512 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



described but in which they have full confidence, the specific gravity at 

 the temperature of combustion is ascertained to be 1.5. The temperature 

 of combustion itself was determined by very careful experiment. The 

 details of the method pursued are interesting, but it is unnecessary to pre- 

 sent them here. It was found that the heat developed by burning a given 

 weight of powder would be sufficient to raise the temperature, of an equal 

 weight of water 619''. 5 C. The specific heat of the mixed products of 

 combustion, was found at constant pressure and at constant volume, by 

 multiplying the specific heat of each ingredient by the amount per cent, of 

 it present, and taking the sum of the products. The elevation of temper- 

 ature produced by the combustion, on supposition of no enlargement of 

 the space occupied by the powder, is then obviously found by dividing 

 619o. 5 C, by the specific heat at constant volume This specific heat being 

 0*18547, the elevation of temperature is equal to 3,340° 0. 



The specific heat at constant pressure is at the same time 0'20698. la 

 order to obtain the thermo-dynamic index of the gaseous portions of the 

 mixture, the sum of the products formed as just described by the several 

 capacities at constant pressure of those portions, must be divided by the 

 sum of the products similarly formed, by the capacities at constant volume; 

 These sums are respectively 0-07612 and 005520. Their quotient is 1-39, 

 which is the value of the thermo-dynamic index. 



/ In order to find the original bulk of the gases, or the magnitude of the 

 space within which they are compressed if liberated without expansion, we 

 consider that the bulk of the powder before combustion will be expressed 

 in cubic centimetres by Wp; a cubic centimetre of pure water at maxi- 



mum density weighing one grame, and Wp being expressed in grames. 

 In like manner if Wr be the weight of the fixed residuum, expressed in 

 grammes, the bulk of the residuum will be Wr. The space occupied by 



Sr. 

 tlie gases will therefore bej^p— Wr=0-50872 c. c. As at 0' C and 0mm 



Sp Sr 

 .760 of pressure, the same gases occupy 193-1 c. c. per gramme weight of 

 powder, the elastic force due to difference of volume only would be exr 

 pressed by 



193- 1 Wp = (if Wp = 1 gramme) 1931 = 193-] == 379-58. 



Wp Wr 1 06806 .50872" 



SpT bT 1039" 1-5 



Thus, the pressures in atmospheres would be 379.58 if there were no 

 elevation of temperature produced by the combustion. 



The original bulk of one gramme of powder being ^^3-^=96246 c. c, 

 and the space originally filled by the gases being 0.50872 c. c, the rela- 

 tive original bulk of gas and powder will be :m^|==0. 52856, which is 

 therefore the numerical value of a, in the foregoing formula, when 1 is 

 unity. 



The volume of the gases having been reduced to zero of temperature, 

 the effect of an elevation by combustion of 3340° C, may be computed by 



