310 
OPTICS. 
contemplates them merely as the natural and 
beautiful effects produced by clouds or va- 
pour in various masses upon the rays of 
light. 
One of the most beautiful and common of 
tnese appearances deserves particular inves- 
tigation,. as, when this subject is well under- 
stood, there will be little difficulty in ac- 
counting for others of a similar nature, de- 
pendant on the different reffangibility of the 
rays of light. Frequently, when our backs 
are turned to the sun, and there is a shower 
either around us, or at some distance before 
us, a bow is seen in the air, adorned with all 
or some of the seven primary colours. The 
appearance of this bow, in poetical language 
called the iris, and in common language the 
rainbow, was an inexplicable mystery to the 
antients ; and, though now well understood, 
continues to be the subject of admiration to 
the peasant and the philosopher. 
AN e are indebted to sir Isaac Newton for 
tne explanation of this appearance; and by 
various easy experiments we may convince 
any man that his theory is founded on truth. 
It a glass globe is suspended in the strong 
light of the sun, it will be found to reflect the 
different prismatic colours exactly in propor- 
tion to the position in which it is placed; in 
other words, agreeably to the angle which it 
forms with the spectator’s eye ami the inci- 
dence of the rays of light. 'Hie fact is, that 
innumerable pencils of light fall upon the 
surface of. the globe, and each of these is se- 
parated as by a prism. To make this matter 
still clearer, let 11 s suppose the circle BAW 
(Plate Ilf. fig. 16) to represent the globe, or 
a drop of rain, for each drop may be consi- 
dered as a small globe of water. The red 
rays, it is well known, are least refrangible ; 
they will therefore be refracted, agreeably to 
their angle of incidence, to a certain point A 
in the most distant part of the globe ; the 
yellow, the green, the blue, and the purple 
rays, will each be refracted to another point. 
A part of the light, as refracted, will be trans- 
mitted, but a part will also be reflected ; the 
red rays at the point A, and the others at 
certain other points, agreeably to their angle 
of refraction. 
It is very evident that if the spectator’s eye 
is placed in the direction of MW, or the 
course of the red-making rays, he will only 
distinguish the red colour; if in another si- 
tuation, he will see only by the yellow rays ; 
in another by the blue, &c. : but as in a 
shower of rain there are drops at all heights 
and all distances, all those that are in a cer- 
tain position with respect to the spectator 
will reflect the red rays, all those in the next 
station the orange, those in the next the 
green, &c. 
To avoid confusion let us, for the present, 
imagine only three drops of rain, and three 
degrees of colours in the section of a bow 
(Plate III. fig. 20). It is evident that the 
angle CEP is less than the angle BEP, and 
that the angle AEP is the greatest of the 
three. This largest angle then is formed by 
the red ravs, the middle one consists of the 
green, and the smallest is the purple. All 
the drops of rain, therefore, that happen to 
be in a certain position to the eye of the 
spectator, will reflect the red rays, and form a 
band or semicircle of red ; those again in a 
certain position will present a band of green, 
&e. If he alters his station, the spectator will 
6 
still see a bow, though not the same bow as 
before ; and if there are many spectators 
they will each see a different, bow, though it 
appears to be the same. 
'1 here are sometimes seen two bows, one 
formed as has been described, the other ap- 
pearing externally to embrace the primary 
bow, and which is sometimes called a secon- 
dary or false bow, because it is fainter than 
the other ; and vvliat is most remarkable is, 
that in the false bow the order .of the colours 
appears always reversed. 
In the true or primary bow we have seen 
that the rays of light arrive at the spectator’s 
eye after two refractions and one reflection ; 
in the secondary bow the rays are sent to our 
eyes after two refractions and two reflections, 
and the order ot the colours is reversed, be- 
cause in this latter case the light enters at the 
inferior part of the drop, and is transmitted 
through the superior. Thus (fig. 19) the ray 
of light which enters at B is refracted fc A, 
whence it is reflected ±0 P, and again reflect- 
ed to W, where, suffering another refraction, 
it is sent to the eye of the spectator. The 
colours of this outer bow are fainter than 
those of the other, because, the drop being 
transparent, a part of the light is transmitted, 
and consequently io,t, at each reflection. 
The phenomenon assumes a semicircular 
appearance, because it is only at certain an- 
gles that the refracted rays are visible to our 
eyes. The least refrangible, or red rays, 
make an angle of 42 degrees two minutes, 
and Hie most refrangible or violet rays an 
angle of 49 degrees 17 minutes. Now if a 
line is drawn horizontally from the spectator’s 
eye, it is evident that” angles formed with 
this line, of a certain dimension hi every di- 
rection, will p reduce a circle ; as will be evi- 
dent by only attaching a cord of a given 
length to a certain point, round which it may 
turn as round Its axis, and in every point will 
describe an angle with the horizontal line of 
a certain and determinate extent. 
