164 MEMORANDA. 



he controverts some opinions expressed by Mr. Wenham 

 and me. On both these I wish to make a few remarks. 



I have stated in the paper to which Mr. Sollitt refers that if 

 rays nearly parallel be sent tlirough the eye-piece of a micro- 

 scope down its axis, their extreme divergence, after passing 

 through the objective, will equal its angle of aperture, which 

 therefore is correctly ascertained by measuring that divergence. 

 The only methods, as far as I know, which do this are the two 

 which I have proposed,* all others depending on the dis- 

 appearance of a light seen obliquely. Of these Mr. Lister's 

 (Mr. Wenham's, which is similar, I have not tried) is alone 

 correct in principle, but it fails practically in extreme cases. 

 In Mr. Sollitt's, and all of the same type, the process is by no 

 means so certain ; on the contrary, they are liable to two serious 

 objections : firstly, that when a pencil of light is inclined at a 

 considerable angle to the axis of an objective, its ultimate 

 angle of divergence is less than the aperture ; and secondly, 

 that this angle is not bisected by the ray which is parallel to 

 the original direction. These are obvious from the theorj' of 

 oblique pencils, and it follows, as a necessary consequence, 

 that we thus measure, not the true aperture, but tivice an angle 

 which is greater than the half of an angle which is less than the 

 aperture. Up to 45° there is no difficulty in seeing that these 

 two errors nearly compensate each other ; but it would be no 

 easy problem to determine their effect at 80° or 85°. To this 

 I may add, that in Mr. Sollitt's method he obtains not the 

 aperture of the objective which he tries, but the sum of it, and 

 that of the lens which he uses as an eye-piece. 



I expressed a belief that objectives of large apertures receive 

 less light from an object in balsam than from one which is dry, 

 and 1 do not see how it can be avoided without also denying 

 the elementary principles of optics. A valve of a diatome 

 (for example) in air disperses light in every direction, as is 

 proved by illuminating it in a dark room with a narrow pencil 

 of sunlight transmitted perpendicularly through it. It is 

 perfectly seen out of the direct beam till its markings disappear 

 by foreshortening, but continues brilliantly visible till the eye 

 comes almost to the very plane of the glass on which it is 

 placed. Now, of this light, so dispersed, all (except what is 

 lost by the reflection of the cover) can come through it to the 



* In measuring an objective of 176°, made by Spence, for my friend, 

 T, F. Bergin, Esq., the diameter of the cone's section was so great that 

 I was obliged to modify the method, by receiving the Hght on a screen 

 made to travel in a cylindric surface concentric with the focal point. 

 This is a decided improvement, but requires the use of a graduated circle. 

 The result must, of course, be corrected for penumbra, &c. 



