82 ADJUSTMENT OF RHOMBOIDS, ACKERMANN 
ii reliable and to give a solution applicable to rhomboids departing further from the 
ideal shape, other formulae, which approximate more closely the rigorous solution 
, are 
developed here. 
Following the same line as in section 5, the coefficients of the linearized condition 
equation are simplified, now however, only second and higher order terms are neglected. 
  
  
  
  
  
Introducing 
li ar Tobs. — "ideal (6.1) 
I and using the expansion 
I ; 
ctg 1 + da | =1—2 Ada (6.2) 
the solution of the normal equation becomes, if the dr’s are given in radians: 
I K = 64 {1— 3% (Arg — Ar, - Ar, — Arg) } (6.3) 
Whence the resulting corrections v are: 
VQ [—2—2 (Arg — Ar] K 
U— | 4+2(4r5—Ar7)}K 
vg = [—2—2 (4r, — Arz) |] K 
  
  
  
  
  
v, — [—2—2 (Arg — Ar, t Arg — Ar) IK 
i oy — [| 2t 2(4r— Ar, Arg — Ar, t Arqy — Arg) ] K 
i vg — [|—2 —2 (Ar, — Arg Ar — Ar) | K (6.4) 
v; —| 2t2(A4ry — 4r, t Ar, — dre + Arg — Ary) |K 
vg — [—2—2 (Ar; — Ar] K 
Il Vg { 4t 2(Ar; —Ar|] K 
WE > 
Wt Vio = [|—2— 2 (Arg — Ar)] K 
i With these results a direct solution for the corresponding corrections to the 
Il preliminary coordinates of the points C, D, and E can be derived. Neglecting again 
IM second and higher order terms of the Ar’s the result is found to be: 
i e de 1 
Ye Be. Td [1 16 (—8 Ar, t 10 Ar; —2 Ar, — 22 Ar, +26 Ary + 2 Ary, — 
I 9 6 Ar; F4 Arg —2 Arg — 2 Ar, 0) } 
i c de 
| Yo 7 We —— *7p (1 + # (—8 dr, + 2 dre + Ar, — 18 Ar, +18 Ar, + 2 Area - 
] € . . 
| 9 2 Ar. Irg —2 Arg Irio) ] 
d Ae 1 
CD c, EP [1 16 (2 Ar, — 10 Ar, +8 Ar 22 Ar, + 6 Ars — 2 Ary 
| 0 26 Ar; + 2 Ars + 2 Arg —4 4ro)}3 
d Ae (6.5) 
yp*73, 1 2 15 {11 + 4 (—4r, —2 Ira - 3 Ar, t 18 Ar, - 2 Ar, —2 176 — 
9 18 Arz — Arg + 2 Ary — A749) ] 
le 
li tp = 3 (x, + x, ) 35 (Ar, — Arg —2 Arg + 2 lr, — Arg 1710) 
A C D ba 
le ; 
| Y=, tup) 39 (— à Ar, + 6 Ary —3 Ary — 14 Ar, + 14 1e + 3 dr. 
" C D 3 6 Ary + 3 Ar40) 
i In each equation of the systems (6.4) and (6.5) the constant term of the corrections 
corresponds to the solution of section 5. The additional terms represent the modifications 
i 
i 
I 
hi 
i 
i 
i 
i 
  
  
Bem 
  
— II —s€ 3