294 PROFESSOR TAIT ON THE ROTATION OF A 



which may be transformed as follows — 



Qz {BV - 2B (A - B) S 2 aa - (A - B) 2 S 2 «4 = - yV , 



Qi (BV - (A 2 - B 2 ) S 2 « £ ) = - yV , 



(B 2 Q 2 + y 2 ) s 2 - (A 2 - B 2 ) Q 2 S 2 a 6 = , 

 and finally 



s 2 cos 2 /3 + S 2 « £ = . 



This might have been written down at once by inspection of (38) and (39). 

 The locus of e in space, i.e., the fixed cone, has the equation 



49. In the preceding solution we began with the very simple equation for r, 

 which immediately presented itself. Let us now apply to the same problem the 

 general equation of § 21, viz., 



2q = q*p~ l (q-iyq) • 



Here, of course, we have 



B 



Hence 



which, because 

 becomes 



2 2 = ? "J (b ~ a) zS ' ^ _1 7? + B q ~ X 7i \ 

 a = qiq- 1 , 



' 1 = (b"a)^ + b^ 



• =-2jy- ] 



which is (40) of § 46, as we see by substituting for Say from § 47. 

 50. Employing this value of e in the kinetic equation 



we have 



a = — g-Vya . 



Hence 



a = - p-Vya = ^ V . yVya 



B '/"-B 2 

 _ 7_ 



B 2 a B 2 



y 2 y 



= 4a> ot, — 4ra Say , 