'Let HO, for instance (Plate III. fig. 19), 
represent the horizon, BVv a drop of rain at 
any altitude, SB a line drawn from the sun to 
the drop, which will be parallel to aline S-M 
drawn from the eye of the spectator to the 
sun. The course of part of the decom- 
pounded ray SB maybe first by refraction 
from B to A, then by reflection from A to 
W, lastly by refraction from W to M. Now 
all drops, which are in such a situation that 
the incident and emergent rays SB, MW, 
produced through them make" the same an- 
gle SNM, will be the means of exciting in 
the spectators the same idea of colour. Let 
MW turn upon IiO as an axis, till W meets 
the horizon on both sides, and the point W 
will describe the arc of a circle : and all the 
drops placed in its circumference will have 
the property we have mentioned, of trans- 
mitting to the eye a particular colour. When 
the plane 11MWA is perpendicular to the 
horizon, the line MW is directed to the ver- 
tex of the bow, and WK is its altitude. 
T his altitude depends on two things, the 
angle between the incident and emergent 
rays, and the height of the sun above the ho- 
rizon ; for since SM is parallel to SN, the 
angle SNM is equal to NM1 : but SMH, the 
altitude of the sun, is equal to KMI ; therefore 
the altitude of the bow WMK, which is equal 
to the difference between WMI and KMI, 
is equal to the difference between the angles 
made by the incident and emergent rays and 
the altitude of the sun. 
The angle between the incident and emer- 
gent rays is different for the different colours, 
as was already intimated ; for the red, or 
least refrangible, rays, it is equal to 42° 2 y • 
lor the violet, or most refrangible, it is equal 
to 40 1-7' ; consequently when the sun is 
more than 42° 2' above the horizon, the red 
colour cannot be seen ; when it is above 40° 
17' the violet colour cannot be seen. 
The secondary bow is made in a similar 
manner; but the sun’s rays suffer, in this 
case, two reflections within the drop. The 
ray SB (Plate III. lig. 19) is decompounded 
at B ; and one part is refracted to A, thence 
reflected to P, and from P reflected to W, 
where it is refracted to M. The angle be- 
tween the incident and emergent rays SNM 
;is equal as before to NM ! ; and NMK, the 
height of the bow, is equal to the difference 
between the angle made by the incident and 
emergent rays and the iieght of the sun. In 
this case the angle SNM, for the red rays, is 
equal to 50° V, and for the violet rays it is 
equal to 54’ 7'; consequently the upper part 
ot the secondary bow' will net be seen when 
the sun is above 54’ 7' above the horizon, 
and the lower part of the bow will not be 
seen when the sun is 50° T above the hori- 
zon. 
In the same manner innumerable bows 
might be formed by a greater number of re- 
flections within the drops ; but as the secon- 
dary is so much fainter than the primarv 
that all the colours in it are seldom seen, for 
the same reason a bow made with three* re- 
flections would be fainter still, and in general 
altogether imperceptible. Since the^-ays of 
light, by various reflections and refractions 
are thus capable of forming, by means of 
drops of rain, the bows which we so fre- 
quently see in the heavens, it is evident that 
there will be not only solar and lunar bows 
but that many striking appearances will be 
produced by drops upon the ground, or air 
on the agitated surface of the water. Thus a 
lunar bow will be formed by rays from the 
moon affected by drops of rain ; but as its 
light is very faint in comparison with that of 
the sun, such a bow will very seldom be seen, 
and the colours of it, when seen, will be faint 
and dim. 
The marine or sea bow' is a phenomenon 
sometimes observed in a much agitated sea • 
when the wind, sweeping part of the tops of 
the waves, carries them alott, so that the sun’s 
rays, falling upon them, are refracted, &c. as 
in a common shower, and paint the colours 
of the bow. 
Rohault mentions coloured bows on the 
grass, formed by the refraction of the sun’s 
rays in the morning dew. 
Dr. Langwith, indeed, once saw' a bow ly- 
ing cm the ground, the colours of which were 
almost as lively as those-ot the common rain- 
bow. it was extended several hundred yards, 
ft was not round, but oblong, being, as he 
conceived, the portion of an In perbola. The 
colours took up less space^ and were much 
more lively, in those parts of the bow which 
were near him than in those which were at a 
distance. 
The drops of rain descend in a globular 
form, and thence we can easily account for 
