584 MR WILLIAM SWAN ON THE GRADUAL PRODUCTION OF 
pasteboard (see Fig. 4, Plate XII.), or other convenient material, having a portion of 
a sector ABCD, cut out from its circumference, be made to revolve, in a plane 
perpendicular to the line of vision, between the eye and a luminous object, the ob- 
ject may be placed so as to be seen through the sector at each revolution of the 
disc. In this manner a succession of luminous impressions will be obtained ; and 
the time during which the light acts on the eye at each impression will depend 
partly on the velocity of the rotation of the disc, and partly on the ratio of the 
arc of the sector to the whole circumference. 
Let ABG (Fig. 1) represent the disc, A C B the sector cut out of it, and E D 
the section, by the plane of the disc, of the pencil of rays proceeding from the 
luminous object to the eye. Then, if 6 =the angle ACB, and ¢ = the time in 
which the disc makes one revolution; the time in which the line AC revolves 
from its present position to the position BC will evidently be s 
Now, if a ray proceeding from any point in the luminous surface is just 
emerging at F, the point from which it emanates will remain visible until A C 
comes to the position BC, or during the time > . Since this is obviously true of 
any other element of the surface, it follows that every part of the surface remains 
visible for the same time. 
The interval of time between the first appearance of the object and its final 
disappearance is obviously greater than that during which each element of its 
surface is visible. For, if E and D be sections of the rays proceeding from the 
points in the luminous surface which are first and last visible, some part of the 
surface will be seen during the interval of time between the instant in which C B 
coincides with CE, and that in which AC coincides with CD, or during the time 
in which the line AC revolves through the sum of the angles ECD, ACB. De- 
noting ECD by A, this time will be Z whe , 
If the luminous object is won and the axis of the pencil of rays proceed- 
ing to the eye is perpendicular to the plane of the disc, putting 
s=the radius of the luminous circle, 
d=its distance from the eye, 
d’=the distance of the disc from the eye, 
c=the distance of the axis of the pencil of rays from the centre 
of the disc, it will be found that A\=2 sin — ; and therefore the time which 
elapses between the first appearance and the final disappearance of the luminous 
circle, is 
oq (2sin 15 ane + 0) 
From this expression it will be seen that the time during which the eye re- 

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