EUGENE SCHNEIDER 95 



Aberrations. — To a certain numerical aperture corresponds a certain 

 limit of definition. But this limit is not always attained; in most 

 cases aberrations distort the image, and the microscope proves inferior 

 to what one might hope for. 



Spherical Aberration. — This aberration can, in general, fairly 

 well be corrected for a given radiation. The properties of the apla- 

 natic points in the front lens facilitate the task of the constructor in 

 a singular measure. When we consider rays of one colour only, there 

 is little more to be achieved from this point of view with well- 

 •constructed objectives. 



Sine Condition. — This condition — which says that, central aberra- 

 tion having been corrected for, the point images outside the axis 

 are exempt from coma — is equally satisfied in all good instruments. 



Curvature of Field. — As regards flatness, everything, or nearly 

 ■everything, remains to be done. The field of better-class objectives 

 is curved to a deplorable degree, so that it is impossible to make a 

 useful observation on the borders of the field when adjustment is made 

 for the central portion. The manipulation of the micrometer screw 

 no doubt admits of rapid focussing and facilitates the successive 

 exploration of different portions of the field. Yet there remains 

 a loss of time and a certain difficulty "in steadying the ensemble. The 

 defect becomes more pronounced in photomicrographic work, though 

 it can be mitigated by the aid of a projection lens, suitably corrected. 

 Eut one must not indulge in illusions. As matters are and w4th the 

 materials at the disposal of the optician, it is impossible to assert that 

 w^e shall some dav succeed in completelv correcting for curvature of 

 field. 



Chromatism. — Chromatism is never eliminated, though it may be 

 toned down. The so-called achromatic objectives, cut out of the 

 customary glasses, always show more or less troublesome coloured 

 fringes on the outlines of objects. Much has been written about the 

 correction for n radiations by the aid of 72- glasses. When several 

 conditions are written for achromatisation it can easily be recognised 

 that the roots are real only for certain values of the co-efficients of 

 partial dispersions of the glasses. In the very simple case of two 

 glasses we may write : 9i , <^2 _ o 



or in another form ±1= —^ 



where (j^, = the focal power of the convergent lens, cji.-, = the focal 

 power of the divergent lens, v.-, — the ratio of {?i2 — 1) to the dis- 

 persion between the two radiations to be achromatised : 



V2 = —'j~ - for the divergent lens, 



«2 — ^2 



and j/j = the same ratio — ^ ,, for the convergent one. If we 



rii — iti 

 possessed pairs of materials such that the ratio were independent 

 of the chosen interval, we might with two glasses achromatise 

 all the radiations. The pupils of Abbe have worked out 

 this problem. The Jena glassworks have produced materials 

 which satisfy the condition defined above imperfectly, but 

 better than the usual glasses. The term apochromatic has 



