﻿ON CONSTRUCTING CANNON OF GREAT CALIBER. 9 



that the external portion will be distended, practically, but one ninth part as much as 

 the internal portion of the solid, and, if we take an infinitely small part for the disten- 

 tion, exactly one ninth. Now it is well known that with most bodies, including 

 iron, within the strain of its elasticity the elongation is in exact proportion to the 

 straining force. Hence with a cylinder such as I have described, if of cast-iron, the 

 inner portion will be rent, or strained beyond its elastic power, at the instant that 

 the outside portion is strained with only one ninth part of the load that it is capable 

 of bearing. If the cylinder be made thicker than in my example, the load borne by 

 the outside will be still less. If it be twice as thick as the diameter of the bore, the 

 outside j)ortion will be strained with only one twenty-fifth part of the load it is capable 

 of bearing, when the inner portion is rent, and all the other parts must be rent in 

 succession, without any increase of the load. The law of the diminution in the power 

 of resistance may be stated as follows. Suppose such a cylinder to be made up of a 

 great number of thin rings or hoops, placed one within another. Tlien the resistance 

 of these rings, compared one Avith anotlier, to any distending force, will be inversely as 

 the squares of their diameters.* With these incontrovertible laws of resistance before 



* If we make a cylinder of 41 concentric hoops of equal thickness, disposed one within another, and 

 exactly fitting, so that the particles of each hoop shall be in equilibrium with each other, the diameter of 

 the largest being 5 times that of the smallest, then the force of each, beginning with the innermost, to 

 resist distention, will be represented by the following numbers : — 



An inspection of these numbers must, I think, impress any one with the fact, that it is impossible to 

 increase essentially the strength of cannon, by a simple increase of thickness. 



Mr. Barlow does not limit the application of his investigation to any kind of metal, but it is evident that 

 his conclusions are not. applicable to any malleable metal like bronze ; for in a cylinder constructed of hoops 

 of this material the i-nner hoops may be elongated by the pressure acting as a crushing force, and by this 

 means be enlarged without any diminution of tenacity. Perhaps some kinds of soft cast-iron may accom- 

 modate themselves to an enlargement in the same way. But with hard crystalline cast-iron, no actual dis- 

 placement of the constituent particles can take place without fracture ; and although the effect of the fluid 

 as a crushing force may act as an au.xiliaiy to the strain, as any estimate of its amount would be a mere 

 guess, I shall not attempt any modification of Mr. Barlow's conclusion, when applied, as in this case, to 

 hard cast-iron gun-metal. 



VOL. VI. NEW SERIES. 2 



