Professor Abbe’s Paper on the Microscope. 247 
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 positive 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 two 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 is not necessarily 
conformable either with that of the image as seen by ordinary illu- 
mination, or with the real structure of the object as known or 
ascertained in other ways. In respect to this last point the follow- 
ing 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 
numerous fresh systems of lines and variously figured fields which 
do not exist at all as such in the object may be made to appear with 
equal sharpness of delineation. These new systems of lines always 
correspond in position and distance from each other with the pos- 
sible forms in which the points of intersection of the real lines of the 
object may arrange themselves in equidistant series. 
With a network crossing at an angle of 60°, there appears, 
besides several smaller systems of lines, a third set marked just as 
