( 833 ) 
point of the base being opposite the middle of the plate. We may 
call the perpendiculars from the extremities of the base the principal 
axes, and their intersections with the plate the foot-points. 
All other cases may be considered as deviations from the normal 
exposure and may be easily derived therefrom. 
For the mathematical reconstruction the mirror-stereoscope is the 
best. The double mirror-stereoscope after the model of the HELMHOL Tz 
telestereoscope is to be preferred, since with this instrument the 
illumination of the plates is the most equable. 
When viewing the reduced pictures of the original negatives, a 
lens stereoscope is best, fitted with plan-convex lenses of 10 Dioptries. 
This is to be recommended, because simple formulae are obtained for 
the mathematical reconstruction. From these formulae, which I have 
already given, it ensues that there exists a simple connection between 
the length of the principal axis (exposing-distance) and the number 
of times the original image must be diminished. If for instance the 
exposure has been made with the normal base, the number of times 
the picture is to be diminished is exactly one more than the length 
of the exposing-distance expressed in decimeters. Thus with an ex- 
posing-distance of 5 decimeters the size of the original exposure 
1 
negative is reduced to er From the degree of diminution we 
ean calculate the distance there must be between the image and 
the lens. 
For convenience’ sake I have always spoken of the left half-image . 
as belonging to the left eye, and the right half-image to the right 
eye. Properly speaking however this applies only to landscape- 
photography, since we never require to view a landscape upside 
down. With ordinary objects however, and this applies both to 
common light as well as the Röntgen rays, it is often of advantage 
to view an object upside down. This is easily accomplished with 
a lens-sterescope by simply turning round the plate on which the 
two half-images are impressed, so that the so-called left half-image 
is placed in front of the right eye and the right half-image in front 
of the left eye. The same thing of course occurs with the original 
plates, if they are turned round in the same manner. Mathematically 
speaking, the image is not altered by turning it upside down. 
Psychically however this is not necessarily the case, and in some 
cases this distinction may be of importance. In what follows I shall 
regard the matter exclusively from a mathematical stand-point, 
the two half-images being considered as a single stereo-image. 
