88 



THE AMEEICAN MONTHLY 



[May, 



corrected by placing a system of 

 strongly over-corrected lenses above 

 or behind a front lens that is under- 

 corrected. When we consider the 

 varying inclination of the rays of 

 light which enter a microscope-objec- 

 tive, especially an objective having 

 a large angular aperture, the difficulty, 

 in truth, the impossibility of correct- 

 ing the chromatic aberrations of all 

 the rays from the axial to the mar- 

 ginal ones, will be evident. Apart 

 from the necessary residual chroma- 

 tism of the system, due to the irrational 

 dispersion of the two kinds of glass, 

 the different angles of incidence 

 greatly complicate the problem of 

 perfect correction. Spherical aberra- 

 tion cannot be eliminated, for in 

 attempting to correct the aberrations 

 of an under-corrected lens by a power- 

 fully over-corrected system, residual 

 errors will always be found. Since per- 

 fect achromatism cannot be obtained, 

 it is evident that the images produced 

 by rays of different colors will each 

 be of a different size from the others. 

 It is also true that there is a differ- 

 ence between the magnification of 

 axial and peripheral rays, so that a 

 certain amount of distortion is pro- 

 duced. The same effect is far more 

 noticeable in the ocular, for there the 

 variation of amplification is consider- 

 able. Nevertheless, the faults of the 

 most perfect objectives are so great, 

 relatively to the imperfections of the 

 ordinary ocular, that it is useless to 

 attempt to improve the performance 

 of an objective by carefully corrected 

 oculars. I do not mean to assert 

 that the improved or patented oculars, 

 such as the ''orthoscopic," periscopic 

 and "solid" eye-pieces possess no 

 points of superiority over the common 

 form, for this is not true ; their supe- 

 riority, however, is apparent mainly in 

 an increased field, or in diminished 

 loss of light by reflection from surfaces, 

 but they cannot render visible details 

 of structure, which an ordinary ocular 

 would not show. 



We pass now to the consideration 

 of the action of an objective in form- 



ing an image of an object. For this 

 purpose we will consider the object 

 to be the siliceous covering of a dia- 

 tom known as P. angulatum. When 

 this object is placed in the focus of 

 a good objective, and viewed with 

 the eye-piece the outline is clearly 

 seen, and also the median line. This 

 outline-image is formed in accord- 

 ance with the ordinary dioptrical 

 rules. But in looking into the micro- 

 scope vv^e see more than the image of 

 the diatom. There is a circular 

 " field of view " which is also an 

 image — an image of something exter- 

 nal to the microscope, it may be an 

 image of the source of light, of the 

 mirror, of the diaphragm, but it is 

 truly an image and it must be regard- 

 ed and studied as such ; for in this 

 image, in connection with the images 

 of objects in the focus of the objec- 

 tive, all the imperfections of the 

 dioptrical action of the objective 

 may be detected. This aperture- 

 image, together with the object-image, 

 may be studied in detail in two 

 places, viz. : in the upper focal plane 

 of the objective, or just above the 

 eye-lens of the eye-piece. It may be 

 studied v^ith the naked eye, or with 

 the aid of an examining lens. The 

 diameter of the aperture-image is 

 determined by the angle of diver- 

 gence of the external cone of rays 

 which enters the objective, and the 

 focal distance. Any ray proceeding 

 from the focal point of an objective 

 is found in the aperture-image at a 

 distance from the axis that may be 

 measured by the equivalent focal 

 length, multiplied by the sine of the 

 angle which the ray forms with the 

 axis. It follows from this that there 

 is a direct relation between angular 

 aperture and the diameter of the 

 aperture-image. It also follows that 

 the exact course of any ray of light 

 can be followed by means of the 

 aperture-image. The objective col- 

 lects the rays of light which diverge 

 widely from the object, the various 

 lenses gradually change the direction 

 of the rays until they become parallel, 



