OF THE MOTIONS OF FLUIDS. 311 



lar causes of agitation, including in the computation those 

 forces only which act regularly upon it as upon the sea. 

 We may therefore consider the sea as covered by an elas- 

 tic fluid of a uniform temperature : and we may suppose 

 the density of this fluid proportional to the pressure, as it 

 is found to be by actual experience. This supposition 

 implies that the height of the atmosphere must be infinite, 

 but it is easy to see that, at a very moderate height, the 

 density is so small that it may be regarded as evanescent. 



If we now call the quantities s, u, and v, for the parti- 

 cles of the atmosphere, s\ u\ and v', the equation (X)(372) 

 will become 



ar^^Q. (-— 2n sm cos d —-- ) 



\dt^ dt J 



«rN / • OA ddv' « . . dw' 2nsm-d ds' \ 



+ ar^d'BT. ( sm«d -j^r--^ 2n sm eos 6 - — + • — ) 



V dr* d^ r at ^ 



+ a3r.(^— 2/irsin2flll'^= i w^^ [ (r + a/)sin (d + oi/) | * 



+ aF— ^^: which, in the 



state of equilibrium, affords us, when integrated, ^ w* r* 



sin^fi + V — r^:izC, a constant quantity. But since 



the pressure p is supposed to be proportional to the den- 

 sity f, we may call pzzlg^, g being the force of gravity in 

 a determinate place, for instance at the equator, and / a 

 constant quantity, which expresses the height of an atmos- 

 phere supposed homogeneous, and of the same density as 

 at the surface of the sea ; a height which is very small in 

 comparison with the radius of the earth, being less than 



yI^ of this radius. The fluenty.^ or fig J- is there- 

 fore Ig hlf : and the equation of the equilibrium of the at- 



