COAST. I ARTILLERY JOURNAL, - Air Defense Artillery

UNIVERSAL MEASURING CAMERA 433
with cas 8 and unite the other members, and (noting that Cas (180a)
= -cos a) we have:
2 sin {3 sin g cas 8=
2 sin {3 cas {3 sin g cas g cas a - sin 2 {3 + sin 2 {3 cos 2 g -
sin 2 g + sin 2 g cos 2 {3=
2 sin {3 cos {3 sin g cas g cas a-sin 2 {3 (1- cos 2 g)sin:!g
(1- cos 2 (3) =
2 sin {3 cos {3 sin g cos g cas a -2 sin 2 {3 sin 2 g
Dividing through by 2 sin f3 sin g, we have, as concluding formula for
computation of the auxiliary angle 8:
cos 8= cos a COS {3 cos g - sin {3 sin g (3)
The computation of the pictured trajectory path is now made by
using the above computed auxiliary angle 8, likewise the known sighting
angle of the camera = e, and the measured distance GP = B for:
m = sin e.Bjsin (180 - e - 8) (4)
Equation (4,) makes possible the computation of all values of m
but in actual practice one can utilize values of m only within definite
determined limits. As soon as m with velocities down to 500 meterseconds
exceeds 100 meters, the assumption that the pictured trajectory
distances or paths are straight lines no longer holds. Furthermore,
the possibility of photographing the projectile in this trajectory is
dependent upon and determined by the size of the projectile. From
these considerations we have, as the outer limit for photographic mtlasurement
of a trajectory interval velocity, a distance of 350 caliber
lengths, in round numbers, in which 100 meters obtains as the outer
limit. Since the trajectory, especially when firing at high angles of
elevation, can generally not be indicated on the terrain, it is also impossible
to point the instrument on the path of the projectile with the
aid of the focusing glass alone. One must rather calculate the inclination
of the objective and set the object glass accordingly. One then
revolves the ground glass plate of the instr!1ment until the muzzle of
the gun appears on a fixed mark on the plate.
The inclination of the object lens r. is determined by the triangle
GFP. (Fig. 1.1.
In this we haw:
OF = OH + HF = OG.sin {3 + GI = OG. sin {3 + B. sin g
OP = B. sin ()! sin (r), wherein: (r) =
180- 8+ e
OG= B. sin ~,sin "', consequently:
OF = B. sin e. sin {3, sin (r) + B sin g
Sin r.= OF .OP
Sin r. = sin je sin {3 ~ s~ng sin (r) (5)
sm ()