11 
at angles of elevation 43^° and 60°, the dispersion of 2 5 cals, 
projectiles was very little different, when the weather was favourable. 
However, an excessive rapid twist might diminish the accuracy in 
vertical fire, and with low velocities from the following causes :— 
With the increase of angular velocity increases also the angle S (the 
other data being the same) between the axis of figure and the tangent 
which increases the air resistance, and this may influence, prejudicially, 
the accuracy. For example, from two 3*4-" mortars, with twists 15 cals, 
and 5 cals, and 2*6 cal. projectiles, the accuracy was the worst from the 
latter/' 
In order to show upon what data the changes of Sf depend, we will 
imagine a sphere described with a radius equal to unity, the centre 
being 0 (Fig. 5). 
Let OT represent up to the time t from the commencement of 
motion the direction of the tangent to the trajectory ; draw through OT 
the vertical plane of fire which, on the surface of the sphere, is 
represented by the arc NTn. 
Let the straight line OA represent, up to the time t, the direction 
of the axis of figure. 
The angle v between the vertical plane NTn, and the plane passing 
through OT and OA will be measured by the angle NT A, and 3 by the 
arc AT. 
At the following moment let the axis of figure transfer itself to OA', 
and the tangent will take up the position OT in the vertical plane of 
fire. 
When the projectile has the proper amount of rotation imparted to it, 
we may assume that the angle AT=§ will not change during the 
rotation of the plane AOT round the fixed axis OT, from this A' T=8 
* Impressions of grooves on driving bands were correct. 
t The author adds, “here we have in view only the case, when S increases slowly 
in the whole extent of trajectory.” (N. Majevski “ Traite de Balistique,” p.p. 201-206). 
