1 48 DYNAMICS OF A RIGID BODY. 



2ft 2 + 2S0ift COS (on, Wz) = I, 



which for brevity we denote as heretofore by 



I? -i, 



Applying the ordinary rules* for maxima and minima, 

 we deduce the n equations 



&c. &c., 



From these ?z linear equations it would seem that 

 ft, . . ., can be eliminated, and that an algebraic equa- 

 tion of the n th degree would remain for p e . The analysis 

 would, therefore, appear to have proved that n screws 

 of maximum or minimum pitch can always be selected 

 from a screw complex of the n th order. 



A moment's reflection will, however, show that this 

 statement needs modification. Take the case of n = 6 : 

 the screw complex of the sixth order is simply another 

 name for every screw in space. In this case, therefore, 

 all the values of p e must be infinite, which implies that 

 each co-efficient of the equation for p 9 must vanish, 

 except the absolute term. 



We are thus presented with no fewer than six for- 

 mulae involving the pitches and angles of inclination of 

 the six screws of a co-reciprocal system. Of these for- 

 mulae we shall in this place only consider one. If the 

 co-efficient oip e be equated to zero it appears that 



i i i i i i 



h i + i + = o 



Williamson's Differential Calculus, 2nd Edition, p. 189. 



