20 
On the Limits of the Optical 
tion) are obtainable only by instruments in which the objective 
admits a cone of light of very large angular aperture from each 
point of the object. 
We have gradually arrived at that stage of improvement in the 
construction of instruments in which rays of light whose direction 
is nearly perpendicular to the axis of the instrument are passed 
into and through the objective, and transmitted towards the ocular. 
This, it is true, happens only when a lens is used dry (i. e. the 
front surface in contact with air), in which case rays inclined to 
the axis at angles up to 87J° actually do enter a well-constructed 
immersion lens. This angle, however, diminishes to about 48° * 
when the lens is used wet, that is, when water is dropped between 
lens and covering glass as in the ordinary practice. This last- 
named angle is nevertheless of far higher amount than any angle 
of aperture in the lens system of a telescope, or photograph 
camera, because with such oblique incidence the spherical aberra- 
tion, even in the carefully calculated and accurately executed lenses 
of these instruments would be simply intolerable. Why then, 
notwithstanding this, is the large incident cone of light in the 
microscope more advantageous than a narrow one of more intense 
light which would deliver an equal absolute quantity ? The 
answer hitherto given to this question appears to me unsatisfac- 
tory. For the so-called " penetration " (i. e. the power of deHnea- 
ting by light and shadow and so rendering visible to the eye 
particles whose refractive quality dififers but slightly from that 
of the matter surrounding them) depends solely upon the pro- 
portion of the aperture of illuminating cone to that of the cone 
passing from points of the object into the lens. Sufficient delinea- 
ting shadow can only be got by narrowing the aperture of the 
illuminating cone, and a comparatively large cone can only be 
applied beneath the object when the cones of light passing from it 
into the objective are also large. 
Now there does, in point of fact, exist in the microscope a 
special cause which under the conditions here given produces a far 
greater aberration of rays from the focal plane than is occasioned by 
spherical and chromatic aberration, and which makes itself most felt 
just when the cones of incident light are smallest. This cause is 
diffraction. 
If, perhaps, occasional allusion has been made to diffraction as 
a cause of deterioration of the microscopic image, I have yet 
nowhere found any methodical investigation into the nature and 
amount of its influence ; but such an investigation shows, as will 
here appear, that diffraction necessarily and inevitably increases 
with the increase of magnifying power, and at length presents an 
* These figures, it must be borne in mind, denote in each case the angle 
included between outermost incident ray and axis of instrument, that is, half 
the so-called " angle of aperture.'' 
