112 MR JAMES CLERK MAXWELL ON THE 




58. 
¢. oA ae — (a? +a, a) 7 5 (2+=) si 
2 a,"—a,” Bea Digit m )- 
When a,=0, as in the case of a solid cylinder, c,=0, and 
oe ey ed =) 
¢,=h,—a, age (2+ = 
=/h Tk {2 2 2 E 3 2 2 59 
qr are (2 +4) + = GPa) | 5 patna oS) 
When /,=0, and r=a,, 
Tka (EH 
=" (G2) Ab St REO! 
When g exceeds the tenacity of the substance in pounds per square inch, the 
cylinder will give way; and by making g equal to the number of pounds which a 
square inch of the substance will support, the velocity may be found at which the 
bursting of the cylinder will take place. 
oe é -2) 6r*, a transparent revolving cylinder, when 
polarized light is transmitted parallel to the axis, will exhibit rings whose diame- 
ters are as the square roots of an arithmetical progression, and brushes parallel 
and perpendicular to the plane of polarization. 

Since I=6 w (g—p) = 
CASE IX. 
A hollow cylinder or tube is surrounded by a medium of a constant temper- 
ature while a liquid of a different temperature is made to flow through it. The 
exterior and interior surfaces are thus kept each at a constant temperature till 
the transference of heat through the cylinder becomes uniform. 
Let v be the temperature at any point, then when this quantity has reached 
its limit, 
rdv 
dr} 

o— COM Cae tae ai een (Gls) 
Let the temperatures at the surfaces be 6, and 6,, and the radii of the sur- 
faces a, and @,, then 
6, —4, _ log a, 6,—log a, 0, 
4 ~ Tog Balog ay aS log a, —log a, 

Let the coefficient of linear dilatation of the substance be c,, then the pro- 
portional dilatation at any point will be expressed by ¢, v, and the equations of 
elasticity (18.), (19.), (20.), become 
doz _ 

=(5,,- 3 =a) (o+p+9)+ = nous bs 
