52 The Rev. S. Haughton on Physical Geology. [Mar. 8 ; 



from which we obtain, finally, 



(C-A)g-g)-Kz 2 +* 2 )=0; 



Z 



or, since tan X, after some reductions, 

 x ' ' 



tan 2 A=^ ( C ~ A )+K (3 ) 



a 2 (C-A)-/^ 2 K } 



This determines the position in which the mass \x will produce the maxi- 

 mum effect in displacing the earth's axis. 



2. In order to make use of the preceding formulae in calculation, it is 

 necessary to determine the absolute numerical values of C and A, which 

 may be done as follows : — 



From Clairaut's theorem* we obtain 



C-A=M^(2e- 2 ), (4) 



where M=mass of the earth, 

 a— equatorial radius, 



e = ellipticity= i, 



q= ratio of centrifugal force to gravity at the equator =-—• 



From observations on Precession and Nutationt we find 

 C-A 1 



C 306 



From equations (4) and (5) we obtain 



> 



Ma 2 

 3-0/ 



Ma 2 



(5) 



C= _ — 

 3-06' 



A== 3H 



C-A = 



935-6' 



Substituting in (2) and assuming p=^, we find 



, aA 935-6 P sin2X 

 — tan 28=- 



l + 935-6p cos 2V 



* Cambridge and Dublin Mathematical Journal (new series), vol. ri. p. 184. 

 t Leverrier and Serret, ' Annales de l'Observatoire de Paris,' 1859, p. 324, 



