554 
OPTICS. 
It has been frequently obferved, that there is a remark¬ 
ably ftrong reflection into water, with refpeCt to rays if- 
fuing from the water; and perfons under water have feen 
images of things in the air in a manner peculiarly diftinCt 
and beautiful. In order to account for thefe faCts, M. 
Bouguer obferves, that, from the fmalleft angles of inci¬ 
dence to a certain number of degrees, the greateft part 
of the rays are reflected perhaps in as great a proportion 
as at the furface of metallic mirrors, or of quickfilver; 
while the other part, which does not efcape into the air, 
is extinguifhed or abforbed ; fo that the furface of the 
tranfparent body appears opaque on the infide. If the 
angle of incidence be increafed only a few degrees, the 
ftrong reflection ceafes altogether, a great number of 
rays efcape into the air, and very few are abforbed. As 
the angle of incidence is farther increafed, the quantity 
of the light reflected becomes lefs and lefs; and, when it 
is near 90 degrees, almoft all the rays efcape out of the 
tranfparent body, its furface lofing almoft all its power of 
reflection, and becoming nearly as tranfparent as when 
the light falls upon it from without. 
The property belonging to the furfaces of tranfparent 
bodies, of abforbing the rays of light, is truly remark¬ 
able ; and, as there is reafon to believe, had not been no¬ 
ticed by any perfon before M. Bouguer. 
That all the light is reflected at certain angles of inci¬ 
dence from air in to denfer fubftances, had frequently been 
noticed, efpecially in glafs prifms ; fo that Newton made 
ufe of one of them, inftead of a mirror, in the conftruc- 
tion of his refleCting-telefcope. If a beam of light fall 
upon the air within thefe prifms, at an angle of 10, 20, 
or 36, degrees, the effeCt will be nearly the lame as at the 
furface of quickfilver, one-fourth or one-third of the rays 
being extinguifhed, and two-thirds or three-fourths re¬ 
flected. This property retains its full force as far as an 
angle of 49 0 49', (the proportion of the fines of the re¬ 
fraction being 31 and 20 ;) but, if the angle of incidence 
be increafed but one degree, the quantity of light reflected 
inwards fuddenly decreafes, and a great part of the rays 
efcape out of the glafs, fo that the furface becomes fud¬ 
denly tranfparent. 
All tranfparent bodies have the fame property, with this 
difference, that the angle of incidence at which the ftrong 
reflection ceafes, and at which the light which is not re¬ 
flected is extinguilhed, is greater in fome than in others. 
In water this angle is about 41 0 32'; and, in every me¬ 
dium, it depends fo much on the invariable proportion of 
the fine of the angle of refraCtion to the fine of the angle 
of incidence, that this law alone is fuflicient to deter¬ 
mine all the phenomena of this new circumftance, at lead 
as to this accidental opacity of the furface. 
When M. Bouguer proceeded to ineafure the quantity 
of light reflected by thefe internal furfaces at great angles 
of incidence, he had to ftruggie with many difficulties ; 
but, by ufing a plate of cryftal, he found, that, at an an¬ 
gle of 75 degrees, this internal reflection diminifhed the 
light 27 or 28 times ; and, as the external reflection at the 
fame angle diminifhed the light only 26 times, it follows 
that the internal reflection is a little ftronger than the 
other. Repeating thefe experiments with the fame and 
different pieces of cryftal, he fometimes found the two 
reflections to be equally ftrong ; but, in general, the in¬ 
ternal was the ftronger. 
Refuming his obfervations on the diminution of light, 
occafioned by the reflection of opaque bodies obliquely 
fituated, he compared it with the appearances of fimilar 
fubftances which reflected the light perpendicularly. 
Ufing pieces of filver made very white, he found, that, 
when one of them was placed at an angle of 75 degrees 
with refpeCt to the light, it reflected only 640 parts out of 
1000. He then varied the angle, and alfo ufed white plaf- 
ter and fine Dutch paper; and drew up the following Table 
of the proportion of the light reflected from each of thofe 
fubftances at certain angles: 
Angles of 
Incidence. 
90 
75 
60 
45 
30 
15 
Quantity of Light reflected from 
Silver. 
1000 
802 
640 
455 
319 
209 
Plafter. 
1000 
762 
640 
529 
352 
194 
Dutch 
Paper. 
1000 
971 
743 
507 
332 . 
203 
Suppofing the afperities of opaque bodies to confift of 
very fmall planes, it appears from thefe obfervations, that 
there are few'er of them in thofe bodies which reflect the 
light at fmall angles of incidence than at greater. None 
of them had their roughnefs equivalent to fmall hemi- 
fpheres, which would have difperfed the light equally in. 
all directions ; and, from the data in the preceding Table, 
he deduces mathematically the number of the planes that 
compofe thofe furfaces, and that are inclined to the gene¬ 
ral furface at the angles above mentioned, fuppofing that 
the whole furface contains 1000 of them that are parallel 
to itfelf, fo as to reflect the light perpendicularly, when 
the luminous body is fituated at right-angles with refpeCt 
to it. His conclufions, reduced to a Table correfponding 
to the preceding, are as follow'; 
Inclinations ofthe 
fmall Surfaces with 
refpeCt to the large 
one. 
o 
15 
30 
45 
60 
75 
The Diftribution of the fmall 
Planes that conftitute the Af¬ 
perities of the opaque Surface 
in the 
Silver. Plafter. Paper. 
1000 
777 
554 
333 
161 
53 
1000 
736 
554 
374 
176 
50 
937 
545 
358 
166 
52 
Thefe variations in the number of little planes, he ex- 
preffes in the form of a curve; and afterwards Ihows, 
geometrically, what would be the effeCt, if the bodies were 
enlightened in one direction, and viewed in another. 
Upon this fubjeCt he has feveral curious theorems and 
problems ; but for thefe we muft refer to the work itfelf. 
Since the planets are more luminous at their edges than 
at their centres, he concludes, that the bodies which form 
them are conftituted in a manner different from ours; 
particularly that their opaque furfaces confift of fmall 
planes, more of which are inclined to the general furface 
than they are in terreftrial fubftances ; and that there are 
in them an infinity of points, which have exaCtly the fame 
fplendour. . 
M. Bouguer next proceeds to afcertain the quantity of 
furface occupied by the fmall planes of each particular in¬ 
clination, from confidering the quantity of light reflected 
by each, allowing thofe that have a greater inclination to 
the common furface to take up proportionably lefs fpace 
than thofe which are parallel to it. And, comparing the 
quantity of light that would be reflected by fmall planes 
thus difpofed, with the quantity of light that was ac¬ 
tually reflected by the three fubftances above mentioned, 
he found that plafter, notwithftanding its extreme white- 
nefs, abforbs much light; for that, of 1000 rays falling 
upon it, of which 166 or 167 ought to be reflected at an 
angle of 77 0 , only 67 are in faCt returned : fo that 100 
out of 167 were extinguilhed, that is, about three-fifths. 
With refpeCt to the planets, Bouguer concludes, that of 
300,000 rays which the moon receives, 172,000, or per¬ 
haps 204,100, are abforbed. 
Having confidered the furfaces of bodies as confifting 
of planes only, he obferves, that each fmall furface, fepa- 
1 rately 
