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Transformation Formulas (Fig. 2) 
  
  
  
V dnm a [(æ"01)o — (x"01)0] [Oo T Qm] — [Q/01)o — Q^ o1)o] [Gc 01) — (x^ 1] i 
[G oi — G^ + (yo): — al 
Vu cos, o c Gl G^ — G3] - [^w — O^] LO^)i— 0^6] 
[G 0) — GT t [070 — O^ ex 
(x"12)0 = Vo1 sin ao1 [(y a2» — (y" a] + Vor cos aor [(x"12)1 — (x"701)1] + (x"01)0 
Oase — = Vo COS 401 [(y 12) mm (^ ^11] sa Vo sin O01 [( X un rr (x! ^a] d (y” ^01)o (2) 
(x^ ^12)o — Voi sin aor [(y 2 — (y” "o1 ] t Va cos ao [( x^ ^12) tm (x^ ‘01)1 ] + (a^ “01)0 f 
(y" 12)0 = Voi cos ao1 [^ 12)1 zu (y' "a1 ] + Voi sin ao1 [x i2) (s^ ‘01)1 ] + (y ‘01)0 
Where: Voi = the scale ratio between the Mo and Mi systems 
aor = the azimuth difference between the My and M; systems 
(x"01)o (Y"01)o and (x"01)1 (Y"01)1 = the coordinates of the connection point 
01° in the Mo and Mi systems respectively 
(x"o1)o (^ 01)o and (x"01)1 (y"o1)1 7 the coordinates of the connection 
point 01" in the Mo and M1 systems respectively 
Transformation Formulas (Fig. 3) 
E e [(x"01)0 — (x?o1)o] [ak es i ]— [(y'o1)o — i 2 ][(x"01)1 — (x°61)1! 
Voaisnenu = a D i 
[o 01)o — ( y? 01 don — y °01)1 ] 
  
  
p + [a^ 01)1 me (x 01 nr 
[(x"01)0 e (x?o1)o] [^ 01)1 mem (x? el ibt 0 
d 
  
  
  
  
V'o91cosa o1 — [(¥ 01)1 — (y?01) t IG'nh— Go). 
pU sno n = jo” «je = (x?o1)o] [Cy e eu e Ge d [(x"01)1 — (x°01)1] 
01 SIN & 01 [(»” 01)1 — ( y? 01 dE [(x^ 01)1 — ( x01 AP 
(4) 
127 s [(x^"1)o — (x?o1)o] [(x^ 01) — (x°01)1] + EGO" o)e — (¥°01)0] [(¥” 01) — On] 
01 COS @ 01 er” 01)1 — ( y "ni B+ | [x^ 01)1 mi 01)1 E 
V'o sin af d- V^oi sin a^9 
l7: cos a" = 2 
V'o cos aoi -- V^ cos a" 9 (5) 
l7^5 sin doi = 2 
(x°12)0 = V™o1 sin a™o1 [(¥°12)1 — (y?o1) V" cos a™o1 [ (x°12)1 — (x%01)1] + (x°01)o (6a) 
(¥°12)0 = V™o1 cos a™o1 [(¥°12)1 — (¥°01)1] + Vor sin a™o1 [(x°12)1 — (x°01)1] + (y?01)o 
(x"12)0 = V" sin a" 
(y'12)o = V" cos a"o; 
[ iH 
[ ] 
[5^ 2)1 — (y? 01)1 ] d V" cos o"9 [x 12) mum (xo 01)1 ] + (x?o1)o 
[(y12). — (y?o1)4] + Vor sin à"o1 [(X 12)1 — (x°01)1] + (9°01)o (6b) 
] 
(x^12)o 7 V"; sin aoi [ ^ 12) 1 — (y?oi] + V™01 cos a™o1 [ (x”12)1 — (x®01)1] + (x%01)0 x 
(y”ı2)0 = V"91 cos a"o1 [^13 — (9° 01)1] + V""o1 sin "os [(x"12)1 — (x°01)1] + (9°01)o (6c) 
Where: V'à V^o = the scale ratio between the Mo and Mi systems computed 
from the connection point 01° and the connection points 01’ and 01” 
respectively; 
a91G0 ^01 = the azimuth difference between the Mo and M1 systems 
computed from the connection point 01° and the connection points 01” 
and 01” respectively; 
(x°01)o (Y°01)o and (x°01)1 (¥°01)1 = the coordinates of the connection 
point 01? in the Mo and Mi systems respectively etc.