168 Mr. Herapath on the Velocity of Sound and 



equations of algebra ; and at the same time open solutions to 

 other phenomena, with which 1 think I may venture to say no 

 analyst ever expected it ha<l the remotest connection. But 

 the theorems will speak best for themselves. 



Let, as usual, S, £, D, g, denote the velocity of sound, elas- 

 ticity of the air, its density, and the velocity acquired by a 

 falling body at the end of the first second. Then, by the theory 

 alluded to, 



W (1) 





And if S be the velocity of sound at any elevation x, and P, p 

 the barometric pressures at the lower and higher stations, 



and 



P- (1-3^2 80 



3V2 (S' -s') =gx. (3) 



For, comparing these formulfe with observations, we have 

 D=r JE488 



r/i (F -f .448)' 

 in which h is the altitude of the barometer at the temperature 

 of water freezing ; r = 10463 by Biot the ratio of the specific 

 gravity of mercury to that of dry air, at 32° Fahr., and baro- 

 metric pressure h = 76 metres, the metre being 3.28085 Eng- 

 lish feet, and F the Fahr. temperature. Therefore since 

 g = 321^ feet, 



S = 1089.41 yZT^Eng. feet. ^ 



Now, from a mean of Captain Parry's experiments in the 

 north, at — 17°. 72 Fahr., it appears the velocity was 1035.2 

 feet per second, or, allowing for the difference in the value of 

 g in that high latitude, probably about 1034 feet reduced to 

 our latitude; our theory gives 1031.5. The French Acade- 

 micians, in 1738, at about 42°.8 Fahr., found it 1103.5 feet; 

 our theory makes it 1101.6. Dr. Gregory, by the mean of 

 his observations, determined the velocity to be 1107 feet at 

 48°62 temp. ; by our theory it should be 1108.1. In 1821, 

 Arago and his colleagues made the mean at 60°.62 to be 

 1118.43; our theoiy gives 1121.5. And from an article on 



