332* Mr Galbraith on Trigonometritul Surveying 



M. Poisson, in his excellent Traite de Mecanique, second 

 edition, published in 1833, gives, on the authority of Dulong, 

 the quantity 1.421, a number exceeding mine slightly. I 

 therefore conclude that the data thus determined possess the 

 requisite accuracy. 



I have been very minute in stating the foundation of the 

 constants employed in my formula, because writers of celebrity 

 have introduced generally too small co- efficients, and conse- 

 quently all the results from their formula.' are defective. This 

 is the case with respect to Sir John Herschel's formula for 

 the velocity of sound in the Encyclopaedia Metropolitana, in 

 which the expansion of moist air in its mean state is assumed 

 at 0.00375 for 1° centigrade, instead of 0.004112 which I have 

 found, or even 0.00421 from the experiments of Dulong, as 

 reported by Poisson in chapter vi. Book Fifth, of his Meca- 

 nique, entitled, " Of the elastic force, and of the heat of gas." 



For this cause it is that the formula of Sir John Herschel 

 gives results all considerably smaller than those from actual 

 experiment. 



By these remarks I by no means design to throw discredit 

 on any of the writings of that distinguished individual. They 

 are merely introduced to guard those who trust the authority 

 of names from condemning the formula which I am now in- 

 vestigating, because the constants employed are different from 

 his. 



From numerous observations on the mountains of Scotland 

 already quoted, I have found that the last factor in formula 



(11), namely, l(l g ^ should be diminished by a quantity re- 

 presented by j * ■ . in which, as already stated, /3' = 



0.004112, and 8 t is the variation of temperature correspond- 

 ing to d h, the variation of height. 



Introducing this into formula (11), it becomes 



_«r , i i A , f\\ 8b a"U Y (i 2 ) 



" _ 2B 1 + fit " 1 + jS'A + 126/ U(l+/S0 M(1 + /30J 



Now the same observations in a mean state of the atmosphere 



