336 
MINUTES OF PROCEEDINGS OF 
undiminished force throughout the mass, it is plain that when the circumference 
of the bore would he stretched a thousandth part of its diameter, i.e. the 
hundredth of an inch, the lamina an inch further would be only stretched -J-gth 
of that amount, and the lamina an inch further still only Ifth, and so on to 
the external lamina which would be only stretched -JJth or ^ the amount, 
that is, when the interior of 10 inches diameter would be on the point of 
rupture the exterior of £0 inches diameter would have only half the strain 
on it which it could bear. Hence, we might lay down the law that the 
resistance of each lamina varied inversely at its distance from the axis ; but 
every one knows a pressure is not transmitted with undiminished force 
through any solid, but that it rapidly decreases as it travels forward, and 
therefore that the opposition which the exterior is called upon to supply 
must be less than that deduced by the foregoing law. In fact, the resisting 
power of the material as well as the distance from the axis must be taken 
into consideration. 
According to the late Professor Peter Barlow, P.B.S., the power exerted 
by the different parts of a metal cylinder varies inversely as the square of 
the distances of the parts from the axis ; in other words, the strains (o- and s), 
on any two laminae are inversely proportional to the squares of their radii, 
(p and r), 
cr V 2 
Dr Hart, Bellow of Trinity College, Dublin, having taken into account 
the compressibility of the metal, which Barlow appears to have omitted, 
calculated that there is a greater strain on the exterior. His formula may 
be written thus, 
or r 2 R 2 + p 2 * 
s p 2 A 2 + ?' 2 
R and r being the external and internal radii, p the radius of an 
intermediate lamina of which cr is the strain, and s the strain on the 
inside. 
If we want to compare the strain on the inside with that on the outside, 
P = R, and we have by inversion, 
s _ R 2 + ?’ 2 
cr %T 2 
In the case of the 10-inch gun before referred to, the strain on the 
interior compared with that on the exterior, w r ould, according to Barlow, be 
as 100 to 25, or 4 times as great, but according to Hart only as 125 to 50, 
or 2| times as great. But whatever be the exact law of resistance it is 
evident that the strength of a homogeneous gun is not in proportion to its 
weight, and that a gun should if possible be constructed in such 
MANNER THAT EACH PART OF ITS MASS WOULD DO ITS DUE PROPORTION OF 
WORK AT THE INSTANT OF FIRING, f 
* Palliser. Treatise on Compound Ordnance, p. 38. 
f This principle was, I believe, first enunciated by the late Captain Blakeley, B.A. 
