Appendix_D 
METHOD OF IMPROVING APPROXIMATE COORDS 
  
For a general coordinate X, let there be m observation 
equations, in which aX. figures, of the form:- 
&.QA. + b udi = C. (5 = 1/to m) vo...) 
and consider the effect of adding to X. ihe increment 
2 M le. 2 x [a] 2 
ax = LI. 
e j71||?3 [231 * EP ad ji \ 23 *£P ad] EODOROUTT 
  
It is seen that, if the approximate value of X, is badly 
out, then all the m terms of the above summation (2), may be 
expected to be of the same sign if the X, error is really 
dominant, and the magnitude will have some relationship to the 
true value of the error. 
One may therefore assign as provisional ‘weight! to the 
error at each X. the value of the corresponding di and apply 
inecrements:- 
  
  
  
i = 2 |2 4X; 2| /m [a.d o'i 
X. = 
2 j=1|\*3 | +04] ad an kl j71 [34 f X; i| 2 Pac? o *n | 
  
(where any d X which are sufficiently close to zero 
on ; 
k may be ignored) 
to all approximate coordinates X. and their position may be 
expected to be improved. 
This process may be iterated if desired, account being taken 
of the second (and even higher) order terms obtained for the change 
in space angle, when evaluating the new residuals C., and the values 
obtained will almost certainly be adequate for the preliminary 
coordinates,