THE LAW OF BURNING OF MODIFIED CORDITK. 257 



Whilst admitting that Table D is merely an expedient, it otters the advantage of 

 la-ing quicker to work with, and the results are fairly consistent with the tubes as 

 supplied. 



5. Investiyrttiim of the Time Rise of Double Tubular M.D. Cordite. It will be 

 clear from a slight consideration that with the propellant in the cord form a 

 decreasing surface is exposed as combustion proceeda With the tube form an 

 approximately constant surface is exposed. If it were not for excess internal 

 pressure the surface would actually be constant. For if dr is the skin burnt 

 at any time, and R and r the external and internal radii, the original surface 

 is proportional to 2ir(R+r) ; so when a skin dr is burnt the surface is proportional to 



Without going deeply into the science of internal ballistics it will be apparent that 

 the longer maximum pressure can be sustained in the gun the greater will be the 

 efficiency of that gun for a given length as regards muzzle velocity. Of course, there 

 are limiting conditions as "regards the capability of the gun to withstand this 

 sustained maximum pressure, but such considerations are outside the scope of this 

 paper. Speaking generally, however, there may be advantages in sustaining the 

 maximum pressure in a gun. Now a double tubular form will present an increasing 

 surface as combustion proceeds, and this will tend to sustain the maximum pressure in 

 the gun. 



The time rise of pressure of a sample of a double tul>e is shown on fig. 7 (left- 

 hand curve). The dimensions of this double tul>e are given on the figure, the firm 

 lines showing the actual shape which in manufacture had not come out as true arcs of 

 circles. A mean circle was therefore determined for the purpose of calculation, and 

 the adjusted double tube is shown by the dotted lines. 



With the view of showing the results given by Table D, I have calculated the 

 time rise of the double tube, using that table. The calculated points are shown on 

 the figure. It will Ije seen that there is a very close agreement in the curves, except 

 at the beginning. The error at the beginning is, of course, due to the excess internal 

 pressure effect being greater with the double than with the single tube. 



The American powder is a multitubular one, that is, short cylinders pierced with a 

 number of holes. Excess internal pressure would have a very magnified effect on 

 such a powder, and this, I think, accounts for the wide difference in value of the 

 exponent of P as used by INUALLS. 



Conclusion. 



In the foregoing I ha,ve, after giving the reconciliation of my law for the cord form, 

 confined myself to the cases where it apparently fails. I have endeavoured to show 

 the cause of the failure and at the same time present the solution. I have not given 

 examples of time rises of the strip form, for with them there is no disturbing cause so 

 long as manufacture is not varied. 



VOL. CO VII. A. 2 L 



