of Edinburgh, Session 1879 - 80 . 
573 
(or at least unverifiable) in a sphere. By properly choosing the thick- 
ness of the cylinder in proportion to its bore, the sensitiveness of 
this gauge may be made as great or as small as we please. And, 
by having two or more, with bulbs of nearly the same internal 
dimensions, but differing considerably from one another in thickness 
of the cylindrical walls, a very important advantage is secured. 
For, under the same pressure, the maximum amounts of distortion 
of the glass are greater in the thinner bulbs, and thus these begin to 
deviate from Hooke’s Law at pressures under which the thicker ones 
are still following it accurately. Thus, by comparison, we can easily 
find through what portion of its range each instrument gives effects 
strictly proportional to the pressure. The thinnest of these is to be 
graduated by comparison with the nitrogen gauge. 
When this method has to be extended to pressures such as would 
crush glass, recourse must be had to steel, and a series of instru- 
ments with different thicknesses of this material is to be prepared. I 
do not yet know whether it may be found practicable to furnish these 
steel bulbs with thick glass tubes of small bore— probably we may 
succeed, if the steel be made to project into the glass. But if not, 
it is easy to construct them entirely of steel, so as to act on the 
principle of the “ weight- thermometer.” Anyhow, they can be 
graduated accurately from one another,, each from a thinner one ; 
until we come to the thinnest, which is to be exactly graduated by 
comparison with one of the thicker of the glass instruments. We 
have thus a series of gauges, each of any desired sensitiveness, 
capable of reading accurately pressures up to those for which steel 
at the interior of a thick tube ceases to follow Hooke’s Law. 
To illustrate this process, and to show what amount of sensitive- 
ness is to be expected from an instrument of known dimensions, I 
append an approximate solution of the problem of the compression 
of a cylindrical tube with rounded ends. The exact solution would 
be very difficult to obtain, and would certainly not repay the trouble 
of seeking it. I content myself, therefore, with the assumption 
that all transverse sections are similarly distorted, which, of course, 
involves their continuing to be transverse sections. 
Let £ denote the displacement of a transverse section originally 
distant x from one end, and let p be the change of r the original 
distance of any point of the section from the axis. Then, as it is 
