288 PROFESSOR TAIT ON THE ROTATION OF A 



These are necessary properties of the strain-function x, depending on the fact that 

 in the present application the system is rigid. 



38. The kinematical equation 



zr = \ssr 



becomes 



(the function x being formed from x by the differentiation of its constituents with 

 respect to t). 



Hamilton's kinetic equation 



2 • marVear = y , 



becomes 



2 . m%aV . £%« = y 



This may be written 



2 • m (x a S • £%« - ea 2 ) = y , 



or 



2 ■ m(oS . a^'e - % _1 s.a 2 ) = x~ l 7 > 



where x' is the conjugate of x • 

 But, because 



S • X a X a i — ^ aa i • 

 we have 



Saa a = S . ax'x<*L . 



whatever be a and a a , so that 



x = x~ l ■ 

 Hence 



2 . »ii«S . ax~ x i— X~ X * ■ « 2 ) = X~ l 7 > 



or, by § 19, 



4>x~ ls = x~ x y- 



39. Thus we have, as the analogues of (17), (17'), the equations 



x~ le = n, 

 x~ x 7 = ?. 



and the former result 



x a == "V ■ £ % a 

 becomes 



Xa. = Y . x^X°- — %V>)a 



This is our equation to determine x, n being supposed known. To find n we 

 may remark that 



4"! = K 



