38 ROYAL SOCIETY OF CANADA 
As already explained, any shape of diaphragm suitable for a chess- 
board screen is adapted to the cross-lined screen by using pairs of aper- 
tures, the distance between the components of a pair being given by (5), 
but it is necessary to have a screen in which the opaque and transparent 
lines are of equal width. Correct gradation cannot be produced with a 
cross-lined screen by means of a diaphragm having a single aperture. 
II. CoPYING FROM POSITIVES. 
The object of the photo-mechanical process is to produce a print 
which will be an exact copy of the original. Before proceeding further 
we must define what an exact copy is in this particular case, 
A print is an exact copy of the original when any tone of the print 
and the tone of the original which it represents, send out or reflect light 
of equal intensity. 
In an original on white paper, a tone is produced by a semi-opaque 
film. The incident light has to pass through this film a first time before 
reaching the underlying surface of the paper, and is partly absorbed on 
the way. The remainder is reflected and diffused by the paper, after 
which it has to pass a second time through the film, where it is again 
partly absorbed. What is left is the light sent out by the tone in ques- 
tion ; it varies, according to a certain law, with the opacity of the film. 
In a half-tone print made with black ink on white paper, the inci- 
dent light falling on the ink is, we will assume, entirely absorbed ; that 
falling on the white surface is reflected and diffused, the intens. y of the 
light sent out being proportional to the percentage of white paper in the 
tone—that is, proportional to the area of the white dots. 
Let Z be the intensity of the light sent out by the pure white paper: 
the intensity for the middle tone of the print is 0°5 Z, because one-half 
of the surface is covered by ink. Reducing the white dots to one-half of 
the middle tone squares, the intensity becomes 0°25 L, because three- 
quarters of the surface are covered with ink. With black dots of this 
size, the intensity is 0-75 L, because three-quarters of the surface are bare. 
I assume that black ink does not reflect any light ; this is not quite 
true, but is sufficient for our purpose. I find from photometric measure: 
ments on a good half-tone print, that the intensity of the light coming 
from the ink is only 4 of the intensity for the white paper; this quan- 
tity is so small that we may neglect it. 
Screens and diaphragms adjusted as we have seen would give very bad 
results in copying from positives. An investigation of the matter shows 
that the illumination is too small in the central parts of the dots, black 
and white, while it is excessive on the edges of the squares of the middle 
tone. With the cross-lined screen, for instance, it would be necessary to 
give a supplementary illumination under the central part of the trans- 
