244 MAJOR J. H. MANSELL: INVESTIGATION OP 



gone straight to the gun and endeavoured to solve the constants a and n in the 

 general form of the above equation by a system of trial and error.* Some have 

 concluded that n is unity, others that n is ^ (!NGALLS, America), (GossoT and 

 LIOUVILLE, France), 0'9 (CENTER VALL, Sweden), &c. These are wide variations, and, 

 as I shall show, are due in part to the form of the explosive that different investigators 

 have experimented with and in part to the following causes. 



The principle of calculation in the gun is that the space behind the projectile is 

 treated as a closed vessel. Now, as the projectile moves down the bore the size of 

 the vessel increases. The size of the vessel therefore directly depends on the distance 

 the projectile will move in a given time under a given pressure. Here at once is the 

 difficulty, and it entirely depends upon what friction or resistance to forward movement 

 is assumed as to what values of a and n may be determined. This friction is made 

 up of (l) the resistance to engraving of the driving band, (2) the resolved part of the 

 rotational thrust due to the lands of the rifling, and (3) perhaps forcement of the 

 projectile through the gun, which is possibly conical in form at any point where the 

 projectile may be during its passage down the bore. 



Now it is obvious that, however elaborate the theory, many large assumptions have 

 to be made in determining the combined effect of (1), (2), and (3), and on these 

 assumptions the whole resulting edifice must stand or fall. 



In my investigations I tried to avoid the pit-fall of the practical application to the 

 gun until I was entirely satisfied that I had determined the law of burning by parallel 

 surfaces in a closed vessel of constant capacity. This paper, then, is a description of 

 the methods I have used and the results I have arrived at in my investigations. A 

 considerable amount of laborious arithmetical calculation has been involved, and I 

 desire here to express my indebtedness to Captains A. K. IZAT and C. H. NEWCOMBE, 

 Royal Artillery, who have rendered me valuable assistance in preparing the diagrams 

 and in working out some of the calculations. 



Description of the Apparatus used. 



Fig. 1 shows a section of the type of closed vessel used. The pressure is registered 

 by the compression of the copper A by the piston B. This piston carries a pen C 

 which traces its movement on blackened paper carried on a revolving drum D (shown 

 in fig. 2). E is a valve for releasing the gases from the vessel after firing. F shows 

 the arrangements for electrically firing the charge. The internal capacity of the 

 vessel I used was 28 '18 cubic inches, and its internal length and diameter were nearly 

 equal. The type of vessel shown in fig. 1 is unsatisfactory, because its great length 

 as compared with its diameter is liable to set up wave actions. 



* GOSSOT and LIOUVILLE (tome XIII., ' Memorial des Potidres et Salpetres ') have recently compared 

 closed-vessel time rises with those calculated when using their factors. The results are not very satisfactory, 

 I think. 



