208 ON Till-: PHYSICAL STRUCTURE OF Till-: EAUTII. 



\' 1 1'f >t du , / dii , dv \ ., , / dn , dr \ ~\ 



A =/,/,- |_ -• ^^^ COS,, + (^^^ + _^j) cOB/f + ( ^^ + ^,^, ) .OS y J, 



,^ ,,.,r/ d>' , du \ , o dv ,. , / du , dir\ ~] 



^ ="''iC'" + 'Hi) "^ dy <=<«' " + (>-. + .lu ) '■"" >■}' 



\\liere u,v,tv are eomponents of velocity ])arallel to the coordinate 

 axes, aud where A: is a coefficient depending on friction and viscidity. 

 If no viscidity aud no friction exists we must have 7t — 0, and hence 

 also 



x=o, r=o, z=o. 



Now, asX, Y, aud Zare the effective components with which the nearly 

 spherical mass of fluid acts at its surface when each of them is separ- 

 ately^ equal to zero, it follows that the fluid can do no work at the sur- 

 face, and the motions of the shell would take place quite independently 

 of the contained mass of fluid when the latter is totally devoid of fric- 

 tion aud viscidity. 



(3) It has long since been clearly shown that the motion of the axis 

 of the Earth, considered as a solid body, may be determined by the 

 difl'erential equations 



V is the potential of the rotating solid, Cits maximum moment of in- 

 ertia, and ?/' direction angles of the axis of rotation. In the case of 

 the Earth, 6 has a i)articular value when it becomes the obliquity of 

 the ecliptic, and ip the longitude of the first i)oint of Aries. It follows 

 that the deterniiuation of ip and H at any time depeiuls upon C and V. 



By analytical transformations, which are fully given by Poisson in 

 his memoir Sur la Rotation de la Terre autour de son centre de Gravite, 

 and by other writers, it finally appears that the variations of f^ and >/• 

 depend on equations in which a factor enters of the form 



2 C - A - 75 



where A, B, C, are the three principal Mionu'nis of iiuTtia of the Earth. 



2 {C A) 



In a spheroid of revolution A = B, and the factor becomes — ^^ — tt 



