DERIVATION, OR DRIFT, OP ELONGATED PROJECTILES. 
127 
For resolving horizontally and normally, 
d\b . 
» “77 = —9 cos xfs; 
and dividing one equation by the other, 
d\fr __ ( w (1000)3 
du ~ (J <P Kv* 
In ordinary flat trajectories we may replace u by v , and then 
/^(IQOO) 3 dv 
w n a Vd IT*? 4 
JC 2 TT 
a 180 
(D v — Df). 
( 1 ) 
This integral has been calculated by Mr. Niven for velocities from 
900 to 1700 f.s., and is given on p. 78 of Major Bladen's “ Principles 
of Gunnery," and he is at present engaged in extending the range 
of velocities from 400 to 2500, using the values of K lately determined 
by Mr. Bashforth from the experiments carried out in 1878 and 1879. 
( cc Report on Experiments-made with the Bashforth Chronograph, &c.," 
Part II.) 
But it is more usual to assume that the angular velocity r dies away 
very slowly, so that we may suppose it constant, and equal to the value 
ttV 
it has at the muzzle—namely, — ; and then 
dz _ _ 
dt n a v dt* 
dz_ — _ Z v — ( 1QQQ ) 3 
du n a d d^ Kv 5 ’ 
and 
e? 2 7T lc 2 TZ P 
— z= - Vg S 
w n a J v 
' v (lOOO) 3 ^ 
so that we shall require the integral / 
to calculate the drift. 
Kv h 
F (1000) 3 
Kv 5 
(3) 
dv to be tabulated 
w 
The drift is proportional to-^, which varies very nearly as the 
fa . d . 
calibre, and also to — , which also varies as the calibre for similar pro- 
Cb 
jectiles; so that the drift varies as the square of the calibre for 
the same initial and final velocity. This explains why the drift is 
insensible in small-arms. 
The preceding explanation is substantially the same as that given 
by Prof. Magnus, except that the consideration of the centre of effort is 
not necessary. 15 
