42 GORHAM, ON THE MAGNIFYING 



from the modifications which a square undergoes in obedience 

 to the laws of isometric perspective ; and it is obvious that 

 if we are enabled to form any kind of rhombic plane at plea- 

 sure, by the mere revolution of one narrow transparent line 

 upon another, we can by simply multiplying these lines mul- 

 tiply also the planes, which when united at their edges will 

 present every appearance of a geometric solid. 



And as a single line held close to the eye appears by in- 

 tersection as a single isolated rhomb, so two or more such 

 lines will form as many images, the relative position of which, 

 as well as their number, can be regulated by that of the aper- 

 tures which produce them. 



If, for example, three fine transparent lines are projected in 

 the form of an equilateral triangle, sufficiently small to be 

 enclosed within the boundaries of a circle not bigger than the 

 pupil of the eye (fig. 1 6), and if such an object be held close 

 to the eye, and examined by the light admitted through the 

 single aperture at the distal end, its image will be that of the 

 triangular prism (see fig. 21, PI. IV.). 



On revolving the distal end of the instrument, which con- 

 tains the single aperture, the prism will appear in a variety 

 of aspects, four of which are shown in the figs. 21, 22, 23, 

 24, PI. IV., in which the image is depicted as seen at each 

 quarter of the circle. 



In order to insure the proper effect, it is essential that each 

 object (that which is held at the near or ocular extremity of 

 the instrument) shall be mere transparent outline (figs. 14 to 

 20), in contradistinction to many of those which were exa- 

 mined by the light from the circular perforations, and which 

 consisted of considerable surfaces of illuminated space. 



A few of the outlines, which I have found to bring out the 

 most satisfactory results, are given in the annexed figures 

 (figs. 14 to 20). 



Fig. 14. Fig. 15. Fig. 16. Fig. 17. Fig. 18. Fig. 19. Fig. 20. 



^^^^^^^^ ^^^^^^ 



Fig. 14. The straight line. 



15. Two straight lines meeting at G0°. 



16. Three straight lines meeting at 60° (the equilateral triangle). 



17. Four straight lines meeting at 90° (the square). 



18. Four straight lines meeting at 60" and 120° (the rhomb). 



19. Six straight lines meeting at 120° (the regular hexagon). 



20. The circle. 



The first of these objects is converted into the rhomb or the 



