OPTICS. 
ftronc light upon the eye, and alfo the impreflion which 
it leaves upon it, makes it infenfible to the effeft of a 
weaker light. M. Bouguer had the curiofity to endeavour 
tivafcertain the proportion between the intenfities of the 
two lights in this cafe; and, by throwing the light of 
two equal candles upon a board, he found that the Iha- 
dow made by intercepting the light of one of them could 
not be perceived by his eye, upon the place enlightened 
by the other, at little more than eight times the distance ; 
from whence he concluded, that, when one light is eight 
times eight, or 64 times, lefs than another, its prefence 
or abfence will not be perceived. He allows, however, 
that the efi'eft may be different on different eyes ; and 
f'uoDofes that the boundaries in this cafe, with refpeft to 
different perfons, may lie between 60 and 80. 
2. Applying the two tubes of his inftrum.ent, mentioned 
above, to mealure the intenfity of the light reflected from 
different parts of the fky, he found that, when the fun was 
25 degrees high, the light was four times Stronger at the 
diftance of 8 or 9 degrees from his body than it was at 
31 or 32 degrees. But what ftruck him the mofc was to 
fmd, that, when the funis 15 or 20 degrees high, the 
light decreafes on the fame parallel to the horizon to no 
or 120 degrees, and then increafes again to the place ex- 
aftly oppofite to the fun. 
3. The light of the fun, our author obferves, is too 
ffrong, and that of the ftars too weak, to determine the 
variation of their light at different altitudes ; but as, in 
both cafes, it muff be in the fame proportion with the 
diminution of the light of the moon in the fame circum- 
ftances, he made his obferyations on that luminary, and 
found, that its light at 19° 16', is to its light at 66° n', 
as 1681 to 2500 ; that is, the one is nearly two-thirds of 
the other. He chofe thofe particular altitudes, becaufe 
they are thofe of the fun at the two foliiices at Croific, 
where he then refided. When one limb of the, moon 
touched the horizon of the fea, its light was 2000 times 
lefs than at the altitude of 66° 11'. But this proportion 
he acknowledges mult be fubjedt to many variations, 
the atmofpbere near the earth varying fo much in its 
denfity. From this obfervation he concludes, that, at a 
medium, light is dirnir.idled in the proportion of about 
2500 to 1681, in travelling 74.69 toifesof denfe air. 
4.. M. Bouguer alfo applied bis inftrument to the dif¬ 
ferent parts of the fun’s difk, and found that the centre 
is confiderably more luminous than the extremities of 
it. As near as he could make the obfervation, it was 
more luminous than a part of the difk fths of the femi- 
diameter from it in the proportion of 35 to 28 ; which, 
as he obferves, is more than in the proportion of the 
fines of the angles of obliquity. On the other hand, 
he obferves, that both the primary and fecondary pla¬ 
nets are more luminous at their edges than near their 
centres. 
5. The comparifon of the light of the fun and moon 
is a fubjeff that has frequently exercifed the thoughts of 
philofophers ; but we find nothing but random conjec¬ 
tures, before Bouguer applied bis accurate meafures in 
this cafe. In general, the light of the moon is imagined 
to bear a much greater proportion to that of the fun 
than it really does; and not only are the imaginations 
of the vulgar, but thofe of philofophers alfo, impofed 
upon with refpeft to it. It was a great furprife to M. de 
la Hire to find that he could not, by the help of any 
burning mirror, colled: the beams of the moon in a fufii- 
cieni quantity to produce the leafl fenfible heat. Other 
philofophers have fince made the like attempts with mir¬ 
rors of greater power, though without any greater fuc- 
cefs ; but this will not furprife us, when we fee the reful t 
of M. Bouguer’s obfervations on this fubjed. In order 
to i’olve this curious problem concerning the comparifon 
Gf the light of the fun and moon, he compared each of 
them to that of a .candle in a dark room, one in the day¬ 
time, and the other in the night following, when the 
moon was at her mean diftance from the earth 5 and, after 
Von. XVII. No. 1203. 
