34 ROYAL SOCIETY OF CANADA 
board screen. The lines of the cross-lined screen are shown dotted in 
Fig. 7. 
There are three important differences to be noted in the behaviour 
of the chess-board and cross-lined screens. 
1st. The squares of the print’s middle tone are, with the chess-board 
screen, equal and parallel to the squares of the screen. With the cross- 
lined screen, they are turned around 45° with reference to the lines of 
the screen, and their area is double the area of the transparent squares. 
2nd. The aperture of the diaphragm with the cross-lined screen is 
twice as large as with the chess-board screen, but the exposure is the 
same for both, because there is never more than one-half of the aperture 
visible from the plate through the cross-lined screen. 
3rd. The relative positions of the diaphragm and of the screen’s 
squares for one of the screens are inverted with the other screen. With 
the chess-board screen, the diaphragm’s perspective is inscribed in the 
square of the screen ; with the cross-lined screen, it is the square of the 
screen which is inscribed in the diaphragm’s perspective. The character- 
istics of the two screens seem to be due to this inversion. Thus the effect 
on the dots produced by increasing the width of the transparent lines in 
the cross-lined screen is obtained with the chess-board screen by in- 
creasing the size of the diaphragm. With the chess-board screen, a modi- 
fication in the shape of the diaphragm’s aperture would require a cross- 
lined screen with transparent figures of the same shape, to produce the 
same dots. 
The two screens do, however, behave exactly alike when the cross- 
lined screen is used in connection with a diaphragm consisting of one or 
more pairs of equal apertures, preferably a 
single pair. This screen then transforms 
itself, so to speak, into a chess-board screen. 
The distance between the centres of the 
components of a pair is: 
a F 
C= WS Te (5) 
A double square diaphragm must fit as 
in Fig. 9 to correspond to the arrangement 
shown in Fig. 2. 
The double aperture produces twice as 
many dots as the single aperture; in the 
shadows, there is a white dot under the middle of each transparent 
square, and another white dot under the intersection of the opaque lines. 
The squares of the print’s middle tone are no longer turned around 45° : 
they are equal and parallel to the squares of the screen. All this can. be 
verified by calculating the curves of equal illumination, in the same 

