1904] the Volume Elasticity of Mastic Solids. 519 



Also (will denote the length of the whole or a part of a generator 

 of a right cylinder or prism, SI its elastic extension 



When a hollow tube of isotropic material, bounded by co-axial right 

 circular cylinders, is exposed to uniform pressures, viz., /over the inne 

 surface, radine n and j,. over the outer surface, radius and to unifom 

 tension P over the flat ends, the elastic displacement parallel to the 

 length, taken as axis of 2, is given by 



n 



Case (i). 



#, = 0, P 



5-2-*Js!L 



/ 2 *V- n i E 



= 0, P ^r- (2), 



Putting for shortness 



81/1 = e, 

 we have 



When the thickness, #, of the cylinder wall is so small that t/n is 

 negligible compared to unity, 



(5). 

 Case (n). 



^ = 0, P= -prfKrJ-n*) .................. (6), 



Thus, with the same notation as in Case (i), 



T. _ Per 2 r 2 

 - 



When ^/r is negligible compared to unity, 



........................... (9). 



Case (iii). - 



pt=p e = -P=^ (10). 



%/l = w / z=s - p /3k (n) f t 



> k = -p/Se (12). 



Case (i) is really that considered by Mr. Mallock. Taking a cylin- 

 drical tube with terminal caps, he applies a uniform internal pressure 

 Pi. This gives on each cap an outwardly directed pressure, whose total 

 amount is Trr-^pi. This leads to a longitudinal tension in the cylinder 



* ' Amer. Math. Soc. Bull.,' 2nd series, vol. 7, 1900, p. 141. 

 t Of. ' Phil. Mag.,' December, 1901, Eqn. (67), p. 594. 



2 Q 2 



