PROBLEM OF THE PROPAGATION OF SOUXD. 35 



we speak, no accurate measure had been established ; and Newton 

 persuaded himself, by experiments made in the cloister of Trinity Col- 

 le^-e, his residence, that his calculation was not far from the fact. 



O " ' 



When, afterwards, more exact experiments showed the velocity to be 

 1142 English feet, Newton attempted to explain the difference by 

 various considerations, none of which were adequate to the purpose ; 

 as, the dimensions of the solid particles of which the fluid air con- 

 .-ists ; or the vapors which are mixed with it. Other writers offered 

 other suggestions ; but the true solution of the difficulty was reserved 

 for a period considerably subsequent. 



Newton's calculation of the motion of sound, though logically in- 

 complete, was the great step in the solution of the problem ; for ma- 

 thematicians could not but presume that his result was not restricted 

 to the hypothesis on which he had obtained it; and the extension of 

 the solution required only mere ordinary talents. The logical defect 

 of his solution was assailed, as might have been expected. Cranmer 

 (professor at Geneva), in 1741, conceived that he was destroying the 

 conclusiveness of Newton's reasoning, by showing that it applied 

 equally to other modes of oscillation. This, indeed, contradicted the 

 enunciation of the 48th Prop, of the Second Book of the Pr'mcipia ; 

 but it confirmed and extended all the general results of the demon- 

 stration; 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 the satisfactory establishment of this physical 

 generalization was to be supplied from the vast generalizations of ana- 

 lysis, which mathematicians were now becoming able to deal with. 

 Accordingly this task was performed by the great master of analytical 

 generalization, Lagrange, in 1*759, when, at the age of twenty-three, 

 he and two friends published the first volume of the Turin Memoirs. 

 Euler, as his manner was, at once perceived the merit of the new 

 solution, and pursued the subject on the views thus suggested. Various 

 analytical improvements and extensions were introduced into the solu 

 tion by the two great mathematicians ; but none of these at all altered 

 the formula by which the velocity of sound was expressed ; and the 

 discrepancy between calculation and observation, about one-sixth of 

 the whole, w r hich had perplexed Newton, remained still unaccounted for. 



The merit of satisfactorily explaining this discrepancy belongs to 

 Laplace. He was the first to remark 7 that the common law of the 



T J/eV. Cel. t. v. 1. xii. p. 96. 



