54 



Mr. Spottiswoode — Equations of Rotation 



[1863. 



(A 

 (A 

 (A 



(a 

 (g 



(8) 



spending equation of motion. The most elegant method of effecting this 

 is to transform (2) and (7) simultaneously into their canonical forms. If 



a /3 y 



Pi 7l 

 ^2 ^2 72 



he the coefficients of transformation, and if □ be the determinant formed 

 by them, the terms involving the products of the variables will be destroyed 

 by the conditions 



F...X/3/3Alyyxy.)=o, 



F...Xaa,a,X/3/3A)=0, 



(^-^...dr...Ia^.«.I^A/3j=0, 

 from the last two of which we have 



Ay.-fty : Ay -/3y, : /3y,+/3,y 



: Ga + Fa, +Ca, : ffia+dra,4- (C-^)a, ; 

 whence, 6 being a quantity to be determined, 



-HO, -a^-^-BO, -F0 *l . (10) 



a -GO, -FO, C-^-C0 J 



Proceeding to develope this expression, we have the term independent of 

 = V'-(33C-hC^+^33)^ + ^'-^' 



The coefficient of —0 



= A { V A - (53 + C)^ + + H(VH +?^^) + G(VG+ ^S^) 



(9] 



=V(AHH2+G2) + V^ 

 + V(H2+B2 + C0 + V^ 

 + V(GHF^-|-C^) + V^ 



= V { AH 3 (BC + C A + AB) - F^ - G=^- H^} 



=V(SH^). 



