30 THE VOYAGE OF H.M.S. CHALLENGER. 



sure which a tube of common lead glass can stand is either 8 J or 14 tons. If it breaks by shearing 

 alone, it is equally resisting to external and internal pressures ; if by mere extension, it resists external 

 pressure more than internal in the proportion of about 5 : 3. 



When the pressure is the same outside and inside the cylinder, we have 



P_ _n df_ _n 



r~ 3k' dx~ 2k' 

 and the diminution per unit volume of the interior is, as in Orsted's experiment 



n 



k 

 The value of this in flint glass is, for one ton pressure, about 



1 



2700' 



When there are, simultaneously, pressures LT^ external and II internal, we have 



HQ 



__ _ 



r 3k al-al 2n (al~aiydx~3k a\-a\ 



whence the increase of unit volume of the walls is at every point 



k a\al 

 and the shear in the transverse sections 



2n (al- 

 The increase of volume of the interior is 



k a\a\ n a\a\' 



which agrees with the special results above when n o or Hi is made to vanish. 

 For a spherical bulb the equations are reduced to 



dr l J 2> r 



9 r* = 

 and we have for external pressure II 



p^-n al ( l \ all \ 



r a\ ajj\3A' i^kn) 



