THE ANGULAR APERTURE OF OBJECT-GLASSES. 45 



be greater as the markings are more delicate, because it would 

 require greater obliquity of the light to exclude one set, and 

 the other would be too oblique to enter the object-glass, unless 

 it be of corresponding large aperture. Now I do not see the 

 cogency of this, because, in this sentence, if he had said, that 

 the obliquity of light required must be greater if the aperture 

 was large, I readily could understand him, though the inverse 

 would be equally clear, viz., that the obliquity of the light 

 I'equired for the exclusion of one set of rays would be less, if 

 the aperture were small ; but why the obliquity must be 

 greater as the markings are more delicate I cannot understand, 

 nor has the author given us any reason for it, but assumes it 

 as a natural consequence, as implied by the word " because." 

 If there was a law in optics, that, by greater obliquity of 

 light, the ratio of con- or di-vergence between two rays was in- 

 creased, I readily could admit the pertinence of the above 

 remark ; but that would be saying that the refractive index of 

 any medium varied with the angle of incidence, while we 

 know that the sinuses of the angles of incidence and refraction 

 stand, with regard to the same medium, always in a constant 

 proportion. The greatest obliquity of light is therefore sepa- 

 rate, the two sets of rays not more than they are under ordi- 

 nary illumination. Further, if the second set is likewise too 

 oblique to enter the object-glass, if not of corresponding large 

 aperture, it would follow, that, under an object-glass of defi- 

 cient aperture, both sets of rays, those corresponding to the 

 depressed (the first), as Avell as those corresponding to the 

 undepressed portion of the valve (the second set), are excluded, 

 and thus nothing at all of the object could be seen, which is 

 simply absurd. In disregard of the simple and plain fact that 

 the efficacy of the greater over the lesser aperture depends 

 upon the admission and not upon the exclusion of certain rays, 

 the author goes on to say : " The most difficult point has been 

 to explain how it is that an object-glass of large aperture will 

 render markings evident which were not visible under an 

 object-glass of smaller aperture." I freely admit that, as I 

 have shown, if we adopt the author^s theory, the explanation 

 is not only difficult but impossible. Nor does this difficulty 

 vanish, as he states it does, when we recollect that the addi- 

 tional rays admitted by the larger aperture are more oblique ; 

 because, how can the admission of additional rays prove the 

 tilting out of others, which is tlie point at issue ? Observe : 

 hence one set of rays will be refracted from the field (pray, 

 why?), whilst the other will enter. In my opinion, there is 

 no sequitur, which that very convenient little word " hence " 

 seems to imply, but the same gratuitous assumption as we have 



