(x; — xj) for j — 1 —i—1 represent the x-gaps between successive models which,
by this formula, are closed. s
Introduction of (32) gives, putting xo — x» according to (52).
xi— x [x/ — x] t - iEw Es + PES (53)
b. Ordinates.
Due to the limited accuracy of observation the spatial models will be affected
with small remaining y-parallaxes which — though their value not generally
exceeds the limit of perceptibility — must be taken into consideration in the
development of formulae. It is assumed therefore that the two parts, into which
the measuring mark splits in consequence of the remaining y-parallax, are set
symmetrically with respect to the point of the model whose coordinates are to
be measured.
If this principle of symmetry is adopted in the absence of other evidence,
the change of the ordinate of a scale transfer point (near the nadirpoint), cor-
responding with corrections to the elements of orientation, is represented by
the formula:
À yi = Yaz (Aou + Aau+ 1) — Ifa b A oi 1 — !fo (A by; + A byi+1) (54)
To reduce the latter term reference is made to (40), which reads if the
indices and j are replaced by j and k respectively:
Aby;—^by;1-—d by; — [bd x]
Summation for j = 1 =i gives, putting A by, = 0 according to (52):
A by, — [d by;]! — [G— j) bd;
Introducing this expression and a similar one for A byi--1 into (54), at the
same time substituting Aw, Awi+1 and At by (35) and (38), we obtain:
A yi = z [d o; + 1o zd Wi-+1— [d by;]hi — U d byı+ rT
+ [G — J) bd ili — 1/, bd Xi+1ı
If the corrections to the orientation elements are expressed by (25), (26) and
(27) this formula becomes:
A yi = Eso + LE» + P E» + Eos (55)
Finally:
n=yit Ay (56)
c. Heights.
The effect of corrections to the elements of orientation on the height of an
x-transfer point near the nadirpoint is represented by the formula:
z z? ‚+
Az= 2 Abxit1 + bzi+ı + TAG TTT Arn (57)
or substituting À pi by (50) and A gi, by an expression similar to (47):
2 2 s ges pa
Azi= 5 Abxi+1 + bz + ir dot (58)
in which according to (42)
A bxi+i RS dhi+1 = dbo + [bd Bile
and from (45):
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