ON THE CHANGES PRODUCED BY THE KALEIDOSCOPE.
The property of the Kaleidoscope, which has excited more wonder,
and therefore more controversy than any other, is the number of
combinations or changes which it is capable of producing from a small
number of objects. Many persons, entirely ignorant of the nature of the
instrument, have calculated the number of forms which may be created
from a certain number of pieces of glass, upon the ordinary principles
of combination. In this way it follows, that twenty-four pieces of
glass may be combined 1,391,724,288,887,252,999,425,128,493,402,200
times—an operation, the performance of which would require hundreds of
thousands of millions of years, even upon the supposition that twenty
of them were performed every minute. This calculation, surprising as
it appears, is quite false, not from being exaggerated, but from being
far inferior to the reality. It proceeds upon the supposition that
_one_ piece of glass can exhibit only _one_ figure, and that _two_
pieces can exhibit only _two_ figures, whereas it is obvious that the
two pieces, though they can only be combined in two ways, _in the same
straight line_, yet the one can be put _above_ and _below_ the other,
as well as upon its right side and its left side, and may be joined,
so that the line connecting their centres may have an infinite number
of positions with respect to a horizontal line. It follows, indeed,
from the principles of the Kaleidoscope, that _if only one object is
used, and if that object is a mathematical line without breadth, the
instrument will form an infinite number of figures from this single
line_. The line may be placed at an infinite number of distances from
the centre of the aperture, and equally inclined to the extremities
of the reflectors. It may be inclined at an infinite variety of
angles to the radii of the circular field, and it may be placed in an
infinite variety of positions parallel to any radius. In all these
cases, the Kaleidoscope will form a figure differing in character and
in magnitude. In the first case, all the figures are polygons of the
same character, but of different sizes. In the second case, they are
stars, differing from each other in the magnitude of their salient and
re-entering angles; and in the third case, they form imperfect figures,
in which the lines unite at one extremity and are open at the other.
If, instead of supposing a mathematical line to be the object, we
take a _single piece_ of coloured glass, with an irregular outline,
we shall have no difficulty in perceiving, from experiment, that an
infinite variety of figures may be created from it alone. This system
of endless changes is one of the most extraordinary properties of
the Kaleidoscope. With a number of loose objects, it is impossible
to reproduce any figure which we have admired. When it is once lost,
centuries may elapse before the same combination returns. If the
objects, however, are placed in the cell, so as to have very little
motion, the same figure, or one very near it, may, without difficulty,
be recalled; and if they are absolutely fixed, the same pattern will
recur in every revolution of the object-plate.