SCREW CO-ORDINATES. 



and four similar equations; hence / n p n is proportional 

 to the determinant obtained by omitting the n th column 

 from the matrix. 



05) 



ft, ft, ft, ft, ft, ft, 



7i> 72, 73> 74, 75* 76> 



The relative values of pi, &c., p 6 , being thus found, the 

 absolute values are given by 37. 



The condition that six screws have a common recipro- 

 cal screw is expressed by the evanescence of a deter- 

 minant, which may be compared with the condition that 

 three straight lines be coplanar, of which the direction 

 cosines are given. 



42. Co-ordinates of a Screw on a Cylindroid. We 

 may define the screw on the cylindroid by the angle 

 /, which it makes with the screw a on the axis of x. 

 Since a wrench of unit intensity on has components of 

 intensities cos / and sin / on a and j3 ( 1 7), and since each 

 of these components may be resolved into six wrenches 

 on any six co-reciprocal screws, we must have ( 36) 



O n = a n COS / + j3 n sin /. 



From this expression we can find the pitch of 6 : 

 for we have 



p e = S/i (ai cos / + ]3i sin If 



whence expanding and observing that as a and ]3 are re- 

 ciprocal 2^ T aij3i = and also that ^p l a^=p a and 

 S^ t j3i 2 = pp, we have the expression already given ( 20) 

 viz. 



= COS 



