of Air and the Gases, and the Velocity of Sound. 13 



uniform density q', then -r^j = , ^ ^ = j- ; which shows 



that P' will impress the same velocity upon every particle of 

 the mass g' x 1, that a row of aerial particles in the length / 

 will do upon a single particle. Let g — 32|^ feet denote the 

 acceleration of gravity in a second of time : then since the 

 weight of one particle will generate the velocity g in a second 

 of time, the weight of / particles will generate the velocity 

 Ixg in the same time. Hence, 



(Idz _ ^ ddz 

 dr- di- 



This is the usual differential equation for determining the vi- 

 brations of a line of air; and the knov.n integral proves that 



c= \/|X/xgis the expression of the velocity of sound 

 in a second of time. 



If, according to the law of Boyle and Mariotte, we had used 



the equation -p- = -^, we should have found c = </ g x I 



for the motion of sound in a second ; and this is Newton's 

 formula. 



At the temperature of S2^ of Fahrenheit, the homogeneous 

 atmosphere is 4350 fathoms, or 26100 feet: and hence the 

 motion of sound in a second is 



v^ i X 32 I X 26100 = 1058 feet. 



Now the French Board of Longitude have lately found, by 

 actual experiment, the velocity of sound at the same tempera- 

 ture equal to 331"^ = 1085 feet. The difference between the 

 theory and observation is therefore only 27 feet, or about -^^^ 

 of the whole. 



If, instead of making e = ^, we adopt the values found by 

 experiment, we shall have to employ the multipliers 1"34'92 

 and 1-3721, instead of | = 1-3333. By this means the cal- 

 culation will approach a little nearer to the experimental 

 quantity, although still short of it. But we should probably 

 deceive ourselves by estimating with too much precision the 

 result of experiments which re(|uire the measurement of very 

 minute variations of length with extreme accuracy. 

 July 4, W2i>. James Ivory. 



II. Obser- 



