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

 one unit. We shall then have V^rrS, and V„='l', which will 

 give M= -; whence it follows that the distorted figure will 



be constructed by reducing the angular distances between the 

 different points of the regular figure to a fourth of their re- 

 spective values. We shall have, moreover, A= - ; that is to 



say, the distorted figure will be found comprised in a right 

 angle, and must be repeated four times. In fine, three slits 

 may be pierced in the black disc. With these elements, we 

 start from the coincidence between one slit and the first point 

 of one of the partial distorted figures. When this slit shall 

 have completed one revolution, the point in question will only 

 have made three-fourths of its revolution, so that it will be 

 removed from the slit an angular distance equal to a right 

 angle. The slit will then have passed before the whole of 

 one of the distorted figures, and consequently a complete 

 regular figure will have been produced. But then the slit 

 will be found before the first point of the following distorted 

 figure, so that its second revolution will cause a second regular 

 figure superposed upon the first, and so on. Moreover, when, 

 after one coincidence, a slit shall have effected one-third of a 

 revolution, another slit will be found in the position which the 

 first occupied at the instant of that coincidence; but also, 

 during this third of a revolution, the transparent disc will have 

 made a fourth of its revolution : the second slit will then cor- 

 respond to the first point of the succeeding distorted figure, 

 and consequently these two slits will produce identical effects ; 

 in short, the same reasoning applies to the third slit with re- 

 lation to the second, and it is seen that an uninterrupted suc- 

 cession of regular images will result from this system, which 

 will be completely superposed upon one another. 



In order to form an idea of the kind of deformed drawings 

 which the case under our consideration gives, I suppose that 

 with the above elements it is wished to obtain, for a regular 

 figure, the word LOI written in white letters upon a black 

 ground (Plate III. fig. 1); the construction of the distorted 

 figures will then give the fanciful drawing represented by 

 fig. 2; and we see that unless accustomed to this kind of 

 anamorphosis, it would be very difficult to divine, from the 

 inspection of this drawing, the regular figure which it will 

 produce. 



It remains for us to"offer two remarks with respect to these 

 figures. In the first place, let us consider a radius traced 

 upon the drawing of the regular figure, and let us take, for 

 example, that which, in the straight position of this figure, is 



