420 



NATURE 



[March 2, 1893 



But now that we are dealing with a higher speed, namely, 

 1295 feet a second, there is evidence of the movement of 

 the bullet in the form of a wave of compressed air in front 

 and of other waves at the side of and behind the bullet. 

 I shall explain this in a moment, but I would rather 

 first show another photograph, Fig. 7, of a bullet travel- 

 ling at a still higher speed, a magazine rifle bullet 

 travelling about 2000 feet a second, in which these air 

 waves are still more conspicuous, and in which a glance 

 is sufficient to make it evident that the waves are much 

 more inclined to the vertical than in the previous case. 



Now as it may not be evident why these waves of air 

 are formed, why their inclination varies with the speed, 

 or why existing they are visible at all, a short explanation 

 may not be out of place, more especially as they form the 

 most interesting feature in the remaining photographs 

 that I have to exhibit, which cannot, as a matter of fact, 

 be properly interpreted without frequent reference to 

 them. 



' I would first ask you to examine some still water into 

 which a needle held vertically is allowed to dip. If you 

 move the needle very slowly not a ripple is formed on 

 the surface of the water ; but as the needle is moved 

 more quickly at first a speed is reached at which feeble 

 waves appear, and then as the speed increases a swallow- 

 tail pattern appears, the angle between the two tails be- 

 come less as the velocity gets higher. Now in the case 

 • of water-waves the velocity with which they travel 

 depends on the distance between one and the next, and 

 for a reason into which I must not now enter either very 

 long or very short waves travel more quickly than waves 

 of moderate dimensions. If they are about two-thirds of 

 an inch long they travel most slowly — about 9 inches a 

 second. Now so long as the needle is travelling less 

 quickly than this no disturbance is made ; but when this 

 speed is exceeded the swallow-tail appears. Suppose, for 

 example, the velocity of the needle to be double the mini- 

 mum wave velocity for water, i.e. let the needle move at 1 8 

 inches a second, and let it at any moment have arrived 

 at the point p, Fig. 8. Then any disturbance, started 



will be smaller, and the angle between 'Lp and M^ will be- 

 come less, while when the velocity is made less the reverse 

 happens, until at last \a V>b, &c. = hp Bp, &c., and then 

 when they exceed these quantities no lines Lp Mp can 

 be drawn touching all these circles, there is no wave 

 surface which the disturbances from all the successive 

 points can conspire to produce, and the consequence is 

 there is still water. 



Now consider the case of a bullet moving through the 

 air. Here again we are dealing with a case in which a 

 wave cannot travel at less than a certain speed which is 

 obviously the velocity of sound (l 100 feet a second under 

 ordinary circumstances), but, as in the case of surface 

 waves on water, higher speeds are possible when the wave 

 is one of very great intensity. The conditions in the two 

 cases are therefore very nearly parallel ; if the bullet is 

 travelling at less than the minimum speed no waves 

 should be formed — the pistol bullet at 750 feet a second 

 did not show any — if the bullet is travelling at higher speeds 

 than 1 100 feet a second waves should be formed which 

 should include a sharper angle as the speed is made to 

 increase. This was found to be so in the case of the 

 Martini-Henry and the magazine rifle bullet. 



The curved form of the wave near the apex is due to the 

 fact that when it is very intense, when the compression is 

 very great, the velocity of travel isgreater and, immediately 

 in front of the bullet, the air is compressed to so great an 

 exent that the wave at this part can travel at the speed of 

 the bullet itself. 



The reason why the waves should be visible at all is 



not difficult to follow. Consider a shell of compressed 



i air though which rays of light from a point are made to 



j traverse. These rays travel in straight lines, except where 



, they meet a medium of different density, and the denser 



! this is and the more nearly they meet this at a grazing 



j incidence the more they will be bent towards the perpendi- 



' cular. In comparison with water or glass a layer of com- 



i pressed air has very little refractive power, and so rays 



which strike the shell anywhere except at the extreme 



edge are practically uninfluenced in their course and 



strike the plate practically in the same place that they 



would do if the shell of compressed air had not been 



when it was at the point A, must have travelled as far as 

 the circle aaa in which Aa is half Ap, similarly for any 

 number of points BC, &c., between A and p any dis- 

 turbance must have travelled as far as the corresponding 

 circles 6l>, cc, &c., the result is that along a pair of lines, 

 pL, PM, touching all the circles that could be drawn in 

 this way, a wave will be found, and it is clear that as the 

 velocity of the point is made greater the successive radii 

 Aa Bd, &c., will become in proportion to A/ less, the circles 



NO. I218, VOL. 47] 



Fig. 9. 



traversed. But those rays ab,ab, Fig. 9, which strike the 

 shell of air almost tangentially are bent inwards slightly at 

 b and again at c, having traversed what is equivalent to a 

 wide angle prism, and strike the plate at e, leaving the place 

 ^, where they would have gone had they not been refracted, 

 dark ; moreover at e they meet other rays which have been 

 hardly at all refracted since they have passed actually 

 into the shell and out again, and therefore e is doubly 

 illuminated. The consequence is that a wave or shell of 



