'258 MAJOR J. H. MANSELL: INVESTIGATION OF 



Undoubtedly it would be a great convenience in working if the integration of these 

 curves were possible. Much thought has been given by different investigators in the 

 past to this problem and much mathematical ingenuity has been displayed. But in 

 these problems one does not obtain expressions which are directly integrable, and 

 assumptions and approximations have necessarily to be made. Such approximations 

 give exceedingly good results within limits, but when one comes to their application 

 to the gun, and its many variables, the limits are so widened that a break-down under 

 certain conditions is an ever-present danger. 



I have, therefore, preferred to follow the system adopted by Mr. BASHFORTH in his 

 calculations of extended trajectories, that is to say, I break up my time-rise curves 

 into small arcs, and, assuming a mean pressure for the interval, find from the 

 calculated end pressure if my assumption has been correct. If not, I have now a 

 guide to the mean pressure to assume, and so on. In this manner each arc can 

 generally be calculated in three trials, and with practice many arcs are obtained at 

 the first attempt. 



The application of this law to the practical case of the gun is outside the scope of 

 this paper, and it is obviously undesirable to publish such investigations in connection 

 with English ordnance. 



For reasons which I have alluded to, the application to the gun presented more 

 complications than the experiments which I have here outlined. 



Having adopted certain frictional laws for the gun, based on the law of burning 

 which I now put forward, I have found that the application holds over a very wide 

 range of varying conditions of loading and calibre, when using cords which is the 

 form with which we have most experience. There can be no higher test than this of 

 the fundamental truth of the law. 



