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MINUTES OF PROCEEDINGS OF 
strain, the conditions would be more favourable; but in the case of 
wrought-iron, where the crushing strain is less, the conditions would 
be less favourable. It would not, therefore, be advisable to discard 
steel entirely from wrought-iron guns. There must be some strongs 
metal to bear the crushing strain which initial tension brings on the 
bore. It is not necessary, however, that the steel be at the bore itself. 
It may be used much more advantageously in the second course. 
Fig. 9 represents my gun with the second course of steel in the 
region of the powder-chamber. The result shows much greater 
strength. In calculating the strength, it is necessary to multiply the 
steel area by 4, as the elasticity is only half, while the tenacity is twice 
that of wrought-iron. 
Fig. 10 shows both 2nd and 3rd courses of steel. The result is 
equally satisfactory. 
The absolute mathematical strengths of these three constructions 
may be given in the order in which they have been considered, as 9, 
8 , 10. This, however, does not take into account any errors of manu¬ 
facture, which will tell more severely against steel than iron, as an 
error of tttooo^ i n dimensions represents a loss of 1 ton per square 
inch in iron, and 4 tons in steel. 
In the all-steel construction, there would be no gain by increasing 
the thickness of metal beyond calibres. It might be made in two 
pieces, the inner \ calibre, and the outer 1 calibre thick, giving \ of 
the useful effect of the metal. The explosion would thus be resisted 
by steel, equal in value to times the dimensions of the bore j and 
thus by working the steel up to 20 tons, or its elastic limits, the pres¬ 
sure in the bore might be 30 tons, if gradually applied. A large 
reduction, however, has to be made on account of the suddenness of 
the strain, as shown in the following calculation:— 
Let P = pressure in the bore suddenly applied, i.e. } uniform during 
the time of expansion. 
r = radius of bore. 
s — space described from the centre by the mass of metal m, in 
the time t. 
T = tension caused by the extension of the metal, and which, 
varying with s } may be put = y- s. 
We have— 
P = 
T , dh 
T + m dT* 
dh 
dfi 
ds d 2 s P ds fxs ds 
dt dfi m dt rm dt 
r r r r% 
== 2P — ~ — 
fxm fjirm, 
