INVERTEBBATA, CRYPTOGAMIA, MICROSCOPY, ETC. 779 



but when the sector arm is swung round, the little circle of light 

 can be neatly bisected on each side of the field, as shown in Figs. 15 

 and 16. A long focus lens may be applied at the eye-hole if neces- 

 sary, or the supplemental tube recommended for Abbe's apertometer, 

 but the Professor finds all that is required is his ordinary reading- 

 glasses, and he can make the bisection of the little bright circle as 

 accurately as when using a compound Microscope to view it even with 

 a yV objective. 



Fig. 15. Fig. 16. 



If we remove the bull's-eye slide, and focus on the lines on the 

 plain slide, we may obtain the air angle with great accuracy by simply 

 looking through the eye-hole in the cap applied at the end of the tube 

 h (Fig. 7), and observing, by aid of a long focus lens, when the image 

 of the hole in / is neatly bisected on either side, as shown in Figs. 15 

 and 16. If, instead of a single lens, a short compoimd Microscope 

 with an objective of 4 inches focus is used, the eye-hole will not be 

 necessary. Except for higher amj^lification, this supplemental part is 

 not needed. The highest air angle objective measured by Professor 

 Smith is an old ^^ by Spencer, 163°. He has no doubt that some 

 of the first-class modern dry objectives of recent date may reach 170° 

 or more ; but even with an angle of 163° the extreme rays strike 

 with such obliquity, that more than half the light is reflected from 

 the front surface, without entering the lens at all, and yet more at 

 higher obliquities. Professor Smith does not mean to say that there 

 is not a gain worth striving for in passing from, say, 160° to 170°, but 

 an objective whose real air angle is more than that last named will 

 have an inconveniently short working distance. 



To compute rigidly the balsam or glass angle from the observed 

 air angle, or vice versa, the objective must not only be accurately 

 focussed, but the intersecting lines must be used ; otherwise an exag- 

 gerated angle (varying very much in different objectives, to the 

 extent of 2° to 12^) may be obtained as the glass angle ; and if from 

 this we should compute the air angle, it might be 10° or 20° too 

 much. 



Carefully used, the instrument will give entirely concordant 

 results. Moving to the right, the point of intersection will travel in 

 the same direction as from Fig. 8 to Fig. 10, and to the left the change 

 will be from Fig. 8 to Fig. 9. This is contrary to what one might at 

 first suppose ; a little reflection will show the reason for this. 



As it seems to have been supposed that Professor Smith intended 

 in his paper to cast doubts on the accuracy of Professor Abbe's 

 instrument, we may point that the Professor himself says in his 



