440 M. J. Plateau on some new and curious applications 



(2.) 



.'— 



Yi+i 



V 



a value necessarily less than unity. Consequently, if we sup- 

 pose that the radius r is that which contains the first point of 

 the distorted figure, that figure will pass entire behind the 

 slit, whilst the latter describes the angle measured by the 

 fraction 



1 



V 



and a regular, perfect figure will thus be produced in this 

 same angle. But as the slit then coincides again with the 

 first point of the distorted figure, a new regular figure will 

 also be produced in a following angle equal to the first, and 

 so on. The figure is multiplied, then, whilst becoming regular ; 

 and if the angle of which we have just spoken is measured by 

 an aliquot part of the circumference, which evident^ requires 



that the relation ^ be an entire number, the regular figures 



will be found ranged symmetrically round the centre, and will 

 be reproduced in the same positions at each revolution of the 

 slit. It is clear that the number of these figures will then be 

 equal to 



In the published anorthoscope we have 

 ^+1=5; 



» n 



and there are produced, in fact, five identical regular figures, 

 symmetrically arranged around the centre. 



The velocities must always be taken such, that the relation 



-^ bean entire number; for otherwise, when the slit shall 



have made one revolution, it is clear, from what precedes, that 

 it will not be found again in coincidence with the first point 

 of the distorted figure, and that, consequently, the regular 

 figures afterwards produced will not be superposed upon tli,^j 

 first, so that there will be confusion. ; . 



If it is desired that each regular figure be seen completely 

 separated from the neighbouring ones, it must evidently be 

 necessary, when the drawing of it is made, that it be comprised 