033 
many trials, he concluded that the light of the fun is 
about 300,000 times greater than that of the moon ; which 
is fuch a difproportion, that, as lie obferves, it can be no 
wonder that philofophers have had fo little fuccels in 
their attempts to colled the light of the moon with 
burning-glaffes. For the largeft of them will not increafe 
the light 1000 times ; which will ftill leave the light ofthe 
moon, in the focus of-the mirror, 300 times lefs than the 
intenfity of the common light of the fun. 
To this account of the proportion of light which we 
adually receive from the moon, it cannot be difpleafing 
to the reader, if we compare it with the quantity which 
would have been tranfmitted to us from that opaque body, 
if it refleded all the light it receives. Dr. Smith thought 
that be had proved, from two different confiderations, 
that the light ofthe full moon would be to our day-light 
as 1 to about 90,900,11’ no rays were loft at the moon. In 
the firft place, he luppofes that the moon, enlightened by 
the fun, is as lu,minous as the clouds are at a medium. 
He therefore fuppofed the light of the fun to be equal to 
that of a whole liemifphere of clouds, or as many moons 
as would cover the furface of the heavens. But on 
this Dr. Prieftley obferves, that it is true the light of the 
fun fhining perpendicularly upon any furface, would be 
equal to the light refleded from the whole hemifphere, if 
every part refleded all the light that fell-upon it; but the 
light that would in fad be received from the whole hemi¬ 
fphere (part of it being received obliquely) would be only 
one-half as much as would be received from the whole he- 
mifpbere if every part of it fnone diredly upon the fur¬ 
face to be illuminated. 
Dr. Smith demonffrates his method of calculation in 
the following manner : “ Let the little circle cfdg, fig. 5. 
reprefent the moon’s body half enlightened by the fun, 
and the great circle aeb a fpherical (hell concentric to the 
moon, and touching the earth ; ab, any diameter of that 
fhell perpendicular to a great circle of the moon’s body, 
reprefented by its diameter cd; e the place of the fhell re¬ 
ceiving full-moon light from the bright heinifphere fd^\ 
Now, becaufe the furface of the moon is rough like that 
of the earth, we may allow that the fun’s rays, incident 
upon any fmall part of it, with any obliquity, are refleded 
from it every way alike, as if they were emitted. And 
therefore, if the legment f^’lhone alone, the points a, e, 
would be equally illuminated by it; and likewife, if the 
remaining bright fegment dg flione alone, the points b, e, 
would be equally illuminated by it. Consequently, if the 
light at the point a was increafed by the light at b, it 
would become equal to the full-moon light at e. And, 
conceiving the fame transfer to he made from every point 
of the hemifpherical furface hbih to their oppofite points 
in the liemifphere haeh, the former hemifphere would be 
left quite dark, and the latter would be uniformly illu¬ 
minated with full-moon light, arifing from a quantity of 
the fun’s light, which, immediately before its incidence 
on the moon, would uniformly illuminate a circular plane 
equal to a great circle of her body, called her dijk. There¬ 
fore, the quantities of light being the fame upon both 
furfaces, the denfity of the fun’s incident light is to the 
denfity of full-moon light as that hemifpherical furface 
heh is to the laid difk ; that is, as any other hemifpherical 
furface whofe centre is at the eye, to that part of it which 
the moon’s difk appears to poffels very nearly, becaufe it 
fubtends but a fmall angle at the eye; that is, as radius 
of the hemifphere to the verfed fine of the moon’s appa¬ 
rent femi-diameter, or as 10,000,000 to iio6-§., or as 90,400 
to x ; taking the moon’s mean horizontal diameter to be 
x6' 7". Striidly fpeaking, this rule compares moon-light 
at the earth with day-light at the moon ; the medium of 
which, at her quadratures, is the fame as our day-light; 
but is lei’s at her full in the duplicate ratio of 365 to 366, 
or thereabout, that is, of the fun’s diftances from the 
earth and full-moon ; and therefore full-moon light would 
be to our day-light as about 1 to 90,900, if no rays were 
loft at the moon. 
7 Y 
“Secondly, 
