50 VISION WITH THE COMPOUND MICROSCOPE 



objectives, one a dry objective, the second a water-immersion, and 

 the third an oil-immersion. These would be compared on the 

 angular aperture view as, say, 74 air-angle, 85 water -angle, and 

 118 balsam-angle; so that a calculation must be worked out to 

 arrive at a due appreciation of the actual relation between them. 

 Applying, however, 'numerical' aperture, which gives '60 for the dry 

 objective, - 90 for the water-immersion, and 1'30 for the oil-immersion, 

 their relative apertures are immediately appreciated, and it is seen, for 

 instance, that the aperture of the water-immersion is somewhat less 

 than that of a dry objective of 180, arid that the aperture of the 

 oil-immersion exceeds that of the latter by 30 per cent. 



When these considerations have been appreciated, the advantage 

 possessed by immersion in comparison with dry objectives is no 

 longer obscured. Instead of this advantage consisting merely in 

 increased working distance or absence of correction-collar, it is seen 

 that a wide-angled immersion objective has a, larger aperture than 

 a dry objective of the maximum angle of 180 ; so that for any of 

 the purposes for which aperture is desired an immersion must 

 necessarily lie preferred to a dry objective. 



1 . There exists then a definite ratio between the linear opening 

 and the focal length of a system, which must be entirely indepen- 

 dent of the composition and arrangement of the system, and solely 

 determined by the above-mentioned aperture equivalent of the 

 admitted cone of rays. When the equivalent is the same we have 

 always the same proportion of opening to focal length, whatever may 

 be the particular arrangement of refracting media in the system. 



2. If the objectives whose apertures are compared work in the 

 same medium, and admit angles of, say, (10, 90, 180, their aper- 

 tures are not in the ratios of those numbers, but are as -50, '70, and 

 1-0. The 180, for instance, does not represent three times the aper- 

 ture of the 60, but t'wice only. 



3. If the objectives work in different media, as air and oil, the 

 latter may have an aperture exceeding that of a dry objective of 

 180 angle. For with the dry objective the refractive index (n) and 

 the sine of half the maximum angle (u) both=l,so that // sin n 

 = 1 also, whilst with the immersion objective n is greater than 1 (say 

 1-5 for oil), and the angle may therefore be much less than in the 

 case of the dry objective, and yet the value of the expression n sin n 

 (i.e. the aperture) may be greater than 1 ('). 



The two latter deductions are so directly opposed to what was 

 accepted by the older opticians and microscopists that a, closer if 

 brief consideration of some of the points which bear upon this branch 

 <>f the subject may here be serviceably summarised. 



Take, lirst, the case of the medium being the same. 



Difference of aperture involves a different <j>iantity of light ad- 

 mitted to the objective provided all other circumstances are equal. 

 1 1 ence the question of aperture leads to the consideration of the photo- 

 metrical equivalent of different apertures or aperture angles. It is 

 not of the essence of the problem, but it affords an additional illus- 

 trnl'nm of numerical aperture, and is thus of great service in its 

 exposition. It is manifest that a pert lire cannot be based on quantity 



