100 MR JAMES CLERK MAXWELL ON THE 
¢—p=¢,—2p, therefore by (21.) 
dp 2p _ , 
dr rah) Mile 
a linear equation, which gives 
a! Cs 
p=e, 7 to. 
The coefficients ¢, and ¢, must be found from the conditions of the surface of 
the solid. Ifthe pressure on the exterior cylindric surface whose radius is a, be 
denoted by /,, and that on the interior surface whose radius is a, by hs, 
then p = h, when r=a, 
and p=h, when r= a, 
and the general value of p is 
OF h SOs he (a saies 



1a ay? — ay? ra as » + + (22.) 
rh =q—p=2% ae) a by (21.) 
eee : a (23.) 
Tabu (p—g)=ba Se ae oe aay 
This last equation gives the optical effect of the pressure at any point. The 
law of the magnitude of this quantity is the inverse square of the radius, as in 
Case I.; but the direction of the principal axes is different, as in this case they 
are parallel and perpendicular to the radius. The dark bands seen by polarized 
light will therefore be parallel and perpendicular to the plane of polarization, in- 
stead of being inclined at an angle of 45°, as in Case I. 
By substituting in Equations (18.) and (20.), the values of p and g given in 
(22.) and (23.), we find that when r=a,, 
Ox ( 1 ) (o+2% has 1 2) f s47 hah, 
2 a NO waa are ) +55 (+ a,?—a,? ) 
1 2 1 1 1 
=o(5 + = 2 ey is i, eat a am) 
=e 2 2n —4a,7h 
Wher pat 1 (o+r2% hy a,’ ok ill (“ hy, +8 a, ue a, ae 
a? —a," 3m a,” —a, 
pe a Li /2a, aE) al 
si =e Sige = see 3m this a, i 3m 
From these equations it appears that the longitudinal compression of cylin- 
dric tubes is proportional to the longitudinal pressure referred to unit of surface 
when the lateral pressures are constant, so that for a given pressure the com- 
pression is inversely as the sectional area of the tube. i 
These equations may be simplified in the following cases:— 


(25.) 


(26.) 



7, 
