1918] on Internal Ballistics 307 



walls of the bore, but any loss from this cause is accounted for in the 

 factor of effect. 



Jf now we consider that some definite fraction of the charge has 

 been converted into gas, the gas expanding according to a definite law 



{v' - a.y = p I j = constant : 



as though no more of the charge would be burnt, but that the 

 proper amount of additional heat from the unburnt part of the 

 charge is imparted to the expanding gases— then a set of curves can 

 be drawn somewhat similar in character to those of Fig. 13 in 

 Clerk Maxwell's " Theory of Heat," 1897. Thus curve 1 may mean 

 that a fraction of 1/10 of the charge has been converted into gas ; 

 curve 2, 2/10 of the charge, and so on up to 10, when the whole 

 has been converted into gas. 



These curves are lines of equal combustion, but for shortness 

 may be called Isopyric Lines. The trace of each isopyric line shows 

 the expansion curve of the gas then generated, on the supposition 

 that the remainder of the gas remained unburnt. 



For each isopyric line, if the position of the shot in the gun is 

 known — that is to say, if the volume is known — then the pressure 

 can be at once determined, or if the pressure is known, the position 

 of the shot can be found. 



If it is assumed that after a fraction z of the charge has been 

 burnt no further combustion takes place, then the energy of the 

 expansion of the powder gas generated from this fraction z will 

 follow the usual adiabatic law. But since the rest of the charge 

 continues to burn, additional heat is imparted to the already generated 

 gases, so that the assumed expansion will not be strictly adiabatic, 

 but will follow some law intermediate between adiabatic and iso- 

 thermal expansion. 



For adiabatic expansion the power to which the volume function 

 must be raised is 1*41 for most gases, but according to actual 

 experiments on petrol engines, a better value for these engines is 

 1 • 23, while with the high pressure used in guns the usual value has 

 been taken at 1*2. For isothermal expansion the volume function 

 power is of course 1. AVe may consequently accept the relation 



P 



(^7= 



a constant where the power lies between 1 • 2 and 1 • 0. 



It has been found that the mean value 1 * 1 gives results closely 

 approximating to those obtained in actual practice. The constant k 

 depends on the resistance offered by the driving band on the shot 

 («) during the initial engraving and (h) during the subsequent 

 motion along the bore of the gun. 



