COAST. I ARTILLERY JOURNAL, - Air Defense Artillery

432 THE COAST ARTILLERY JOURNAL
is provided with the Universal Measuring Camera after the manner of
the theodolite.
Figure 1 will serve to explain the method of computing the trajectory
path s passed over by the projectile from the muzzle of the
gun to the limit taken in by the sighting field of the instrument.
Let: G = Gun muzzle = initial point of the distance measured
M = Terminal point of measured distance m
P = Position of camera
PG = Measured distance between camera and gun muzzle
HGM = Angle of elevation of gun = f3
GPI = Terrain angle between camera and gun muzzle = y
FIP = Angle between muzzle-camera line and firing
direction = a
GPM = Sight angle of the camera = e
OPF = Inclination of the optical axis = 7r
MGP = Auxiliary angle in.the triangle GPM = 8
GOP = Auxiliary angle in the triangle GOP = w
The pictured length of trajectory GM is computed by using the
auxiliary angle 8. In order that the assumption upon which the measurements
are based may actually obtain and the optical axis of the
camera may intersect the trajectory at the point 0, it is necessary to
compute also the angle 7r and to incline the object glass through this
angle.
The computation of the auxiliary angle 8 is most easily made by
using the adjoining pyramid APIG. In the four triangles of this
pyramid, let:
AP=A GP=B DI=Rsing=D AG=Rsing/sinf3=C
IP = Rcos g = B' AG = D/sin f3 = C AI =B. sin g. cos f3 = C'
sin f3
By application of the cosine proposition one now establishes a
relation in the two triangles AGP and AlP between the four angles a,
7r, g, and 8, namely:
N= B2+ C:}- 2 BC. cos 1.l80 - 8)
A2= B'2+ C'2_ 2 B' C'. cos (ISO - a)
(1)
(2)
Equalizing (1) and (2) and introducing the angle functions in
place of the triangle sides give:
B o> 0> I B2 sin2 g cos 2 f3 2 BO> (180 cos f3 sin g cos g
- cos- g.- sin:!f3 - cos -aJ sin f3 -
B2-L B2sin 2 g 2 B2cos (ISO - 81 s~ f3g •
I sin2 f3 ., Sill
After multiplying through by sin 2 f3. B2 we isolate the member