412 



K A L E I D O S DO P E. 



ed image is greatly inferior to that of the sector AOB 

 seen by direct visiari , but if the number of reflections 

 is 1 6, 18, or 20, or even above 8 or 10, the last reflect- 

 ed image is scarcely if at al' perceptible, even when a 

 pretty strong light is thrown upon the aperture. If 

 the picture consequently had been symmetrical and 

 agreeable to the eye in so far as the arrangement of its 

 parts was concerned, it would have lost all its beauty 

 from the extreme inequality in the light of the reflected 

 images of which it is composed. When the reflectors 

 are made of glass, or of glass covered on one side 

 with black varnish, this difference is so very striking, 

 that the circular field can scarcely be completed. By 

 very powerful illuminat-on, indeed, the last image may 

 be rendered visible ; but the difference of the intensi- 

 ties of the sectors remains the game, and therefore the 

 imperfection of the picture cajihot be corrected even by 

 the application of the strongest lights. 



As the eye advances from C to B, the angles of inci- 

 dence increase, the Joss of light diminishes, and the 

 difference in the intensity of the reflected images is the 

 least possible when the eye arrives at E. In the case of 

 blackened glass, the last reflected images are sufficiently 

 bright, when the number of sectors is 12 or 16. Hence 

 it follows, that in order to obtain a perfectly symmetrical 

 picture from the images formed by reflection, and to pro- 

 cure as much equality as possible in the light of the dif- 

 ferent images, the eye should be placed in the planes of 

 both the reflectors, or as near as possible tu the angular 

 point at E. 



SECT. III. On the Effects produced by varying the 

 Position <fthe Object. 



If the object is placed within the reflectors at any 

 point D, between their object end O and their eye end 

 E, a perfectly symmetrical picture will obviously be 

 formed from it ; but the centre of this picture will not 

 be at O, the centre of the lunvnous sectors, but at the 

 point D, or its projection rf, Fig 1 and 2, where the ob- 

 ject is placed, so that we shall have a circular luminous 

 field enclosing an eccentric circular pattern- Such a 

 position of the object is therefore entirely unfit for the 

 production of a symmetrical picture, unless the object 

 should be such as wholly to exclude the view of the 

 circular field, formed by the reflected images of the aper- 

 ture AOB. 



As the point D approaches to O, the centre of the 

 symmetrical picture will approach to O, and when D 

 coincides with O, the centre of the picture will be at 

 AO, and all the images of the object placed in the 

 plane AOB will be similarly disposed in all the sec- 

 tors which compose the circular field of view. Hence 

 we may conclude, that a perfectly symmetrical pat- 

 tern cannot be exhibited in the circular field of view, 

 when the object is placed between O and E, or any 

 where within the reflectors. If the eye could be placed 

 exactly at the angular point E so that every point of 

 the line EO should be projected upon O,then the images 

 would be symmetrically arranged round O ; but this is 

 obviously impossible, for the object would, in such cir- 

 cumstances cease to become visible when this coin- 

 cidence took place. But independent of the eccentrici- 



half, one-third, or one-fourth of it, as when we have it 

 in our power to move the objects across the aperture, or 

 the aperture over the objects. * 



Another evil arising from the placing vf the objects 

 within the mirrors is, that we are prevented from giving 

 them the proper degree of illumination which is so es- 

 sential to the distinctness of the last reflections. 'ITie 

 portions of the mirrors, too, without the objects, or be- 

 tween D and O, are wholly unnecessary, as they are 

 not concerned in the formation of the picture. Hence 

 it follows, that the effects of the Kaleidoscope cannot 

 be produced by any combination of mirrors in which 

 the objects are placed within them. 



Let us now consider what will happen, by remo- 

 ving the object beyond the plane pa.-sing through 

 AOB. In this case the pattern will lose its symme- 

 try from two causes. In the first place, it is manifest, 

 that, as the eye is necessarily raised a little above the 

 point E, and also above the planes AOE, BOE, it 

 must see through the aperture AOB a j>ortion of tfie ob- 

 ject situated below both of these planes. This part of 

 the object will therefore, appear to project beyond the 

 point, or below the plane where the direct and reflected 

 images meet. If we suppose, therefore, that all the re- 

 flected images were symmetrical, the whole picture 

 would lose its symmetry in consequence of the irregu- 

 larity of the sector AOB seen by direct vision. But 

 this supposition is not correct; for since the image m n, 

 Fig. 3. seen by direct vision does not coincide with the 

 first reflected images mn' ', nm', it is clear, that all the 

 other images will likewise be incoincident, and there- 

 fore that the figure formed by their combination must 

 lose its symmetry, and consequently its beauty. 



As the eye must necessarily be placed above a line 

 perpendicular to the plane ABO at the point O, it will 

 see a portion of the object situated below that perpen- 

 dicular continued to the object. Thus, in Fig. 1. if the 

 eye is placed at e above E, and if MN is the object 

 placed at the distance PO, then the eye at e will ob- 

 serve the portion P o of the object situated below the 

 axis POE, and this portion, which may be called the 

 aberration, will vary with the height E e of the eye, 

 and with the distance OP of the object. 



Let us now suppose E e, and OP to be constant, and 

 that a polygonal figure is formed by some line placed at 

 the point Q of the object MN. Then if PQ is very great 

 compared with P o, the polygonal figure will be toler- 

 ably regular, though all its angles will exhibit an im- 

 perfect junction, and its lower half will be actually, 

 though not very perceptibly, less than its upper half. 

 But if Q approaches to P, Po remaining the same, so 

 that P < bears a considerable ratio to PQ, then the po- 

 lygonal figure will lose all symmetry, the upper sector 

 being decidedly the largest, and the lowest sector^ the 

 smallest. When Q arrives near P the aberration becomes 

 enormous, and the figure is so distorted, 'that it can no 

 longer be recognised as a polygon. 



The deviation from symmetry, therefore, arising from 

 the removal of the object from the extremity of the re- 

 flectors, increases as the object approaches to the centre 

 of the luminous sectors or the circular field, and this de- 

 viation becomes so perceptible that an eye accustomed 

 to observe and admire the symmetry of the combined 

 objects, will instantly perceive it, even when the dis- 



Kaleid*- 

 scope. 



ty of the pattern, the position of the object within the tance of the object or PO is less than the 20th part of 



mirrors prevents that motion of the objects without an inch. When the object is very distant, the defect 



which a variation of the pattern cannol be produced, of symmetry is* so enormous, that though the object is 



An object between the reflectors must always be ex- seen by direct vision, and in some of the sectors, it is 



posed to view ; and we cannot restrict our view to one. entirely invisible in the rest, 



