366 THE THEORY OF SCREWS. [337 



P = + bcx ((A - A) (73 - 74) ~ (A - A) ( 7s - 7.)), 



+ ca y ((75 7) (& ~ &) ~~ (71 ~ 72) (& A))&amp;gt; 



Q = + bcx ((a, - a 4 ) (75 - 7 6 ) - (a 5 - a 6 ) (73 - 7,)), 

 + acy ((71 - 7 2 ) ( 5 - 6 ) - (i - &amp;lt;* 2 ) (75 - 7e)) 

 + abz ((! - 2 ) (73 - 74) - (a, - 4 ) (7! - 7,,)) ; 



- a a) (A&quot; A) (& /3 2 ) ( 5 tte)), 



^ = a 3 (: + a) (A - &) + 6 s (a, + a 4 ) (A - A) + c 3 (* 5 + a 6 ) (/3 6 - /3 6 ), 

 Z^ a = a 3 (A + /3 2 ) (aj - 2 ) + 6 3 (/3 3 + A) ( 8 - &quot;4) + c 3 (A + A) ( a s - e) I 

 Z ay = a 3 (d + a) (71 - 72) + b 3 ( 3 + 4 ) (73 - 74) + c 3 (cc 5 + 6 ) (75 - 7), 



^ya = tt 3 (7x + 7 2 ) (! - a s ) + 6 3 (7s + 74) (3 ~ 4 ) + C 3 (75 + 7e) (s - a e) I 



X 0y = a 3 (A + A) (7i - 72) + ^ 3 (A + &) (73 - 74) + c 3 (A + A) (7s ~ 7e), 



The required equation is then as follows : 



= 



A, -R + L^, 

 R + L afi , B, - 



Q + L ay , P + Lfiy , 



C 



