Elias Loomis.

A treatise on meteorology : with a collection of meteorological tables online

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the ship in the direction of the last refracted rays, and the object
appears inverted because the rays have suffered reflection.

Other rays, that never could reach the eye at E in the ordinary
state of the atmosphere, may likewise be bent into curves which
do not cross before reaching the eye. In this case an erect image
of the ship may be seen, and both the direct and inverted images
may be seen simultaneously.

404. Lateral Mirage, — ^In mountainous countries, or near a high
coast, it may happen that tl^e air is divided by a nearly vertical
plane into two portions, one of which is heated by the sun, while
the other is in the shadaw of a hill or a bank. The transition
from the warm to the cold air will not be abrupt, but the density
of the vertical sections will increase gradually from the warmer to
Fig. 88. the colder portion. If an ob-

A ^^dHHISH^zX^ server were situated at B, Fig.
^^ ^^^^^^^HHHlBtaf ^^' ^^^^ ^^^ bounding plane,
-^^^^^^^^^^^ he might see in the warmer

part a symmetrical image, CD',
of objects, CD, situated in the
colder part, as if in a vertical
mirror. This is called a later-
al mirage. It is less frequent-
ly seen than the other varieties, and its duration is more transient.


405. Displacemmts. — Under certain circumstances, objects near
the horizon may appear displaced ; sometimes laterally, as in the
vicinity of mountains, but more frequently in a vertical direction,
in which case they appear elevated above their true position.
Sometimes an object appears double, certain rays reaching the
eye without sensible deviation, while others, traversing strata of
increasing density, describe a curve line. This phenomenon dif-
fers from the true mirage in this respect, that the image is not
inverted, showing that the light has not suffered reflection.

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406. Abs()rp,ym of Light — ^The atmosphere is never perfectly
transparent, but absorbs a portion of the light which traverses it
Hence distant objects, as the summits of mountains, generally ap-
pear dim, as if enveloped in a mist or a bluish smoke. This loss
of light is due partly to the presence of minute particles of con-
densed vapor, and sdso small particles of dust, and partly to the
difference of density of the strata arising either from a difference
of pressure or a difference of temperature. In passing from one
stratum to another of a different density, a portion of light is re-
flected, so that the transmitted portion is continually diminished.
After a rain, when by a general mingling of the strata the tMi-
perature of the air has been rendered nearly uniform, its trans-
parency is greatly increased.

407. Bedness of the Evening Sky, — The redness of the evening
sky is due principally to the condensed vapor of the air, a portion
of which begins to be precipitated as the temperature of the day

If we transmit the sun's light through a glass prism at different
hours of the day, we shall find that the spectrum changes with
the altitude of the sun. As the sun approaches the horizon, the
violet part of the spectrum contracts, and at length disappears al-
together, while the red end of the spectrum remains entire. We
hence conclude that the violet rays, which are the most refrangi-
ble, have the least power of penetrating the dense atmosphere, in-
cluding the dust and the condensed vapor near the horizon, and
therefore, when the sun is near the horizon, his light exhibits an
excess of those rays bordering upon the red end of the spectrum,
and this color is communicated not only to the evening sky, but
also to the clouds which float in the atmosphere.

From the same cause, tne sun, just before setting, sometimes as-
sumes a deep red color, as if seen through a smoked glass, and
this redness is more noticeable in the setting than in the rising
sun, because in the morning the condensed particles of vapor have
descended to the earth, or are converted again into invisible va-
por by the increasing heat of the morning.

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408. Beflected Light of the Sky. — An observer at night, in the
neighborhood of a large city, may notice a decided illumination
of the heavens, arising from the light of the city reflected from
the sky, and during an extensive conflagration this illumination
is sometimes very brilliant. The atmosphere therefore reflects a
portion of the light which, falls upon it It is this light of the
.sky which prevents our seeing the stars in the daytime, and its
brightness is but little inferior to that of the moon, for during the
day the moon appears like a small white cloud. It is chiefly
from this source that, during the day, apartments which are not
accessible to the direct rays of the sun derive their illumination.

The brightness of the sky is variable. It depends upon the
purity of the air, increasing ^with the number of the particles of
condensed vapor suspended in it. It depends also upon the
weight of the air above the observer, being less on the summits
of mountains than at the level of the sea.

