ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 



309 



dry objective of 180° air-angle having a larger aperture than one of 

 100° and the latter than one of 50*^. The most important of the 

 differences between the two theories arises, however, when for air is 

 substituted a medium of greater refractive index, such as oil. This 

 constitutes the special difficulty of the angular aperturist, for having 

 in his consideration of aperture confined himself to the angles in 

 front, and those being of course always limited to a maximum of 180'^, 

 he is not unnaturally led to consider 180'^ in air to be an absolute 

 limit as regards aperture which cannot be surpassed by any kind of 

 objective, a limit, moreover, imposed by fundamental natural laws in 

 whichever way the matter is regarded. 



If we examine the emergent pencils corresponding to the dif- 

 ferent angles, and, for simplicity, take objectives of the same focal 



Fig. 54. — Eelative diameters of the 

 (utilized) back lenses of various dry 

 and immersion objectives, of the same 

 power, from an air-angle of 60° to an 

 oil-angle of 180°. 



180° oil-angle. 

 (1-52 Num. Ap.) 



length throughout, we see that 

 the diameters of the emergent 

 pencils of the dry objectives en- 

 large with the increase in the 

 angles of the admitted pencils 

 (though, as will be shown here- 

 after, not in the same proportion), 

 the maximum diameter for a dry 

 objective being obtained when the 

 angle is 180°. If now the dry 

 objective of 180° is replaced by 

 an oil-immersion objective of 82°, 

 and the angles at the radiant are 

 increased (from 82°) as those of 

 the dry objective were increased 

 (up to 180°), the plain fact is that 

 the emergent pencil goes on en- 

 larging in the same manner as 

 before. Thus if we commence 

 with an air-angle of 10° and pro- 

 ceed by successive additions of 

 10° up to 180° air-angle, passing 

 then to 82° balsam-angle, and 

 again progressing up to the nearest 

 practicable approximation to 180° 

 balsam-angle, the emergent pen- 

 cils will show a continuous in' 

 crease* There is no break at 

 the 180° air-angle nor does any- 

 thing abnormal occur at that 

 point, but we have a regularly 

 progressing series from the lowest 

 air-angle to the highest balsam-angle, the diameter corresponding 

 to the 180° air-angle not being at the top of the series but only two- 



o 



180° water-angle. 

 (1-33 Num. Ap.) 



180° air-angle. 

 96° water-angle. 

 82° oil-angle. 



(1-00 Num. Ap.) 



97° air-angle. 

 (0-75 Num. Ap.) 



60° air-angle. 

 (0-50 Num. Ap.) 



* If the objectives have the same focal length throughout, tlien, as before 

 explained, the absolute diameter of the emergent beam is all that need be 

 regarded ; while if the focal lengths vary, it is the ratio of the diameter to the 

 focal length that must be considered. 



