l68 PHILOSOPHICAL TRANSACTIONS. [ANNO 1797. 



to be as the densities, as Mr. Robins supposes them to be, the initial force of this 

 generated elastic fluid must be at least 20 times greater than Mr. Robins deter- 

 mined it ; for , 4 6 8 o ? tne density of the elastic fluid in the experiments in question, 

 is to 1, its density when the powder quite fills the space in which it is confined, as 

 Q43 1 atmospheres, the measure of its elastic force in the experiments in question, 

 to 20108 atmospheres ; which, according to Mr. Robins's theory respecting the 

 ratio of the elasticities to the densities, would be the measure of its initial force. 

 But all my experiments tend uniformly to prove, that the elasticities increase faster 

 than in the simple ratio of the corresponding densities ; consequently the initial 

 force of the generated elastic fluid must necessarily be greater than the pressure of 

 201 OS atmospheres. In one of my experiments which I have often had occasion to 

 mention, the force actually exerted by the fluid must have been at least equal to 

 the pressure of 54752 atmospheres. The other experiments ought no doubt to 

 show, at least, that it is possible that such an enormous force may have been exerted 

 by the charge made use of; and this I think they actually indicate. 



In the first set of experiments, which were made when the weather was cold, 

 though the results of them uniformly showed the force of the powder to be much 

 less than it appeared to be in all the subsequent experiments, made with greater 

 charges, and in warm weather, yet they all show that the ratio of the elasticity of 

 the generated fluid to its density is very different from that which Mr. Robins's 

 theory supposes }* and that this ratio increases as the density of the fluid is in- 

 creased. Supposing, what on many accounts appears to be extremely probable, 

 that this ratio increases uniformly, or with an equable celerity, while the density is 

 uniformly augmented ; and supposing further, that the velocity and limit of its in- 

 crease have been rightly determined from the result of the set of experiments, 

 table 1 , which were made with that view ; then, from the result of the experiments 

 of which we have just been giving an account, in which 12 grs. of powder exerted a 

 force equal to 9431 atmospheres, taking these experiments as a standard, we can, 

 with the help of the theorem a»i +0.0004* = y, deduced from the former set of ex- 

 periments, compute the initial force of fired gunpowder, thus : 



The density of the elastic fluid, when 12 grs. of powder are used for the charge, 

 being = 468, it is 468 Il8 7 2 = y = 1479.5 ; and in order that this value of y may 

 correspond with the result of the experiment, and be expressed in atmospheres, it 

 must be multiplied by a certain co-efficient, which will be found by dividing the 

 value of y expressed in atmospheres, as shown by the experiment, by the number 



* Though this circumstance, of the ratio of the elasticity to the density of the fluid, be here mentioned 

 as if it related to the same thing in the 2 cases, they are yet however quite different : in these experi- 

 ments it means the ratio of the charge of powder, or quantity of generated fluid in the same space, to its 

 strength or elasticity ; but in Mr. Robins it means also that the elasticity of the same quantity of fluid, 

 when it occupies different spaces, as when following and impelling a ball along the barrel of a gun, is in 

 the ratio of the decreasing densities, or inversely as those spaces. Besides, this property, in both these 

 respects, is not merely a matter of supposition in Mr. Robins's theory, but the consequence of experi- 

 mental proof, both by himself and other eminent members of the a. s. 



