1. hh a paper published under the above title in the Philosophical 
Magazine and Journal of Science for 1892, Lord Kelvin described a 
graphic method for the solution of dynamical problems. We will quote 
from his paper the following account of his method. 
«In dynamical problems regarding the motion of a single particle in 
a plane the following plan is given for drawing any possible path under 
the influence of a force of which the potential is given for every point of 
the plane. Suppose, for example, it is required to find the path of a par- 
ticle projected, with any given velocity, in any given direction through 
any given point P, (see fig. 1)». 
«Calculate the normal component force at this 
point, and divide the square of the velocity by this 
value, to find the radius of curvature of the path at 
that point. Taking this radius on the compasses, 
find the centre of curvature C, in the line P,K, per- 
pendicular to the given direction through /,, and de- 
scribe a small arc, P)P,Q,, making P,Q, equal to 
about half the length intended for the second arc. 
Calculate the altered velocity for the position Q,, 
according to the potential law, and, as before for P,, 
calculate a fresh radius of curvature for Q, by find- 
ing the normal component force for the altered direc- 
tion of normal, and for the velocity corresponding to 
the position of Q,. With this radius, find the po- 
sition of the centre of curvature, C,, in P,C,L, the 
Pig. I. 
line of the radius through P,. With this centre of 
curvature and the fresh radius of curvature, describe an are P,P,O,, 
making P,Q, equal to about half the length intended for the third arc; 
calculate radius of curvature for position Q,, draw an arc P,P;Q3, and 
continue the procedure». 
Vid.-Selsk. Skrifter. I. M.-N. Kl. 1908. No. 1. 1 
