of the significance of the elevation discrepancies to determine the accuracy of the
hana Or the standard error of this quantity.
This standard error must be expressed as a function of the accuracy (standard
error) of the basic observations /1,, ..., h,, which are assumed to be affected by the
same standard error so»
The problem is first to determine the accuracy (the standard error) of the
correction dAcorr Of the expression (6) which was determined from the expression (1)
dhcomr = dhy + xdn + yd. rss CH)
Since dh,, dy and d£ have been computed from the expressions (3)-(5) and conse-
quently are indirectly measured quantities, it is most convenient to apply the
general law of error propagation.
The weight number of the correction dh, is consequently in general shape
found as
Quan other ^ Qus, t X Qut Qut 2xQag t 2yQact 2Xy One. 24. (8)
Since the standard error of each measured elevation Ameasurea iS assumed to be so the |
corresponding weight number is 1. From (6) we consequently have
Qhfinaltfinal edu Q an gorrdtoor tt (9)
Finally the standard error of /gina is
He |
Pana] — Soq Oanal^ünal* .... (10)
The wéight numbers Q;,4,, Q,, and Q;; according to (8) can be determined from
the expressions (3)-(5) as the square sums of the coefficients of dh,, dh, and dh;
respectively. The correlation numbers in the expression (8) are found as the
product sums of the coefficients of dh,, dh, and dh; from (3)-(5) when the expres-
sions for dhy, dn and dé are pairwise combined.
3. PRACTICAL EXAMPLE
In order to demonstrate the procedure under somewhat simplified conditions
the points 1-3 are assumed to be located according to Fig. 1 and with the co-
ordinates
KS am MI MC m d ei)
y170 va = a vs = a
The expressions (3)-(5) become
dis hd thy a2)
| —2dh, t dh, * dh;
dn = dà , ni (13)
_ dh, — dh,
d£m P (14)
The weight numbers become
Quan, 7 i (13)
3
Qv 7 adi ust (16)
Qi 7 yn a;