278 



American Quarterly Microscopical Journal. 



into unity, the quotient will be, of course, the index of refraction 

 of the glass semicircle. 



Provided the glass semicircle is nicely centered, the silvering of 

 the glass cover, which prevents vision from taking place except 

 through the small hole or slit directly over the center of the semi- 

 circle, would be unnecessary with the highest powers ; for the dia- 

 meter of the circular spot through which rays can pass into the 

 objective is so small, as compared with the diameter of the semi- 

 circle, that the greatest possible chance of error from this source 

 will be very small indeed. But with dry lenses of low power, this 

 is not the case ; the greater the transverse diameter of the objective, 

 the more readily would those rays enter it, which, having passed 

 through the semicircle, but not through its center, would indicate a 

 greater aperture than the objective actually possessed. This is, I 

 suppose, the source of the erroneous readings which Professor Smith 

 obtained {loc. cit. p. 203) when he attempted to use his apparatus 

 after the method of Abbe with low-power objectives. He did not 

 use the opaque cover with a small central hole, which is indispen- 

 sable in this case. On the other hand, his apparatus gave sub- 

 stantially the same results with high-power objectives, whether 

 used after Abbe's method or his own, and for reasons obvious, 

 I trust, from the above remarks. 



I append a list of the angles of several objectives, as actually 

 measured by my apparatus in the crown-glass semicircle of 1.534 

 index, together with the corresponding angles computed for an 

 index of 1.5, the so-called "balsam angle," and for an index of 

 1.525, which will be what I propose to call the "interior angle." 



To illustrate the performance of these objectives, I send here- 

 with photographs, by each, of a frustule oi Amphipleura pellucida^ 



