ON APERTURE AND DEFINITION OF MICROSCOPE OBJECT GLASS. 447 



be compared as they stand in each column, one fraction under the 

 other, they clearly prove that the number of distinguishable lines 

 and interspaces (or, as Mr. Sorby puts it, the number of lines 

 *' defined" at very small intervals) varies as the wave length of the 

 colour with the same angle of aperture. And this would be true of 

 all the colours of the spectrum. Taking the extremes and means as 

 here given, the variation of tvhat is called " defining" power is as 

 1 : r63/(?r the same aperture. 



Or again, if the fractions in the two columns, headed respectively 

 97*^ and 180° (a difference of more than 80'^), be compared, we 

 find that the lens of 97° aperture^ with blue rays, "defines" — 

 supposing, with Mr. Sorby, that his table *' clearly shews the 

 value of a large aperture in defining " — as well as the lens of ISO*^ 

 aperture with white light. 



Eut it may perhaps be said that when the figures are read in line 

 instead of column they do show increase of defining power with 

 increase of aperture. Yet, on nearer consideration, it will be found 

 that the denominators of the fractions denoting approach to extreme 

 limits of *' definition," although rising to a higher figure, 

 actually indicate a diminishing rate of increase. If, for instance, 

 the " defining " power of an objective of 60° aperture be called 

 1, then the difference of increased ** defining " power of an 

 objective of 90° aperture is — compared with the first — as 

 1'5 : 1. But the rate of defining power of an objective of 120° 

 aperture to that of the objective of 90° is only as 1*16 : 1. And 

 the rate of defining power of an objective of 150° aperture to that 

 of the objective of 120° is only as 1*1 125 : 1. Lastly, the ratio 

 of " defining " power of the objective of 180° to that of an objective 

 of 150° is only as 1-0337 : 1. Prom this it is clear that a few 

 degrees of aperture beyond 110° cannot give any appreciable 

 increase of value ivhen th^ effect of a rise of 2>0° at a time is so little. 

 And this too, in spite of the fact that every 30*^ of additional 

 aperture, gives a largely increasing zone of marginal light. But, 

 while the figures of this table fail to prove the value of large 

 aperture in *' defining," they indicate still less respecting the 



