651 
.0 P T 
& lens adjufted exaftly to the neareft part of the pifture. 
Confequently, the focal length of the lens mu ft be a mean 
between the diftances of different parts of the pifture; that 
as, a little greater than that which is fuited to the feftor 
feen by direft vifion. 
When fmall kaleidofcopes are made with four or with 
three mirrors, the preceding directions are equally appli¬ 
cable, the greateft care being taken that the reflectors taper 
nearly to a point at the eye end, fo as not to leave an 
aperture greater than 1-15th of an inch in diameter. 
The preceding inftruments may alfo be fitted-up with a 
draw-tube and lens. 
Curious Properties. —-The fplendid difcoveries which 
have been made with the telefcope and microfcope have 
inverted them with a philofophical character which can 
never be attached to any other inftrument. It is only, 
however, in the hands of the aftronomer and the natura- 
lift that they are confecrated to the great objeCts of fci- 
ence : their ordinary poffeffors employ them folely as in-«> 
ftruments of amufement; and it is fingular to remark how 
loon they lofe their novelty and intereft when devoted to 
this inferior purpofe. The folar microfcope, the camera- 
obfcura, and the magic lantern, are equally fhort-lived in 
their powers of entertainment; and even the wonders of 
the electrical and galvanic apparatus are called forth at 
long intervals, for the occafional purpofes of inftruCting 
the young, or aftoniftiing the ignorant. A ferenity of Iky, 
very uncommon in our northern climate, is abfolutely 
neceffary for difplaying the powers of fome of the prece¬ 
ding inftruments ; and the eftefts of the reft can only be 
exhibited after much previous preparation. From thefe 
caufes, but principally from a want of variety in their ex¬ 
hibitions, they have conftantly failed to excite, in ordi¬ 
nary minds, that intenfe and continued intereft which 
3night have been expeCted from the ingenuity of their 
r.ouftruCtion and the fplendour of their eftefts. But we 
have heard of many cafes where the tedium of fevere and 
continued indifpolition has been removed, and where 
many a dull and folitary hour has been rendered cheerful 
by the unceafing variety of entertainment which the ka- 
leidofcope afforded. In one refpeft, indeed, this inftru- 
ment is luperiorto all others. When it is once properly 
conftruCted, its effeCts are exhibited without either Ikill 
or labour; and fo numerous are its applications, and fo 
inexhauftible its ftores, that theobferveris conftantly flat¬ 
tered with the belief that he has obtained refults which 
were never feen before, and that he has either improved 
the inftrument, or extended its power, by new applications. 
That property of the kaleidofcope which has excited 
more wonder, and therefore more controverfy, than any 
other, is the number of combinations or changes which 
it is capable of producing from a fmall number of objeCts. 
Many perfons, entirely ignorant of the nature of the in¬ 
ftrument, have calculated the number of forms which may 
be created from a certain number of pieces of glafs, upon 
the ordinary principles of combination. In this way it 
follows, (fee p. 318 of this volume,) that 24 pieces of glafs 
may be combined 1391724188887252999425128493402200 
times, an operation, the performance of which would 
■take hundreds of thoufands of millions of years, even 
upon the fuppofition that 20 of them were performed 
every minute. This calculation, furprifing as it appears, 
is yet falfe, not from being exaggerated, but from being 
far inferior to the reality. It proceeds upon the fuppofi¬ 
tion that one piece of glafs 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 fame Jlraight line, yet the 
one can be pilt above and below the other, as well as upon 
its right fide and its left fide, and may be joined, fo that 
the line connecting their centres may have an infinite 
number of pofitions with refpeft to a horizontal line. It 
follows, indeed, from the principles of the kaleidofcope, 
Shat, if only one objed is ufed, and if that objed is a mathe- 
I c s. 
