160 DYNAMICS OF A RIGID BODY. 



potential complex, then it is well-known that one set of 

 axes of reference can be found which will reduce both 

 U and V to the sum of n squares. These axes of refer- 

 ence are the harmonic screws. 



We may here also make the remark, that any screw 

 complex U* = o of the (n - i} th order and second degree 

 can always be transformed in one way to the sum of n 

 square terms with co-reciprocal screws of reference ; for if 

 UQ and p Q = o be transformed so that each consists of 

 the sum of n square terms, then the form of the expres- 

 sion of p 6 ( 40) shows that the screws are co-reciprocal. 



