1918] on Internal Ballistics 305 



Noble aud Abel's formula Ijecomes a much more convenient 

 expression by introducing the volume notation instead of that of 

 densitv, viz. : — 



R 



p = . 



V — a 



With the old black powder a was supposed to represent the 

 volume of the solid part of the charge which always remained in the 

 vessel, and so reduced its capacity, after the powder had been 

 exploded. The space occupied by this solid mass was 57 per cent 

 of the volume of the original powder. 



Clausius and Van cle Waals, experimenting on air and other 

 gases at pressures and temperatures far below those obtained by Sir 

 Andrew Xoble, arrived at more complicated formulas, but involving 

 very similar constants to those of the Noble and Abel formula. 



AVith colloidal smokeless powders, such as cordite when fired in 

 closed vessels, the a term still makes itsappearance, although there is 

 no solid residue after the explosion. 



Now, the unit of volume we have dealt with up to the present is 

 that due to the whole charge, but as the powder burns gradually it is 

 evident that the unit of volume will vary as the charge is consumed. 

 If we put v', the varying unit of volume, as that due to any fraction z 

 of the charge which has been burnt, then if 8 is the density of the 

 solid powder compared with water, i.e. 1 • 58, we have for the actual 

 available space, the capacity of the vessel less the content in cubic 

 inches of the unburnt powder, viz. : — 



0-27-73(1-2)^' 

 o 



C - 27-73 (1 - 0) ^ 



so that v' = — 



if we write ^ = '^ 



27*73 z IV 



. . . , 1 , V - a 



It IS lound that v - a = 



z 



where v is the gravimetric volume, supposing the whole charge had 

 been - converted into gas, and a is a constant commonly called the 

 CO- volume. This constant may be described generally as proportional 

 to the space occupied by unit-volume of gas if compressed by infinite 

 pressure. 



This formula is true both for the closed vessel of constant 

 capacity and for the gun with which the capacity varies according to 

 the travel of the shot in the bore. 