The light of the sky is greatest in the vicinity of the sun, and
diminishes rapidly as we recede from his disc.

409. Blue Color of the Sky. — ^While the red rays of the sun have
a greater power of penetrating a dense atmosphere, the blue rays
are more readily reflected by it, but this difference is not sensible
until the light has traversed large masses of air. The azure color
of the sky is therefore due to the light reflected by the air, and
the purer the air the more decided is this azure tint When
mountains covered with snow are illumined by a rising sun, they
appear of a rosy or orange tint upon the eastern side, while on
the western side they exhibit a bluish tint The blue color of
the sky is therefore due to the reflection of light, and not to a
peculiar color belonging to the particles of air.

410. Cyanometer. — The intensity of the blue color of the sky
exhibits very great variety. In order to measure it, Saussure in-
vented an instrument which he called the cyanometer. This
instrument has 27 colored surfaces, of which the first is almost
white, and the last is of the deepest cobalt blue, while the inter-
mediate surfaces present every gradation between white and blue,
and the surfaces are numbered from 1 to 27. It has also a sec-
ond series of colored surfaces, beginning with the deepest blue of
the preceding series, and ending with a jet black, while the inter-

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mediate surfaces present every gradation between blue and black,
and these surfaces are numbered from 27 to 63.

In using this instrument, the observer selects that particular
tint upon the scale which corresponds nearest to the color of. the
sky, and the color of the sky is denoted by the number attached
to that tint Other cyanometers have been invented depending
upon the properties of polarized light

The blueness of the sky generally increases from the horizon
to the zenith. When the color of the sky near the zenith is
indicated by 20 on the cyanometer, it will generally be about 4
near the horizon.

The blueness of the sky is greatest after a rain, when the air is
most pure, and it diminishes with an increase of the particles of
condensed vapor suspended in the air. Hence a pale sky is a
sign of rain.

The blueness of the sky decreases as we recede from the equa-
tor. At Cumana,in latitude 10^, the average blueness of the sky
is 24, while in Europe it is only 14. On a clear, bright day, the
average blueness of the sky at New Haven corresponds to about
18 on the cyanometer.

The blueness of the sky increases with the altitude, and at an
elevation of 16,000 feet the heavens become almost black. On
the top of Mount Blanc, Saussure found the color of the sky 39,
while at the foot of the mountain the color of the sky near the
zenith was represented by 18.

411. Twilight — If there were no atmosphere, night would com-
mence as soon as the sun descends below the horizon, and the
day would begin with equal abruptnes& The astronomical limit
of twilight is generally understood to be the instant when stars
of the sixth magnitude begin to be visible in the zenith at even-
ing, or disappear in the morning. In our climate the evening
twilight generally terminates when the sun is 17° or 18° below
the horizon. The morning twilight commences at a somewhat
less depression, since the vapor of the atmosphere condensed dur-
ing the night does not rise to so great a height in the morning as
at evening. These limits, however, are variable, the duration of
twilight depending upon the state of the atmosphere. When the
sky is of a pale color, indicating the presence of an unusual amount
of condensed vapor, twilight is of longer duration. This happens

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habitually in the polar regions. On the contrary, within the trop-
ics, where the air is pure and dry, twilight sometimes lasts only
fifteen minutes.

412, Twilight Curve. — A little before sunset the western sky
grows yellow, and in the east we observe a purple tint arising
from the reflection of the sun's rays, which have traversed the
atmosphere horizontally, and which communicate their color to
whatever they illumine. After the sun has set, we perceive near
the eastern horizon a dark blue segment, above which we notice
the purple tint already mentioned. As the sun declines this seg-
ment .rises higher ; it subsequently reaches the zenith, and finally
the western horizon, when the twilight entirely ceases. The out-
line of this segment sometimes appears very sharply defined, and
is called the twilight curve. This segment is a part of the coni-
cal shadow of the earth, which intercepts the sun's rays from a
portion of the atmosphere, and this portion reflects only that dif-
fuse light which comes from other parts of the sky.

