C34 
OPTICS. 
“ Secondly, I fay, that full-moon light is to any other 
moon-light as the whole diflc of the moon to the part that 
appears enlightened, confidered upon a plane furface. 
For now let the earth be at b, fig. 6. and let dl be perpen¬ 
dicular to fg, and gm to c l; then it is plain, that gl is 
equal to dm; and that gl is equal to a perpendicular fec- 
tion of the fun’s rays incident upon the arch dg, which 
at h appears equal to dm; the eye being unable to diltin- 
guilh the unequal dillances of its parts. In like manner, 
conceiving the moon’s furface to confifl of innumerable 
phyfical circles parallel to cfdg, as represented at A, the 
fame reafon holds for every one of thefe circles as for cfdg. 
It follows then, that the bright part of the furface vilibie 
at b, when reduced to a flat, as reprefented at B, by the 
crefcent pdqmp, wil,l be equal and fnr.ilar to a perpendicu¬ 
lar fe&ion of all the rays incident on that part, reprefented 
at C by the crefcent pgqlp. Now the whole diflc being in 
proportion to this crefcent as the quantities of light in¬ 
cident upon them, and the light falling upon every rough 
particle being equally rarefied in diverging to the eye at b, 
confidered as equi-diftant from them all; it follows, that 
full-moon light is to this moon-light as the whole difk 
pdqc to the crefcent pdqmp. Therefore, by compounding 
this ratio with that in the former remark, day-light is to 
moon-light as the furface of an hemifphere whole centre 
is at the eye to the part of that furface which appears to 
be pcfTefied by the enlightened part of the moon.” 
Mr. Michell made his computation in a much more 
fimple and eafy manner, and in vVhich there is much lefs 
danger of falling into any miftake. Confidering the dis¬ 
tance of the moon from the fun, and that the denfity of 
the light rnufl decreafe in the proportion of the fquare of 
that diftance, lie calculated the denfity of the fun’s light, 
at that diftance, in proportion to its denfity at the furface 
of the fun ; and in this manner he found, that, if the 
moon reflected all the light it receives from the fun, it 
would only be the 4.5,000th part of the light we receive 
from the greater luminary. Admitting, therefore, that 
moon-light is only a 300,000th part of the light of the 
fun, Mr. Michell concludes, that it reflects no more than 
between the 6th and 7th part of what falls upon it. 
Count Rumford con ft meted a photometer, in which 
the fhadows, inftead of being thrown upon a paper fpread 
out upon the wainfeot, or fide of the room, are projeded 
upon the infide of the back part of a wooden box inches 
wide, io| inches long, and jj- inches deep, in the clear. 
This inftrument is reprefented at fig. 5-8. The light is 
admitted into it through two horizontal tubes in the 
front, placed fo as to form an angle of 6o°; their axes 
meeting at the centre of the field of the inftrument; fee 
fig. 7. In the middle of the front of the box, between 
thefe two tubes, is an opening through which is viewed 
the field of the photometer. This field is formed of a 
piece of white paper, which is not fattened immediately 
upon the infide of the back of the box, but is palled upon 
a fmall pane of very fine ground-glafs; and this glafs, 
thus covered, is let down into a groove’, made to receive 
it, in the back of the box. The whole infide of the box, 
except the field of the inftrument, is painted of a deep- 
black dead colour. To the under part of the box is fitted 
a ball and focket, by which it is attached to a Hand which 
fupportsit; and the top or lid of it is fitted with hinges, in 
order that the box may be laid quite open as often as it is 
neceflary to alter any part of the machinery it contains. 
