﻿8 ON CONSTRUCTING CANNON OF GREAT CALIBER. 



the ratio of increase in thickness, but that the ratio of increase of strength is such, 

 that, where they become of considerable thickness, the strength falls enonuously 

 below that given by the ratio of thickness. Mr. Barlow has carried out his reasoning 

 in an analytical form, which I shall omit, wliile I endeavor to give the physical 

 principles of the problem, as he has laid them down, in a form more clearly within 



Fig. 1. 



Fig. 2. 



30 

 60 



34-ei 



the conception of all.* For this purpose 

 let us suppose Fig. 1 to represent the cross- 

 section of a hollow cylinder, like a cannon; 

 A, the bore, 10 inches in diameter, B, the 

 walls or body, 10 inches thick. Let this 

 cylinder be distended by internal fluid pres- 

 sure until the bore is 20 inches in diameter, 

 as in Fig. 2. The external diameter will be 

 increased only to 34:.641 inches. For in 

 Fig. 1 the whole diameter is 30 inches, and 

 contains an area of 30^ = 900 circular inches. From this take the area of the bore 

 10* = 100 inches, and we have 800 inches in the area of the solid walls. Now after 

 it is distended, the area of the bore becomes 20^^ = 400 circular inches, and as the 

 walls contain the same area as before the distention, viz. 800, we have 800 + 400 

 = 1200 circular inches for the area of the whole section, and /\/1200 = 34.641 for 

 the external diameter. Before the distention the circumference of the bore was 

 10 X 3.141 = 31.41, and the external circumference of the body was 30 X 3.141 

 = 94.23. After the distention the circumference of the bore is 20 X 3.141 = 62.82, 

 and the circumference of the outside solid is 34.641 X 3.141 = 108.81. Every inch 

 of the inner portion of the wall, then, by the distention has been doubled in length, 

 while the external circumference of the wall has been distended only in the ratio of 

 94.23 to 108.81, or from 1 to 1.155, less than one seventh part. 



I have taken a case of extreme distention, for the purpose of showmg more clearly 

 the physical condition of the problem. But this makes the ratio of the differences less 

 than they ai-e when the distention is kept within the bounds of practice with iron 

 cylinders. If, in the preceding case, the distention of the bore be made, what it may 

 be in practice just before fracture, namely, ToVoth part of the diameter, we shall find 



* Mr. Barlow's paper may be found in the first volume of the Transactions of the Society of Civil 

 Engineers, and likewise in the Encyclopsedia Metropolitana, and in the Treatise on the Manufactures of 

 Great Britain, p. 326. 



