Observations on Prof. Abbe’s Experiments. By J.W. Stephenson. 85 
An examination by the eye-piece shows that this is so; by the 
reduction of the aperture the finer lines (the spectra of which are 
excluded) have disappeared and been replaced by a plain silver 
band, the coarser lines appearing in their normal condition, as 
anticipated by theory (Fig. 6). 
3rd EKxperiment.—This experiment, like the former, illustrates 
the necessity of an amount of angular aperture sufficient to admit 
some spectral rays; in it the central slit is simply reduced to 35 
of an inch, which is sufficient to exclude the spectra of the coarser 
as well as the finer lines (Fig. 7). The examination shows that, 
- even as far as lines 1780 to the inch go, all resolving power has 
departed, the two gratings being replaced by a plain silver band 
without any trace of lines. 
In all these experiments in which a slit has been employed, it 
will have been observed that the sides of the slit are parallel to the 
direction of the lines; but it will be found that if the diaphragm is 
turned so that the slit is at right angles to the lines, all the spectra 
will be readmitted and perfect definition result, proving that it is 
the position of the stops relatively to the striz, and not their form 
alone, which produces the phenomena. 
The ordinary adapter used for rotating the analyzing prism of a 
binocular microscope is a convenient instrument for adjusting the 
stops, which may be placed at the end of a small tube of a size suit- 
able for entering the objective when necessary. The same effects of 
duplication or obliteration of lines may be produced on such an 
object as Lepisma saccharina by using higher powers with suitable 
diaphragms. 
The limit of visibility is a direct consequence of the demonstra- 
tion that no resolution can be effected unless at least two pencils 
are admitted; and as the admission of a secondary or spectral 
image is absolutely dependent on the aperture of the objective, it 
follows that the resolving power is a function of such aperture, of 
which we know the superior limit to be 180°; when the limit 
of resolving power with oblique light has been reached, the illumi- 
nating ray will be seen at the extreme edge of the back lens with 
the spectral image on the opposite margin, as in Fig. 11. 
The rule given by Professor Abbe for determining the greatest 
number of lines per inch which can be resolved by oblique light 
will be found (taking any given colour as a basis) to be equal to 
twice the number of undulations in an inch multiplied by the sine 
of half the angle of aperture. 
As the sine of an angle can never exceed unity, the maximum 
will be equal to twice the number of undulations in an inch in that 
ray of the greatest refrangibility which will afford sufficient light for 
the purpose. With central light, the maximum for any assigned 
colour will be equal to the number of undulations in an inch. 