The count had found it very inconvenient to compare 
two fhadows projected by the fame cylinder, as thefe were 
either neceflarily too far from each other to be compared 
with certainty, or, when they were nearer, were in part 
hid from the eye by the cylinder. To remedy this incon¬ 
venience, he now makes ufe of two cylinders, which are 
placed perpendicularly in the bottom of the box juft de- 
icribed, in a line parallel to the back part of it, diftant 
•from this back 2^ inches, and from each other 3 inches, 
meafuring from the centres of the cylinders ; when f^ie 
two lights made ufe of in the experiment are properly 
placed, thefe two cylinders project four fhadows upon the 
white'paper upon the infide of the back part of the box, 
or the field ol the inftrument; two of which fhadows are 
in contact precifely in the middle of that field, and it is 
thefe two alone that are to be attended to. To prevent 
the attention being diftradted by the prefence of unnecef- 
fary objects, the two outfide fhadows are made to difan- 
pear ; which is done by rendering the field of the inftru¬ 
ment fo narrow, that they fall without it, upon a black¬ 
ened furface, upon which they are not vilibie. If the cy¬ 
linders be each of an inch in diameter, and z~ inches 
in height, it will be quite fufticient that the field be 2y’j 
inches wide ; and as an unnecefiary height of the field is 
not only ufelefs, but difadvantageou’s, as a large furface 
of white paper not covered by the fhadows produces too 
ftrong a glare of light, the field ought not to be more than 
fa of an inch higher than the tops of the cylinders. That 
its dimenfions, however, may be occafionally augmented, 
the covered glafs fhould be made inches long, and as 
wide as the box is deep, viz. 3^ inches; fince the field of 
the inftrument can be reduced to its proper fize by a fereert 
of black pafteboard, interpofed before the anterior furface 
of this covered glafs, and refling immediately upon it. A 
hole in this pafteboard, in the form of an oblong fquare, 
j t 7 o inch wide, and two inches high, determines the di¬ 
menfions, and forms the boundaries of the field. This 
fereen fhould be large enough to cover the whole infide 
of the back of the box, and it may be fixed in its place 
by means of grooves in the fides of the box, into which 
it may be made to enter. The pofition of the opening 
above mentioned is determined by the height of the cy¬ 
linders; the top of it being] of an inch higher than the 
tops of the cylinders ; and, as the height of it is only two 
inches, while .the height of the cylinders is 2f 6 inches, it 
isevident that the fhadows of the lower parts of thecylin- 
ders do not enter the-field. No inconvenience arif’es from 
that circumftance; on the contrary, feveral advantages 
are derived from that arrangement. 
That the lights may be placed with facility and preci- 
fion, a fine black line is drawn through the middle of the 
field, from the top to the bottom of it, aud another (ho¬ 
rizontal) line at right angles to it, at the height of the 
top of the cylinders. ■ When the tops of the fhadows 
touch this hill-mentioned line, the lights are at a proper 
height; and farther, when the two fhadows are in contaft 
with each other in the middle of the field, the lights are 
then in their proper directions. 
We have fa id that the cylinders, by which the fnadows 
are projected, are placed perpendicularly in the bottom of 
the box; but as the diameters of the fhadows of thefe cy¬ 
linders vary in fome degree, in proportion as the lights 
are broader or narrower, and as they are brought nearer 
to, or removed farther from, the photometer, to be abm 
in all cafes to bring thefe fnadows to be of 'the fame dia¬ 
meter, which is very advantageous, in order to judge 
with greater facility and certainty when they are of 
the fame denfity, the count renders the cylinders movable 
about their axes, and adds to each a vertical wing of 
an inch'wide, of an inch thick, and of equal height 
with the cylinder itfelf, and firmly fixed to it from the 
top to the bottom. . This wing commonly lies in the mid¬ 
dle of the fhadow of the cylinder; and, as long as it re¬ 
mains in that fituation, it has no effefl whatever; but, 
when it is neceflary that the diameter of one of the fha¬ 
dows be increafed, the correfponding cylinder is moved 
about its axis, till the wing jull def'evibed, emerging oitt 
of the fhadow, and intercepting a portion of light, brings 
the fhadow projefted upon the field of the inllrument to 
be of the width or diameter required. In this operation 
it is always neceflary to turn the cylinder outwards, or 
in fuch a manner that the augmentation of the width of 
the fhadow may take place on that fide of it which is op- 
pofite to the (hallow correfponding to the other light. 
The neceflity for that precaution will appear evident to 
any one who has a jull idea of the inllrument in queftion, 
