126 CAPTAIN NOBLE AND ME. E. A. ABEL ON FIEED GUNPOWDER. 
of heat, we are able, from equation (15), to deduce the law connecting the tension and 
the pressure. For if we call v' and v' 0 the volume at any instant and the initial volume 
of the permanent gases, we have from (15) 
P=l>o(^) Cv > ( 17 ) 
but if a he the ratio which the volume of the non-gaseous products at the moment 
of explosion bears to that of the unexploded powder, we have 
v' 0 =v 0 (l — cc), v'=v—ctv 0 , (18) 
and equation (17) becomes 
and this is the relation between and v on Bunsen and Schischkoff’s hypothesis. 
Taking, as before, j9 0 =4T477, w 0 =l, and remembering that we have found the value 
of a to be '6, we have 
J»=«-477(^)^ (20) 
Q 
The value of the exponent ^ can be deduced from the data given in Table XYI. 
Table XYI. — Showing the percentage weights, specific heats at constant volume, and 
the specific heats at constant pressure of the permanent gases produced by the 
explosion of powder. 
Nature of gas. 
Percentage weight 
of gas. 
Specific heat at 
constant pressure. 
Specific heat at 
constant volume. 
Sulphuretted hydrogen 
•0262 
•2432 
•1840 
Carbonic oxide 
•1036 
•2450 
•1736 
Carbonic anhydride 
•6089 
•2169 . 
•1720 
Marsh-gas 
•0012 
•5929 
•4680 
Hydrogen 
•0023 
3-4090 
2*4110 
Nitrogen 
•2579 
•2438 
•1727 
From the data in this Table the value of C p is found to be= , 23528, of C 0 =T782, 
and that of the fraction ^=T3203; and equation (20) becomes 
( •A \ 1-3203 
^=i) ( 21 ) 
The results of (16) and (21) are given in Table XVII. ; and in the same Table are 
given the values of j?, both as deduced from actual experiment in the bore of the 10-inch 
and 11-inch guns (see Plate 22), and also as deduced from our experiments in a close 
vessel. The results of the experiments upon the tension of different densities in a close 
vessel represent of course the elastic force which would exist were the gas allowed to 
expand in a vessel impervious to heat, without production of work. 
