On Prof. H. L. Smith's Apertometer. 281 



Professor Smith's conclusions are based upon the following 

 facts : 



1. That the front lenses of microscope object glasses only 

 admit incident rays through a central area, far within their actual 

 diameter. 



2. That angle of aperture strictly means the angle measured by 

 a triangle taken from the extremities of the diameter of this light 

 spot as a base line, up to the focal distance in the axis, whether 

 that distance is in air, water, or glass, with the difference of angle 

 due to the refraction of each. 



3. That rays extending laterally from places without the central 

 focal point, do not constitute a proper angle of aperture, but cover 

 an area known as field of view. 



4. That rays from every part of the field of view pass through 

 every portion of the transmitting diameter of the front-lens, and, 

 together, enter the pupil of the eye from the eye-piece. 



5. That, in the optical methods of measuring angles of aperture 

 heretofore in use, rays from the light, or index points, have tra- 

 versed and intersected all these exterior rays or oblique angles, in 

 succession, to the limit of the field of view, which has been er- 

 roneously assigned as angle of aperture. 



We appear to be in agreement upon these five conditions. I 

 venture, however, to offer a few remarks for Professor Smith's 

 consideration. I have formed a high opinion of the utility of his 

 apertometer, as it can be used in the same manner, but with better 

 defining effect than Professor Abbe's for distant objects ; but it 

 has the much greater advantage of possessing an examining mi- 

 croscope rotating about the center of a sector in the focus of the 

 object glass, which may traverse the whole of the rays in succes- 

 sion, and ascertain their direction from the focal point up to the 

 transmitting diameter of the front lens, enabling us to discriminate 

 between the rays converging to the focus and those surrounding 

 it, so that they may not be included in the measurement. 



I have one of Professor Smith's apertometers constructed in ac- 

 cordance with his description. For a stand I utilized a sturdy 

 little microscope with a swing tail-piece, made by Zentmayer, and 

 sent over here as a model. The only addition needed was a divided 

 sector, or protractor, attached to the lower limb, so that the degree 

 of inclination of the tail-piece could be easily read. The center of 

 rotation coincided with the upper portion of the glass slide. The 

 fine motion of the microscope enabled the lines to be focussed 



