TRANS. OF PROF. ABBE’S PAPER ON THE MICROSCOPE. 169 
may be—organized particles or mere differences of molecular 
aggregation (centres of condensed matter)—they will always 
present a delineation of the familiar form. All ground for assum- 
ing these elements to be depressions or prominences fails, after 
proof that neither the visibility of the markings nor their greater 
distinctions under oblique illumination has anything to do with 
shadow effects. The distribution of light and shade on the surface 
of the valve in the form of a system of hexagonal fields, is the 
mathematically necessary result of the interference of the seven 
isolated pencils of light which is caused by diffraction, whatever 
may be the physical condition of the object causing this diffraction: 
the position of the hexagonal fields, with two sides parallel to the 
middle ribs, has its sufficient reason in the visible disposition of the 
diffracted spectra towards the axis of this valve, and can be deduced 
by calculation without any necessity for knowing the actual struc- 
ture of the object. 
That the same state of things obtains in numerous instances of 
organic forms, the study of which belongs to the province of 
histology, we may learn from the instance of striated muscular fibre. 
The manifold changes in the characters of the images which 
present themselves account, to a certain extent, for the notorious 
discordance between the representations of different observers. 
In connection with the foregoing conclusions, which have an im- 
portant bearing on the scientific application of the microscope, it 
appears, further, that the limits of “resolving” power are deter- 
minate for every objective and for the microscope as a whole. 
No particles can be resolved when they are situated so closely 
together that not even the first of a series of diffraction pencils 
produced by them can enter the objective simultaneously with the 
undiffracted rays. As even with immersion objectives the angular 
aperture cannot, by any possible means, be increased beyond the 
degree which would correspond, in effect, to 180° in air, it follows 
that whatever improvement may be effected in regard to serviceable 
magnifying power, the limit of resolving power cannot be stretched 
sensibly beyond the figure denoting the wave-length of violet rays 
when direct illumination is used, nor beyond half that amount 
when extreme oblique illumination is used. The last limit is, in 
point of fact, already reached by the finest lines of the Nobert 
plate and the finest known markings on diatom valves, as far as 
seeing is concerned. Only in the photographic copy of microscope 
images can resolution of detail be carried any farther. 
From these facts it appears that the microscope image—ex- 
cluding two cases of a similar and exceptional kind—consists, as a 
general rule, of ¢wo superimposed images, each being equally dis- 
tinct in origin and character, and also capable of being separated 
and examined apart from each other. Of these, one is a uegatve 
