550 Prof. Orr on the Forced Precession and Nutations of 



Replacing <£ by (n — i/r cos«)£, these are respectively the 

 real parts of 



— zg^+^o cos a_ n )t ^ " ± fa i(—8+\J/ cos a— n)t 



1 



and of }- • ( 17 ) 



1/ 4- M 7 • 1/ M / 



J 



2 ~ 2 



Comparing these couples with those which enter into 

 equations (2), it appears that the first terms of these corre- 

 spond to a disturbance whose speed in the sense of the rule of 

 Art. 3 is a=s+ ^ cos a, and the second terms to one whose 

 speed is cr'— — s + yjr cos a. 



5. For the case of precession 1/ is zero, s is zero, and 

 the two disturbances just mentioned have coincident speeds, 

 the value of a being ty cos a. From the known value of 

 yjr and the preceding results it appears that if e be large 



compared with 77-77 — ^,.^ , the precession is almost the same 

 060 . zbOUO 



as if the whole were rigid, whatever the thickness of the shell 



may be. Actually ^ is negative, and accordingly the rate 



of precession of the shell is less than if the whole were rigid. 



It should be noted, however, that if the applied couples were 



of such a nature as to make the polar axis revolve in the same 



direction as that of the rotation, the precession of the shell 



would be greater in amount than if the whole were rigid. 



If the mass of the shell be neglected, and if e be supposed 



to be 3 ^tj, the period of precession of the shell would exceed 



that of a rigid earth by [cos a f 1) =1 274 days. This 



agrees substantially with Lord Kelvin's result. 



6. The period of any of the nutations which are to be con- 

 sidered is very small compared with that of the precession, 

 and therefore f cos a may be neglected compared with s. 

 Accordingly the values of 0, ^ we obtain by means of (13), 

 (14), when the two equivalent disturbances are considered as 

 in Art. 4, are 



+ W- W ]>, -^rr-, W, (18) 



; (0 + U')+,(A + A')+ (A '-' t6) ^ 



en — s 



±a\ 



