TRANS. OF PROF. ABBE’S PAPER ON THE MICROSCOPE. 143 
surface whatever magnifying power be used, or whatever mode of 
illuminating (direct or oblique). | Even a couple of lines ruled on 
a glass will, under the circumstances above stated, be not otherwise 
distinguishable than as one broader line with sharp outlines. With 
the most powerful immersion lens nothing at all can be seen of the 
markings of Pleurosigma angulatum, and even the coarse lines of 
LHipparchia Janetra remain unrecognizable with a power of 200. In 
the case of granular objects and other irregularly shaped particles, 
diffracted light cannot be completely separated from undiffracted 
light, and accordingly there is no absolute disappearance of all the 
particles; but such indefiniteness of image ensues that the finer 
particles of the preparation fuse into a homogeneous grey cloud. 
(ii.) When all light is shut off, excepting a single pencil. of 
- diffracted rays, a Zositive image of the particles in the object which 
caused the diffraction is formed, and appears more or less brightly 
on the dark field, but without any detail. Ruled lines appear as 
uniformly clear flat stripes on a dark ground. 
(iii.) But when not less than ¢o separate pencils are admitted 
the image always shows sharply defined detail, whether it appears 
in the form of system of lines, or of separate fields; nor does it 
matter whether undiffracted light passes in with the incident cones 
or not: that is to say, whether the image appears on a bright or a 
dark field. If fresh pencils be set in operation fresh details appear, 
but always different, according to the degree of minuteness, or to 
the nature of the markings; and this detail 1s not necessarily con- 
Jormable either with that of the tmage as seen by ordinary illumina- 
tion, or with the real structure of the object as known or ascertained 
zn other ways. In respect to this last point the following particulars 
are noteworthy. 
(iv.) A simple series of lines will be always imaged as such when 
two or more illuminating pencils are set in operation, but the lines 
will appear doubly or trebly fine when, instead of the pencils being 
consecutive in order of position, one, two, or more intervening 
pencils are passed over. Thus a group of two lines only in the 
object appears as if composed of three or four separated sets. The 
phantom lines thus created cannot be distinguished by help of any 
magnification from the normal image of actual lines of double or 
treble fineness, either in respect to sharpness of definition or con- 
stancy of appearance, as may be shown by a conclusive experiment, 
in which namely, the falsely doubled image appears side by side 
with the image of an object actually ruled with lines of double 
fineness. 
(v.) When two pieces of simple lattice cross each other in the 
same plane at any selected angle, the systems may, by suitable 
regulation of the admitted pencil of light, be rendered visible 
together or separately, and by varying the form of illumination 
