THE EQUILIBRIUM OP ELASTIC SOLIDS. 



From these equations we find that 



,_fJ__ J_\ (zp+r&} 



\9fji 3m/ \ * dr] 



63 



._ 



3m 



and hence v = c,logr + c t , p may be found in terms of r. 



Hence 



Since 



v 



1 



/= 60, - = &o, + - 



2 1 \ 

 + J 



( 



the rings seen in this case will differ from those described' in Case III. only 

 by the addition of a constant quantity. 



When no pressures act on the exterior and interior surfaces of the tube 

 ^=5^ = 0, and 



2 . _1_\ " 

 + 3m/ 



' 



ofo* log . - log a, a.* log a. - a, 8 log aA 

 -- -- 



,/2 J^X- 1 

 6 fe 3m/ ^" 



a 1 i a > Moga 1 -loga i \ 



a.'-a/ 



. 

 ' 



...(62). 



There will, therefore, be no action on polarized light for the ring whose 

 radius is r when 



a, 2 a, 2 , a, 

 r = 2- Jog-. 

 i a/ & a, 



CASE X. 



Sir David Brewster has observed (Edinburgh Transactions, Vol. vm.), that 

 when a soHd cyUnder of glass is suddenly heated at the cylindric surface a 

 polarizing force is developed, which is at any point proportional to the square 

 of the distance from the axis of the cylinder; that is to say, that the dif- 



