OPTICS. 
G‘45 
whereas in the femicircle Mae, containing the movable 
mirror, 
The i 
images 
formed' 
by 
' i and 2 ( 2 times the 
) 3 and 4. ( a .«• • , > 4 f velocity 
| 5 and 6 / reflections, move mtbj f ofth / 
.7 and 8 •> 1 16 * mirror; 
a progfeflion which may be continued to any length. 
It h as been taken for granted, not only that the object 
feen by direct viiion is in a date of perfect junction with 
the images of it formed by reflection ; but that the objeCt 
and its images have the fame apparent magnitude, and 
nearly the fame inteniity of light. As thele conditions 
are abfolutely necefiary to the production of fymmetrical 
and beautiful forms, and may be all effected by particular 
methods of conftruCtion, we (hall briefly inveftigate the 
principles upon which thefe methods are founded, in fo 
far as the polition of the eye is concerned. 
When any objeCt is made to touch a common looking- 
glafs in one or more points, the reflected image does not 
touch the objeCt in thefe points, but is always feparated 
from it by a fpace equal to the thicknefs of the glafs, in 
confequence of the reflection being performed by the 
pofterior furface of the mirror. The image and the ob- 
jeCt mult, therefore, be always difunited ; and, as the in¬ 
terval of reparation mult be interpofed between all the 
reflected images, there cannot poflibly exilt that union of 
forms which conftitutes the very effence of fymmetry. In 
mirror glafs there is a feries of images reflected from the 
firft furface, which unite perfectly with the objeCt, and 
with one another. When the angles of incidence are not 
great, this feries of images is very faint, and they do not 
much interfere with the more brilliant images formed by 
the metallic furface. As the angles of incidence increafe, 
the one feries of images deftroys the effeCt of the other, 
from their overlapping or imperfect coincidence ; an effeCt 
which increafes with the thicknefs of the glafs; but, when 
the reflections are made at very oblique incidences, the 
images formed by the metallic furface become almolt in- 
vifible, while thofe formed by the firlt furface, are as bril¬ 
liant and nearly as perfeCt as if the effeCt of the pofterior 
metallic furface had been entirely removed. In the fol¬ 
lowing obfervations, therefore, it is underftood that the 
images are reflected either from a poliflied metallic furface, 
or from the firft furface of glafs. 
In order to explain the effeCts produced upon the fym¬ 
metry of the picture by a variation in the pofition of the 
eye, we mult fuppofe the objeCt to be placed at a fmall 
diftance from the end of the mirror. This pofition is re- 
prefented in fig. io. where AE is a feCtion of the mirror 
in the direction of its length ; MNOP an objeCt placed at 
~a diftance from the extremity A of the mirror, and mnop 
its image,.which, by the principles of catoptrics, will be 
fimilar to the objeCt, and fimilarly fituated with refpeCt to 
the mirror AE. Now, if the eye is placed at C, it will 
fee diliinCtly the whole objeCt MNOP, but it will only fee 
the portion nrso of the image cut off* by drawing the line 
CAr through the extremity of the mirror; fo that there 
cannot be a fymmetrical form produced by obferving at 
the fame time the objeCt MNOP and this portion of its 
image; and the. deviation from fymmetry will be ftill 
greater, if MNOP is brought nearer the line BA ; for the 
image mnop will be entirely included between the lines 
A r and AB, fo that no part whatever of the image will 
be vifible. As the eye of the obferver moves from C to 
e, the line CAc will move into the pofition eAx; and, 
when it has reached the point e , the whole of the image 
fmxop will be vifible. The fymmetry, therefore, arifing 
from the flmultaneous contemplation of the objeCt and 
its image will be improved ; but it will ftill be imperfeCt, 
as the image will appear to be diftant only by the fpace 
mx from the plane of the mirror, while the diftance of the 
objeCt is Mai. As the eye moves from e to E, the line 
eAx will move into EAB, and the objeCt and its image 
will feetn to be placed at the equal diltances, MB, mB, 
from the plane of the mirror, and will therefore form a 
Vol. XVII. No. i 204. 
fymmetrical combination. When the objeCt is moved, and 
arrives at BA, the image wall touch the objeCt, and they 
will form one perfeCt and united whole, "whatever be the 
fliape of the line MP. Hence we conclude, that, “ when 
an objeCt is placed at a little diftance from the extremity 
of a plain mirror, its image formed by reflection from the 
mirror cannot unite with the object in forming a conjoined 
and fymmetrical picture, unlefs the eye is. in the plane of 
the mirror.” 
