(386) 
raphy taken on glass plates can be due only to the bending of the light rays by 
zones of atmospheric disturbance caused by density differences and not follow- 
ing the normal laws of a changing index of refraction with altitude zones but 
acting like an optical prism in bending the light rays that pass through them. 
The transverse (y) component of such a deviation changes the y-parallax 2 
on which the corrections of relative orientation are based. It results in an error 
in the relative orientation of a pair of photographs which in a strip of photo- 
graphs is reflected in the orientation of all the photographs that follow. An 
erroneous residual y-parallax produces a warp in the model and error is pro- 
pagated throughout the strip. 
The points which are important in analyzing these deformations are N 
having the ordinate y —0 in the planes x—0o and x=b which are used for the 
correction of errors of adjustment of y” and y“ and the points A and A’ of the 
same plane for which the absolute value of y/z is minimum and which serve for 
the adjustment of a' and «^; these quantities y” y” and a’ a” represent the errors 
of adjustment of the perspective pair about the y and z axes. 
The orientation in a plane xo furnishes the values byo and bzo of the adjust- 
ments and removes the error f of the relative adjustment of the two photographs 
about the x-axis. The expression of the parallax 4 that remains after this orien- 
tation is: 
  
/ / / 
A= [x (a —a") T^ be" + ix (7 2” = by}, 
This can be removed at all the points of the same plane perpendicular to 
the base by introducing the two components: 
by = —[x(¢'—»") t br"] and bz = +[x(¢’—a”) + bal, 
which are linear functions in x. But this is not exactly the hypothesis on which 
the equation of the perspective pairs is derived. 
In the case where it is not true, the expressions become: 
by = —[x (F—7") + by" + fi + a) 
  
/ HU HU xz | 
bz = + |x (a—a”) + ba” + ( P = E p— y (€ — €) 
B is the residual error of adjustment about x-axis which propagates the 
deviation of the light ray in the orientation; 
¢ is the y-parallax at a part considered to have y-parallax in the photo- 
graphs; 
to Is the proper error at a point N of the planes corresponding to the zo 
distance from the first point. 
Were they are the only causes of the systematic deformation of the model, 
the errors of alignment in by and bz, functions of f, v, and eo, are generally too 
small to be detected, but they are evident as limits of accuracy in the correction 
of 4. This is not true, if the errors arise from local deformations. 
To diagnose the errors of alignment, the method consists of performing the 
orientation in the most favorable plane and removing 4 successfully in the planes 
X — 0,x — b/2, x — b, at first with by at N, then by bz at points À and A’ 
without changing the by. One obtains this according to whether the plane of 
orientation is or is not one of the preceding planes. 3 or 4 values of by and 6 or