PRINCIPLES OP GUNNERY. 
248 
supposing the projectile to move in a straight line, unaffected by 
gravity; 
ds (1000) 3 to 
then dv ~ Kv 2 ' d 3 ’ 
or s 
_ w /’(1000 )*dv ^ 
~ 3» J IP ; . 1 J 
the limits of this integral being the velocities at the beginning and 
end of the distance, s> 
For velocities between 1100 f.s. and 1350 f.s., where the cubic law Approxi- 
holds, the coefficient K may be given a constant value for the same Stf 0 Vof 
form of projectile. Between these velocities for service ogival-headed ^toSty 18 
projectiles with regard 
K= 108-5. 
to range. 
When K is constant, equation (3) becomes 
_ w (1000) 3 rdv 
S ~J* K J 
which may be integrated thus : 
K d 2 
( 1000) 3 w 
10 
1 1 
V V * 
(1 1 \( 1000) 3 
\v r) ~ k ; 
(4) 
where V is the muzzle velocity, and v the remaining velocity, at a 
given distance, s, from the muzzle. 
Or, transposing, 
V 
d - 2 
(1000) 3 w 
Vs 
(5) 
which gives the remaining velocity at a given distance, s } from the 
muzzle» 
For velocities where the cubic law holds^ and the projectile moves 
approximately in a straight line, the remaining velocity at a given 
distance may be fairly accurately determined by this formula by sub¬ 
stituting the mean value of K given above. 
For example : suppose it were required to find the remaining velo¬ 
city of the 10-in. M.L. gun of 18 tons at 1000 ft.* 
V= 1364 f.s., - = -24, K= 108-5, and 4 = 1000. 
w 
These values substituted in equation (5) will give (w) the remaining 
velocity at 1000 ft. 
* Vide Tablej “Comparison of M.L; Guns,” p. 20. 
