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IX . — Some additional Remarks on the Measurement of the Angle 
of Aperture of Object-glasses. By F. H. Wenham. 
A paper by myself on this subject was read before the Boyal 
Microscopical Society at the November meeting in 1876, wherein 
I pointed out how in all previous methods of measurement serious 
errors had arisen from the admission of rays from oblique pencils 
which falsified the results by a considerable addition to the angle 
proper. 
Angle of aperture simply means a pencil of rays starting from 
the axial centre of the focal plane, up to the diameter of trans- 
mission of the object-glass. The angle included represents the 
number of degrees of aperture, each ray of which gives an image of 
a near object, or a telescope view of a distant one in the same line 
of direction with a special eye-piece arrangement. But if another 
line be taken from the light boundary of the object-glass beyond 
the centre of the field plane, and to the opposite extreme of its 
margin, the direction of the ray is one of excessive obliquity ; but 
still, notwithstanding its direction, it also gives an image of a near 
and distant object either without or with the special eye-piece for 
distance. In all methods of measurement for aperture hitherto 
employed, these very oblique pencils have been included in the 
amount, thus causing some object-glasses to show near double the 
number of degrees that the cone or pencil of rays should properly 
indicate ; and so from the earliest history of the achromatic object- 
glass till now, one of the most astounding fallacies in science has 
been perpetuated, not much to the credit of those who have given 
attention to the subject. 
The method described in my paper consists of placing an opaque 
screen, with a straight-edge set in focus in the centre, exactly 
bisecting the field of view so that a ray from the exterior or margin 
of transmission of the object-glass shall be confined to the centre 
only, by the edge of the screen. The direction of this ray, as in- 
dicated by a distant image, is marked as zero on a sector scale. 
The screen is then reversed, readjusted for focus and position, so as 
to cut off the other half, leaving the first open. A ray would thus 
pass from the opposite extremes of the circle of light transmission 
of the object-glass and through the centre of focus ; the true angle 
is now indicated, as all the oblique rays deviating away on either 
side of the centre of focus are stopped off during the measurement. 
The rationale of this principle is so plain and comprehensible that 
no one has ventured forth to controvert its truth, notwithstanding 
that it must be extremely unwelcome to many, and may be left to 
posterity to recognize. 
Several, who have been measuring their object-glasses for true 
