86 THE THEORY OF SCREWS. [97, 98 



screws of reference. The six co-ordinates of a, with respect to the same 

 screws, are therefore 



A^j, + B 1 a 2 + Ojttg + D^t, 



A^ + B 6 a, + C 



We can now express the condition that a and /3 are conjugate screws of inertia. 

 This condition is ( 81) 



Sp! 2 (A lttl + B^, + 0,0, + A4&amp;gt; (A& + B& + C& + A/3 4 ) - 0. 



Denoting pfAf + ... +p 6 A/ by uf y and observing that S l p 1 2 A l B 1 and similar 

 expressions are zero, we deduce 



A similar proof may be written down for each of the remaining degrees 

 of freedom. 



