326 THE NORTHERN MICROSCOPIST. 

jective. This process is now much better performed by Abbe’s 
Apertometer, which is a semi-circular disc of glass of high refrac- 
tive index, having graduated scales on its surface ; and as it also 
acts as a wide-angled condenser, it permits of the highest balsam- 
angles being measured by it. 
“ Angular aperture” was thus regarded as the correct measure 
of the capacity of the objective for receiving and transmitting light. 
This theory rests upon the assumption that light is emitted from 
the minute radiant elements of the object with equal intensity in 
all directions, and that, in a vertical plane section of a hemisphere 
of such light, an angle of 120° would contain twice as much as 
one of 60°. This assumption is incorrect, as, in accordance with 
the established laws of optics, the light must be of the greatest 
intensity in the line of perpendicular emission, and must diminish 
towards the sides of the hemisphere in the ratio of the cosine of 
the obliquity from the perpendicular, as shown in Fig. 35. The 
nie true _—sanigle of 60°, or 30° 
THEORY. THEORY. On each side of the 
perpendicular line, 
will, therefore, con- 
tain more than half 
the quantity of light 
in the angle of 120°, 
their relative pro- 
portions being as 
50 to 87, which is 
the ratio that the 
sines of their semi- 
angles (30° and 60°) bear to each other. This will be evident on 
referring to Fig. 36, where the angular equivalents of light on the 
two theories are represented, as well as the sines of the angles of 
30° and 60°, and the relative quantities of light received by these 
sines in each case. ‘The same principle holds with regard to all 
other angles in air, viz., that they must be compared with each 
other by means of the sines of their semi-angles. 
Now as the areas of circles are to each other as the squares of 
their radii, so the ¢ofal quantities of light received by objectives of 
different angular capacity must be in the relative proportion of the 
squares of the sines of their semi-angles. The ¢/uminating powers 
of lenses must, therefore, be compared with each other by means of 
the squares of the sines of their semi-angles of aperture. So that 
if we express this power in an air-angle of 60° by the number 250, 
in an angle of 120° it will be 757, and in one of 180” it will be- 
come 1000, 
If light were emitted from every minute surface-element with 
equal intensity in all directions, we should see the illuminated disc 


Fig. 37. 
