216 Mr. Galbraith on the Velocity of Sound. 



we shall call k, to be 1*3492, and Gay-Lussac and Welter 

 1:37.48. The mean of these two is 1*362, by which the re- 

 sult must be multiplied before the root is extracted in the for- 

 mula of Newton. If the law of Boyle and Mariotte be adopted, 



then -— = — r, in which p is the elastic force of the air in 



p s x 



agitation, p' that in equilibria; and s and 5' the corresponding 

 densities. This equation leads to the formula of Newton, 



that is, v = */ I x g, in which I is the height of the homo- 

 geneous atmosphere, and g the gravitating force. But if the 



constant k = 1*362 be introduced, then v — \/ I x g x k ... (1) 

 Now if p be the pressure or height of the mercury in the 

 barometer, and D the density of a homogeneous elastic me- 

 dium, then Newton's formula becomes v = * / -~. Biot 



has determined the ratio of the weight of mercury to air at 

 the temperatm*e of the freezing point, and under a pressure of 

 29*921 inches in the parallel of 45°, to be 10466*82. But 

 when the barometric pressure varies and becomes 7?, and the 

 temperature t by the law of Boyle, adopting the metrical 

 barometer and centigrade thermometer, 



D — ■ 1 (Q) 



10466-82x0-76 (1+0-00375 ^ ' 



It is necessary to introduce into this formula a correction 

 for the effect of aqueous vapour. According to Watt and 

 Saussure the weight of vapour of water is f of that of dry air 

 under the same pressure. Gay-Lussac's result, which is per- 

 haps the more accurate, is ■§. Now if we suppose that there 

 is in the air all the water that can exist in a state of vapour 

 at the temperature of 86° Fahrenheit, there is then a degree 

 of saturation greater than to be met with in nature. In this 

 case the tension of the vapour would be 1*22 inch by the table 

 of Dalton. 



In designating this by f, p being the barometric pressure, 

 the density of the humid atmosphere would be the same as 

 that of dry air which would support a pressure indicated by 

 p —f -f- ^f = p — § f. Making this correction, formula (2) 



becomes D = —-g-I^^—^ (3) 



Introducing this value of D into the formula of Newton, we 



demicians in 1738, from experiments on sound, found it T4254. Laroclie 

 and Berard,l -4954: Gay-Lussac and Welter, 1*3748; and Clement and Des- 

 onnes, 1-3492: and the mean of all these is 1-4112. We have, however, 

 used a mean of the two last only, though perhaps that of the whole is 

 more conformable to experiments on sound. 



have 



