250
when the distances dyx, dl 2 and d13 are increased, thus approaching
the condition of freedom of correlation.
The formula (12) will now be developed for 2 and 3 orientation
bearings which are chosen in the directions
iz
<Pi 9i.p J
92 9i.P -
and further that
d d^ d2 d3 p d].p
where p is a changing factor.
It is found respectively that with 2 orientation bearings
3 _Pl f~P V_2 „I (45)
av - 2 a*i df p 1 pi I OR
and with 3 orientation bearings
„2 4 P2 (9P* (>P (i V 2) (i V 2li±22) g« (,fi)
V - 3 ffal V 8lp2
When is taken equal to 2 in formula (45) we find (43)
formula (44) can be derived from (46) by taking p
The coefficients p2fi(P) and p%{p) in the second term on the right
hand side of the equations (45) and (46) are plotted in the figure 5,
being indicated by y1 and y2 respectively.
The first function of p shows a minimum for p 1 and the second
one for p 2.
In some literature [2] the formula
av a* 'iï~ aR (47)
is used, where aR c y dA} the standard deviation of the coordi
nates of the occupied stations. The da is the mean of the distances
at the occupied stations to the unknown station viz. di.p, du.p,
diu.p etc. The corresponding coefficient of the above formula (p2)
is plotted as the line y3.
The values of oj obtained by (45) are tabulated in table 1,
taking c 3; 5, 10 cc, for several values of p and di.p (in
meters). In the formula (47) is taken di.p= du.p d\u.p etc.
The increased precision of the intersecting line I.P with three
orientation bearings is very remarkable. The minimum value of ay
occurs when p 2, which means that the orientation bearings
should be twice as long as the distance di.p.
The minimum ay with two orientation bearings occurs when
p 1.
ai-p
