Full text: Commissions I and II (Part 4)

  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
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; 
  
  
     
  
  
  
  
   
    
   
  
  
  
  
  
   
     
    
    
    
   
   
     
    
   
  
	        
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