Mr. Bashforth on the Resistance of the Air to Projectiles. 303 



(4) the numerical values of bl 2 , where 1=150 feet, the distance be- 

 tween the screens. And assuming that, for a given form of head, 

 the resistance of the air varies as the square of the diameter, the 

 mean values of 25 have been adopted for shot] weighing W lbs., and 

 having a diameter of d inches, or 2R feet. 



When a body is moving in a straight line under the action of a 

 force which varies as the cube of the velocity, it appears that the 

 actual velocity v r at the middle of any space 2s f is such that, if an- 

 other body moved over the same space 2s' with a uniform velocity v\ 

 it would describe it in the same time as the first-named body. For 

 the time t' would 



= ±2s' + b(2s') 2 , 



uniform velocity 



2s f 2s f 1 , 



l r 2s< + b(2s f ) 2 ±r+2bs' 



the actual velocity at the distance s f . 



M. Helie, in his 'Traite de Balistique' (1865), adopted, for elon- 

 gated projectiles, a law for the resistance of the air which varied as 

 the velocity cubed. The law was deduced from some experiments 

 made at Gavre, when a great number of velocities (V, v") of shot fired 

 with various charges were measured at two points x metres apart. 

 The mean values of v f and v ff were taken and substituted in the 



formula —rj-r- ; and it was found that this was approximately con- 



v"v'tf 

 stant, and consequently that the resistance varied as the (velocity) 3 . 

 The French measures and weights have been converted into English 

 measures for M. Helie's best experiment, in order to facilitate com- 

 parisons with my own experiments. The contents of M. Helie's work 

 were quite unknown to me for several months after my report on the 

 above experiments had been given in. For an ogival-headed shot 

 struck with a radius of two diameters M. Helie's value of 25 is 



26 = -000036?-! =-000000062^, 



w w 



while my experiments for the same form of head, but with much 

 higher velocities, give 



26=-000060^ =-000000104 ^. 



w w 



There is reason to expect that my value of b will require a small 

 reduction for the low velocities used in M. Helie's experiments ; but 

 it is extremely improbable that it can be reduced to M. Helie's value. 

 It will thus appear that M. Helie and I agree in adopting a law of 

 the resistance of the air, but that we have followed quite independent 

 methods in experimenting, and have arrived at different numerical 

 results. 



