4 CARL STORMER. M.-N. KI. 
The practical utility of this method is dependent upon the ease or 
difficulty with which the radius of curvature can be calculated. If the 
potential on which the force depends is a somewhat complicated function 
of the coördinates of the point, the method immediately becomes so 
troublesome to use, that recourse should rather be had to one of the many 
numerical methods of integration for the calculation of the path. 
We intend, however, to demonstrate an extremely simple, approximate 
construction of the radius of curvature by the aid of a number of equipo- 
tential lines, whereby the above difficulty is avoided. 
Let the differential equations for the motion of the point be 
dx _2U 
dt? — %x 
dy aU 
FEET (D) 
where U is a given function of x and y. Let us further assume that 
we have drawn in advance a number of equipotential lines, 
Let 4 MB be a part of the path, and M its point of intersection 
P 
with the equipotential line U= Further let M N be the normal, with 
n 
direction towards increasing ©, i.e. towards the centre of curvature of 
the path. Jf we designate as D the part of the normal between the two 
nearest equipotential lines, er WE en we have for the 
radius of curvature @ in the point M, the approximate formula 
ge = pD. 
By the aid of this formula, the radius of curvature may be easily and 
quickly constructed, when the equipotential lines have been drawn once for 
all. The construction of the path of the point by the aid of the radu of 
curvature thereby becomes very simple and easy of accomplishment. We 
will return later to the question of the possibility of modifying the method 
when the radius of curvature is very large, or when the equipotential 
lines lie far from one another. 
