solution of the pro- 

 blem of the motion of sound was first assailed (in 1741) by 

 Cramer of Geneva, who succeeded in showing that his reasoning 

 applied equally to other modes of oscillation than that which was 

 assumed. It is true this contradicted the enunciation of the 

 47th proposition of the second book of the Principia ; " but it 

 confirmed and extended all the general results of the demonstra- 

 tion ; for it left even the velocity of sound unaltered, and thus 

 showed that the velocity did not depend mechanically on the 

 type of the oscillation " *. But this, as well as other unsatisfac- 

 tory points in Newton's theory, was first distinctly perceived 

 and pointed out (in 1759) by the illustrious Lagrange, and re- 

 placed by an exact and rigorous investigation. But still the 

 expression for the velocity of sound remained identical with that 

 originally delivered in the 49th proposition of the second book 

 of the Principia. It is obvious therefore that, although Newton's 

 solution of this problem was incomplete, it nevertheless contained 

 the true principles of this physical generalization. With a just 

 appreciation of the importance of the step taken by the great 

 legislator of physical science, the illustrious author of the Meca- 

 nique Celeste appropriately characterizes it : a sa theorie, quoique 

 imparfaite, est un monument de son genie " f. 



But notwithstanding the confirmation and extension which 

 the Newtonian theory received from the mathematical labours of 

 Lagrange and Euler, the obvious discrepancy between the velo- 

 city of sound as given by the physical theory and by direct expe- 

 riment, and which had arrested the attention of Newton, re- 

 mained a perplexing fact. Lagrange suggested that Mariotte's 

 law, which assumes the pressure to be directly proportional to 

 the density, might not be true ; and that if we assume the pres- 

 sure to vary as the | power of the density, the discordance would 

 be explained. But he assigned no physical cause for this more 

 rapid variation of the elastic force of the air J. On the other 

 hand, Euler considered that the deviation of fact from theory 

 might possibly arise from an incorrectness of analysis in assu- 

 ming the factor ( -j- \ =1 in the equation prev iously to integra- 



* Whewell's ' History of the Inductive Sciences,' vol. ii. p. 315. London, 

 1837. 



t Mecanique Celeste, vol. v. book 12. p. 95. Paris, 1825. 



X Poisson, in the Journal de I'Ecole Poly technique, vol. vii. (cahier 14) 

 p. 325. Also Poisson's Traite de Mecanique, 2nd edit. vol. ii. pp. 716, 717» 

 Paris, 1833. 



