TESTING THE CHROMATIC ABERRATION. 165 



achromatism, and to this extent the traditional method of explana- 

 tion is well grounded. Yet it does not by any means follow that 

 an under-corrected objective-image will receive a red or orange- 

 coloured border by the dispersion in the eye-piece. For since the 

 image-points v" and r" are the apices of the emergent cones of 

 light, and therefore approach each other to a certain extent on 

 approximation or withdrawal of the eye-lens (while the distances 

 remain constant), it is always possible to give them such a position 

 that they will coincide for the observing eye. In this case, how- 

 ever, the resulting image appears either perfectly colourless or 

 bordered only by colours of the secondary spectrum. 



The elimination of the blue or red coloured borders does not 

 therefore afford any criterion of true achromatism ; it is equally 

 possible with under-corrected and achromatic objectives, as with 

 over-corrected ones, and so far the usual method of explanation 

 is inaccurate. 1 



This explanation becomes quite untenable when the real image 

 is formed by an excentric part of the objective-system, e.g., by one 

 half, which occurs most frequently in microscopical examinations. 

 The defect of achromatism must therefore manifest itself, as was 

 above pointed out, in the displacement of the different colours 

 laterally, so that on the one side red, and on the other violet, pre- 

 ponderates. It is evident that under such circumstances a correc- 

 tion of the objective-image by means of the eye-piece is impossible. 

 The coloured borders may certainly be somewhat modified, but 

 never eliminated on both sides simultaneously. 



The chromatic aberration of the objective cannot, as a rule, be 

 eliminated by means of the opposite aberration of the eye-piece, 

 except in certain particular cases. This is also unconditionally 

 true with regard to spherical aberration. For since the incident 

 cones of light in the eye-piece generally meet less than a square 

 millimetre of the refracting surfaces, it can hardly be assumed 

 indeed it is almost impossible that, with proportionally weak 

 curvatures, considerable aberration, capable of elimination, could 

 still be present, or that aberration already present could be 

 compensated. 



1 The absence of the coloured borders shows only, according to what has been 

 stated, that the field-lens and eye-lens form, in the effective peripheral zone, 

 a combination which is aplanatic for red and blue light. The points of con- 

 vergence of the differently coloured pencils do not here come into account. 



