TRANSACTIONS OF SECTION A. 323 
measures of plates. It may be expressed, with a probable error of under one 
micron, as a function of the radius from the centre of the plate, with the addition 
of terms representing the effect of the deviation of a central ray in passing along 
the optical axis of the lens, a deviation due to small errors in centreing of the 
system of lenses. ‘The symmetrical part of the distortion is nearly represented by 
a parabola of the second degree. 
A ‘standard’ value of the focal length at a given temperature results from 
the determination of the distortion. It is the distance on the réseau scale of 
the silvered surface of the réseau plate from the back nodal point of the lens for 
small elements of the picture near the centre. The temperature coeflicient of 
that standard, being equal to the difference between the coefficients of expansion 
of aluminium and glass values for different temperatures of exposure, may be 
computed and used for all subsequent work. 
The corrections for distortion are taken out at sight from a diagram of 
correction curves over the plate. They become large near the corners of the 
plate, reaching then 200p or more. 
_ No other correction is applied to the plate co-ordinates, the remaining errors 
being treated as accidental. From a discussion of measures it results that the 
principal sources of these errors and their probable amounts are as follows :— 
Error of seale and screw, treated as accidental . : . +£0'3p 
Uncorrected distortion of lens and error in taking out dis- 
tortion from diagram : : - ; : +1lp 
Distortion of film and error inherent to the photograpbic 
image 7 . : 5 : - ; : : . +) By 
There are, in addition, errors in the relative orientation of the pair of plates 
(+1'5y), and in their absolute orientation and that of the base line, The 
vertical co-ordinate z is estimated on the glass scale to the nearest 10p, it being 
unnecessary to measure z with the same accuracy as the stereoscopic difference e. 
The combined effect of all the errors on the measures of an ordinary topo- 
graphical object is: 
Ae=+4y, Av=+10p, Az=+47p. 
The probable errors in the co-ordinates of a point resulting from these values 
are as under :— 
Y AY Ax AZ 
Base 800 m. 
1,000 m. 01 01 01 | 
2,000 ,, 0-4 0:2 01 
3,000 ,, 09 0:3 0:2 
4,000 ,, 15 04 0:3 
5,000 ,, 2-4 06 04 
6,000 ,, 3:4 0:8 0-6 
7,000 ,, 4°7 11 0-3 
8,000 ,, 61 1-4 10 
9,000 ,, V7 18 1:2 
10,000 ,, oD 2:2 14 
11,000 ,, 11°5 2°6 7 
12,000 ,, 137 31 2:0 
Base 500 m., 
15,000 m. 12:9 3:0 2:0 
Base 1,000 m. 
20,000 m. 11°4 ; - 2°8 ge 
A test survey was made, in which the co-ordinates of 265 points were 
computed from a pair of plates. Of these twenty-five were either determined by 
independent survey or compared with their positions derived from the overlap of 
Y¥2 
