:3!0 CELESTIAL MECHANICS. 1. vil. 37- 



which the particles are impressed, by the action of the 

 spheroid, is of the same order with the relation of the mass 



of the fluid to that of the spheroid, or of the order — , and 



that it may therefore be neglected in the calculation of SF'. 



§ 37. Of the earth's atmosphere, considered first in 

 the state of equilibrium. Of the oscillations which it un- 

 dergoes in the state of motion, having regard only to the 

 regular causes which agitate it ; and of the variations 

 which these motions produce in the height of the baro- 

 meter, P. 105. 



377. Theorem. The oscillations of the 

 atmosphere may be determined by the equa- 



tions r^d9. (-^^ — -2n sm cos 9 ^j + r^S'sr .^— . sm 6 

 + 2n sin cos 5 ■^)'=^V'—gdy'—gBy; andy= 



, / du' dv' u' cos Ok ,, .... , , 



— / (-77 +-1 — + — ^—TrY the quantities u and 



^ dd d'23- sm 9 / ^ 



t?' being analogous to u and v in the case of a 

 hoEfiogeneous fluid (372), SF' being the por- 

 tion of ^F which belongs to the state of 

 motion only, ay the elevation above the level 

 of the sea, y the variation of height corres- 

 ponding to the temporary change of density, 

 and g the force of gravitation. 



In examining the motions of the atmosphere, we may 

 omit the consideration of the variation of heat, in different 

 latitudes and at different heights, as well as all the irregu- 



