Ca j X, Ul P (9)
These are the correction equations from which is to be calculated.
It is easily seen that the observations (4>i.» ai.») are correlated.
2. Equation (i) will be expressed in another form viz.
"r, Yi Yi AY»— AYi
Z. (ar° Xi Xi AXi AXi a" i1
Ol ^i(6)
The following formula can now be derived for the bearings of the
line P I introducing approximate values for the coordinates
of station P:
Yi AYi —Y'p AYp s
arc tan AXp tt oci.p vaip 01 (7)
where the expression (6) has to be used for
After expanding (7) according to Taylor and putting
1 4>V.I7T—ai,pV arc tan 4 an
the equation becomes:
ap.iAYp bpjAXp 1 AYi j ap\ I ai
AAijöp.i wyi èi.»j
nZX~T 2 ^a-i.iAYi bi+AXi vaj J vaup. (8)
The right hand side of equation (8) will be denoted by V1.
NowS «iand 1Y bn represent the coordinates of
the centroid of points on a coordinate system of which the -j-a and
-j-b axes are the negative X axis and the positive Y axis respectively,
the distances from the origin being the inverse of the distances from
the origin (I) to the station pertinent to the coefficients a and b
(see figure 2).
As apj «i.p and bp, 1 bj.p it is
and i_1
(io)
240
n i w
i"n- 1
n 1 X{ ai
i-i L
i-tt 1
i - 1
<-1
n 1 n 1
,i" n l
I
1