TRANS. OF PROF. ABBE’S PAPER ON THE MICROSCOPE. 95 
solves 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 accumu- 
lation 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 fortioré 
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 com- 
bined with a strongly over-corrected system of lenses. The dis- 
covery 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 sufficiently the spherical aberration, except 
by lessening the focal distance of front lens from the object to a 
degree which makes it practically useless. The application of 
the immersion principle renders it possible to overcome spherical 
aberration, where even the maximum angular aperture is used. 
It is in this power of using very large angles of aperture, and also 
in avoiding loss of light, that the real advantage of the immer- 
sion plan lies. It will indeed be seen from what follows, that 
these two facts fully explain the undoubted superiority of the im- 
mersion lens. 
Every appliance by which the amending of spherical aberration 
has been attempted—whether by correcting lenses placed above 
the objective or by construction of ocular—will produce no better 
result than what is already effected by changing the distance of the 
front lens of the objective from those behind it. They simply 
permit the existing residual aberration to be transferred—shilted 
backward or forward between the centre and outside border of 
the aperture—and by this means to keep, for a time, some par- 
ticular zone of the objective more or less free from aberration, a¢ 
the cost of the rest / 
In an analysis of the conditions which belong to a perfect con- 
struction, it becomes obvious that the factors on which correctness 
of image in the centre of the field, and the maximum of good 
performance depend, namely, chromatic and spherical aberration, 
pertain to the functions of the odjective alone, upon which no 
influence of the eye-piece, however constructed, can produce any 
