322 Transactions of the Boyal Microscopical Society. 
from rays proceeding at extremely oblique angles from flat surfaces 
having a raised conHguration or structure. Take, for the first 
example, a piece of coarse-grained canvas or other fabric. Throw 
light upon or through this obliquely, and examine it at various angles 
with a shallow magnifier. At visual incidences greater than 45"^ or 
50° no advantage will be gained ; on the contrary, there will be a 
positive loss of definition. The same effect is seen on a different 
surface consisting of uniform glistening particles, such as bird-seed. 
To this dissentients will say, “You are comparing observations under 
a low magnifying power or with none at all to those made with the 
microscope,” but relatively the conditions do not differ. Perhaps 
the most trying work for a hand magnifier is in examining the 
polish of glass surfaces in order to ascertain if all the “ greys ” are 
worked out. For small lenses a half-inch achromatic is used, held at 
an angle of about 45° ; at a greater angle the extremely fine specks 
cannot be discovered. Light is directed at a great obliquity on the 
surface or is transmitted. Uneducated workmen do not reason 
about any theory of angles, but adopt the one that gives the best 
result, simply because they find out at once that it does so. 
My argument is that the angular aperture of microscope object- 
glasses has hitherto been erroneously measured by all the usual 
means, in which the outer oblique rays extending to the margin of 
the field of view have been in all cases included, and, in fact, constitute 
the false measurement. The true angle is the cone of rays diverging 
from an atom or point in the centre of the field. Other pencils of 
greater obliquity defining atoms at the margin, are exclusive and 
independent of the central rays as much as the different objects 
themselves, yet it is the direction of these exterior rays that we 
have hitherto been measuring. There seems to be an absence of 
experiment, or disinclination to admit the evidence of such an error. 
For one proof of an example wherein angle of direction is erro- 
neously measured as angle of aperture, unscrew and remove the 
back lenses of high-power objectives, and measure the apparent 
apertures of the fronts alone by any of the usual methods, such as 
the traversing sector, or by the angle of direction to two distant 
images. The angle of the front lens alone of a ^ thus measured 
came out as 83°, simply because the back lens included nearly a 
hemisphere, which admits lateral rays from a wide angular direc- 
tion. The aperture of the front of a yV appeared as 110°, and 
that of a T 3 as 122°, because more rays entered sideways, as the 
back surface in these last lenses is almost a hemisphere. This 
exemplifies the absurdity and utter inaccuracy of the usual mode of 
measuring angle of aperture, as we know that these single lenses 
have in reality an angle of aperture of a few degrees only. 
In order to define more clearly the direction of these outer rays, 
that cause indications of false aperture, I tried the following expe- 
