OF THE MOTIONS OF FLUIDS. 315 



sin-9 ^ (/) — or^Sy, this part of the second member of the 

 equation derived from (L), combined with the former part, 

 which is here an~r s'ln^h', affords us the equation here laid 

 down.] 



If we suppose that all the particles of air, originally situ- 

 ated on the same radius of the earth, remain constantly on the 

 same radius during their motion, as has been shown to take 

 place with respect to the sea, we may proceed to examine 

 whether this supposition is consistent with the equations of 

 motion and of continuity. For this purpose, it is necessary 

 that the values of u' and v' [representing the motions in 

 latitude and longitude,] should be the same for all these 

 particles : now it will appear hereafter, when we consider 

 the forces concerned, that these forces are very nearly the 

 same for all the particles : the variations ^(p and St/ must 

 therefore necessarily be the same for all the particles, and 



the quantities 2/irS'ar sin^fl, and nrr sin^ 6^^ s' — («') > must 

 be so small as to be capable of being neglected in the pre- 

 ceding equation. 



At the surface of the sea, we have ?'=y, ay being the 

 elevation of the surface of the sea above the surface of 

 equilibrium. We may therefore inquire whether the sup- 

 positions of ^ny, and of y being constant for all the par^ 

 tides of air situated on the same radius, are consistent 

 with the equation of continuity of the fluid, which, by article 



374,isO=r^{,'+(,)(-+^~+-_^)+0.^-:hence 



we have ^^-l l^^^^^^^f^"^), [since /= 

 ^ V r^dr dd dw sm d ^ ^ 



— p'l- Now, r^as' is equal to the value of r at tbe aur- 



