OF THE MICROSCOPE. .. 71 



(ttbnit widely divergent pencils, but which fail to give distinct 

 and sharply-defined images. Such lenses, when measured by 

 the older methods, indicate extraordinarily large angles, and 

 yet fail to have a resolving power at all commensurate with 

 the aperture claimed. Indeed, when such objectives are 

 diaphragrned down to moderate angles, their performance is 

 frequently greatly improved. The action in this case is similar 

 to that of the diaphragms in the "hand magnifiers, shown in 

 Figures 2 and 3. In these simple lenses, it is found that by 

 cutting off the outer rays, which do not come to the same focus 

 as the central ones, the definition is greatly improved. 



It is a fact no longer open to dispute, that the efficiency of 

 an objective, supposing it to be properly corrected, may be 

 more nearly expressed by its angular aperture than by its focal 

 length. For example, if we have two objectives, one of one- 

 fifteenth of an inch focal length, and 150 angular aperture, and 

 another of one-fifth of an inch focal length, and 180 angular 

 aperture, the latter, although magnifying only one-third as 

 much as the other, will actually show more of the more delicate 

 .'. tract ural features of any object ; and if its magnifying power 

 be increased by suitable eye-pieces until it is equal to the mag- 

 nifying power of the one-fifteenth, it will give a better image 

 than the latter. Our own experience has long since convinced 

 us of the truth of this, and we believe that it is the opinion 

 held to-day by all who are familiar with glasses of both kinds. 

 Prof. Abbe, who is, perhaps, the highest living authority on the 

 mathematics of the microscope, goes so far as to say that the 

 angular aperture of an objective is an exact expression of its 

 power, and he gives a table in which he lays down the number of 

 lines to the inch which may be resolved by any given aperture. 



It is not difficult to give a practical demonstration of the im- 

 portance of a comparatively wide angle of aperture, for as we 

 have just said, object-glasses possessing this feature are capable 

 of giving important results, which cannot be obtained by means 

 of lenses of lower angle. Thus, when we examine, by means 

 of a superior French triplet of one-sixth of an inch focus, 

 the silicious remains of certain very minute plants of the species 

 Pkurosigma Ballicum, we are able to see certain lines or mark- 

 ings which exist upon their surfaces. That we may be able 



