202 Dr Searle, The determination of the effective ) 
Third method. 
Here two apertures were used. The diameter of the first was dt, =0°80 
and that of the second was d)=0-42 em. The diameter of the bright patch 
due to the first was ¢,=3'31, as found above. The readings for the bright — 
patch for the second aperture were as follows: 
Right edge of bright patch, 7-90, 8:05, 8-22 cm. 
Left edge of bright patch, 4°64, 4°80, 4:97 cm. 
Differences, 3°26, 3:25, 3:25 cm. 
Mean value of diameter of patch =c,=3-25 cm. 
Hence, by (6), we find for the effective diameter of the stop, 
dy, (G = €9) arene 0:80 x 0:06 ee - 4 
eas ea ee 31—0:13=3:'18 cm. 
The mean of the three values gives ~=3'18 cm. Hence 
n=f /a=2159/3:18=6:79. 
The marking of the stop on the “f” system is therefore 7/679, and the 
aperture ratio is 1/6°79 or 0°147. 
a—C; 
§9. Hffect of distance of object on effective aperture. The 
foregoing discussions refer to the case in which the light which 
falls on the photographic plate comes from an object at an infinite 
distance so that the plate is in the focal plane of the lens system. 
When, however, the object is not at infinity, as when the camera is 
used in copying, the plate will not be in the focal plane /,G anda 
fresh investigation becomes necessary. It appears, however, that 
the speed of the lens can be calculated for any position of the object, 
when, in addition to the data obtained in the second method (§ 5), 
we know the position relative to the lens system of the other 
principal focus F,. 
The speed of the lens will be proportional to the light which 
reaches unit area of the image when the object is a surface of 
standard brightness. Let an infinitesimal element dS of this 
surface be placed at O (Fig. 5), the centre of a geometrical 
hemisphere of unit radius, the plane of the element coinciding 
Zs 
‘ 
19, 
Oo.” 
Fig. 5. Fig. 6. 
with the base of the hemisphere. Let Ids be the light which 
passes, per unit area, through the surface of the hemisphere in the 
neighbourhood of the pole Z, where ZO is normal to dS. Then J 
is called the intrinsic brightness of the surface. 
The light which passes, per unit area, through the surface of 
