Mr. Galbraith on the Velocity of Sound. 217 



have /-^f- = /l0166-82x 0-76(1 +0-00375 0-£4t"( 4 ') 

 into which we must introduce the constant factor k, and 



V= /l0466*82x 0-76 (1+0-00375*) ~ ff x Jc. 

 By extracting the square root and simplifying 

 V = (104-0385 + 0-19496 t)(l + J ^ ? ) yj m 



Now if g* be the gravitating force at 45° of latitude, then at 

 any other latitude A, g = g' (1—0-00268 cos 2 A). 



From numerous observations on the length of the pendulum, 

 we have found g* — 9*8058 metres, as also the constant quan- 

 tity.-^ = 0*00268 in the usual formulae relating to the pen- 

 dulum, or the excess of the polar above the equatorial pendu- 

 lum divided by twice the length of the latter. By introducing 

 these quantities there will be obtained, after a little reduction, 



V = (104-0885 + 0-1 9496 *)(l+^ r ^—) (3-1 31 4 -0-00420 



cos 2 a) (5) 



the velocity of sound per second in metres. 



But the velocity of wind (as I have shown in the 66th volume 

 of the Philosophical Magazine) has an effect on the velocity of 

 sound. Let that velocity be represented by w, and the angle 

 which it makes with the direction of the sound by <$, the 

 complete formula becomes 



V= (104-0885 + 0-19496/) (l + ^-Z_) (3-1314-0-0042 



cos 2 A^) + w cos $ .... (6) 



the velocity per second in French metres. 



When the English barometer and Fahrenheit's thermome- 

 ter are used, 



V= | 104-0885 + 0-10831 (*-32°) j (l + ^ f_ 2 ) (lO'273S 



— 0-01378 cos 2 a) + co cos $ = the velocity per second in 

 English feet (7) 



The formula in its present state will be found, it is hoped, 

 more easy in its application than that usually given, while tit 

 the same time it possesses all the precision which the most 

 accurate data we could procure, can give. 



To conduct a series of experiments to which this formula 

 is applicable, it is necessary to possess a complete set of in- 



Vol. 68. No. 341. Sept. 1826. 2 E struments, 



