166 ANNUAL OF SCIENTIFIC DISCOVERY. 



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iron cannon the strength of which was known to me, leads me to believe that 

 he has not over-estimated its power, although I am aware that it is generally 

 considered as excessive. If, following an opposite course to that herein 

 described, the powder be at liberty to expand upon any side the force thrown 

 in the other directions is very small. Thus, if a charge be placed loose in a 

 gun, without shot or wad, the force upon the walls of the gun is very trifling ; 

 no more than is produced by the restraint of the inertia of the charge itself, or 

 the fluid formed from it. If we would divest a charge of this property of 

 inertia, and fire it in a constantly maintained vacuum, it would not rend walls 

 made of cartridge paper, if a single end were left open for its escape. From 

 the preceding statement it will be seen that gunpowder will take any force, 

 from perhaps 50,000 atmospheres, when confined to a close cavity, down to 

 zero, if it be deprived of inertia and fired in a vacuum constantly maintained. 

 In artillery practice, the restraining power which causes the powder to act 

 against the walls of the cannon, is derived principally from the inertia of the 

 shot. This is so much greater than the inertia of the powder itself, that the 

 latter may be neglected in the considerations that are to follow. Now, 

 bearing in mind what has been already said, let us compare the difference of 

 the force of powder as exerted upon a small and large gun respectively. It 

 is perfectly well known, that, if we have a pipe or hollow cylinder of say 

 two inches in diameter, with walls an inch thick, and if this cylinder will bear 

 a pressure from within of 1,000 pounds per inch, another cylinder, of the same 

 material, of ten niches in diameter, will bear the same number of pounds to 

 the inch if we increase the walls in the same proportion, or make them five 

 inches thick. A cross-section of these cylinders will present an area pro- 

 portional to the squares of their diameters, and if the pressure be produced 

 by the weight of plungers or pistons, as in the hydrostatic press, the weight 

 required in the pistons will be as the squares of the diameters, or as 

 4 to 100. 



Now carry this to two cannon of different calibres, and take an extreme 

 case. Suppose the calibre of one to be 2 inches irf diameter and the other 

 10 inches, and that the sides of each gun equal, in thickness, the diameter of 

 its calibre. Then to develope 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 calibres, 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, will 

 weigh 1 pound and 125 pounds respectively ; the weights being as the cubes 

 of the calibres. 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 rates of ball is in a ratio as high as that 

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

 before us, an increase 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 foregoing statement and comparison, however, do not present the 



