GEOGRAPHICAL SURVEY OFFICE OF SWEDEN NO A 34 
7 
2.2. The differential formulas. 
The x-obliquity (x-deviation) and the width-correction (y-deviation) have 
the following influence upon the image coordinates in the A 7 and A8 accord 
ing to Lycken [3] : 
ta'. -■ÉBL-dt+i-dl 
s s 
dy * = - — dt - dl 
J s s 
( 1) 
x' and y' are the coordinates in the grid plane, where the origin of the 
coordinate system is located in the projection centre, s = \J x'^ + (g-y') 2 
and g = 230 mm (A7) , g = 240 mm (A8) • The well known differential formulas 
relating the image and the machine coordinates are as follows; 
2 
dx=-dx + — dz + y dpe + (l + — 0 ) zdcn - ¿SL den 
OZO ¿. ' z 
z 
2 
dy = - dy + -^ dz - x d9e + d<p - (l + ^ ) zden 
( 2) 
x and y are the machine coordinates, dx Q , dy Q and dz Q are the translations. 
These translations can be written as follows; 
ta o = Ô ^ ^ 
ây 0 - f % - % 
( 3 ) 
dz = — dc - dz 
o c 
After inserting formula (l) into (2) and formula (3) into (2) the following 
working correction equations are obtained in the image scale; 
^2 , , , , 
v x “ "^p + *” < k^ ,+ ~àc- “d2H- y 'dae +(l+ ) edep - ~^-dcj - ^^L-dt+ ^dl-dx' 
c 
. / / 
*2 
( 4 ) 
v' ss -dyp+ -^dy^+^dc- ^dz- x'dae + -df -(l+ edej - -fdt- ■^^-dl-dy" 
dx'— — x ^ = X ^ _ x ^ 
z measured given 
<3y'= - 7' = y 
measured 
- 7 
given