Professor Abbe’s Paper on the Microscope. 199 
at the same time, to be able to distinguish and recognize the images 
which each zone delivers separately. For this purpose the illumi- 
nation is so regulated that every zone of the aperture shall be 
represented in the image formed at the upper focal plane by tracks 
of the entering pencils of light, yet so that for each zone a small 
streak only of light he let in, and that the tracks be kept as widely 
apart from each other as possible. If an objective be absolutely 
perfect, all these images should blend with one setting of focus into 
a single, clear, colourless picture. 
A test image of this kind at once lays hare in all particulars the 
whole state of correction of the microscope, With the aid which 
theory offers to the diagnosis of the various aberrations, a com- 
parison of the coloured borders of the separate partial images, and 
an examination of their lateral separation and their differences of 
level, as well in the middle as in the peripheral zones of the entire 
field, suffice for an accurate definition of the nature and amount of 
the several errors of correction, each of them appearing in its own 
primary form. 
Assuming the theoretical knowledge and practical experience 
necessary tb carry out such an inquiry properly, and to estimate 
its results correctly, the mode of procedure above described affords 
so exhaustive an analysis of the qualities of an objective, that when, 
in addition, its focal length and angle of aperture are ascertained, 
its whole capacity of performance may he determined beforehand. 
Whoever has once examined in this manner even good objectives 
which have proved to be excellent in practice, will be as little 
disposed to accept childish assertions of their perfectness as to 
advance on his part absurd pretensions which no one has yet made 
good. 
That the performance of the microscope does not always 
depend solely on the geometrical perfection of the image, but also, 
in addition to this, in certain classes of objects, upon amount of 
angular aperture, is a fact long recognized. The exact significance 
of this fact has nevertheless remained as problematical as the exact 
nature of the quality of “ resolving ” or discriminating power. It 
remained a question, What value might be assigned to the quality 
thus related with angular aperture, and does its significance extend 
any farther than to certain cases in which shade effects were sup- 
posed to be produced by oblique illumination ? 
In the endeavour to establish a theoretical basis for the con- 
struction of the microscope, it was a matter of the first importance 
to define the exact function of angular aperture in the normal per- 
formance of the microscope, lest I should fall into a misdirection of 
my labours towards aims of very problematical worth. 
As, then, it was important above all things to ascertain more 
exactly than has been hitherto set forth the actual facts respecting 