matical line without breadth , the inftrument will form an in¬ 
finite number of figures from this fingle line. The line 
maybe placed at an infinite number of diftances from the 
centre of the aperture, and equally inclined to the ex¬ 
tremities of the refleftors. It may be inclined at an infi¬ 
nite variety of angles to the radii of the circular field, and 
it may be placed in an infinite variety of pofitions paral¬ 
lel to any radius. In all thefe cafes, the kaleidofcope will 
form a figure differing in charafter and in magnitude. In 
the firft cafe, all the figures are polygons of the fame cha¬ 
rafter, but of different fizes. In the fecond cafe, they 
are ftars, differing from each other in the magnitude of 
their falient and re-entering angles ; and in the third cafe, 
they form imperfeft figures, in which the lines unite at 
one extremity and are open at the other. If, inltead of 
fuppofing a mathematical line to be the objeft, we take a 
Jingle piece of coloured glafs, with an irregular outline, 
we fliall have no difficulty in perceiving, from experiment, 
that an infinite variety of figures may be created from it 
alone. This fyftem of endlefs changes is one of the mod 
extraordinary properties of the kaleidofcope. With a 
number of loofe objefts, it is impoflible to reproduce any 
figure which we have admired. When it is once loft, 
centuries may elapfe before the fame combination re¬ 
turns. If the objefts, however, are placed in the cell 
fo as to have very little motion, the fame figure, or one 
very near it, may, without difficulty, be recalled ; and, if 
they are abfolutely fixed, the fame pattern will recur in 
every revolution of the objeft-plate. 
As the kaleidofcope is of great ufe in the ornamental 
arts, particularly to carpet and lace manufacturers, calico- 
printing, paper-ftaining, jewellery, See. Sic. its adaptation 
to their purpofe is effected by occafionally furnifhing the 
inftrument with aftand, in order that the pattern may be 
fixed whilft the artift is engaged in copying it. It is alfo 
capable of being ufed with Dr. Wollafton’s camera lu- 
cida, by which means thofe who would otherwife be un¬ 
able to copy the patterns may do it with perfeft facility 
and accuracy. The eftefts of the inftrument may alfo be 
exhibited to many perfons at once, on the principles of 
the folar microfcope, or magic lantern. The inftrument 
for fcientific purpofes is occafionally fo conftrufted as to 
admit of the inclination of the refleftors being varied at 
pleafure. Under the authority of Dr. Brewfter, kalei¬ 
dofcopes of all the different forms are manufactured by 
the opticians with great accuracy and perfection ; but the 
popularity of the inftrument has been fuch as to induce 
a great number of individuals, who have been ignorant 
of its principles, to infringe upon the patent, and impofe 
upon the public a wretched imitation of the original, pof- 
feffing none of the properties which are effentially necef- 
fary to the production of beautiful and fymmetrical forms; 
and, in order to juftify fuch proceedings, it became ne- 
ceffary to fearch out for fome combination of mirrors, al¬ 
ready deferibed, which might have fome refemblance to 
Dr. Brewfter’s inftrument; and the firft fuppofed antici¬ 
pation of it was found in Prop. XIII. and XIV. of Wood’s 
Optics ; but profeffbr Wood, in a letter to Dr. Brewfter 
on the fubjeft, has molt handfomely difclaimed having 
in contemplation the eftefts produced by the kaleido¬ 
fcope in giving the propofitions alluded to. 
The next fuppofed anticipation, was an inftrument pro- 
pofed and made by Mr. Bradley in 1717; which con- 
lifted of two pieces of filvered looking-glafs, five inches 
wide, and four inches high, jointed together with hinges, 
and opening like a book. Thefe plates being fet upon a 
geometrical drawing, and the eye being placed in front 
of the mirrors, the lines of the drawing were feen multi¬ 
plied by repeated reflections. This inftrument had been 
deferibed long before by Kircher, and did not receive a 
Angle improvement from the hands of Bradley. It had 
been often made by the opticians; but no perfon ever 
thought of applying it to any purpofe of utility, or of 
ufing it as an inftrument of rational amufement by the 
creation 
