62 THE EQUILIBRIUM OF ELASTIC SOLIDS. 



Since 7= but (q p) = ( -- 2j&r*, a transparent revolving cylinder, when 



polarized light is transmitted parallel to the axis, will exhibit rings whose 

 diameters are as the square roots of an arithmetical progression, and brushes 

 parallel and perpendicular to the plane of polarization. 



CASE IX. 



A hollow cylinder or tube is surrounded by a medium of a constant 

 temperature 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 tem- 

 perature 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 



(61). 



Let the temperatures at the surfaces be 0, and 0,, and the radii of the 

 surfaces a, and c^, then 



,' logOj-loga, 



Let the coefficient of linear dilatation of the substance be c,, then the 

 proportional dilatation at any point will be expressed by c t v, and the equations 

 of elasticity (18), (19), (20), become 



dSx I 1 1 



d8r 

 8r 



The equation of equilibrium is 



and since the tube is supposed to be of a considerable length 



d8x 



-j *=c t a constant quantity. 



-*+ <). 



