36 ROYAL SOCIETY OF CANADA 
Designating by À the height of a triangle, by b the base, and by m the 
ratio between the second and the first exposure, we must have : 
= 36 (m+ 1) (6) 
The length of b is given by the equation : 
Sats [ii - (G—}) (=+1) | (7) 
in which 4 is the diagonal of the figure and 7 the ratio of the circum- 
ference to the diameter. The first exposure is given through the whole 
aperture ; the second one through the central cross shown by broken 
lines on the figure. 
It would unduly expand the limits of this paper to give the full 
theory of this diaphragm, and it is quite sufficient for our purpose 
to calculate the curves which it gives, without inquiring any further. 
YY) This diaphragm is adjusted 
77 ‘oO that its perspective will fit in 
| fly the squares of the screen as in 
Z Fig.11. The aperture of Fig. 10 
a bs Z is calculated for equal exposures ; 
LA 1Q - 


VOI the value of bis: 
Fie. 11 Di "0 19224 
The calculated curves are shown in Fig. 12. The smaller dots still 
are circles; the larger ones! are 
composite curves, consisting of arcs 
of circles, ellipses and hyperbolas. 
Their areas are given hereunder. 





q Area. | q | Area. 
0°05 0:05 ||, 0:30 | 0:2921 
0°10 010 || 0:35 | 03349 
0-15 015 || 0-40 | 0:3794 
0-20 0-20 | 045 | 0-4386 
0°25 0-25 | 0:50 | 0°50 

The first five dots are circles: 
their areas are absolutely correct. 
The square of the middle tone is, of 
course, correct. The errors in the 
remaining four dots are very much 
reduced. 
The perfection of this result may 
be improved by increasing the ratio Fie. 12. 

