1908. No. I. ON THE GRAPHIC SOLUTION OF DYNAMICAL PROBLEMS. 
LT 
the axis xx” is tangent to the equipotential curve through M, and the 
distance, 6, from the point marked on the paper to the axis xx", is read 
b 
off. Then cos y = z and thus 
a 
OT AED) 
whereupon @ is quickly calculated with a sliding-rule. 
In the case of o being so large that the centre of curvature falls out 
side the paper, the following method may be employed. 
et 
Fig. 6. 
In this figure, where MM’ is an arc of a circle with radius @ and 
centre in O (centre of curvature), we have 
n =o (1 — cos à) 
c=osina 
consequently, with sufficient accuracy, 
c—h=-c 
Here c is assumed, as also a. The position of M’ is thereby determined, 
n and Ah being easily calculated with a sliding-rule. As also the position 
of P, is known, we have the direction of the radius of curvature in the 
point M". 
If the gelatine-paper is used, it is turned about M so that the one 
axis falls along MN’. By the aid of the cross-rule paper, the points M' 
and P' may then easily be marked. 
This is the description, in its principal details, of the graphic con- 
struction of the path. 
Printed 26 May 1908. 
