Professor Ahhes Paper on the Microscope. 
195 
of the lens yield unequally magnified images, according as their 
inclination to the axis varies, and according also to the unequal 
refrangibility of the different colours — an inequality which obtains 
just as much whether the several partial images are compared with 
each other, or whether within the area of each image different 
positions in the field of vision are compared. 
This class of anomalies affects exclusively the constitution of the 
image outside the centre of the field. The perfection with which 
the rays unite in the central region, and therewith the maximum 
capacity of performance, depends on the contrary entirely on the 
real aberration spherical and chromatic, as commonly understood. 
Chromatic aberrations, as they show themselves where a large 
angular aperture is used, do not depend alone on those differ- 
ences of focus which affect the image-forming beams as a whole ; 
but quite as much in an unavoidable inequality of coincidence of 
colours of variously inclined pencils of rays within the angle of 
aperture, which manifests itself in this, that an objective which 
is perfectly achromatic when direct illumination is used must be 
more or less o^;er-corrected for use with oblique illumination. 
Although the first-mentioned ordinary form of colour dispersion 
(primary and secondary) may be entirely removed or rendered 
scarcely noticeable, the last-named source of chromatism cannot 
be counteracted or removed by any known material or any known 
technical treatment. 
Spherical aberration on a stricter examination of its causes 
resolves itself into a series of independent elements which as they 
increase in number, follow, with the increasing inclination of the 
rays towards the axis, a more and more unequal course. An 
absolute effacement is only possible theoretically for the two first 
members of the series. As soon as the angular aperture exceeds a 
small number of degrees, the counteraction of spherical aberration 
can be effected in no other manner than by compensating the 
irremovable errors of the higher elements through intentionally 
introduced residual aberrations of the lower ones. The accumulation 
of unavoidable deficits which this method of compensation necessarily 
leaves unremedied, compels a limitation of the angle of aperture. 
For angles of aperture exceeding 60^ and a fortiori for the very 
large angles of modern objectives, the pre-supposition of an adequate 
compensation is found in the well-known type of construction where 
a plain nearly hemispherical front lens is combined with a strongly 
o-yer-corrected system of lenses. The discovery of this mode of 
construction must be looked upon as the basis of every improvement 
which has been introduced since. For a system of lenses made to 
use in air, the limit of serviceable aperture proves to be from 105° 
to 110°, beyond which it is not possible to counteract sufiiciently 
the spherical aberration, except by lessening the focal distance of 
VOL, XIV. p 
