Vol. 6, 1920 PHYSICS: THOMPSON, HICKMAN, RIFFOLT 
173 
analysis of these curves, the velocity-time and pressure- space curves, 
as well as data regarding the resistance of the barrel, are all available. 
An extensive application of this procedure is to be made in a determina- 
tion of the resistance of air at various densities, to the flight through it of 
bodies moving with relatively high velocities. Heretofore, measurements 
have been made out-of-doors, shooting over a comparatively long range 
in order to get the desired accuracy. By making use of this velocity ap- 
paratus we are able to make two determinations in a length which is to 
be obtained in a building of laboratory size. The resistance is measured 
by the work which is done in the passage of the projectile from one point 
to another through the medium. This will require the two determinations 
of the velocity for the change in kinetic energy. It is necessary that the 
velocity be found with a precision which is sufficient to give the difference 
in the squares of the velocities with an acceptably small error. For a 
Government thirty caliber (Vso lb.) projectile the resistance of the air 
at normal pressure is such that the velocity will decrease an amount of 
the order of 225 feet per second in travelling 300 feet from the muzzle. 
At densities greater than normal the decrease will, of course, be greater 
and at pressures less than normal (which will be obtained as described be- 
low) the decrease will be less than this. 
Rds _ 
Si - S2 2< 
is the mean value of the retardation over the distance of observation 
(100-200 feet). 
An approximate idea of the effect upon the final value of the resistance 
of an error in the measurement of the velocity of one part in ten thousand 
is obtained by an examination of the above expression. 
8R ^ 2v6v _^ 2vodVo _^ ^ 4 X 2500 X V4 _^ . . approximately, 
R ~ Vo^ ~ Vo^ "' 650000 or about 0.4%. 
Here Av = 125; Vo = 2650; v = 2525; dv = 8vo = ^U- At higher pres- 
sures the error will be still less and at pressures down to one-half normal 
the substitution in this expression shows that the error for a single observa- 
tion will still be below 1%. 
Inasmuch as the ratio of the resistance of the medium to the weight 
of the projectile decreases as the diameter increases and in direct pro- 
portion, the precision which would be expected with large projectiles 
would be correspondingly less. Nevertheless, by increasing the distance 
of observation the same order of accuracy would be possible with pro- 
jectiles up to perhaps 3 inches in diameter. If the firing is done in 
a tube of from i to 3 hundred feet in length, having a diameter suffi- 
cient to make observation possible without great inconvenience, the air 
pressure in this tube being controlled by a pump, the observations of the 
