32 SCREW CO-ORDINATES. 



The facilities presented by rectangular axes for 

 questions connected with the dynamics of a particle have 

 perhaps their analogues in the conveniences which arise 

 from the use of co-reciprocal groups of screws in the 

 present theory. 



If the six screws of reference be co-reciprocal, then 

 the formula of the last section assumes the very simple 

 form 



34. Co-ordinates of a Wrench. We shall henceforth 

 usually suppose that the screws of reference are co-reci- 

 procal. We may also speak of the co-ordinates of a 

 wrench,* meaning thereby the intensities of its six com- 

 ponents on the six screws of reference. So also we may 

 speak of the co-ordinates of a twist, meaning thereby 

 the amplitudes of its six components about the six screws of 

 reference. 



The co-ordinates of a wrench of intensity p" on the 

 screw p are denoted by p/ 7 , &c. p 6 x/ . The co-ordinates of 

 a twist of amplitude p' about p are denoted by pi', &c. 



P.'. 



35. The Work done in a twist of amplitude a' about 

 a screw a, against a wrench of intensity j3 7/ on the screw 

 /3, can be expressed in terms of the co-ordinates. 



Replace the twist and the wrench by their respective 

 components about the co-reciprocals. Then the total 

 work done will be equal to the sum of the thirty-six 

 quantities of work done by each component twist against 

 each component wrench (10). Since the screws are co- 



* Pliicker has introduced the conception of the six co-ordinates of a system 

 offerees Phil. Trans., vol. 156, p. 362. See also Battaglini, " Sulle dinami 

 ip. involuzione," Atti di Napoli IV., 1869; Zeuthen, Math. Ann., Band I., 

 p. 432. 



