Neiv Apertometer. 277 



refraction, as they enter and leave the immersion fluid, resume in 

 the crown-glass front precisely the same course they had in the 

 semicircle. In this case, the angle measured in the semicircle 

 would be precisely equal to the aperture of the pencil passing 

 through the crown-glass front, and might be called the first inte- 

 rior angle of aperture, or briefly, the interior aperture of the 

 objective. As this is the angle which, after all, determines the 

 resolving power of the objective (provided its aberrations are pro- 

 perly corrected), I think it would be better hereafter to express 

 the angle of objectives in degrees of interior aperture instead of 

 speaking of air, water or balsam angles, or using the numerical 

 scale of Abbe. This end will be obtained with sufficient exactness 

 if the crown-glass semicircle has an index of refraction of 1.525. 

 In this case, the angles read by the apparatus with each objective 

 will be its interior aperture, and no computation will be necessary. 

 But equally exact results can be obtained from a glass semicircle 

 of higher or lower index, provided only its index of refraction is 

 known ; in this case it is simply necessary to compute the corre- 

 sponding angle in a medium of 1.525 from the observed angle, by 

 the method already explained. I have ordered a semicircle of the 

 desired index to be constructed for my own apparatus, but as it 

 has not yet reached me, I am still using the one I originally had 

 constructed from the first material that came to hand. This is a 

 piece of dense crown-glass of the index 1.534, and, of course, all 

 the observed angles must be correspondingly corrected. 



The index of refraction of the glass semicircle may be exactly 

 determined, in the ordinary way, by measuring' the angular devia- 

 tion produced by a prism cut from the same piece of glass. But 

 in the absence of conveniences for this determination, it is one of 

 the advantages of this apertometer that it affords the means of 

 measuring the index of the glass semicircle with sufficient accu- 

 racy ; for, if the angle of any immersion objective that exceeds 90° 

 of interior aperture be measured by it, and then the immersion 

 fluid wiped away, and the angle measured with a very thin film of 

 air between the front of the objective and the semicircle, the ob- 

 served angle will be reduced to a figure which is constant for all 

 •objectives of the same or greater aperture, and which is indepen- 

 dent of variations in the angles of such objectives, representing, in 

 fact, double the angle of total reflection from the glass of the semi- 

 circle to air. If the sine of half this constant angle be divided 



