VOL. LXXXVII.] PHILOSOPHICAL TRANSACTIONS. ] 65 



The agreement of the elasticities, computed from the theorem x 1 + o -°°°4* = y } 

 with the actual elasticities as they were measured in the experiments, may be seen 

 in the foregoing table; but this agreement may be seen in a much more striking 

 manner by a bare inspection of the figure before-mentioned; for the line ad in this 

 figure having been drawn from the computed elasticities, its general coincidence 

 with the line ac of the experiments, shows how nearly the computed and the actual 

 elasticities approach each other. And when the irregularities of the line ac, which 

 must be attributed to the unavoidable errors of the experiments, are corrected, these 

 2 curves will be found to coincide with much precision throughout a considerable 

 part of the range of the experiments; but towards the end of the set of experi- 

 ments, when the charges of powder were considerably increased, the elasticities 

 seem to have increased faster than, according to the assumed law, they ought to 

 have done. From this circumstance, and from the immense force the charge must 

 have exerted in the experiment, when the barrel was burst, I was led to suspect that 

 the elastic force of the fluid generated in the combustion of gunpowder, when its 

 density is great, is still much greater than these experiments seem to indicate; and 

 a further investigation of the subject served to confirm me in this opinion. 



It has been shown that the force exerted by the charge in the experiment in which 

 the barrel was burst could not have been less than the pressure of 54752 atmos- 

 pheres; but the greatest force of the generated elastic fluid, when, the powder 

 filling the space in which it is confined, its density is = 1000, on computing its 

 elasticity by the theorem x 1 + 0000 4* = y 3 turns out to be only equal to 29178 at- 

 mospheres. In this computation the mean of the results of all the experiments in 

 the foregoing set is taken as a standard to ascertain the value, expressed in atmos- 

 pheres of y, and it is y X 1.841 = 29 178. 



But if, instead of taking the mean of the whole set of experiments as a standard, 

 we select that experiment in which the force exerted by the powder appears to have 

 been the greatest, yet in this case even the initial force of fired gunpowder, com- 

 puted by the above rule, would be much too small. In the experiment N° 84, 

 when the charge consisted of 18 grains of powder, and the density or value of x 

 was 702, a weight equal to the pressure of 10977 atmospheres was raised. Here 

 the value ofy (= x l + °- 000 4*) is found to be (702 12808 ), = 4421.7; and to express 

 this value of y in atmospheres, and at the same time to accommodate it to the actual 

 result of the experiment, it must be multiplied by 2.4826; for it is 4421.7 (the 

 value of y expressed in equal parts) to 10.977 (its value in atmospheres, as shown 

 by the experiment), as 1 to 2.4826, and consequently 4421.7 X 2.4826= IO977. 



If now the value of y be computed on the same principles, when x is put = 

 1000, it will turn out to be y = l000 I + o - 4 = 15849; and this number expressed 

 in atmospheres, by multiplying it by 2.4826, gives the value of y = 39346 atmos- 

 pheres. This however falls still far short of 54752 atmospheres, the force the 

 powder was actually found to exert when the charge filled the space in which it was 

 confined. But in the 84th experiment, when 18 grains of powder were used, as 



