252 Mr KELLAND, ON THE MOTION OF 



relations which shall furnish arguments in favour of anj-^ particular 

 assumption. With this object let us compare the equations for the 

 motion of light with those before us, limiting their interpretation by 

 the phenomena of wliich they are the mathematical expressions. 



In both cases the variation of velocity due to the length of a 



wave must depend on the magnitude of the term (-) , and, from the 



smallness of this variation in the case of sound, (if it does vary at all), 

 we conclude that e cannot be large in sound compared with its value 

 in light, yet the velocity of sound is very small compared with that 



p 

 of light, whence it appears tliat tiie term -;;3y i'^ small, not by reason 



of the comparative increase of e'~', but by the diminution of P. 



We will then endeavoui; to ascertain the value of n which renders 

 the expression 



„ 217' - Wf . ..Trff 



(r - 'r + D^ 



(taken from to infinity with respect to each of f, »/ and ^) a small 

 quantity. 



20. It is obvious that this may be effected by making 11 very 

 large, but it is doubtful whether this will be the mode by which it 

 actually becomes small from the circumstance that e'"' becomes pro- 

 portionally small by the same hypothesis. 



In order to find another value of n, which will satisfy the same 

 conditions, we p\irsue the following process. After writing x, y, x 

 instead of ^, v and ^ for convenience, let the above function be 

 expanded in a series ascending by poAvers of x; then the finite sum of 

 the expansion with respect to z, will be the value of the expression 

 corresponding to given values of x and y. 



But -(, + !)» = -^ + | + &c. 



