863.] of a Solid Body about a Fixed Point. 59 



whence the equations of motion (19) become 



q\='7-Hd,-e)r,p^A (21) 



In order to compare these results with the ordinary known form, we must 

 make 



F=0, G=0, H=0, 

 which values reduce (13) to the following : 



(A^py+(B^qy+(c^ry=zh, 



- (B + C) - (C + A) B(?^ - ( A + B) Cr^ = - ; 

 which last is equivalent to 



( A -S) (A^i?) -h (B - S(B*^)^ + (C - S) (cKy^ /c-Sk, 



or 



A{A^py+B{B^'qy-\-c(cKy=:k\ 



Also, on the same supposition, 



V = ABC, 6=-(B + C), 0,= -(C + A), 0,= ~(A + B), 

 which, when substituted in the above, give 



a/'=(ABC)"^(B-C)B*cV. b^^'=..., cV=..., 



or 



Aj)' = (B - C)qr, Bq' = (C- A)rp, Cr' = ( A - B) pq, 

 as usual. 



It remains onlj to determine the absolute values of the coefficients of 

 transformation, the ratios of which are given in (15). For this purpose let 



V(A + 0J + T,H=^„ VF +TJ=J„ 

 V(B+0,) + T,B=i3o, VGH-T,(K=ffi^^, ^ . . . (22) 

 V(C + 0„)+T,C=Co, VH + T,?^=|^[. 



Then, from (15), 

























(A...H...X^J 



!offi„)'~ 



(A, 





~(A 











38, 





if„ 



«'=(A...H...Xaj 





(A 





A 



...Iffi.iF.C„/' 



ffi. 







f„ 







' (A...H...Xaj 





(A. 





-(A. 



•.Iffi.P?.c.) ■ 



VOL. XIII. 



