584 ME WILLIAM SWAN ON THE GRADUAL PRODUCTION OF 



pasteboard (see Fig. 4, Plate XII.), or other convenient material, having a portion of 

 a sector A B C D, 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 dm-ing 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 A B G (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 = the angle A C B, and « = the time in 

 which the disc makes one revolution ; the time in which the line A C revolves 



t s 

 from its present position to the position B C will evidently be — . 



Now, if a ray proceeding from any point in the luminous surface is just 

 emero-ing at F, the point from which it emanates will remain visible until A C 



comes to the position BC, or during the time 2^. 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 gi-eater 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 \ this tmie will be '^ ^ . 



If the luminous object is circular, and the axis of the pencil of rays proceed- 

 ing to the eye is perpendicular to the plane of the disc, putting 

 it = the radius of the luminous circle, 

 6?= 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 X=2sin-i^ ; and therefore the time which 



elapses between the first appearance and the final disappearance of the luminous 

 circle, is 



From this expression it will be seen that the tune during which the eye re- 



