70 SELECTION AND USE 



Dr. Goring- devised several practical methods of measuring 

 the angular aperture of different objectives, and he gives a very 

 full and clear description of an arrangement adapted to his own 

 instrument, in which the foot was made to rotate on a carefully 

 centered and graduated base, and modifications of this plan 

 have since been adopted by several of our prominent micro- 

 scope makers. It has been pointed out, however, that, as 

 usually employed, the angle which is measured by this method 

 is not the angle a b c, and although the angle which is actually 

 determined may be of great value in determining the qualities 

 of an objective, it can hardly be denied that to apply the term 

 angular aperture to any other angle than the one that has been 

 described, must tend to introduce a confusion of terms, and is 

 altogether wrong. But in order to be strictly accurate, this 

 statement presupposes a condition which is unfortunately too 

 frequently overlooked, and that is that all the proportions and 

 curves of the different parts of the objective are perfect. To 

 make this clear, let us assume that Fig. 16 truly represents an 

 objective of which the diameters, curves, and distances apart of 

 the several lenses, are absolutely correct for the kind of glass 

 used. It is obvious that by slightly increasing the diameter of 

 lens 1, or by changing the relations of the three lenses, the ap- 

 parent angular aperture might be considerably increased. We 

 would soon find, however, that this increase was of no advan- 

 tage, because after passing a certain degree the back combina- 

 tions would fail to utilize the additional rays admitted, and the 

 result would be that the performance of the lens would be in- 

 jured rather than improved. Therefore, although in a properly 

 constructed lens the angle a b c shows the true angular aperture, 

 this will not be the case if the optician has made the front, a c, 

 larger than it ought to be in relation to the other parts of the 

 objective.* 



It is an unfortunate, but an indisputable fact, that this very 

 mistake is frequently committed by makers of objectives, who 

 either have not studied, or do not appreciate the qualities of 

 lenses of v/ide angles. They therefore make objectives which 



*The reader who desires to pursue this subject will find it fully dis- 

 cussed in Dr. Blackhaui's paper on Angular Aperture, which has beeu 

 published in a separate form. 



