PROCEEDINGS OF THE POLYTECHNIC ASSOCIATION. 615 



the combustion of cannon powder is far from complete, even when the shot 

 leaves the muzzle. A medium sized cannon powder has grains three-tenths 

 of an inch in diameter, the largest sized from six to nine-tenths. Piobert 

 gives, as the conclusion arrived at after a very long und elaborate series of 

 experiments on the rapidity of combustion of powder in lumps, that the 

 combustion advances at the rate of half an inch per second; his conclu- 

 sion is, moreover, positive that neither heat nor pressure aflfect, to any sen- 

 sible degree, this rate. A grain of powder 0. in. 3 in diameter, would 

 therefore be nearly a third of a second in burning, while Rodman's experi- 

 ments prove that the shot of a 42-pounder, with ten pounds of powder, is 

 but little more than five thousandths of a second in the gun after the fire 

 takes the cartridge. We may, also, by a very simple process of calcula- 

 tion, show that Rodman's experimental determination cannot be far from 

 correct. The actually observed velocity with which a round shot leaves a 

 12-pounder gun of sixteen calibres length, when the charge is a quarter of 

 the weight of the shot, is 1635 feet; the length of the bore is six feet, which 

 is, therefore, about the space through which the pressure acts on the pro- 

 jectile; if this pressure were constant, it would expel the ball in the time 

 which it would take the ball to move twelve feet after leaving the gun — 

 that is to say, ^^^ Taiz = j-tq <^f ^ second nearly. But as the pi'essures near 

 the muzzle are very far below the mean, those near the breech must be 

 greatly above, or the time must be much less than this calculation gives. 

 Since, therefore, the powder is not by any means completely burned, not 

 even probably'' on supposition that Piobert's conclusions in regard to the 

 effect of heat and pressure on rapidity of combustion are erroneous, before 

 the elastic force of the developed gases ceases to act on the projectile, we 

 have reason to suppose, that if our determination of maximum theoretic 

 pressure is correct, the velocities computed by our formula will be much in 

 excess of those obtained in actual experiment. Again, all the circum- 

 stances of the actual experiment, of which the calculation takes no account, 

 are in favor of excess on the sioe of the calculation ; the weight of the 

 sabot, the envelopes of the gun, the resistance of the air, &c., all these par- 

 ticulars, if allowed for. would reduce the computed velocity. It is evident 

 that there is error somewhere, either in the determination of the volume of 

 gas, or in that of the heat developed, or in the assumption that the relation 

 of elasticity to volume is the same under all pressures. Wliat is known of 

 carbt)nic acid, however, under high condensation at ordinary or at low 

 temperature, does not encourage the belief that its elasticity can, under 

 any circumstances, increase more rapidly than in the inverse ratio of its 

 bulk (temperature remaining> constant, but makes it nearly certain that 

 any change which should occur in this respect would be in the opposite 

 direction. 



There is one particular in which it is probable that our formula ought to 

 be cori-ected. We have employed the thermodynamic index of the expand- 

 ing gases, 1.39, as determined by the Heidelberg experimenters and by 

 ourselves; in doing this we have disregarded the fact, that the fixed pro- 

 ducts of combustion which have originally the same high temperature as 

 the gaseous, are intimately mingled with the gases in a state of minute 

 division, that is in the form of smoke. A true thermodynamic index for 



