Mr. Galbraith on the Velocity of Sound. 



113 



Now let <p be the angle which the direction of the wind 

 makes with that of the sound, and w the velocity of the wind ; 

 then w cos ;p will be the correction to be applied to the velo- 

 city of sound, on account of the velocity and direction of the 

 wind. 



Hence the complete formula embracing all these corrections 

 ■will be 



\ = V-{-ci{p'—p) + ^{t' — f) + y {h' — /i) + 0) COS (p . ... (8) 



or, by substituting the values previously found, 



V = UOO -\- 18-8 {p'— p) + l-l'i^it' — t) +2-87 {h'—h) +M cos (p ...(^Q) 



Applying this formula to Mr. Goldingham's observations, we 

 shall then see how it corresponds in each individual case, and 

 be able to form some estimate of its accuracy, though there 

 must be some slight discrepancies, on account of the velocity 

 and direction of the wind being unknown, as well as on ac- 

 count of unavoidable small errors of observation. 



As it is not likely he would make observations during high 

 winds, but most frequently in moderate weather, when, ac- 

 cording to Smeaton's estimate in the 51st volume of the Philo- 

 sophical Transactions, the velocity of the wind might vary from 

 about 4 to 8 feet per second, then the error of Mr. G.'s ob- 

 servations might vary on that account, from to about 10 or 

 12 feet, according as the wind contributed to augment or di- 

 minish the apparent velocity of the sound ; and this, perhaps, 

 may be about the maximum error of the formula. 



We shall now present a table embracing all these deduc- 

 tions. 



Table of Mr: Goldingha7n's Experiments. 



Vol. 66. No. 328. Au'T. 1825. 



On 



