4* Other possibilities. 
4.1. Choice of the measured points. 
In the above case 27 points, 3 planes, and one principal distance were used, 
but it is obvious that the numbers of the points, planes, and principal 
distances could have been varied. It could also have been possible to vary 
the locations of the points and planes. In the solution as presented here 
the standard errors of the corrections are very small which is importantj 
and this must also be the aim in other solutions of the adjustment. For this 
reason, it is important to use a large number of points, several planes, 
considerable distances between separate planes, considerable distances bet 
ween separate points, and a symmetrical location of the points. 
4.2. Choice of the orientation elements. 
Five elements of the interior orientation and 6 elements of the exterior 
orientation have been used in every projector which is the minimum number of 
elements which can be used in a solution of this problem. Thus there is no 
possibility of reducing the numbers of the elements but it is possible on 
the other hand, to increase the numbers of elements. There are various 
eccentricity errors in the gimbal axes which are the result of the adjust 
ments carried out at the factory by the instrument manufacturer and these 
errors can be taken into account in the computations. There are 3 gimbal 
joints in an autograph and there are 3 separate errors in every joint. Thus 
we have a total of 20 elements. Differential formulas have been derived by 
Hothmer [4] • We obtain the following formulas for the A7 autographs 
according to [4 ] and (4): 
v' = -dXp+ •|dy- |dc- y'dx. +(l+ ^~)càf - -^^-dw - ■ S j 2 -d-b+ f 41- 
_ (<*z) _ (<*z) /s' 2 +y* 2 -<-c 2 ae Zls\SL de^-^'A"- 
( 18) 
cz 
Jr 
2, 2 
+c 
1 r +c 
/ ,2 2 
z |/y +c 
z _de 21 + 
♦ ^ ^V 2 ±o_ 2 . dei , + (-T4-T - (irr) de 22 + rrars 
r*2, 2 
s yx +c 
|/x' 2 + 
*'r 
s /x'^+c" 
de_ 0 -dx" 
32 
GEOGRAPHICAL SURVEY OFFICE OF SWEDEN NO A 34 
19