454 MB. B. HOPKINSON ON MEASURING THE PRESSURE PRODUCED IN THE 



cushion of air f inch thick is interposed some flow takes place.* In consequence of 

 this, the pressure wave which emerges and is propagated elastically cannot he quite the 

 same as the wave of applied pressure. It is easy to see that the general effect of the 

 setting up of the end must be to deaden the hlow, that is to reduce the maximum 

 pressure and prolong its duration. In fig. 14, A is the (conjectural) curve representing 



Fig.14. 



Time io' 5 sees. 



the pressure applied to the end of the rod. If the rod were perfectly elastic, the. 

 pressure across a section 2 inches from the end would be represented on the same time 

 base by the curve B, which is the same as A, but moved 10~ 5 seconds to the right. 

 The momentum in the end 2 inches at any time is the difference between the areas of 

 the curves up to that time. For instance at 2 x 10~ 5 seconds it is represented by the 

 shaded area under curve A. But if the end be not completely elastic, the higher 

 pressures developed over section B will be less than those acting on the end at 

 corresponding times. Thus the record of pressure over the section 2 inches from the 

 end will be a curve such as B' and the momentum in the end two inches at any time 

 will be greater than it would be if the end were elastic by the difference between the 

 areas of curves B and B' which is double shaded in the figure. This extra momentum 

 is transferred to the remainder of the rod later on, causing the curve B' to rise above 

 B. The curve B' represents the wave of pressure actually sent along the rod. It is 

 this curve which is determined by the method which has been described, and it is 

 evident that that method under-estimates the maximum pressure and over-estimates 

 the duration of the blow. 



A few experiments were made with the gun-cotton touching the end of the shaft. 

 The average total momentum given to the shaft and piece in this case is about 

 90 units or roughly twice as great as that transmitted through f-inch air-space. Of 

 this total about 80 per cent, is caught in a piece 4 inches long, and about 50 per cent, 

 in a piece 1 inch long. When the gun-cotton is at a distance of f-inch these figures 

 are 90 and 60 respectively. The apparent duration of the pressure is therefore 

 rather greater at the surface of the explosive. The setting up of the end of the 

 shaft is, however, much more marked when the gun-cotton is in contact and it may 



h This is when the steel is in the form of a shaft, so that there is no lateral support of the part 

 subjected to pressure. It is, of course, possible to make a plate with hardened face which will withstand 

 the attack of gun-cotton on a portion of the face. 



