78 HARMONIC SCREWS. 



J_dV_ _l_ dV 



~1 Wf 2p n dW 



we therefore have the equation : 



tp+ffsL-v- * dv 



e ~dt' " ^T^T; 



or 



and 72-i similar equations ; but we see from 67 that 



Differentiating this equation with respect to the time, 

 and regarding e as constant, we have : 



_ 



' 'dt ' J^~d 



whence 



JOS dV 



the same equation as that already found by Lagrange's 

 method. 



To integrate the equations we assume : 



where /i, . . .f n are certain constants, which will be 

 determined, and where Q is an unknown function of the 

 time: introducing also the value of F", given in 70, 

 we find for the equations of motion : 



= o, 



&c. 



nti +'...'+ wQ = O. 



