OPTICS. 
the proportion which they would have borne to each other 
at the fame diftance, or in the fame circumftances. 
To afcertain the quantity of light loft by reflection, he 
placed the mirror, or reflecting furface, B, (Plate I. fig. i.) 
on which the experiment was to be made, truly upright; 
and, having taken two tablets of precifely the fame co¬ 
lour, or of an equal degree of whitenefs, he placed them 
exaCtly parallel to one another at E and D, and threw 
light upon them by means of a lamp or candle, P, placed 
in a right line between them. He then placed himfelf fo, 
that with his eye at A he could fee the tablet E, and the 
image of the tablet D, reflected from the mirror B, at the 
fame time making them, as it were, to touch one another. 
He then moved the candle along the line ED, fo as to 
throw more or lefs light upon either of them, till he could 
perceive no difference in the ftrength of the two lights 
that came to his eye. After this, he had nothing more 
to do than to meafure the diftances EP and DP, and then 
the intenfity of the lights was as EP 2 to DP*. 
To find how much light is loft by oblique reflection, he 
took two equally-poli/hed plates, D and E, fig. a. and 
caufed them to be enlightened by the candle P. While 
one of them, D, was feen at A, by reflection from B, 
placed in a pcfition oblique to the eye, the other, E, was 
fo placed as to appear contiguous to it; and, removing 
the plate E, tiil the light which it reflected was no ftronger 
than that which came from the image D, feen by reflec¬ 
tion at B, he eltimated the quantity of light that was loft 
by this, oblique reflection, by the fquares of the diftances 
of the two objeCts from the candle. 
In order to afcertain the quantity of light loft by reflec¬ 
tion with the greateft exaCtnefs, M. Bouguer introduced 
two beams of light into a darkened room, as by the aper¬ 
tures P and Q, fig. 3. which he had fo contrived,that he could 
place them higher or lower, and enlarge or contract them 
at pleafure; and the reflecting furface (as that of a fluid 
contained in a veflel) was placed horizontally at O, from 
which the light coming through the hole P, was reflected 
to R, upon the fcreen GH, where it W'as compared with 
another beam of light that fell upon S, through the hole Q j 
which he made fo much lefs than P, as that the fpaces S 
and R were equally illuminated ; and, by the proportion 
that the apertures P and Q bore to each other, he calcu¬ 
lated what quantity of light was loft by the reflection at O. 
It w’as neceffary, he obferves, that the two beams of light 
FO and QS (which he ufually made 7 or 8 feet long) lhould 
be exaftly parallel, that they might come from two points 
of the Iky of the fame altitude, and having precifely the 
fame intenfity of light. It was alfo neceffary that the 
hole Q fliould be a little higher than P, in order that the 
two images lhould be at the fame height, and near one 
another. It is no lefs neceffary, he fays, that the fcreen 
GH be exaftly vertical, in order that the direct and re¬ 
flected beams may fall upon it with the fame inclination ; 
fince, otherwife, though the two lights were perfectly 
equal, they w’ould not illuminate the fcreen equally. 
This difpofition, he fays, ferves to anfwer another im¬ 
portant condition in thefe experiments ; for the direCt 
ray QS mull be of the fame length with the fum of the 
incident and reflected rays, PO and OR, in order that 
the quantity of light introduced into the room may be 
fenfibly proportional to the fizes of the apertures. 
The great difference between the quantity of light re¬ 
flected from the furface of water, at different angles of in¬ 
cidence, is truly furprifing. M. Bouguer fometimes fuf- 
peCted that, when the angles of incidence were very 
fmall, the reflection from water was even greater than 
from quickfilver ; though he rather thought that it was 
fcarcely fo great. In very fmall angles, he lays that water 
reflects nearly g of the direCt light. 
The light reflected from a lake is fometimes f or £, or 
even a greater proportion, of the light that comes direCtly 
from the fun, which is an addition to the direCt rays of 
Vox. XVII. No. 1197. 
553 
the fun that cannot fail to be very fenfible. The direCt 
light of the fun diminifhes gradually as it approaches tha 
horizon, while the reflected light at the fame time grows 
ftronger; fo that there is a certain altitude of the fun, in 
which the united force of the direCt and reflected light 
will be the greateft poflible, and this, he fays, is 12 or 13 
degrees. 
The light reflected from water at great angles of inci¬ 
dence is extremely fmall. M. Bouguer w r as affured, that, 
when the light was perpendicular, it reflected no more 
than the 37th part that quickfilver does in the fame cir¬ 
cumftances ; for, it did not appear that water reflects more 
than the 60th, or rather the 55th, part of perpendicular 
light. When the angle of incidence was 50 0 , the light 
reflected from the furface of water was about thfe 3id part 
of that which mercury reflected ; and, as the reflection 
from water increafes as the angle of incidence diminifhes, 
it was twice as ltrong in proportion at 39 0 ; for it was 
then the 16th part of the quantity reflected from mercury. 
In order to procure a common ftandard by which to 
meafure the proportion of light reflected from various 
fluid fubftances, he feleCted water as the molt commo¬ 
dious ; and, partly by obfervation and calculation, he 
drew up the following Table of the quantity of light re¬ 
flected from its furface at different angles of incidence: 
Angles of 
Incidence. 
Rays reflected 
of xooo. 
Angles of 
Incidence. 
Rays reflected 
of 1000. 
i 
721 
* 7 ! 
x 7 8 
I 
69a 
20 
I 4 S 
669 
2 5 
97 
2 
639 
30 
65 
614 
40 
34 
5 
501 
5 ° 
2 2 
/ a 
409 
60 
19 
IO 
333 • 
70 
18 
12 a 
271 
80 
18 
15 
2 11 
90 
18 
In the fame manner he conftruCted the following 
Table, containing the quantity of light reflected from the 
looking-glafs not quickfilvered : 
Angles of 
Incidence. 
Rays reflected 
of 1000. 
Angles of 
Incidence. 
Rays reflected 
of 1000. 
a£ 
4 584 
30 
I I 2 
5 
543 
40 
57 
7 h 
474 
50 
34 
JO 
41 2 
60 
27 
ja| 
356 
70 
2 5 
*5 
299 
80 
2 5 
20 
222 
90 
2 5 
2 5 
157 
When water floats upon mercury, there will be two 
images of any objeCt feen by reflection from them, one 
at the furface of the water, and the other at that of the, 
quickfilver. In the largeft angles of incidence, the image 
at the furface of the water will dilappear, which will hap¬ 
pen when it is about a 60th or an 80th part lefs luminous 
than the image at the furface of the quickfilver. De¬ 
prefling the eye, the image on the water will grow ftronger, 
and that on the quickfilver weaker, in proportion; till at laft 
the latter will- be incomparably weaker than the former ,- 
and, at an angle of about 10 degrees, they will be equally 
luminous. According to the Table, -j%Vo of the inci¬ 
dent rays are reflected from the water at this angle of 10 
degrees. At the furface of the mercury they were re¬ 
duced to 500 ; and of thefe, part being reflected back 
upon it from the under furface of the water, only 333 re¬ 
mained to make the image from the mercury. 
It 
