346 HISTORY OF ACOUSTICS. 



solution by the two great mathematicians; but 

 none of these at all altered the formula by which 

 the velocity of sound was expressed ; and the dis- 

 crepancy between calculation and observation, about 

 one-sixth of the whole, which had perplexed New- 

 ton, remained still unaccounted for. 



The merit of satisfactorily explaining this dis- 

 crepancy belongs to Laplace. He was the first to 

 remark 7 that the common law of the changes of 

 elasticity in the air, as dependent on its compres- 

 sion, cannot be applied to those rapid vibrations in 

 which sound consists, since the sudden compression 

 produces a degree of heat which additionally in- 

 creases the elasticity. The ratio of this increase 

 depended on the experiments by which the relation 

 of heat and air is established. Laplace, in 1816, 

 published 8 the theorem on which the correction 

 depends. On applying it, the calculated velocity of 

 sound agreed very closely with the best antecedent 

 experiments, and was confirmed by more exact ones 

 instituted for that purpose. 



This step completes the solution of the problem 

 of the propagation of sound, as a mathematical 

 induction, obtained from, and verified by, facts. 

 Most of the discussions concerning points of ana- 

 lysis to which the investigations on this subject 

 gave rise, as, for instance, the admissibility of dis- 



7 Mec. Cel. t. v. 1. xii. p. 96. 



8 Ann. Phys. et Chim. t. iii. p. 288. 



