SCREW CO-ORDINATES. 35 



Thus, to compute each co-ordinate a n , it is only ne- 

 cessary to ascertain from the tables half the virtual co- 

 efficient between a and w n and to divide this quantity by 



A- 



39. The Virtual Coefficient between two screws may 

 be expressed with great simplicity by the aid of screw 

 co-ordinates. 



The components of a twist of amplitude a' are of 

 amplitudes a'cti, &c. a'a 6 . 



The components of a wrench of intensity fi" are of 

 intensities /3" ft &c. /3"ft. 



Comparing these expressions with 34, we see that 



t ' /3 // /Q// ft 



a n = a a n , p = p Pi 



and the expression for the work done by the twist about 

 a, against the wrench on /3, is 



a'j3" [2/ lfll ft H-, &C., + 2/ fl a 6 ft]. 



The quantity inside the bracket is the virtual coefficient, 

 whence we deduce the important expression 



^a/3 = S/ia,ft. 



Since a and /3 enter symmetrically into this 1 

 sion, we are again reminded of the reciprocal character 

 of the virtual coefficient. 



40. The Pitch of a screw is at once expressed ' 

 terms of its co-ordinates, for the virtual coefficient of two 

 coincident screws being double the pitch, we have 



41. Screw Reciprocal to five Screws. We can deter- 

 mine the co-ordinates of the single screw p y which is 

 reciprocal to five given screws, a, j3, 7, S, c. ( 27). 



The quantities p,, &c., p 6 , must satisfy the condition 



= o, 

 D 2 