413. Cohrs of the Morning Twilight. — ^When the sun is still 12°
below the eastern horizon, the horizon generally appears border-
ed with a red or orange band, above which the twilight curve
rises 7°. The orange zone gradually extends, becomes bordered
with yellow, and afterward with green, while the twilight curve
ascends toward the zenith. When the sun is only 2° below the
horizon,^the eastern horizon becomes yellow, the green zone be-
comes more decided, and extends from 8° to 18°, the twilight
curve extends to within 8° of the western horizon, and is border^
ed with a purple zone about 12° in breadth. As the sun rises,
the western horizon appears bordered with a rosy band, sur-
mounted by yellow. The red in the east disappears, and is suc-
ceeded by yellow, surmounted by green, which continues after
'"he yellow has disappeared, when the sun is 2° or 4° above the

The red and yellow zones are ascribed to the absorptiqn pro-
duced by the different thicknesses of air traversed by the rays of
light The green color results from a combination of the yellow
rays with the blue rays of diffuse light reflected from the parti-
cles of the atmosphere, green being produced by a mixture of
yellow and blue.


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414. Height of the Atmosphere deduced frorrri Twilight — Attempts
have been made to compute the height of the atmosphere from
the position of the twilight curve at a given instant after sunset;
but the results thus obtained are not uniform, being greatest when
the sun is lowest below the horizon. From such computations it
has been inferred that the height of the atmosphere can not ex-
ceed 36 miles ; but this can only be regarded as the height of
that portion of the atmosphere which has a density sufficient to
reflect an appreciable amount of light. Other phenomena indi-
cate that an extremely rare atmosphere extends to a much great-
er height

415. Prognostics derived from Twilight — Since the colors and
, duration of twilight, especially at evening, depend upon the

amount of condensed vapor which the atmosphere contains, these
appearances should afford some indication of the weather which
may be expected to succeed. The following are some of the rules,
which are relied upon by seamen. When, after sunset, the west-
ern sky is of a whitish yellow, and this tint extends to a great
height, it is probable that it will rain during the night or the
next day. Gaudy or unusual hues, with hard, definitely outlined
clouds, foretell rain and probably wind. If the sun, before setting,
appears diffuse and of a brilliant white, it foretells a storm. If
it sets in a sky slightly purple, the atmosphere near the zenith
being of a bright blue, we may rely upon fine weather.

A red sky in the morning presages bad weather, or much wind
if not rain ; but if the sky presents simply a rosy or grayish tint^
we may expect &ir weatber.



416. The rainbow consists of a series of circular bands colored
with the tints of the solar spectrum from red to violet, and is sit-
uated in that part of the sky which is opposite to the sun. It is
caused by the refraction and reflection of the sun's light from
drops of rain whose form is sensibly spherical.

It is proved in Natural Philosophy (Olmsted, p. 419) that, if
i represents the angle of incidence of a ray of light,
r " " " refraction " "

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D represents tbe angle of deviation of a ray of light,
n " the index of refraction for water;
then, for the maximum deviation after one reflection, we have

COS. i=Y ^ 7" ; sin. t=n sin. r; D=4r— 2i. »

If we assume the index of refraction for the red rays to be
1.3309, and for the violet rays 1.3442, we shall find

for the red rays, t=69° 32' ; D=42° 24' ;
" violet rays, t=68'° 46' ; 0=40° 28'.
For the minimum deviation after two reflections we have

cos. i= \/ — -— ; sin. t=n sin. r ; D=ir+2i— 6r.
V 8

Whence, by computation, we find

for the red rays, i=71° 55' ; 0=50** 20' ;
" violet rays, i=71° 29' ; D=53° 46'.

The exterior radius of the primary bow should therefore be
42^ 24', increased by half the diameter of the sun; and its breadth
should be V 56', increased by the apparent diameter of the sun,
which is about 30', making 2^ 26'. The mean of numerous care-
ful measurements gives 41^ 38' for the radius of the middle part
of the primary bow.

The interior radius of the secondary bow should be 50® 20', di-
minished by half the diameter of tbe sun, and its breadth should

417. Necessary Qmdiiions ofVisibiiiiy. — If the altitude of the
sun be greater than the radius of the bow, then no rainbow can.
be seen. For this reason, during more than six months of the
year at New Haven, the primary bow can never be seen at noon,
and near the summer solstice the primary bow can not be seen
for more than six hours near the middle of the day.

