OF TUB, MOTIONS OF FLUIDS. 313 



ddF 



being multiplied by the very small square r'^, we 



may find its value upon the supposition that the earth is 

 spherical, and we may also neglect the density of the at- 

 mosphere in comparison with that of* tbe earth. We may 

 therefore take [, by anticipating the law of gravitation], — 



- — n: cr =: —— - m being the mass of the earth, conse- 

 dr ° ic% 



. ddF 2m 2(/' . , in 2mdr "l 

 quently —-———7—-:= ^,, [smce d---=: 'I 



we have therefore /^hlp zi C — r'cj j^g'- consequently 



n being a constant multiplier representing the density of the 

 air at the surface of the sea, and hlezzl. If we make A 

 and K equal to the length of the pendulum vibrating se- 

 conds, at the surface of the sea under the equator, and in 

 the latitude of the particle of the atmosphere in question, 



we shall have -^zz— and consequently « iz-— (l +-„)' 



Hence it appears that the strata of air of equal density are 

 every where equally elevated above the sea, with the excep- 

 tion of the quantity —-- ; but in the exact calculation 



of the heights of mountains, by observations of the baro- 

 meter, this quantity must not be neglected. 



We may now proceed to determine the oscillations of a 

 stratum which is on a level, or of the same density, in the 

 state of equilibrium. If we make a(p the elevation of a 

 particle of air above the level of the surface to which it 

 belongs in the state of equilibrium, it is obvious that in 

 virtue of this elevation the value of 8F will be augmented 



