42 ROYAL SOCIETY OF CANADA 
aperture of the diaphragm, of which the full area À was formerly visible 
from the plate, is partly hidden by the opaque lines of the screen, leaving 
only the portion r uncovered. The illumination becomes : 
r 
i= CpL R 
or, if we designate by @ the largest portion of the diaphragm’s aperture 
visible through the screen, and by g the fraction thereof visible from the 
particular point of the plate under consideration : 
i— Cpt a 
We can take for i the critical amount of illumination which determines 
the formation of the dots; it is approximately what Messrs. Hurter and 
Driffield call the “inertia” of the plate. The outlines of the dots will 
then be the curves for which the uncovered fraction of the diaphragm is: 
iR 
= cho (8) 
For p = 1, that is, for the pure whites, the illumination at the dark- 
est point, O, of the plate (Fig. 15) must not be less than 7, otherwise a 
black dot would be found in the print. It must not be more than à, 
because a tone, pL, of the original, less bright than pure white, would 
be represented by pure white in the print. It must, therefore, be equal 
2 
toi. As the value of g for this point, O, is te must have : 
AD he ete 
ms CLO) 
Introducing this value in equation (8), it becomes : 
4b° 
Ne 9 
17 pQ ny 
We now have only to calculate by means of equation (9) the value of 
q for each tone p of the original, and, with these values of g, to plot the 
curves of equal illumination in the same way as we did before. They are 
represented in Fig. 18 for values of p increasing in arithmetical ratio from 
3, to 1, and for a screen in which the opaque lines are one-half the 
width of the transparent lines ; these lines are shown dotted in the figure. 
The values of g are given hereunder. 







p q ey ae BU Ai or tod al ony ed ean 
1-00 0143 || 0:70 0-204 040 | 0357 | 0110 | 1429 
0-95 0-150 0°65 0-220 035 | 0408 | 005 | 2857 
0-90 0-159 0°60 0-238 0:30 | 0-476 | 0:00 | co 
0-85 0-168 0-55 0-260 || o2 | 0572 | | 
0°80 0-179 050 | 0-286 020 | 074 | | 
0°75 0191 0 O45.) 0st el 0815; I> 10952, 7) | 





For p = 1, q is 4 or 0148, 