When two mirrors, therefore, are combined, as in fig. r, 
the eye muft be in the plane of both, in ord?r that the 
object and its image may have a fymmetrical coincidence, 
and therefore it muft be at the point E where the two 
planes cut each other. The neceflity of this pofition, and 
the effeCts of any conflderable deviation from it, will be 
underftood from fig. 1. where AOB is the angle formed 
by the mirrors, and MN the place of the objeCt. Then, 
if the eye is placed at C, the aperture AOB will be pro¬ 
jected into afb upon the plane MN ; but the orthographic 
projection of ABO upon the fame plane is A'B'O', or, 
what is the fame thing, the reflecting furfaces of which 
AO, BO, are feCtions, will, when prolonged, cut the plane 
MN in the lines A'O', B'O'; hence, rays from the objeCts 
fituated between A'O'B' and afb cannot fall upon the 
mirrors AOE, BOE, or images of thefe objeCts cannot be 
formed by the mirrors. The images, therefore, in the 
different lectors formed by reflection round O as a centre, 
cannot include any objeCts without A'O'B'; and,flncethe 
eye at C fees all the objeCts between A'O'B' and afb, there 
can be no fymmetry and uniformity in the picture formed 
by the combination offucli an objeCt with the images in the 
feCiors. When the eye defcends to e, the aperture AOB 
is projected into a'o'b', which approaches nearer to AOB ; 
but, for the reafons already afllgned, the fymmetry of the 
picture is ftill imperfeCt. As the eye defcends, the lines 
a!o', b'o', approach to A'O', B'O'; and, wdien the eye arrives 
at E, a point in the plane of both the reflecting furfaces, 
the projection of the aperture AOB will be A'O'B', and 
the images in all the feCtors will be exaCtly fimilar to the 
objeCt prefented to the aperture. Hence we conclude in 
general, that,_ “ when an objeCt is placed at any diftance 
before two mirrors inclined at an angle which is an even 
aliquot part of 360°, the fymmetry of the picture is per¬ 
fect, when the eye, confldered as a mathematical point, is 
placed atE;” and that “ the deviation from fymmetry 
increafes as the eye recedes from E towards C.” If the 
objeCt were a mathematical furface, all the parts of which 
were in contaCt with the extremities AO, BO, of the 
mirrors, then it is eafy to fee that the fymmetry of the 
picture will not be affeCted by the deviation of the eye 
from the point E, and, in confequence of the enlarge¬ 
ment of the feCtor, feen by direct viflon. The fymmetry 
of the picture is, however, affeCted in another way, by 
the deviation of the eye from the point E. 
We have already feen that, in order to poffefs perfeCt 
fymmetry, an objeCt muft confiftoftvvo partsin complete 
contaCt, one of which is an inverted image of the other. 
But, in order that an objeCt, poffefiing perfeCt fymmetry, 
may appear perfectly fymmetrical, four conditions are 
required. The two halves of the objeCt muft be fo placed 
with refpeCt to the eye of the obferver, that no part of 
the one half {hall conceal any part of the other; that, 
whatever parts of the one half are feen, the correfponding 
parts of the other muft alfo be feen ; and that the corre^ 
fponding parts of both halves,and both halves themfelves, 
muft fubtend the fame angle at the eye. When we ftand 
before a looking-glafs, and hold out one hand fo as to 
touch it, the hand will be found to conceal various parts 
of its image ; and, in fome pofitions of the eye, the whole 
image will be concealed, lo that a fymmetrical picture 
cannot poflibly be formed by the union of the two. If 
the eye is placed fo obliquely to the looking-glafs, that 
the hand no longer interferes with its image, it will ftill 
be feen, that parts of the hand which are not direCtly 
vifible are vifible in its reflected image; and therefore, that 
2 B a fymmetrical 
