104 Prof. Potter on the solution of the Problem of Sound. 



which we may do from the undetermined minuteness of the 

 atoms of matter, we have 



^ _3 <fe^ 



\da:) 



which differs from the ordinary differential equation of vibratory 



3 

 motion only in the coefficient 5. Taking, on the usual conside- 

 rations, -^ =1, we have the well-known integral 



>/ = 'P{x-af)+f{x-\-at); 

 and from the property of wave motion, the velocity of transmis- 

 sion = \/- K, since this is the value of a in the integral. 



Now if the above process be correct, we shall find the velocity 

 of sound equal to \/ - k, when we ha\e in the ordinary method 



supplied the value of K—gH, as at the commencement of the 

 paper. Taking the data given by Poisson, page 715, vol. ii. 

 second edition of his Traitede Mecanique, at the temperature 15°-9 



Centigrade, we find A/ - ^ . H = 1 132-3 English feet, velocity 



per second; M'hilst Poisson gives 340-89 metres, or 1118-4 feet 

 per second as the result of the experiments of the " Commissaires 

 du Bureau des Longitudes." 



Sir John Herschcl, in his Treatise on Sound, says " we may, 

 therefore, adopt 1090 feet without hesitation (as a whole number) 

 as no doubt within a yard of the truth, and probably within a 

 foot." This is for the temperature of freezing ; and allowing for 

 the 15°-9 Centigrade above freezing by his rule, "that every ad- 

 ditional degree of atmospheric temperature, on Fahrenheit's 

 scale, adds 1-14 foot to the velocity," we find the velocity 1122-6 

 feet per second, which is within half a foot of our theoretic value 

 found above. 



The same method of procedure which is here followed, the 

 author intends shortly to apply to the general equations of fluid 

 motion for elastic media. 

 Loudon, December 28, 1850. 



