Methods for Improving Sphe7'ical Correction. By Prof. Abbe. 819 



As is obvious from a glance at the diagram, this plan is con- 

 nected with a peculiar difference of the image-forming pencils. 

 Owing to the effect of the distance M N, the blue pencil must 

 pass to the image with less angular convergence than the red one. 

 According to the general theorem, established by Lagrange, this 

 difference indicates a different amplification of the blue and 

 the red image (the blue larger than the red), notwithstanding 

 their identical position on the axis, or, expressed in another way, 

 a chromatic difference of focal length, coexisting with identical 

 position of the conjugate foci for different colours. The practical 

 result of this deviation must be a defect of achromatism outside the 

 axis. The images of different colours coinciding on the axis, the 

 centre of the field will appear perfectly achromatic ; but the blue 

 image overlapping more and more the red one, coloured outlines 

 will appear outside the centre, increasing with the distance from the 

 axis. 



Achromatic defects of this kind are of subordinate importance, 

 as they do not injure the definition in the central part of the field. 

 They are to be found in all objectives of somewhat considerable 

 aperture, and are generally overlooked by microscopists, though the 

 difference of amplification in such object-glasses exceeds 1 per cent, 

 (the more brilliant rays of the red and blue considered only), and 

 much more still in systems with duplex front. But such defects 

 of amplification, if they become too obvious, may be easily corrected 

 either by specially constructed eye-pieces or by a separate cor- 

 recting lens added to the ordinary eye-piece. Hence the fact above 

 noticed, though not of course advantageous, is no serious objection 

 to the plan here considered. 



On the other hand this mode of construction much facilitates 

 the correction of another kind of amplificatory defect of still greater 

 importance, which cannot be overcome by the eye-pieces or similar 

 means, but must always be corrected in the objective. "What is 

 generally called by microscopists " curvature of field," is in fact 

 in its principal part the result of different amplification by different 

 zones of the apirture, — the axial pencil yielding a dift'erent linear 

 amplification of the image to those of the various oblique pencils ; 

 and for correcting these anomalies, which are a grave difficulty in 

 the construction of wide-angled systems, the elements of a separated 

 posterior lens can be readily made available. 



Eespecting the practical application of this plan of correction, 

 it can be used in both telescopic and microscopic objectives. But in 

 telescopes of small and moderate focal length the residual spherical 

 aberration is not of any practical importance ; and in large objec- 

 tives, where it has an injurious influence, there are much greater 

 aberrations arising from the disproportional dispersive powers of 

 crown and flint (secondary colours). As long as these exist the 



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