556 Dr. C. Chree : Applications of 



and stresses are as follows, the notation being as before, and 

 the cylinder being supposed suspended : — 



u=~E-h[(l-2 V )U+ 9 z{ VP -(l~ V y\] ~] 



^ ^ 1 77 



4 ~a T- 1 — qpq(a 2 — r 2 ) —gp qz% 



r^> = ?'c = ^ = 0. 



Over the base ^ = the mean value of —^ is II, that being 

 by hypothesis the pressure at this depth in the liquid. 



If h be the height of the cylinder, the suspending forces 

 are given by 



the mean value over the cross section being — H+gph. This 

 is a pull or a push according as gpli or II is the larger. 

 The elastic change in the radius at height z is given by 



Za\a= - { (1 -2 V )U+gp V z-gp'(l- V )z(l -qz) |/E. (57) 



The moan change in height (i. e. the mean difference 

 between the values of iv over the cross sections z = h and 2 = 0) 

 is given by 



tf/A={8^-(II-j0>A)}/B, . . . (58) 

 where p=Ti-lg P 'h{l-lqh) (59) 



is the mean value of the liquid pressure throughout the height 

 of the cylinder. 



The modification required to adapt the preceding solution 

 to the case when the cylinder is supported on its base is 

 easily applied. 



General Properties ; Influence of Cavities ; Gravitation, fyc. 



§ 16. Some general conclusions may be derived from (2) 

 as to the influence of cavities in solids exposed only to 

 surface forces. If we distinguish the external surface and the 

 several internal surfaces limiting cavities, with their respective 



