transform the machine ordinates of the stations 0 and 7 respectively into the 
terrestrial system. Since the models in question have already been set to the hori- 
zontal and therefore need no vertical rotation, these corrections are equal to the 
corrections of the corresponding nadirpoints or in formulae: 
— A byo == 20 and — A by, en (72) 
Introducing (70) and (72) into the right-hand part of (12) we obtain: 
Wy — 10 — nn + a(n +1) bKo + Ya(n —1) BK, (73) 
  
A formula for the closing error w. is derived as follows. 
Reverting (63) we obtain for the x-transfer point (x = xo, y — 0, X = Xo 
and Y = Yo): 
Xo = (Xo — &o) cos Ko + no sin Ko 
Yo = (xo — £o) sin Ko — mo cos Ko 
Similarly it follows from (64) for the x-transfer point in the last model: 
An = (Xn — En) cos Kn + 5n» sin Ks 
Y, — (Xn — En) sin K, — 9 cos Ks 
If we insert these expressions into the right-hand part of (15) we obtain, 
putting Ko — K, and yo — » approximatively: 
wo = fg — En — [3i— xi Ju. — (Xn — X) (74) 
The differences xi—xi in this formula are the x-gaps between consecutive 
models, which are thus eliminated. 
Appendix II. Derivation of a formula for the angle between two consecutive air 
bases. 
From fig. 5 which represents three air stations ;—1, ; and ;--1 and their 
verticals, we read in the left triangle: € 
sin ‘Ja (R1 — S) = : (r — s) cos !J» yi 
or approximately, R, — § and y being 
small: 
a (R—5)= 56 —5 
Evidently » — 5 is the difference be 
tween the stations’ heights Hi; and Hi 
whence: 
  
  
1 
Uo (Ri— 8) = y (Hi — Hii) C (Earth's Centre) 
Figure 5 shows also: 
1s (Ri + S) = 4% (a — y 
Subtracting these equations we obtain: 
Fig. 5 
1 
S1, (z — Vi) ET b (Hi = Hi) 
20