1 62 DYNAMICS OF A RIGID BODY. 



- )32') + j3(02' - 7*0 + y(P* - ay') o, 



gives the equation which determines p. 



To express this equation concisely we introduce two 

 classes of subsidiary magnitudes. We write one magni- 

 tude of each class as a determinant. 



= P. 



i, i, 71 



p2/3l + 2 2 2 - -#272, P272 + #2/32 - JV202, 2 , j3 2 , 72 



~ #373, p373 + #3/33 - JK303J 3, 03, 73 



4 , /3 4 , 74 



5, /3 5 , 75 



By cyclical interchange the two analogous functions 

 Q and R are defined. 



= z. 



Pzy2 + Z2p2-J>za2> ft, 72 



/>33 +JV/3 - z sft> Psft + 2 3 a 3 - ^373, ps7 3 + # 3 ft -J'sOs, ft, 73 



ft, 7* 



ft, 75 



By cyclical interchange the two analogous functions 

 M and N are defined. 



The equation for p reduces to 



= o. 



The reduction of this equation to the first degree is 

 an independent proof of the principle, that one screw, 

 and only one, can be determined which is reciprocal 

 to five given screws; p being known, a, /3, 7 can be 

 found, and also two linear equations between .A/, y, 2', 

 whence the reciprocal screw is completely determined. 



