Motion of a Spinning Projectile. 333 



velocity than to the cube, except over a range of velocities 

 between 900 and 1200 feet per second. Denoting resistance 



by R and velocity by V, it is found, on plotting ^ against 



V, that the curve is very nearly a horizontal line for veloci- 

 ties below 800 feet per second, then it rises rapidly till 



V = 1300 feet per second, after which it is nearly horizontal 

 again as far as observations go. Thus R is nearly propor- 

 tional to V 2 when V is below 800 feet per second, and again 

 when V is greater than 1300 feet per second. The steepest 

 part of the curve is somewhere near the point where 



V = 1080, which, it should be observed, is about the velocity 

 of sound. It is reasonable that there should be a change in 

 the law of resistance at the velocity of sound, for, when the 

 velocity of the projectile is less than that of sound, the 

 particles of air encountered by it at any instant had already 

 been set in motion, before the projectile arrived, by the 

 pressure which was transmitted ahead of it, this pressure 

 being transmitted with the velocity of sound. But when the 

 projectile is travelling with a velocity greater than that of 

 sound no pressure waves are transmitted ahead, so that the 

 projectile meets, and has to set in motion, stationary air 

 particles. 



3. This change in the behaviour of the air is shown in 

 photographs of flying bullets. When the bullet is travelling 

 faster than sound, there is a great density of air round the 

 nose and, as the bullet travels, this leaves behind it a single 

 wave of compression consisting of a pair of straight lines 

 equally inclined to the direction of motion, and joined to- 

 gether by a curve surrounding the nose of the bullet. When 

 the velocity is less than that of sound no such compression wave 

 is seen ; but in this case also there must certainly be high 

 density at the nose, which, however, will not be so great as 

 in the other case, and, moreover, it will decrease gradually 

 from the nose outwards, which will explain why photographs 

 do not show it. The essential difference between the two 

 cases is that, in the first case, the air is at rest at normal 

 pressure a very short distance in front of the nose, while in 

 the second case the air has a pressure which gradually 

 decreases from the nose forward, and all this air under extra 

 pressure has a forward motion. 



4. Bashforth also states that his observations show that 

 the resistance of the air is exactly proportional to the area 

 which the shot presents to the air in its motion. This means 

 that the resistance to elongated shot, which travel nose fore- 

 most, is proportional to the square of the diameter of the shot. 



PHI. Mag. S. 6. Vol. 34. No. 202. Oct. 1917. 2 A 



