106 LAPLACE'S THEORY OF SOUND. 



experiments on fluid friction with his now nearly perfected 

 apparatus, using sperm-oil as well as water, and had 

 obtained 781 '8 as the equivalent resulting from nine 

 experiments with water, and 782* 1 as resulting from nine 

 experiments with sperm-oil. He communicated these 

 results in June, 1847, to the chemical section of the British 

 Association. 



In a letter to the PJiilosopJiical Magazine, dated Oak 



Field, near Manchester, July 17th, 1847, Joule says — "The 



equivalent of a degree of heat per lb. of water, determined 



* by careful experiments made since those brought before the 



British Association at Oxford is 7751b. through a foot ! " 



This letter is primarily " On the Theoretical Velocity 

 of Sound." This, according to Laplace, depends on the 

 ratio of the specific heat of air at constant pressure and 

 that at constant volume. 



The values of these specific heats, already determined, at 

 that time were known to be inexact, particularly that at 

 constant volume. Joule now sees that he can, by means of 

 the mechanical equivalent of heat, determine the value of 

 specific heat at constant volume relatively to that at 

 constant pressure with a close approximation. He uses 

 the new equivalent 775 in making this calculation, and 

 obtains the ratio 1*36. This is not far from the true value. 

 1*408; the difference being solely attributable to the error 

 of the specific heat of air at constant pressure. Using 

 this ratio in the formula of Laplace, Joule found that it 

 brings up the velocity of sound " from Newton's estimate of 

 943 to 1095, which is as near 11 30, the actual velocity at 

 32, as could be expected from the nature of the experi- 

 ments on the specific heat, and fully confirms the theory 

 of Laplace." This determination was in a few years to 



