35 
sions (99)—(102) above, the errors of the center points of the photo- 
graphs evidently can be expressed as functions of the original image 
coordinate measurements. Consequently the influence of systematic 
and accidental errors of the basic measurements upon the results of 
the triangulation can be investigated. 
Below we will particularly pay attention to the accumulation of the 
inevitable accidental errors. We therefore assume that systematic 
errors of the fundamental image coordinates are corrected as completely 
as possible. Residual errors are then regarded to be of accidental charac- 
ter. The statistical expression for the magnitude of the accidental 
error in each image coordinate is given by the standard error of the 
image coordinate measurements and is denoted sy. Special investigations 
should be performed for the determination of this very important factor 
for each type of camera, plotting instrument and operator. 
1.223. The error accumulation in a cantilever extension 
Assuming only accidental errors in the basic measurements the error 
accumulation in the functions (111) and (112) can be found from the 
corresponding weight numbers and the standard error of the basic 
measurements. First the weight numbers of DX, and DY, are expressed 
in terms of the weight and correlation numbers of the elements of the 
coordinate transformations. Then the latter are obtained from the 
expressions (103)— (106) above. 
Evidently uniform conditions are assumed within the strip. 
After development of the expressions (111) and (112) the weight 
numbers of X, and Y, are found in the usual wellknown way 
Qu xz, 77 Op (^ - (n — 1 (n — 29 T... + 22 + 12} + nQ,,, + 
T 3Q4, Ín + (n — 1) + (n —2) + ....+2+ 1} (113) 
Ory. =F [m - (0 - 3 3 23 LLL + 22 + I} + #0, + 
F25Q n -n—13) 3 »—2) 9 ..... +2 + 1} (114) 
But 
1 
12 4-22 -- 33 4-..... + (n — 1)? + W = 6 (2»--1)(n-4- 1)» (115) 
and 
"n | 
| + 2+3+..... F(n—l1)T^-—5 (n + 1) (116) 
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