If the observer be sufficiently elevated above the earth, as in a
balloon, he may see the rainbow as a complete circle, but on the
sur&ce of the earth we only see a semicircle when the sun is in
the horizon.

Lunar rainbows are occasionally seen, but the colors are faint,
and generally only a white or yellowish arc is distinguishable.

418. Supeniumerary Bows. — ^The Newtonian theory of the rain-

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bow is incomplete, inasmuch as it only considers those rays which
experience the maximum or minimum deviation, and entirely
neglects those rays which pass a little beyond these limits. The
eflfect of these other rays is to extend the breadth of the primary
bo^ upon the inside, and also to produce secondary bands which
the Newtonian theory does not explain. When the rainbow is
brilliant, we often perceive faint bands alternately red and green
within the violet of the primary bow, or perhaps superposed upon
the violet, which then assumes a purplish tint Near the violet
bow we frequently see an arch of rose-red, succeeded by one of
yellowish-green ; then perhaps a second arch of rose-red and a
second of yellowish -gjreen. Two supernumerary bows are not
very uncommon ; three have repeatedly been seen, and occasion-
ally even four.

These supernumerary bows are due to the interference of rays
which traverse a drop in a direction dififering but little fi-om that
of maximum deviation. To every angle of deviation a little less
than the maximum, there correspond two rays, one whose angle
of incidence is a little greater, and the other whose angle is a lit-
tle less than that which gives the maximum deviation. These
rays, having pursued routes slightly unequal, interfere and pro-
duce alternations of light and darkness, or alternately bright and
dark bands. The bands resulting from these interferences for
each of the colors of the spectrum, being superposed upon the
sky, produce bands analogous to the colored rings of thin plates.

419. Theory exphined frcm a Diagram, — A ray of light, SA,
once reflected from the inner surface of a drop of rain at B, ex-
Fig. 84. periences its greatest deviation, viz.,

s; -^ -.^^^^ 41®, when the angle of incidence, FEA,

„^ .^j^^^^^^^^^^^^^^^ .^ ggo Suppose a ray of light, S'A',

/ \ ^^^ f^^'s upon the drop at an angle great-
d -^ J-\ er than 59®, it will experience a devia-

V /7 / *^^^ ^®^ ^^^ ^■'■°* ^^ * ^y* ^"

\ '//// A", which falls upon the drop at an

^^^""""y^/TC angle less than 59®, will experience a

//Y deviation less than 41®. That is, there

//V are always two rays which experience

^ an equal deviation (for example, 40°),

and therefore emerge parallel, one of them making with the

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drop an angle greater lihan 59°, and the other a less angle. The
paths of these two rays within the drop are slightly unequal,
and there are two rays the diflference of whose paths within the
drop is equal to half the breadth of a wave of light These
waves, being in opposite phases, will interfere with each other,
and produce darkness. There are two other rays the difference
of whose paths within the drop is equal tdfche breadth of a wave
of light These waves, being in the same phase, will conspire to
produce a double illumination. There are two other rays the
difference of whose paths is equal to one and a half undulations,
and which consequently interfere with each other.

Thus we have rays the difference of whose paths is equal to 1,
2, 8, 4, etc, undulations, and which therefore conspire ; and there
are other rays the difference of whose paths is equal to ^, 1^, 2-J^,
8^, etc., undulations, and which therefore interfere.

420. Gmsequence of these Interferences. — If, then, the sun fur-
nished red light only, we should see opposite to the sun, when
drops of rain are falling, circular arcs, alternately red and black.
If the sun's light were entirely violet, we should see circular arcs
alternately violet and black, but the diameter of the violet arcs
•would be less than that of the red arcs. The other colors of the
spectrum would produce arcs of intermediate dimensions. Now,
since the sun's light contains all the colors of the spectrum, all
these colored arcs are in fact formed simultaneously and super-
posed, and, being of unequal diameters, the colors are partially
blended. But near the usual primary bow two or three of these
narrow bands of prismatic colors are often suflSiciently distinct to
be visible. In consequence of this reflection of light from the
drops of rain, it results that the sky within the primary bow is
brighter than that without it

421. Size of the Drops of Rain, — ^The smaller the drops of rain,
the broader will be these colored banda In order that the su-
pernumerary bows may be formed beyond the first violet bow,
the drops. must be extremely minute. It is found by computa-
tion thtft if the drops be ^ inch in diameter, a second red band
will be formed 2^ from the outer red of the primary bow, and it is
near this point that the first supernumerary bow is usually seen.

