THE ROYAL ARTILLERY INSTITUTION. 
149 
of its internal to its external diameter multiplied by its thickness. 
The more nearly this ratio is unity, the greater will be the proportion 
of work obtained; also, as the calibre increases, so may the thickness 
be advantageously increased. 
By taking the internal radius as the unit of thickness, we can readily 
see the very small addition of strength which is gained by increasing 
the thickness. A thickness of \ calibre gives a strength of \ of \ 
calibre; a thickness of 1 calibre gives a strength of J of 1 calibre or § 
of i calibre; a thickness of calibres gives f of \ calibre. So that 
we have | for the first \ calibre, § - | or i for the second J calibre, 
-fa for the third, and so on; the total is therefore | + 374 4* 473- 
+ ad injin . for an infinite thickness. Now, as the sum of this series 
can never reach unity, it follows that, even with an infinite thickness, 
we can never obtain as much useful effect as we shall from \ calibre of 
thickness if all the metal could be made to do its work. This law is 
fatal to a very heavy gun ever being made of one homogeneous piece 
of metal. 
2. Armstrong Guns. 
It was for the reason above stated, that Sir William Armstrong gave 
initial tension to the successive coils adopted in his system, so that, if 
properly arranged, they should have all their interior surfaces at their 
greatest tension at the moment of maximum strain. The great amount 
of strength gained by this method will be seen in Fig. 3 , which repre¬ 
sents a 9 -inch gun, on the Armstrong plan, with all the coils extended 
so that the inner surfaces are all at the elastic limits of the iron. 
The area below the continuous curve is all the strength that could 
be obtained if the whole gun were of one piece. The areas between 
the continuous and discontinuous curves are the additional strengths 
obtained by initial tension. It will be noticed that more waste power 
is rescued as the distance from the centre increases. But this also 
involves greater initial tension; and for this purpose, at one calibre 
thickness, the initial tension must be eight-ninths of the strain the coil 
is to bear. If so much initial tension as this is put on, there is a 
danger, on the one hand, of overshooting the mark and overstraining 
the coil so much that it may break; and this was actually the case in 
a 600 -pr. which burst one of its coils, while the barrel and all the 
other coils remained sound. On the other hand, if too little tension be 
put on, it may so happen that the iron beneath is more compressible 
than usual, and the greater part of the tension may be absorbed without 
compressing the bore. These two dangers both increase as the thick¬ 
ness of the metal increases; and, for this reason, Major PalliseFs 
remarks are very appropriate—viz., that the circumferential strength 
should be obtained as near the bore as possible. This useful maxim, 
however, cannot be carried out in the Armstrong gun, on account of 
the breech-piece, which surrounds the most vital point at the powder 
chamber (see Fig. 11). The breech-piece has its fibre arranged longi¬ 
tudinally, for the sake of longitudinal strength, and gives in consequence, 
circumferentially, only half the strength coiled iron would give, inas- 
