532 M. J. Plateau on some new and curious applications of 



angle, and so on up to tlie sixteenth, and let us arrange these 

 sixteen figures according to the principle of the phenakisticope ; 

 that is to say, in such a manner, that, in going from the first to 

 the last, we pass gradually through all the modifications of form 

 and position which compose the movement the appearance of 

 which it is desired to produce. Let us afterwards divide the 

 transparent disc into sixteen equal angles, and then transfer into 

 each of these last one of the above figures, distorting it angu- 

 larly in the relation of 4 to 5, and arranging all these distorted 

 figiu-es in the same order as the regular figures to which they 

 correspond. Lastly, let us make four slits in the black disc. 



The two discs thus constructed are attached to their axes, 

 placing them in such a manner that the radius, which would divide 

 into two equal parts one of the angles in which are represented 

 the distorted figures, is directed vertically from the centre of the 

 disc upwards, and one of the slits is before this radius. This done, 

 we illuminate strongly from behind the transparent disc, place 

 ourselves in front of the black disc, as in the case of the anor- 

 thoscope, and set the apparatus in motion. When the above 

 slit, starting from the position we have given it, shall have tra- 

 versed I of a revolution, the transparent disc Avill have effected 

 m a contraiy direction y^^^th of a revolution ; and, consequently, 

 the radius which would divide into two equal parts the angle adja- 

 cent to that under consideration, will occupy the vertical position. 

 But the following slit wdl then also be in this vertical position ; 

 and it is clear that the same thing will take place with all the 

 radii occupying respectively the centres of the sixteen angles 

 which contain the distorted figm-es : at the moment when each 

 of these radii ])asses through the vertical drawn from the centre 

 of the disc upwards, it w^ill coincide with one of the slits. Each 

 of the sixteen angles, with the distorted figure it contains, will 

 then be traversed in its turn by one of the slits, in such a manner 

 that the middle of its image will be directed vertically from the 

 centre upwards, and all these successive images will be exhibited 

 consequently at the same spot. But these images will be con- 

 tracted in the relation of 5 to 4, so that each distorted figure 

 will give a pei'fect image in an erect position. The rapid suc- 

 cession of all these at the same place will then produce, as in 

 the ordinary phenakisticope, the continuous appearance of a 

 figure executing the desired motion. 



Beside this erect iuuige, which results from the coincidence of 

 the distorted figures and the slits in the upper part of their revo- 

 lutions, it is clear that there is also produced, as in the ordinary 

 phenakisticope, a scries of other regular images symmetrically 

 arranged with relation to the centre of the disc. But, in the 

 present instrument, it is easy to manage so that the erect image, 



