NATURAL PHILOSOPHY. 167 



9 



whole case; for they are made upon the supposition that the charge of 

 powder, in each instance, is as the square of the diameter of the shot, or that 

 the cartridges of the' 2 and 10 inch guns are of the same length. This, if we 

 take the charge of the small gun at of a pound, would give but 8^- pounds 

 for the large, or y 1 ^ of the weight of the shot. The velocity obtained from this 

 charge would produce neither range nor practical effect, and to obtain these 

 results, that is, 1,600 feet a second, we must either increase the force through 

 the whole length of the gun to 5 tunes that required for the small gun, or, 

 the force remaining the same, we must provide for its acting through 5 times 

 the space. Neither of these conditions can be practically accomplished. 

 However, by an increase of both the charge and the length of the bore, the 

 result may, in the limits under consideration, be attained. Thus, taking the 

 large bore, if we double its length and make the cartridge 5 tunes as long, 

 increasing the weight from 8^- to 41f pounds, or perhaps, having an advan- 

 tage from the comparative diminution of windage and the better preservation 

 of the heat, with a charge of from 30 to 35 pounds we may obtain the full 

 velocity of 1,600 feet a second. But this again increases enormously the 

 strain upon the gun. 



It does not appear obvious, at a first view, how an increase in the charge 

 should increase the tension of the fluid produced from it, if the cavity inclosing 

 it be proportionably enlarged. If a steam pipe a foot long will sustain the 

 pressure of a given quantity of steam, of a given temperature, a .pipe two feet 

 long, of the same thickness and diameter, will sustain the pressure produced 

 by a double weight of steam from the same boiler. Why then should the 

 pressure upon a cannon be increased by a double length of cartridge ? The 

 difference seems to be this : With the steam, the pressure is as in a closed 

 cavity ; with the powder, the tension depends upon the movement of the 

 shot while the fluid is forming. Now, whether the charge be large or small, 

 the motion of the shot commences while the pressure is the same in both 

 cases, and before the charge is fully burned, and with the same velocity in 

 both cases ; but with the large charge the fluid is formed faster than with the 

 small, while the enlargement of the cavity by the movement of the shot is 

 nearly the same in both cases. This destroys the proportion between the 

 sizes of the two cavities, and the tension must increase faster, and become 

 greater, from the larger charge. The law of this increase cannot, from the 

 complicated nature of the problem, be stated with any reliable exactness, but , 

 we may, I think, conclude, from the increased velocity of the shot, and many 

 other effects, that the stress thrown upon the gun by different charges of 

 powder, within ordinary limits, will not vary essentially from the square 

 roots of those charges. If then we increase, in the example under considera- 

 tion, from a charge of 8 pounds to one of 32 pounds, the stress upon the 

 gun, being as the square roots of these numbers, is raised from 2.88 to 5.65, 

 or from 1 to 1.96. Having already increased the stress upon the gun, by the 

 shot, from 1 to 1.71, if we multiply these together, we have a total increase 

 of from 1 to 3.35. That is to say, if, under the conditions here stated, we 

 load a gun of 2 inches calibre with 1 shot and 4 of a pound of powder, and 

 a gun of 10 inches calibre with 1 shot and 32 pounds of powder, the stress 



