Universal Apertometer. 201 



passing through the objective, when used to form an image in 

 the field of the eye-piece of the microscope. 



So much for the air angle; for balsam, or what we will here 

 consider as the same thing, angle in glass, the slide [g) is 

 replaced by another (Fig. 8) of the same thickness, but with 

 a small bull's eye — say 0.25 inch radius — cemented to it, and 

 of such thickness that its center of curvature is in the 

 front surface of the slide ; fine lines are also ruled on this 

 slide, passing through the center of curvature of the lens. 

 When the bull's eye is properly adjusted, it will make no dif- 

 ference in the distinctness with which the images of external 

 objects are exhibited, when using the objective and eye lens 

 (/) as a little telescope, whether the glass slide and bull's eye 

 are in position or whether they are removed, the rays pass 

 through the slide and bull's eye, emerging without refraction 

 at the convex surface ; they will emerge, indeed, at a much 

 smaller angle, as shown in Fig. 11, from the refraction at the 

 front surface; and in this refraction, nearly all the rays which 

 give the exaggerated angle disappear, and the angle of the 

 emergent rays is the true angle in glass, from which the true 

 air angle may be computed. To avoid this computation, M. 

 Zeiss constructs the apertometer with another scale, upon 

 which an arc of 82° corresponds to 180°, and one of 77°. 5 to 

 144°, &c. No objective ever made, or that can be made to 

 work as a dry lens, will pass rays through the slide and 

 bull's eye at a greater angle than, say 82*^, when air intervenes. 



The I -8th inch already alluded to, when the systems were 

 closed and it was adjusted on the cross lines in the center of 

 curvature of the hemispherical lens, transmitted rays making 

 an angle of 77°. 5. The natural sine of half this angle is .6259, 

 and this, multiplied by 1.52, assumed as the index of refraction 

 of glass, gives .9513, the natural sine of 72°. 05, twice which, or 

 144°. I, is the air angle. [The degrees are here given in 

 tenths.] Measured directly, using the glass slide {g) and the 

 lines, as before described, I obtained 144°. Measured on the 

 sector in the old way, I had no difficulty in getting 179° before 

 the light disappeared. 



A I -6th inch Gundlach, which, measured in the old way, 

 gave 141°, as the air angle, gave but 72^.75 with the bull's eye, 

 from which the computed air angle is 128°. 7; when measured, 

 using the glass slip (^), I obtained 129°. It will be understood 



