3.3. The lacking flatness of the glassplates 
As has been mentioned repeated times above, the lacking flatness of 
the glass plates probably has a very important influence upon the geo- 
metrical conditions of the photographs. In particular the standard err- 
ors of unit weight of the image coordinate measurements of the photo- 
graphs from the R. C. 5 Aviogon camera have been influenced by the 
lacking flatness. Therefore some measurements have been performed 
of the flatness of these plates. For such measurements a microscope and 
a surface plate of high precision have been used. The small depth of 
focus has been used for the measurements of the differences between 
the emulsion surface and the surface plate in a great number of points. 
The procedure is described in details in reference [5]. 
The glass plates can become deformed due to their own weight in 
addition to the deflections of the glass and emulsion. 
In reference [6] Oswal has published an investigation of the flexure 
of photographic plates under their own weight and some modes of 
support, In a series of experiment he also has determined the deforma- 
tions empirically. It seems possible, however, that his results do not 
entirely correspond to the deformations which occur in a plate support- 
ed by a frame as in the camera. 
The deformation w of a plate of the size a X a due to the own weight 
can according to reference [7] be expressed in a formula: 
  
  
. mn ART InTX muy 
sin —— sin — cos ——- cos ——-— 
192p(1 — v2) 2 2 : 
w= a + BA + (37) 
5T 9h3 mn , 9 
— (m2 + n2)^ 
a4 
where v = constant, about 0.3 
E = Young's modulus 
h = the thickness of the plate 
m and n = whole odd numbers 
x and y = orthogonal coordinates in a system the origin of which is 
located in the center of the plate and the axes of which are parallel to 
the edges of the plate. 
For a plate of the size 23 X 23 cm and the thickness 2 mm the maxi- 
mum deflection will become 0.0112 mm. In Fig. 9 the deformation of 
an octant is demonstrated. Evidently these deformations can have a 
systematic influence upon the radial distortion amounts which are de- 
termined according to the grid method. It is evidently important to use 
sufficiently thick glass plates. 
A thickness of 5 mm will result in a maximum deformation of 0.0007 
mm which can be neglected. 
'The deformations of some glass plates were measured with the micro- 
28