o8fi 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 a single 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 n times during 

 each revolution of the driving-wheel, the time of revolution of the disc, ex- 

 pressed in seconds, is — ; 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 

 revolution of the disc is ^ ^^^ ^^ ^ . 



In order to compai'e the brightness of the aperture D, seen by uninteiTupted 

 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 

 ft'om the screen A C, 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 gi'eater distance 

 from the screen A C* 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, wiU 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 0, of the prism is constant, we may conceive that face of the prism as the 

 source of light of a constant intensity. Let />, =the apparent brightness of this 

 light seen by uninteiTupted vision ; />2=its apparent brightness seen during the 

 revolution of the disc. Then if r=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 r, 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 ^/,, will be — j, and at the dis- 



"i 



(I T i 

 tance d., its apparent brightness wiU be -p,. Now since the apparent brightness 



of both apertures is made equal, we have 



* This is conveniently done by means of a pulley and coi-d. When the apertures are lieing made 

 equally bright before the disc is made to revolve, it is necessary that the aperture D should be fidly 

 exposed. Where the sector is too narrow to admit of the whole aperture being seen at once, another 

 sector is cut in the disc for this purpose, which admits of being closed by a slider of pasteboard be- 

 fore the disc is made to revolve. 



