174 ELECTRIC-SPARK PHOTOGRAPHS. 



not a ripple is formed on tlie 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 sw^allow-tail pattern apiiears; 

 the angle between tlie two tails become 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 loug or very short waves 

 travel more quickly than waves of moderate dimensions. If they are 

 about two-thirds of an iuch loug 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 w^heu this speed is exceeded the swallow- 

 tail appears. Suppose, for exami^le, the velocity of the needle to be 

 double the minimum wave velocity for water, i. e., let the needle move 

 at 18 inches a second, and let it at any moment have arrived at the point 

 p, PI. V, fig. 1,~ then any disturbance, started when it was at the 

 point A, must have travelled as far as the circle a((a in which Aa is half 

 A^), similarly for iiiiy number of points BC, etc., between A and_2> any 

 disturbance must have travelled as far as the corresponding circles bb, 

 cc, etc., the result is that along a pair of lines, ^>L,pM, touching all the 

 circles tliat 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 A^f Bb, etc., will become in proportion to Ap less, the circles will 

 be smaller, and the angle between Lj? and Mp will become less, while 

 when the velocity is made less the reverse happens, until at last Aa 

 Bb, etc., = A^ Bp, etc., and then when they exceed these quantities no 

 lines hp Mp can be drawn touching all these circles, there is no wave 

 surface which the disturbances from all the successive points can con- 

 spire 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 can not travel at less 

 than a certain speed which is obviously the velocity of sound (1,100 

 feet a second, under ordinary circumstances), but as in the case of sur- 

 face waves on water, higher speeds are possible when the wave is oue 

 of very great intensity. The conditions in tlie two cases are therefore 

 very nearly i^arallel; if the bullet is travelling at less than the mini- 

 mum 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. Tliis 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 veloc- 

 ity of travel is greater and, immediately in front of the bullet, the air 

 is compressed to so great an extent 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 difiicult to 



