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



sure which a tube of common lead glass can stand is either 8i 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 



£__n rf|__n 



r~ 3k' dx~ 3k' 



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 IIj external and II internal, we have 



p_ i_ rio^-n^f rio-ii! a\ai d%_ i_ iio^-n^ 



r 3k a\-al + 2ra (of- al)r 2 ' dx 3k af-og ' 



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



i n o ft5-IIi«? 

 % a*— a* ' 



and the shear in the transverse sections 



1-fc. IIo— Hi ajajj 



2n (ai-aiy 



The increase of volume of the interior is 



i n «?-n>f n„-n! 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 



and we have for external pressure II 



2^=J;(A), 



af- a%\3k^ 1*471 J 



