x y 
REPORT OF COMMISSION V GV-23 
It may be seen that 
Xo z 0 vo = R 
xz; = R sin 6, 41 = R cos 6, 
and 
x1 — Ax 
tan (nı — An) = — — — 
Yi Ay 
Since R relates only to scale, we may put R=1, in which case, 
sin 0 — Ax' 
tamn(y— 29) = ———7 
cosf — ^v 
where 
Ax 
Ax’ = — = 
R 
Ay 
Ay = — 
R 
Expanding, 
(tan n — tan An)(cos 8 — Ay’) = (1 + tan n tan An)(sin 0 — Aa”) 
Here n=true angle and 0=observed angle. 
he 
tan » cos 0 — tan nAy’ — tan An cos 6 + tan AnA y” 
= sin # — Ax’ + tan n tan An sin® — tan y tan AgAx' 
> ~~ Se - : 3 
Fhe unknowns are An, Ax’, and Ay’. Collecting coefficients of common un- 
knowns, 
tan n cos 0 — sin 0 
= [tan An|(tan » sin 0 + cos 6) + [Ay' — tan AnAx'] tan 5 — (Ax' + tan AnA y”) 
Now 
Ax 
tan &y = — 
1 — Ay 
tan An — tan Anây" = Ax’ 
Therefore 
(Ax" + tan AnAy") = tan An 
) Letting 
Ay' — tan AnAx’ = v 
tan An =» 
a = tang 
b = tan n sin 0 + cos 0 — 1 
c = tan n cos 0 — sin 0 
^ dr