29 PROFESSOR TAIT ON THE ROTATION OF A 



[It shows, for instance, that, as 



while 



S . /3%a = S. (3quq~ l =S . uq~ 1 Bq , 



we have 



and therefore that 



xxP = q.ia.-^q- 1 = e , 

 or 



X = % _1 > as above.] 

 Differentiating, Ave have 



Hence 



= 2V.V( ? -ij)«. 

 Also 



so that the equation of § 40 becomes 



2V . V(rt) a = V . ^- T (? _1 7!?)« ■ 



or, as a may have any value whatever, 



which, if we put 



Tj = constant 



as was originally assumed, may be written 



2y = q<p~\q-^ 7 q) 



as in § 21. 



43. Let f be the vector joining the extremity of s to the intersection of y with 

 the invariable plane. Then 



g + Xy — i . 



Operating by S . y , and remembering the condition 



Sty = - h\ 



we have 



xy ' =-h 2 ; 



so that 



In the initial position of the body this vector, considered as being drawn from 

 the fixed point, was 



i , h * i 



<r = q-hq + - 2 q-iyq 



