1908. No. 1. ON THE GRAPHIC SOLUTION OF DYNAMICAL PROBLEMS. 5 
We will first prove the correctness of the approximate formula @ = pV. 
If we designate the projection on the normal M N of the force acting on 
the point M, as K,, and the velocity of the point as v, we have, as we 
know, the mass of the point being equal to 1, 
7 
9 7) 
= = © 
According to system I, v? = 2U, and A, = 5,,, where 
ON 
Pr 
= indicates the 
° 
oN 
Fig. 2. 
derivative of U along the normal M N. This gives 
1 OU 
Let us now consider an assumed point M’ on the normal, and call 
its distance from a fixed point on the latter &, £ to be reckoned positive 
in the direction MN. If M' moves, U will be a function of &, and if 
this function be developed in series, we easily obtain the desired approxi- 
mate formula, 9 = pD. It was in this way, moreover, that I first demon- 
= 
strated this formula. 
