THE EOYAL ARTILLERY INSTITUTION. 
349 
We have, then, 
/= % = a (WsmD-vf; 
dt 
Integrating, 
dt 
dv a (JF sin D — v ) 2 
* = !. „.b. + a 
a JF sin D — v 
But it is clear that 
when t — o then v = o, 
1 
<7 = 
aJF sin D’ 
t = ± . 
JF sin D — v aJF sin D 
Disentangling v , we have 
v—fFsinD — 
TF sin 7) __ds 
atJF sin D + 1 dt 
Integrating, we obtain 
S= IF sin Dt -log e ( atJF sin D + 1) + C' ; 
Oj 
and when t — o then 8 = o } 
and * *» C s= o ; 
and thus, substituting its value for a , we have 
Deviation in ft. = ^sin Dt - - -log, f 00232438 ^- - - 1 — + l) • 
•00232438^ 8 \ w ) 
In this formula, the first term of the right hand side of the equation 
gives the amount of distance travelled by the wind across the range at 
any given time t from the starting of the projectile ; and the second 
term gives the amount of space lagged behind by the shot at that time; 
the difference being, of course, the actual sideways travel of the shot. 
In the third series given in the table of practice, taking the wind 
at 3, as estimated, the formula would give the deviation due to this 
cause as 12*8 yds., reducing the observed deflection to 22 yds., against 
15 in the second series. It appears probable, as before mentioned, 
that the wind was really rather more than 3. 
I append a second table, showing the results obtained by applying 
this formula to the correction of practice for accuracy. The wind was 
evidently observed with great care by the officer conducting the 
practice, and its frequent shifts are, no doubt, faithfully registered. 
An inspection of the table clearly indicates, however, that to record 
accurately the force and direction of the wind during the actual flight 
of the shot, an efficient instrument is absolutely necessary. 
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