40 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
terference figure may be observed directly as it is formed in the rear focus 
of the objective at C"D" or it may be viewed with the Bertrand lens and 
ocular, which together constitute a magnifying microscope focussed on 
C"D". The conjugate image C'"D'" is viewed directly through the posi- 
tive ocular by the eye at A'"B'" and appears in the position C""D"". 
The interference figure can also be viewed directly, as it forms in the eye- 
circle of the ocular in Fig. 3 1 . For the measurement of optic axial angles a 
scale can be introduced at any one of the conjugate images CD or C"D" 
or C'"D'" and by its use the angular direction corresponding to any point 
in the field determined. 
In the arrangement of Fig. 32 the image A'" B'" is located at the eye- 
circle of the ocular and can be seen with the aid of a hand lens at that point. 
From Figs. 30 and 32, the reciprocal relation between the object or entrance 
port and the entrance pupil is clearly shown. In case the entrance pupil 
or one of its con jugate images serves as object, the original object or entrance 
port serves as entrance pupil, and vice versa. The recognition of the func- 
tions of the apertural planes in a lens system and the reciprocal relation 
between such planes and the object or its image planes is of great assistance 
in tracing the actual path of the rays through the lens system in the micro- 
scope. The importance of diaframs to the designer of the optical system 
in restricting the aperture of the transmitted beams of light and thus im- 
proving the quality of the image will not be considered in this paper. 
MAGNIFICATION. 
In lens systems used for projection (objective magnification) the lateral 
magnification is directly the ratio of the linear size of the image to that of 
the object; with a given lens system it is possible to obtain any desired 
magnification if mere magnification is sought. In instruments used to aid 
vision (subjective magnification) the eye is an essential part of the optical 
system and the magnification is determined by the size of the image on the 
retina rather than by its actual size, the purpose of the lens system of the 
instrument being to increase the size of the retinal image. The retinal 
image depends primarily on the angle subtended by the principal rays at the 
eye-circle of the instrument (the angle u', Fig. 30). This angle of view u' 
can be expressed in terms of the relative positions of the pupils and images. 
In Fig. 33 let PM be an object viewed through the lens by the eye 0' ; let 
C'D' be the diameter of the pupil of the eye and CD its conjugate image, 
which is the entrance pupil of the system; let P'M' be the virtual conjugate 
image of the object PM; F and F' the principal foci of L, and the distances 
OM = {, O'M' = ', FM = x, F'M' = x', FO = A', F'O' = A". Then 
' ' = ?! tan u' _y r _ i _0 
' y y ' 
On the assumption that the system is free from distortion we find or the 
*' 
lateral magnification = t ; but ' = *' X' and therefore 
