PROCEEDINGS 
OF THE 
ROYAL SOCIETY OF EDINBURGH. 
yol. yii. 1869-70. No. 81. 
Eighty-Seventh Session. 
Monday, 7 th February 1870. 
Dr CHEISTISON, President, in the Chair. 
The following Communications were read : — 
1. On Eeciprocal Figures, Frames, and Diagrams of Forces. 
By J. Clerk Maxwell, Esq., F.E.SS. L. & E. 
The reciprocal figures treated of in this paper are plane recti- 
linear figures, such that every line in one figure is perpendicular 
to the corresponding line in the other, and lines which meet in a 
point in one figure correspond to lines which form a closed polygon 
in the other. 
By turning one of the figures round 90°, the corresponding lines 
become parallel, and are more easily recognised. The practical 
use of these figures depends on the proposition known as the 
“ Polygon of Forces.” If we suppose one of the reciprocal figures 
to represent a system of points acted on by tensions or pressures 
along the lines of the figure, then, if the forces which act along 
these lines are represented in magnitude, as they are in direction, 
by the corresponding lines of the other reciprocal figure, every 
point of the first figure will be in equilibrium. For the forces 
which act at that point are parallel and proportional to the sides of 
a polygon formed by the corresponding lines in the other figure. 
In all cases, therefore, in which one of the figures represents a 
frame, or the skeleton of a structure which is in equilibrium under 
YOL. VII. II 
