RAINBOW. 
^^eight in ounces by .173, which gives the 
depth in inches and parts of an inch. In 
fixing these gauges, care must be taken that 
tlie rain may have free access to them ; 
hence the tops of buildings are usually the 
best places. When the quantities of rain 
collected in them at different places are 
compared, the instruments ought to be fix- 
ed at the same heights above the ground at 
both places, because, at different heights, 
the quantities are always different, even at 
the same place. 
RAIN BOW. The rainbow is a circular 
image of the sun, variously coloured. It is 
thus produced : the solar rays, entering the 
drops of falling rain, are refracted to their 
further surfaces, and thence, by one or 
more reflections, transmitted to the eye : 
at their emergence from the drop, as well 
as at their entrance, they suffer a refrac- 
tion, by which the rays are separated into 
their different colours, and these, therefore, 
are exhibited to an eye properly placed to 
receive them. That this is the true ac- 
count of the formation of the rainbow, 
appears from the following considerations ; 
1 . Tliat a bow is never seen but when rain 
is falling, and the sun shining at the same 
time, and that the sun and bow are al- 
ways in opposite quarters of the heavens : 
this every one’s experience can testify. 
2. That the same appearance can be 
artificially represented by means of water 
thrown into the air, when the spectator 
is placed in a proper position with his 
back turned to the snn : experiment will 
show this. 3 . That its formation, as above 
described, can be clearly explained from 
the properties of light, already demon- 
strated in the former parts of this dic- 
tionary. 
Let AB, (Plate XIII. Miscel. fig. 10) be 
a drop of water, and C D, a pencil of solar 
rays incident thereon ; if all the rays of any 
one colour, as red, belonging to the pencil, 
CD, be refracted to the same point, G, and 
thence reflected, they will fall on the 
space, R Q, with the same obliquity, and 
at the same distances from each other, as 
the refracted rays, if proceeding backward 
from G, would fall on the space, T S, but 
these, at their refraction, would emerge in- 
to T D, C S, &c. parallel to each other 5 
the rays, GR, GQ, will emerge from the 
drop parallel to each other, and therefore 
will enter an eye properly placed copiously 
enough to cause a sensation ; a red colour 
will therefore appear in the direction of 
these rays, and so of others. But if the re- 
fracted rays do not meet in the same point, 
the reflected rays, (fig. 11) I V, PQ, will 
not fall on the surface at the same distance 
from each other that PT and IS do, 
though their obliquity to the surface be 
equal to that of tlie latter ; therefore the 
refracted rays will emerge, diverging fi'om 
each other, and consequently will not enter 
the eye copiously enough to cause a per- 
ception of their colour. It is plain that 
where the rays of any colour emerge pa- 
rallel, all these emerging rays will be in- 
clined to the incident rays in the same an- 
gle. And by calculation it is . found, that 
the red rays when they emerge parallel to 
each other, make with the incident rays an 
angle, ABO, (fig. 12) of 42“ 2', and the 
violet an angle, A C O, of 40° 17', and the 
rays of the other colours, angles greater 
than the latter, and less than the former. 
If through the eye which receives the 
emerging rays, there be drawn a line; A X, 
parallel to tlie incident rays, it will make 
with tlie emerging rays of each colour an- 
gles, RAX, and VAX, &c. equal to the 
above. This line, A X, is called the axis 
of vision. The several drops placed in the 
lines, AR, A V, &c. will exhibit to the eye 
at A, the several prismatic colours respec- 
tively, as appears from what has been said ; 
and if those lines be supposed to revolve 
with a conical motion round the axis of vi- 
sion, it is evident, for the same reason, that 
all the drops placed in each of the conic 
surfaces, so generated, will transmit the 
rays of each colour respectively to the eye, 
and therefore, that a number of circular, 
concentric arches of the prismatic colours, 
adjoining to each other, will be exhibited 
to the eye. This explanation relates to the 
interior bow, whose colours, beginning 
from the outside, are red, orange, &c. as in 
the prismatic spectrum. This bow can ne- 
ver be seen if the sun be elevated more 
than 42“ 2' above the horizon ; for the ho- 
rizon, H O, (fig. 13) always makes with the 
axis of vision, A X, an angle equal to the 
elevation of the sun, in the case here 
stated, the line, A Q, marking the vertex of 
a rainbow, would fall entirely below the 
horizon. As the interior bow is formed by 
one reflection and two refractions, the ex- 
terior bow is formed by two reflections and 
two refractions at the surfaces of the drops 
of falling rain. If the red rays of any pen- 
cil, C D, (fig. 14) of solar yays after refrac- 
tion intersect each other at R, so that when 
reflected at T V, they may proceed paral- 
lel within the drop, after a second reflec- 
M ra 3 
