12 
and the angle A ' TA, represented by dv', is obtained from (8) so that 
dv 
A[x 
2 B cos 8 
1-1 
4 KB I 
A 2 p 2 tan8j 
*} 
dt. 
Since p is large, we need only retain the first terms in the expansion of 
the second term within the brackets, so that 
dv' = 
K 
Ap sin 8 
dt 
(19) 
Let 0 denote the angle OT makes with the horizontal plane and 
8'=A'T. 
From the triangle A ' TT’ , S' = 8 + dS ; hence dS is greater, the greater 
A' TT = 180—v— dv\ or the less dv '. 
From (19) we see dv' diminishes with the increase of the angular 
7 tV 
velocity p = —, or with the decrease of the pitch; and, therefore, 
Jtir) 
the angle 8 will increase. 
This last conclusion serves to confirm the remarks above regarding 
the influence of an excessive twist on the accuracy, when firing at high 
angles of elevation and with low velocities. 
September 9th, 1891. 