If we consider the interval between the first and second maxi-

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mum unity, the breadths of the succeeding intervals for the same
color will be expressed by the numbers,

second interval, 0.587 ; fourth interval, 0.440 ;

third interval, 0.493; fifth interval, 0.404.

Supernumerary bows are sometimes seen on the outside of the
secondary rainbow, and they are to be explained in a similar
manner. ^

422. Fog-how eocplmned, — If the drops be less than ^ inch in
diameter, the primary bow will be wider than two degrees, the
breadth of the bow depending simply upon the size of the drops.
But as the breadth of the bow increases, the colors are spreisul
over a greater surface, and consequently they are less vivid and
distinct When the diameter of the drops is i^ih inch, which is
the average diameter of particles of fog, the bow becomes a very
faint arch 4° or 5^ in breadth, with only a slightly rosy tint upon
the outside. Such is the bow actually observed when the sun
shines upon a dense fog.

The undulatory theory of light, therefore, explains not only
the supernumeraiy bows, but the variable breadth of the prima-
ry bow.



423. The sun and moon, when partially covered by light, flee-
cy clouds, are often seen encircled by one or more colored rings,
which are called coron(3R, This phenomenon is most frequently
noticed about the moon, since we are too much dazzled by the
light of the sun to distinguish faint colors surrounding his disc.
In order to examine coronsB about the sun, it is best to view them
by reflection from a blackened mirror, by which means the bril-
liancy of the sun's light is very much reduced.

424. Order of the Colors, — ^When a corona is complete, we may
observe several concentric colored circles. The one next to the
sun is blue, the second is nearly white, and the thir^is red.
These form the first series of rings. In the second series the or-
der of the colors is purple, blue, green,. pale yellow, and red. In
the third series the colors are pale blue and pale red. These
rings are partially represented in Fig 88.

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The diameter of these rings is not always the same. The di-
ameter of the fiVst red ring varies from 8° to 6°, and that of the
second red ring from 5^ to 10°.

426. Cauae ofCoToncR. — Coronas are produced by the diffraction
of the rays of light in their passage through the small intervals
between the particles of condensed vapor in a cloud. If we look
at the moon through a very small aperture (as a pinhole in a
plate of sheet-lead) we shall see the hole surrounded by colored
rings, whose tints are the same as those observed in coronas. The
light of the moon, passing through the small interstices between
the particles of a cloud, is difiracted in a similar manner. The
particles of a cloud must not be too numerous, otherwise no rays
can pass between them; and the smaller the intervals between the
particles, the greater will be the diameter of the rings.

426. CoroncB produced artifidaUy. — ^If we sprinkle upon a pane
of glass a little lycopodium, or any very fine dust of nearly uni-
form fineness, and look at the moon through this glass, we shall
see it surrounded by rings of the prismatic colors, precisely like
those formed by a cloud.

If, on a cold winter evening, we breathe upon a pane of glass,
the breath will condense in small globules and freeze; and if we
look at the moon, or even at a street lamp, through this glass, we
shall see a similar system of colored rings, having violet on the

427. Ohw surrounding the Shadow of an Observer. — ^When the
sun is near the horkon, and the shadow of the observer falls on
grass covered with.aew, one may often observe a vivid glow sur-
rounding^ the shadow of his head. If the shadow falls upon a
cloud or a fog, the head will appear surrounded by a luminous
glory, exhibiting the prismatic colors. The order of the colors is
the same as in coronas, and sometimes four and even five series
of rings have been observed.

The light of the sun is reflected to the eye most powerfully by
the particles of fog near the head ; for the light reflected both
from the anterior and posterior face of such particles will reach
the eye. This explains the glow of light surrounding the shad-
ow of the observer. The color is produced by the diffraction of
the Ught thus reflected, precisely as in the case of a corona.

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Online LibraryElias LoomisA treatise on meteorology : with a collection of meteorological tables → online text (page 18 of 28)