3^o 



NATURE 



[August 14, 1890 



that when the gun is fired the interior of the tube is still in a 

 slight state of compression, so that the circumferential firing 

 stresses of the tube are insignificant pressures, the chief stress 

 being thrown upon the wire. 



This theoretical result appears to be of great practical ad- 

 vantage in prolonging the life of the gun, as it is found that 

 the tube of the wire gun has hitherto shown an unexpected 

 vitality ; a very gratifying result, when it is considered how 

 short the life of our large guns is, in consequence of the erosion 

 of the bore. 



An empirical formula, N = 2400 -f- ^ - 50, given by General 

 Maitland (Proc. I.C.E., vol. Ixxxix. p. 205) for the life of a 

 gun, where c denotes the calibre in inches, and N the number of 

 full charges that can be fired before the gun requires relining, 

 will illustrate forcibly the comparative longevity of large and 

 small guns : thus, if ir = 16, N = 100 ; if c = 12, N = 150 ; but 

 if c = o"3, as in the new magazine rifle, N = 7950. 



We have now determined graphically the firing stresses in the 

 wire gun, where the powder pressure, p^, is exactly adjusted, so 

 as to produce uniform t in the wire ; a less powder pressure 

 would obviously strain the inner fibres less, and less than the 

 outer fibres ; vice versd, a powder pressure greater than p^. 



(49) But now the gun-maker has to determine the initial 

 stresses in his gun from the above state of firing stress, by the 

 operation of stripping off the powder stresses, assuming the gun 

 to behave as if homogeneous. 



As a first consequence, the initial stresses in the jacket C will 

 be reduced to zero, as they should be ; because we have sup- 

 posed the jacket c slipped on with merely a mechanical fit. 



Secondly, in the wire coil B, the state of initial circumferential 



tension will be obtained by subtracting the ordinates of the 

 prolongation of the Barlow curve t'^t^ from the ordinates of the 

 straight line ^Vi '■> whence we obtain the symmetrical Barlow 

 curve (pi'Pv by reflexion of the Barlow curve t'^t^ ...» produced. 



The curve of radial pressure rjcS^ in the wire coil B, obtained 

 by subtracting the ordinates of the Barlow curve /j A ^fO"^ the 

 hyperbola p^Pif is now easily plotted, but is of a more com- 

 plicated analytical character. 



Finally, we come to the state of initial stress in the tube A, 

 obtained also by stripping off the powder stresses from the firing 

 stresses ; and consisting of the curve of initial radial pressure 

 U^r(„ a Barlow curve, and its reflexion, t^Tq, the curve of circum- 

 ferential pressure in the tube A ; th e position of t^Tq being 

 settled so as to make the area ^iTiTo^q equal to the area r-^<pi<t>or2 ; 

 and now the state of initial stress is represented in Fig. 10. 



(50) We notice that t,, is considerable, and may with im- 

 perfect design become dangerously near the crushing pressure of 

 the material of the tube A ; practically, however, the great 

 crushing pressure Tq is considered advantageous, as tending to 

 improve the resisting power of tbe material against the great 

 enemy, erosion. 



In the Severn tunnel, as a different exemplification of these 

 principles, the crushing effect in the brick tube, due to the head 

 of water of the land springs, was not allowed for sufficiently ; if 

 the land water around the tunnel is not kept down by pumping, 

 the head of water soon becomes sufficient to cause the bricks on 

 the interior of the tunnel to crush and splinter ; and until the 

 interior is strengthened considerably with steel or cast-iron curbs, 

 the expense of pumping cannot be avoided. 



(51) There is considerable divergence of opinion as to the 



Oi 



Oa 



proportions to be given to the tube A and the wire coil B ; 

 Longridge preferring a comparatively thin tube. A, of some 

 softer material, like cast-iron, while Schultz made his tube of 

 steel, and considerably thicker in proportion, with the advant- 

 age of throwing the longitudinal strength into the tube. 



As the theory is considerably simplified if we take the tube A 

 and the wire of the coil B of the same elasticity, we shall make 

 Fig. 9 represent the design of one of the Schultz guns, as 

 described by Moch, altering the dimensions and stresses to 

 round numbers in inches and tons. 



Now Figs. 9 and 10 represent the section across the chamber 

 of the Schultz 34-centimetre (is^-inch) gun, in which we have 

 made r^ = 7, r^ = 10, r^ — 14, r^= 18, in inches, to the nearest 

 integer. 



(52) We assume that, under a powder-pressure, pQ, of 20 tons 

 on the square inch, the wire coil is under a uniform circumfer- 

 ential tension of 30 tons on the square inch ; a very moderate 

 estimate for what steel wire is capable of sustaining, as 60 

 would not be excessive. 



Numerical calculation by means of the formulas of Part I. 

 gives the following values of the stresses, in round numbers : — 



15; i'-i= 7, ^2 = 9. ^'2 



30, whence • 



A = 2, /i ^ 



<l>i = 14; ^'1 — - 5'5> U — - 0'S> all in tons per square inch. 



In Fig. 10 the initial stresses are represented ; and we find, as 

 before, (^2 = 21, (^j = 14, ffij = 7, t\ = 20, Tj, = 27, while the 

 initial stresses in the jacket c are nil. 



(53) There still remains an important practical detail to be 



NO. 1085, VOL. 42] 



settled theoretically — the formula for the varying tension with 

 which the wire must be wound on the tube A, in order that 

 when the coil is complete the curve of initial tension of the wire 

 should become finally ^x'/'2- 



The formula has been investigated in all its generality by 

 Mr. Brooks in Longridge's "Treatise," but we shall follow 

 Moch in his article in considering the very much simplified case 

 of uniform modulus of elasticity. 



As we have already used the word initial to distinguish the 

 stresses in a gun in a state of repose when finished, we shall 

 call the varying tension with which the wire is wound on the 

 gun the tvinding tension, and denote it by Q, in tons per square 

 inch. 



(54) Now, to determine for any radius, r, of the coil B, Moch 

 assumes that the winding tension of the wire is equal to the 

 initial tension, <^, increased by the circumferential tension (pres- 

 sure) due to the initial radial pressure. Si, at the radius r, acting 

 on the partly finished tube and coil between the radii r^ and r ; 

 and thus 



e = <^ -f 



r- At r. 



In other words, it is assumed that the tension of repose, (p, is 

 less than the winding tension, 6, by the amount due to the pres- 

 sure as at a radius r, and zero pressure at the radius r^, treating 

 the material as homogeneous. 



