348 Transactions of the Society. 



Hitherto plane objects only have been considered. When we 

 deal with objects of other shape it is self-evident that angular 

 aperture as such will have a marked influence on the appearance 

 of the object, and whether that influence is useful or not, it must 

 of course be taken into account in interpreting what is actually- 

 seen on viewing an object. 



It would seem then that the " angular aperture" of an objective 

 should be stated as well as the " numerical aperture." "When 

 it is known that a lens admits a pencil of such and such angular 

 breadth from an object in a medium of given refractive index, the 

 complete description of the lens is given in all qualities except 

 magnifying power, though we still want the standard of com- 

 parison afforded by the numerical aperture notation. Take the 

 case referred to by Prof. Abbe, say a cubical crystal of common 

 salt. We do not see clearly at the same time the horizontal face of 

 the crystal and its vertical sides, but by lowering the objective a 

 narrow band on the four vertical sides is fairly focused, and by 

 observing the apparent dimensions of this square band we are able 

 to say that the crystal is a true rectangular parallelepiped at any 

 rate. Moreover the clearness of the image of the band will depend 

 evidently on the angular aperture of the lens. 



Again, if oblique illumination is employed, what was at first 

 symmetrical about the axis of the instrument is now symmetrical 

 about an axis forming a definite angle with that axis, and so angular 

 aperture will be important as such. 



These considerations are perhaps too evident to require notice, 

 but they appear to me to have some weight. 



Lastly, it may be remarked that by law C the " depth of focus " 

 in an immersion lens is greater than that of a dry air lens in the 

 proportion of N : 1, by formula 0. 



Note ly Prof. Able. 



On the preceding paper Prof. Abbe writes as follows : — 

 I agree that the measure of aperture is a photometrical one in 

 principle. But by the expression, " number of rays " as opposed to 

 " mere quantity of light," I desire to convey that the bearing of 

 the notion is not confined to the photometrical functions of the 

 lenses. The expression " quantity of light " would imply the 

 intensity of the rays, which must be excluded in the estimation of 

 aperture, because a greater intensity does not compensate for a 

 smaller angle in regard to " aperture " ; whilst it does so in regard to 

 quantity of light, and a purely photometrical measure would have 

 to be based on the estimation of the rays in the whole cone, not 

 only in a plane section. In that respect the difference is, in fact. 



