52 ROYAL SOCIETY OF CANADA 
intensity of the subject, and pZ another tone, O and O, the opacities 
by which they are represented ; we must have 

PL REO; 
REO’ 
or 
O, 
ae 
and 
DE DIE — lozup, 
D and D, being the densities of the transparency which represent the 
light intensities pL and Z. Ina transparency developed more or less 
than required to produce a perfect one, the last equation becomes : 
D — D, = — a log. p, (12) 
a being the development factor. 
A vignetted screen is produced by exposing a photographie plate to 
illumination which varies in amount at different points of the plate. 
Let / be the greatest illumination of this plate, and gl another illumin- 
ation. The de 0, and o produced, being orne to the light 
intensities, we have 
LDC 
(NE 0, 
or 
and ‘ 
d,—d = — log. q, 
d, and d being the densities of the screen produced by the light inten- 
sities, / and gl, the development factor being one. With another factor, 
f, the equation becomes : 
d,—d= — f log. q. (13) 
We place this screen and the transparency in the printing frame, and 
through both give the proper exposure to the plate. The negative is 
developed, the engraved block made and the print struck off as usual. 
The final result is that wherever the sum of the superposed densities of 
the transparency and screen has been greater than a certain density, M, 
there is ink on the print, and wherever this sum is less than M, the white 
paper of the print is left bare; the outlines of the dots are, therefore, the 
lines for which we have : 
DEA —— ys (14) 
This density, M, is the one which lets through just that critical amount 
of illumination which was stated to be about equal to the inertia of the 
plate, and which is the illumination on the outlines of the dots. 
