of Edinburgh, Session 1874-75. 
443 
(2.) On the Equipotential Surfaces for a Straight Wire. 
Some results given in Yol. I. of Thomson and Tait's Natural 
Philosophy may be much more simply obtained by calculating the 
potential of a wire rather than its attraction. That potential is 
easily found as 
p lo s- 
r i + r 3 + c 
r x + r 2 - c ’ 
where c is the length of the wire, p its line density, r x and r 2 the 
distances of its ends from the point at which the potential is to be 
found. 
In this form we see at a glance that the equipotential surfaces 
are prolate ellipsoids of revolution with common foci at the ends 
of the wire. 
The method is extended to polygons plane or gauche, closed or 
unclosed. 
(3.) On a Fundamental Principle in Statics. 
The principle that, while additional constraints cannot disturb 
equilibrium, unnecessary constraints may be removed without dis- 
turbing equilibrium, is of very great use in the statics of fluids 
and of elastic and flexible bodies. But it seems not to have been 
made use of to the extent its importance deserves. 
My attention was recalled to it when attempting to compare the 
shares taken by gravity and cohesion in resisting the tendency of 
the so-called centrifugal force to split a planet. The problem 
which first proposed itself was to determine the gravitation attrac- 
tion of one- half of a uniform sphere upon the other. 
The sextuple integral which a direct solution of this problem 
would require may be entirely dispensed with, and its place sup- 
plied by a simple single integral, if we imagine a thin film of the 
solid on each side of a diametral plane to be converted (without 
change of bulk or density) into an incompressible liquid. 
Or we may commence with a sphere of homogeneous incom 
pressible liquid. If a be its radius, p its density, it is easily shown 
that the whole pressure normal to any diametral plane — which is 
of course the attraction of the hemispheres on one another — is 
