7 
The angular velocities round the former are p, q, r ; and round the 
latter 
d8 d£ dv 
dt ’ dt ’ dt * 
Resolving the latter along x, y, z , then 
8£ . dv 
> ,= M + cosS dt 
<1 = 
dS 
dt 
r — — sin 8 
dv 
dt 
1 
( 13 ) 
If we suppose the projectile turning round 0 so transpose itself that 
8 remain constant, and q = 0, and, taking this into consideration, we 
obtain 
q' = —r sin £, r' =- r cos i. 
By differentiating these last two expressions, and combining with the 
last two in (12) we get two equations, which lead to following equation 
-Br^ + (B—A) rp = K 
which combined with the first and third of (13) lead to the equation 
dv 
Ap sin 8 -jj—B sin 8 cos 8 ( ) =K 
dv\ 2 
dt) 
identical with (7). 
The first equation of (12) showsj? is constant the whole time, i.e.,p=p 0 . 
V. 
If r] denote the pitch of rifling expressed in calibres from (11) we get 
7 TV 
P ° - • 
From (11) we see p will be greater, the greater 
K 
tan S’ 
. ( 14 ) 
we ought then, in 
K . 
(11) to substitute the greatest magnitude of -—- in order to determine rj. 
tan 8 
Assuming for ATthe expression (1) we find 
= h R p cos 2 S 
tan 8 r 
The maximum rotation will be at departure, when v = V and 8 = 0. 
Bearing this in mind, we get from (11) and (14) 
t rV 2 
r]R A s/ 
Bh Bp 
_ i 
A 3 7T* V 2 
B h IBp 
whence 
(15) 
