July 24, 1890] 



NATURE 



307 



(14) Thus, with pilpo - rilr'o = \, and P = 15, the powder 

 stresses are given by circumferential tensions — 



T = T, 



/.• = 5 ; 



so that, with a shrinkage pressure &><, = pi = 3, the principal 

 firing stresses are given by circumferential tensions — 



T,- = 1 7 - 8 = 9, a great reduction on 1 7, 

 /.• = 5 + 5 = lo. 



while 



T<, = 5 - 5 = o, 



to = 2 + 2 = 4. 



We need not consider the radial pressures for practical 

 purposes. 



To equalize these maximum tensions, t, = 9 and ti = 10, the 

 tube might be made slightly thicker and the jacket thinner, or 

 else the shrinkage pressure to,, or/, slightly diminished, keeping 

 to the same bore and external diameter. 



(15) We have thus shown how the initial stress, the powder 

 stress, and the firing stress at any point of a gun composed of 

 a tube and a single jacket is found, and exhibited graphically in 

 Figs. 3 and 4. 



The curves in the figure are seen to be all similar to a curve 

 whose equation is of the form_y = ax — ", now called the Barlow 

 curve. 



When the gun is built up of three or more concentric cylinders, 

 the method of procedure is the same ; the initial pressure 

 between the cylinders may be supposed known from the amount 

 of shrinkage given in the manufacture ; and now, taking any 

 intermediate cylinder of the gun under initial pressures pi and 

 po at the internal and external surfaces, of radii r,- and ;■<,, we 

 erect ordinates to represent /,• and /<,, and draw the Barlow curve 

 joining their ends. 



The Barlow curve representing the circumferential tension or 

 pressure will always appear as an equal reflection of the pressure 

 curve, the position being assigned so as to make the area of the 

 circumferential tension curve equal to /,r,- - pgro ; and it may 

 happen that this area may vanish or become negative, showing 

 that some or all of the initial circumferential tensions are really 

 pressures. 



(16) But practically the gun-maker reverses this procedure ; 

 with him it is the maximum circumferential firing tension /,• of 

 a tube or hoopwhich is limited by the strength of the metal ; 

 so that, starting with these ti's, as given, he calculates the 

 pressures between the successive coils of the gun, proceeding 

 inwards, and finally determines the maximum allowable powder 

 pressure in the interior of the bore. 



Afterwards he subtracts the powder stresses from these firing 

 stresses, and thus obtains the initial stresses in the gun ; 

 and then from these initial stresses he calculates the amount 

 of shrinkage to be given to the coils or hoops to obtain 

 the requisite state of initial stress. But we shall show subse- 

 quently that the requisite amount of shrinkage is given just as 

 simply from the firing stresses as from the initial stresses ; so 

 that henceforth we need only determine the firing stresses. 



(17) Then Fig. 5 represents the maximum allowable firing 

 stress over the powder-chamber of the American 8-inch gun, 

 shown in cross-section, as composed of an inner tube, A, over 

 which a jacket, B, and two hoops, c and D, have been shrunk on. 



In practice, the maximum allowable tension in the jacket and 

 hoops is restricted to l8 tons per square inch, but in the inner 

 tube to 15 tons per square inch, so as to allow for erosion of the 

 bore, the weakening due to the rifling grooves, and the possible 

 failure of the tube. 



(18) In the notation of the "Text-book of Gunnery," 1887^ 

 by Major Mackinlay, R.A., supposing there are n cylinders in 

 the cross-section of the gun, the successive radii of the cylindrica 



Fig. 5. 



surfaces, beginning from the outside, are denoted in inches by 

 ''«, r„ _ 1, . . ., ^2, ^1, ^0 ; and 'the firing pressures at the 

 surfaces of separation are denoted by/„_i, . . ..A'A; ^^^ 

 /o finally denotes the powder pressure at the radius r^ of the 

 bore. 



We notice that there is no sudden change in the value of the 

 radial pressure ; but that the circumferential tension, /, changes 

 suddenly from one cylinder to the next. 



As we are concerned principally with the maximum tensions, 

 which occur practically at the inner surface of a cylinder, we 

 denote them, proceeding inwards, by /„_i, t„-.n, . . . t^, t^, 

 /■„ ; and we shall suppose them to change suddenly to /'„ _ 1, 

 t'„ -„,.,. t'2, t\, in proceeding inwards to the next cylinder. 



(19) Starting from the outside cylinder, the stress formulas 

 give, since /« = o, 



while 

 so that 



t'r. = a;- 



= -(' 



-:'). 

 •■:')■ 



/>„-< = 



(22) 



giving ^,---i.w}iep /«-! is assigned by its maximum allowable 

 value. 



Also 



- t'n=p„ 



(23) 



giving /'„, if required for the diagram. 



Proceeding inwards to the next cylinder, we have (witb 

 different values of a and b) — 



/„ _ 2 = ar~2_ .^ + ^, /„ _ 1 = ar~-_ ^ -f b, 



t,t — 2 = ^^^1 2 ~ ^'> i'n — \ = '^^T— 1 ~ ^ ' 



so that, eliminating the a and b, fir,t b and then a, 

 Pn-,-Pn-,=^a{r-l^-r-i;), 



and therefore, by division, 



r-^ - r-^ 



Pn-, - Pn-x = ^^ '^\t„-.,+p...,), 



Pu 



(A<-!,+A-l)+. 



■1.(24) 



giving/,,- 2 when/,, _ , is known, and when t,,-^ is assignedl 

 by its maximum allowable value in practice. 

 Also 



NO. 1082, VOL. 42] 



-/'„-,=/ 



(25) 



