1818.] Dr. Roget on the Kaleidoscope. 377 



direction only, and the images arrange themselves in stripes 

 without any extended lateral connexions.' Of the triangular 

 kaleidoscopes, the first, having for the base of the prism an 

 equilateral triangle, produces very regular appearances of 

 images, disposed in three lines crossing each other at angles 

 of 60° and 120°, and, therefore, presenting connected triangles. 

 The instrument in this form might be distinguished by the name 

 of trigonoscope, or more shortly triascope. The second triangle, 

 which may be taken as the base of the prism, is the right-angled 

 isosceles triangle, that is, as may be perceived by the figure, a 

 triangle composed of two contiguous sides, together with the 

 diagonal of a square. This construction divides the field of 

 view into regular squares, which, by their perfect symmetry, 

 compose very beautiful arrangements ; and the instrument, 

 under this form, may be denominated a tetrascope, since the 

 predominant character of the appearances it exhibits is that of 

 images grouped together by fours, and symmetrically disposed 

 about the sides and angles of squares. The third mode of con- 

 struction, which takes for its base the half of an equilateral 

 triangle, resulting from its division by a perpendicular from the 

 vertex to the base, as is seen in the third figure, affords also 

 appearances of great beauty. The predominant form is the 

 hexagon, and the images' are grouped together in compartments 

 of this figure ; a circumstance which may entitle this variety of 

 the instrument to the appellation of hexascope ; for although 

 hexagonal arrangements also occur in the field of the triascope, 

 they are by no means so striking to the eye, or give so exclusively 

 the character of symmetry, as those which are conspicuous in 

 the construction now described. 



As a plane surface of indefinite extent admits of subdivision 

 by regular polygons of the same kind only in three ways, namely, 

 by triangles, by squares, and by hexagons ; so each of these 

 modes of division is the result of a separate arrangement of three 



{>lane mirrors, namelv, by the triascope, the tetrascope, and the 

 lexascope. Of these, the last two appear more especially calcu- 

 lated for affording assistance to artists in suggesting ornamental 

 patterns. All the polygonal kaleidoscopes, indeed, have a 

 material advantage over the common one, in the greater exten- 

 sion they give to the field of view. This field would, in 

 theory, appear to be infinite ; but in practice it soon becomes 

 limited, from the great loss of light attendant on repeated 

 reflections. With glass mirrors the light still more rapidly 

 diminishes from the polarisation it receives by being subjected 

 to so many reflections from planes of different relative inclina- 

 tions. This latter inconvenience might, however, be obviated 

 by employing metallic reflectors. More light being reflected in 

 proportion as the incident rays are more oblique, the instruments 

 above described should be of sufficient length to allow of great 

 obliquity of reflection, and thus afford more numerous repetitions 

 of images before the diminution of light renders them invisible. 



