6 GOKHAM, ON THE 



As the apertures are arranged in lines which cross each 

 other at angles of 60^ and 120°, the outlines of the transparent 

 figures should bear the same angular relation. Thus the 

 modifications of the equilateral triangle, the rhomb of 60° and 

 120 , and the regular hexagon, a few of which are given in the 

 above examples, are well suited for the purpose. 



When a transparent hexagonal star (fig. 19), slid into the 

 eye-piece of the instrument and brought close to the eye, is 

 examined by the light admitted through a combination of 

 apertures, that, for instance, marked No. 4, at the 225th 

 page, placed at the other end, the images of a number 

 of stars are apparent. These stars are seen to change their 

 relative position with every movement, however slight, of the 

 revolving plane. Sometimes they are observed to touch each 

 other by one ray, at others by two, while in intermediate 

 positions the rays alternate. The patterns which are thus 

 formed are as variable as the parts into which a circle can be 

 divided. They are shown in two of their phases of revolu- 

 tion in the 4t]i and 5th figures of Plate VIII., Vol. II. 



The concentric circles, fig. 25, thus multiplied display 

 themselves with good effect. Their appearance is represented 

 in the 6th figure of Plate VIII., which is produced by using 

 the arrangement of apertures mai'ked No. 5, page 225. 



But the combinations effected by the mutual coalescence of 

 the images of the imperfect figures into one entire composite 

 form are the most curious. Thus if the three-rayed star, 

 fig. 26, be examined, its images will be seen either to alter- 

 nate (fig. 9, Plate I., Vol. III.), or to resolve into one hexa- 

 gonal reticulation with a dot in the centre of each mesh, as 

 shown in fig. 10, Plate I., Vol. III. And the images of the 

 figure, composed of the straight and curved lines, fig. 30, unite 

 into many fresh devices ; two of which are copied in the 

 figures 7 and 8, Plate I. 



But it is needless to multiply examples, as those which have 

 been already given will doubtless have sufficed to explain the 

 construction of the instrument, and one of the purposes at 

 least to which it may be legitimately applied. 



Hitherto we have confined our attention chiefly to the mul- 

 tiplication of the images of artificial objects prepared expressly 

 for tlie purpose, and viewed by the aid of the light admitted 

 through small apertures. 



We are now to consider how the images of natural objects 

 are magnified by the same means 



Here let us notice, in limine, that we are not about to insti- 

 tute a comparison between two optical instruments, the eye 

 and the achromatic microscope, which although they are con- 



