586 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF 
to revolve in time with a metronome adjusted to beat seconds; so that, by ascer- 
taining the number of revolutions which the pulley, Q, makes during each revolu- 
tion of the driving-wheel, the time of asingle revolution of the disc is readily de- 
termined. This time multiplied by the ratio of the arc of the sector to the whole 
circumference of the disc, gives the length of each luminous impression. Thus, 
if the driving-wheel revolves m times in a second, and the disc times during 
each revolution of the driving-wheel, the time of revolution of the disc, ex- 
pressed in seconds, is seal: and if 6 be the angle of the sector, the time during 
which the eye receives light from each element of the luminous surface at every 
P een, 6 
revolution of the disc is Tee 
In order to compare the brightness of the aperture D, seen by uninterrupted 
vision, with its brightness as seen during the revolution of the disc, the illumina- 
tion of the apertures is first made equal by varying the distance of the flame L 
from the screen AC, until both apertures seen by reflexion in the prism appear 
equally bright. When the disc is then made to revolve, the apparent brightness 
of the aperture D immediately diminishes, and the equality of the brightness of 
the apertures is again restored by withdrawing the light L, to a greater distance 
from the screen AC.* Since the distance of the light S, from the screen B D, re- 
mains constant during this operation, the ratio of the apparent brightness of the 
aperture D, seen by uninterrupted vision, to its apparent brightness during the 
revolution of the disc, will be that of the square of the distance of the light L, from 
the screen A C, before the disc has begun to revolve, to the square of its distance 
during the revolution of the disc. For since the intensity of the light incident on 
the face O, of the prism is constant, we may conceive that face of the prism as the 
source of light of a constant intensity. Let 6,=the apparent brightness of this 
light seen by uninterrupted vision; b,=its apparent brightness seen during the 
revolution of the disc. Then if 7=the intrinsic brightness of the flame L, d, and 
d, its distances from the screen before and during the revolution of the disc, a, 
the ratio of the brightness of the light transmitted by the glass in the aperture 
C’, to that incident upon it, and 7, the ratio of the brightness of the reflected light 
to the light incident upon the face N, of the prism; the apparent brightness of the 
aperture C, when the light L, is at the distance d,, will be a and at the dis- 
1 
ari 
ay 
of both apertures is made equal, we have 
tance d, its apparent brightness will be Now since the apparent brightness 
* This is conveniently done by means of a pulley and cord. When the apertures are being made 
equally bright before the dise is made to revolve, it is necessary that the aperture D should be fully 
exposed. Where the sector is too narrow to admit of the whole aperture being seen at once, another 
sector is cut in the dise for this purpose, which admits of being closed by a slider of pasteboard be- 
fore the disc is made to revolve. 

