Petrograjphic Microscope Work. 65 



(2) The principle on which the second method is based is 

 illustrated in tigs. 2 to 5. 



In fig. 2 the paths of parallel beams of rajs entering the 

 condenser under different angles of incidence are shown. Such 

 beams are readily obtainable and their significance most easily 

 appreciated by using the plane side of the substage mirror and 

 observing distant points on the horizon as they appear reflected 

 in the mirror. The parallel beams of light are brought to 

 focus by the condenser in its upper focal plane where the dis- 

 tant points K, L, M are imaged at K', I/, M'. From the figure 

 it is evident that the greater inclination of an incident beam of 

 light the farther from the central axis does it come to focus ; 

 conversely, points near the center of the field, K', L', M' are 

 formed by beams of light incident under relatively small angles. 



Fig. 3. Fig. 4. Fig. 5. 



^v^L 



This relation has an interesting bearing on the object field of 

 view of objectives. In modern objectives, the shorter their 

 equivalent focal length (E. F.) the smaller their object field of 

 view, and hence the smaller the angle of the incident cone of 

 illumination required to cover the field, and vice versa ; in 

 general, the longer the E. F. of an objective the greater the 

 angle of the cone of incident illumination required for the 

 same condenser ; for the same cone of illumination, the longer 

 must be the E. F. of the condenser to increase the width of 

 cone of illumination in the object field. For this reason the 

 large Abbe condensers with relatively long E. F. can be used 

 for observations both in parallel and in convergent polarized 

 light without disturbing the upper lens of the condenser sys- 

 tem ; but with such large condensers correspondingly large 

 polarizers are required. The relation between the actual width 

 of the upper focal plane of the condenser (image plane for inci- 



Am. Jour. Sci.— Fourth Series, Vol. XXXV, No. 205.— January, 1913. 

 5 



