98 MR JAMES CLERK MAXWELL ON THE 
dices is nearly the same as that of Canada balsam, while the other is very differ- 
ent, the common surface of the gutta percha and Canada balsam will transmit 
one set of rays much more readily than the other, so that a film of extended gutta 
percha placed between two layers of Canada balsam acts like a plate of nitre 
treated in the same way. ‘That these films are in a state of constraint may be 
proved by heating them slightly, when they recover their original dimensions. 
As all these permanently compressed substances have passed their limit of 
perfect elasticity, they do not belong to the class of elastic solids treated of in this 
paper; and as I cannot explain the method by which an uncrystallised body 
maintains itself in a state of constraint, I go on to the next case of twisting, which 
has more practical importance than any other. This is the case of a cylinder 
fixed at one end, and twisted at the other by a couple whose moment is M. 
Case II. 
In this case let 6 6 be the angle of torsion at any point, then the resistance to 
torsion in any circular section of the cylinder is equal to the twisting force M. 
The resistance at any point in the circular section is given by the second 
Equation of (14.) 

This force acts at the distance 7 from the axis; therefore its resistance to torsion 
will be g,7, and the resistance in a circular annulus will be 
doe 
dz 

Qr2nrdr=mT r dr 
and the whole resistance for the hollow cylinder will be expressed by 
M="" ae ok etna athe 
m=4M 5 a =i 
wv sph (a,*—a,*) 
720 M b 
ary a (=a) . . (17.) 
In this equation, m is the coefficient of linear elasticity; a, and a, are the 
radii of the exterior and interior surfaces of the hollow cylinder in inches; M is 
the moment of torsion produced by a weight acting on a lever, and is expressed 
by the product of the number of pounds in the weight into the number of inches 
in the lever; 4 is the distance of two points on the cylinder whose angular motion 
is measured by means of indices, or more accurately by small mirrors attached to 
