BALSAM APERTURES. 123 



We have thus again endeavored to make manifest 

 that the idea that angular aperture is accompanied by a 

 sacrifice of working distance has no real existence 

 that is, in the form popularly accepted. 



Thus far we have discussed "angular aperture" in its- 

 popular signification, and, in several of its aspects, 

 from the definition given from the micrographic dic- 

 tionary. Taken in conjunction with the remarks we 

 have thus far had occasion to offer, the reader would 

 probably infer as axiomatic that the range of apertures- 

 would necessarily be confined within the axial pencil 

 and the one striking the underside of the slide at near 

 coincidence, thus traversing and limited by an arc 

 measured by nearly 90 the latter being equal to 180 

 of aperture. This, too, is the precise aspect to which 

 the author desired to restrict his observations. Now 

 there is another kind of aperture of which very little 

 is generally known, we refer to 



BALSAM APERTURES. 



From a theoretical or mathematical standpoint, the 

 study of balsam angles fairly bristles with difficulties ; 

 it has been to us a problem to which our school boy 

 wrestlings with Euclid seem a pleasant and simple exer- 

 cise. While we frankly admit our incompetency to 

 properly present the subject, we have to remark, on 

 the other hand that we were not willing to send forth 

 this little book without at least some mention of the 

 matter. 



Observers interested in the history of the American 



