96 MR JAMES CLERK MAXWELL ON THE 
In these cases the co-ordinates 2, y, 2 are replaced by the co-ordinates 
x=X, measured along the axis of the cylinder. 
y=r, the radius of any point, or the distance from the axis. 
z=r6, the arc of a circle measured from a fixed plane passing 
through the axis. 





aes ied as , p,=0, are the compression and pressure in the direction of the 
axis at any point. 
ay ze au , py=p, are the compression and pressure in the direction of the 
radius. 
don 4 ee =r p;=q are the compression and pressure in the direction of the . 
tangent. j 
Equations (9.) become, when expressed in terms of these co-ordinates— 
m do 
PaaS her re 
m dod 
% = ae (14.) 
_ Mm a On 
%~ 2° dr 

The length of the cylinder is 4, and the two radii @, and @, in every case. 
Cass I. 
The first equation is applicable to the case of a hollow cylinder, of which the 
outer surface is fixed, while the inner surface is made to turn through a small 
angle 66, by a couple whose moment is M. 
The twisting force M is resisted only by the elasticity of the solid, and there- 
fore the whole resistance, in every concentric cylindric surface, must be equal to M. 
The resistance at any point, multiplied into the radius at which it acts, is ex- 


2400 
pressed by 7g, = aed ek: 
Therefore for the whole cylindric surface 
a0 mirrb= M. 
dr 
M 1 i 
Whence s0=5-—, (Gr - az) 
M 1 1 
and m= 5-739 (Gr = = eee (Ly) 
The optical effect of the pressure of any point is expressed by 
Pap 6a (16.) 
7 r* 
