DYNAMICS OF A RIGID BODY. 1 69 



We may easily verify with these co-ordinates that 

 each pair of principal screws of inertia are recipro- 

 cal : for let xf, yd' be a pair of roots, then the differ- 

 ence between the two equations 



= o and 2 - o is 



but this is equally the condition that the two screws of 

 which the co-ordinates are 



shall be reciprocal ( 57). 

 It is also easy to see that 



* ~ 



' 



Since each of the terms on the left-hand side of this 

 equation is zero, it follows that the right-hand side must 

 be zero ; but this is equivalent ( 54) to the statement that 

 the principal screws of inertia are conjugate screws of 

 inertia ( 57). 



