318 SUMMABY OF CURRENT RESEARCHES RELATING TO 



being (in accordance with Fraunliofer's formula) proportional to the 

 sine of the semi-angle multiplied by the refractive index of the 

 medium, n sin u f is the true measure of the resolving power of an 

 objective ; so that 180° air-angle ( = 1 num. a]).) represents not the 

 v^hole (=1*5 num. ap.) but only two-thirds of the total possible 

 effect as regards resolving power. 



Sometimes it is objected, as it was in the recent discussion,^ that 

 resolving power must not be dealt with in considering aperture. It 

 is somewhat difficult to appreciate how it can be consistently, or even 

 seriously, suggested that resolving power is to be excluded from a 

 discussion of the aperture question from the point of view of angular 

 aperture, for even in the height of the predominance of that theory 

 it was resolving power, and resolving power alone, that was always 

 accepted as representing the proper function of increased aperture. 



The true function of aperture is in fact to be found not merely 

 in resolving power, but in the increased and more perfect delineating 

 power of the Microscope (to use Professor Abbe's term), i. e. the 

 power of the Microscope to show things as they are. This view is, 

 however, founded on considerations which the angular aperturist 

 necessarily does not accept, and which to him has always been repre- 

 sented only by the more limited term of " resolving power," which 

 is one only of the particular manifestations of delineating power. 

 When, therefore, he does not object to the use of the expression of 

 n sin u as the proper expression for resolving j)ower, he may well 

 be asked to define those other benefits, not being resolving power, 

 which he contends are attendant ujion increased aperture, and for 

 which the angle is alleged to be the correct expression. 



(7) The "Angular Grip." — Having seen that illuminating power 

 and resolving power vary not as the angles, but as {n sin uy or 

 n sin u, we reach the last point suggested by the angular aperturist 

 in support of the supposed maximum of 180° in air, which has come 

 to be known as the " angular grip " theory. If " angular grip " existed 

 in reality, the use of the angular expression would of course be estab- 

 lished, as it must obviously increase with the angles and attain a 

 maximum at 180° whether in air or any other media. 



Taking Figs. 61 and 62, and forgetting that it was they themselves 

 who raised the photometrical question or the resolution question and 

 at first based all their argument on that alone, they say, "Your demon- 

 stration has not touched the real point at issue, which has nothing to 

 do with greater or less amount of light, or with greater or less re- 

 solving power. Is it not clear that the pencil in Fig. 61 is of larger 

 angle than that of Fig. 62." 



If it is explained that no objection is intended to be made on that 

 point, and that every one must readily admit that the pencils are 

 different as regards angular extension, the angular aperturist exclaims 

 triumphantly, " If you admit that the angular extension of the pencils 

 at the object is different — that the pencil of 180° in Fig. 61 is in that 

 respect larger than the pencil of 82° in Fig. 62 — I have proved my case. 

 The angular grip of the object is greater with the 180° than with the 

 t i.e. the "numerical aperture." J See this Journal, a7it(', p. 160. 



