PHOCEEDINGS OF THE SOCIETY. 377 



respectively 34 and 35 on page 164 of the number of tlie Journal 

 above cited, 



"It is abundantly evident that a dry lens of 170'' aperture 

 (assuming such an instrument to be in existence) would refract the 

 pencil of rays shown in Fig. 34 just as readily as it would refract 

 that of Fig. 35 after refraction from the cover-glass as shown in the 

 figure, and in both cases the pencil would be brought to the same 

 focus behind the objective. 



" Let us now put x = each degree of angular pencil from the 

 radiant. Then in Fig. 34 the objective will take in a pencil of 

 170 a;^; but as the radiant pencil in Fig. 35 is only 80^, diluted on 

 emerging from the glass cover, in that case the objective will only 

 take in a pencil of 80 x\^ ; it is therefore clear that the one is not the 

 ' optical equivalent ' of the other. 



" The comparison of a pencil after refraction with one in its 

 original condition, when the question under discussion is one solely 

 as to the size of pencil direct from the radiant, has no bearing upon 

 the point at issue. If compared after one refraction, why not after 

 any number of them ? 



" If two pencils of 20° each — radiant from points in air — fall, one 

 on a concave lens which it exactly fills and refracts so that on 

 emergence it is diluted into a pencil of 40°, and the other similarly 

 falls on a convex lens which refracts it so that it is compressed into 

 an angle of only 10°, their angular aperture is not changed by the fact 

 of their subsequent dilution or condensation — they are still both of 

 20° aperture. 



" In order to bring the radiant in Fig. 34 into the same condition 

 as that in Fig. 35, it would be necessary to cover 

 the former with a slip of glass having a semi- 

 globular cavity on its under side, and so placed 

 that the radiant point is in the centre of the 

 cavity as in the annexed diagram, Fig. 110, 

 which upon the ' optical equivalent ' theory 

 involves the assertion, that the angle c, r, d is equal to the angle 

 a, r, h. 



" I understand now that it is contended that the radiant pencil c, r, d 

 in balsam, that is 80° angular, emits as much light under a given 

 illumination as the angle a, r, d in air, 170° angular. I have not, until 

 after the last meeting of the Society, imagined that any such assump- 

 tion was in existence. I stated as much in my previous communica- 

 tion ; I am yet without a shadow of proof of its accuracy — it may be 

 my fault or my misfortune — but even if proved to be true, I submit 

 that the term ' aperture ' to express the difference is inappropriate, to 

 say the least." 



Mr. Crisp said * that (1) Mr. Shadbolt had unnecessarily com- 

 plicated his own view of the matter by introducing the concave 

 hemisphere. All he need have done was to take Figs. 34 and 35 and 

 point out that the 170° in air in the two cases could not, on his 

 view, be equivalent, inasmuch as one originated from a pencil of 

 * This note also was taken asi'3ad. 



