﻿ON CONSTRUCTING CANNON OF GREAT CALIBER. 5 



Now cany this to two cannon of clifFcvcnt calibers, and take an extreme case. 

 Suppose the caliber of one to be 2 inches in diameter and the other 10 inches, and 

 that the sides of each gun equal, in thickness, the diameter of its caliber. Then 

 to develop the same force, per inch, from the powder of each gun, the inertia of 

 the balls should be as the squares of the diameters of the calibers, respectively ; that 

 is, one should be 25 times as great as the other. But the balls, being one 2 and the 

 other 10 inches in diameter, wUl weigh 1 pound and 125 pounds respectively; the 

 weights being as the cubes of the calibers. Hence each inch of powder in the large 

 gun will be opposed by 5 times as much inertia as is found in the small gun. This 

 produces a state of things precisely similar to that of loading the small gun with 5 

 balls instead of 1 ; * and although the strain thrown upon the gun by 5 balls is by 

 no means 5 times as great as that by 1 ball, there can be, I think, no doubt that 

 the strain produced by different weights of ball is in a ratio as high as that of the 

 cube roots of the respective weights.f This would give, in the example before us, 

 an increase of from 1 to 1.71, or the stress upon the walls of the 10-inch gun would 

 be 71 per cent greater than upon those of the 2-inch gun. 



* The state of things here described will be comprehended by 

 a glance at this figure. The two cylinders A and B, made 

 in the proportions of 1 to 5, will resist an equal hydrostatic 

 pressure, and the weights or plungers a and b, with which they 

 are loaded, will remain supported upon the water in equilibrium, 

 if an open communication be made between them by the pipe 

 d. But if we load the larger one with the ball c instead of b, 

 we shall require 5 balls, as shown in the small cylinder A, to 

 balance the pressure of c. 



t Hutton inferred that the velocities of balls of different weights with the same charges of powder were 

 inversely as the square roots of the weights, and Captain Mordecai, in his excellent book of experiments, 

 makes the same inference. This would give no increase to the force of the powder, and must be impossi- 

 ble ; and I find from comparing their experiments, and computing the forces developed by the same charges 

 of powder with shot of different weights, that the forces are almost exactly as the cube roots of the shot. 

 Thus Button's experiments with balls of 1.21b. and 2.91b., velocities 973 and 749, give forces almost ex- 

 actly proportional to the cube roots of 1.2 and 2.9. Captain Mordecai's experiments with balls of 4.421b., 

 9.281b., and 211b., velocities 2,696, 2,150, and 1,520, all furnish, by computation, forces very nearly 

 proportional to the cube roots of the respective weights of the balls. Every one knows that a small 

 increase in the weight of the shot in a fowling-piece increases in a sensible degree the recoil and the 

 stress upon the gun. This is so universally received as true by ordnance officers, that it is a common 

 practice to use two or more balls, instead of an increased charge, in proving guns. 



