OV THB MOTIONS OF flUIDS. 509 



It may be observed that, in this equation, the angles 

 Q and ** «< + 'V are reckoned from a fixed point, and a 

 fixed meridian, on the earth, while in the equation {31) the 

 same angles are referred to the axis x, and to a plane 

 passing- through that axis, and having a rotatory motion 

 round it expressed by n : now this axis and this plane are 

 not precisely fixed with regard to the surface of the earth, 

 because the attraction and the pressure of the fluid, which 

 covers it, must alter in a slight degree their position on the 

 surface, as well as the rotatory motion of the spheroid. 

 But it is easy to see that these alterations must be to the 

 values of au and av, almost in the proportion of the mass 

 of the sea to that of the solid spheroid : consequently in 

 order to refer the angles 6 and *' n^+"'2r to an invariable 

 point and an invariable meridian on the surface of the 

 spheroid, in the two equations (M) and (N), it must be 

 suflBcient to alter u and v by quantities of the order 



— and — , which we have neglected in this computation : 

 r r 



it may therefore be assumed, in these equations, that au and 



av are the motions of the fluid in latitude and longitude. 



[It seems more natural to call the angle made by the plane 



in question with the first meridian la ov 's:-\-av only, and to 



express by nt the rotatory motion of the earth only : and 



perhaps nt-\-is may have been an error of the pen only for 



'Zir-f-ai;.] 



It may also be remarked, that the centre of gravity of the 



spheroid being supposed immoveable, we must transfer to 



the particles of the fluid in a contrary direction, the efi*ect of 



the reaction of the sea on that spheroid : but since the place 



of the common centre of gravity of the solid spheroid and 



of the sea is not changed in consequence of this reaction, 



it is evident that the relation of this Telocity to that with 



