10 
Proceedings of the Royal Irish Academy. 
adapted to a frds object glass, with the binocular tube, and I think 
the results there exhibited (which the Members can view after the 
meeting) will be found to be satisfactory. 
The size and curvature of the paraboloid is easily made out, if the 
focus be chosen y^^h of an inch above the upper surface, the equation 
of a perpendicular section \f = ax will become = <^ ^ ^ + I ^ind solv- 
ing the equation for «, we shall have « = - -J + ^/ 4y^+^^g ; and if the upper 
surface of the paraboloid be made |ths of an inch in diameter (a size most 
convenient in practice), a becomes = to J, and the equation y"^ - is 
that of the paraboloid form. Should the focus be taken at a distance of 
jJ^th of an inch above the truncated paraboloid, and its upper surface 
be one inch in diameter, then the equation becomes y^ — jX quam 
proxime :* this latter form will admit of a hollow cone of light of 
120°- 185°, and will almost give a dark ground illumination for an 8th 
immersion object glass. I have also on the table another microscope, 
in which, by this illuminator, the Pleurosygma formosa is well seen. 
A useful addition to this instrument will be found in cementing an 
Abraham's prism to the bottom of the paraboloid, adapted to a focus 
of about 14 inches, so that the rays from a lamp, at that distance, will 
be easily concentrated on the object {see Plate II., fig. 2). 
Should direct light be required for any mode of investigation, even 
with some of the highest powers, another form of microscope could be 
made, by turning the paraboloid upside down, and placing the object 
glass in its centre ; and by using a perforated reflector, placed in the 
body of the microscope, and the immersion principle, a new instrument 
can be produced, and which, I think, may be useful for some kinds of 
objects (566 Plate III., fig. 2). 
The same principle of immersion is applicable to all kinds of axial 
condensers, and I am sure, when they come to be tried, will give re- 
sults equally satisfactory, and possess advantages similar to those I 
have observed in the form of dark ground illumination, which I have 
had the honour to bring before you. 
Allow me briefly to recapitulate the advantages which I claim for 
this mode of illumination : — 
1. The object under the microscope will be seen by light reflected 
from its surface and from its interior (if transparent) ; 
2. It will allow no disturbing light to impinge on the retina ; 
3. It will get rid of almost all shadows ; 
(*) The above calculations have been simplified by not allowing for the deviation 
caused by the intermediate fluid, and also by the medium in which the object is 
placed. Should water be used (as required in many cases) some modification of the 
above will be necessary, and the ■ araboloid should be formed accordingly ; = ax 
will then assume the form = — or y^ = - and the focus will be or 1th of 
10 8 
an inch above the upper surface of the paraboloid ; in the latter case, a rather 
thick slide M'ill be required. 
