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



we determine the arbitrary constants, and it is easy to see that 



(c) f=_n-^- 8 (e-2/) =-n 



do: a\—a\ of— affile 



These quantities express the change per unit of length : (a) tangentially to a cross-section of 

 radius r ; (b) radially for the same section ; and (c) longitudinally for all parts of the tube. They 

 indicate a strain made up of two parts : a uniform compression of 



n a\ 



oka\ — a% 



in all directions ; and a shear of 



1± 



II a\ af, 



2na\— a\r 



in the plane of a transverse section. 



The diminution per unit volume of the interior of the cylinder is 



VV« ax a\ — ai\n kj 



When II is a ton-weight per square inch, the value of the quantity 



"(H)' 



is, according to the best determinations, somewhere about j^ 6 q for ordinary specimens of flint glass, 

 and about ^oVg ^ or steel- This expression is very simple, and enables us at once to calculate the 

 requisite length of bulb, when its internal and external radii are known, which shall have any assigned 

 sensitiveness when fitted with a fine tube of a given bore. To obtain great sensitiveness, increasing 

 the diameter of the bulb is preferable to diminishing its thickness, as we thus preserve its strength ; 

 and we have seen how to avoid the complication of temperature corrections. 



It is obvious from the expressions above that the change of unit volume is the same throughout 

 the whole of the substance of the walls of the tube, having the value 



k a\ — «l' 



But the shear is greater as r is less. Its greatest value is therefore at the interior surface, where 

 it is 



In en — ik. 



