rain sometimes occurs, and in many instances it is due to very simple
causes. In some cases the coloring matter is found to be nothing but
the pollen-dust shaken out of the flowers on certain trees at such
times as a strong wind happened to be blowing over them. Fir trees
and cypress trees, when grouped together in large forests, at certain
seasons of the year give off enormous quantities of pollen, and this
vegetable dust is often carried many miles through the atmosphere by
the wind, and frequently falls to earth during a shower of rain. The
microscope clearly reveals the origin of such colored rain, which has
on more than one occasion puzzled and mystified the inexperienced.
Pollen is, therefore, very largely responsible for the reports sent
from different parts of the world of golden, black, and red rain.
Fish and insects also descend to earth during showers of rain; but
since it is probable that these and other unwonted visitors to the
atmosphere were originally drawn up into the air during the passage
across the country of a whirling storm, with powerfully ascending
currents of air, there is no need to look for any far-fetched
explanation of what, after all, is a very simple occurrence.
The history of a raindrop, then, has some very romantic and
interesting episodes connected with it; but, wonderful as are the
incidents in what is really a very remarkable career, it is not until
the raindrops fall on the earth that the full purport of the work
they do is wholly realized. Contemplated by itself, a raindrop seems
a very insignificant thing; but when the drops combine in a heavy
downpour of rain the result is truly wonderful. The information
that one inch of rain has fallen over a certain area is not very
impressive; the amount does not seem very great. A fall of one inch
of rain means, however, that no less than one hundred tons of water
have fallen on each acre of surface, or no less than sixty thousand
tons on each square mile. Instead of expressing the amount of water
in tons, it may be thus stated in gallons, taking the Thames basin
as a convenient area for reference: a rainfall of three inches over
that area means that one hundred and sixty thousand million gallons
of water have been precipitated from the atmosphere. At times, too,
when the rainfall is still heavier, rivers overflow their banks and
floods occur, and still further evidence is then forthcoming of the
power and the might of the raindrops working toward one common end.
Sooner or later the raindrop, whether it runs off the surface of the
earth in a river or in a disastrous flood, finds its way, under the
influence of evaporation, back into the atmosphere, and is then ready
to start on another journey, which, like all its predecessors, will
be full of incident from start to finish.
THE RAINBOW
--JOHN TYNDALL
The oldest historic reference to the rainbow is known to all: “I do
set my bow in the clouds, and it shall be for a token of a covenant
between me and the earth.... And the bow shall be in the cloud; and
I will look upon it, that I may remember the everlasting covenant
between God and every living creature of all flesh that is upon the
earth.”
To the sublime conceptions of the theologian succeeded the desire for
exact knowledge characteristic of the man of science. Whatever its
ultimate cause might have been, the proximate cause of the rainbow
was physical, and the aim of science was to account for the bow on
physical principles. Progress toward this consummation was very slow.
Slowly the ancients mastered the principles of reflection. Still more
slowly were the laws of refraction dug from the quarries in which
Nature had imbedded them. I use this language because the laws were
incorporate in Nature before they were discovered by man. Until the
time of Alhazan, an Arabian mathematician, who lived at the beginning
of the Twelfth Century, the views entertained regarding refraction
were utterly vague and incorrect. After Alhazan came Roger Bacon and
Vitellio, who made and recorded many observations and measurements on
the subject of refraction. To them succeeded Kepler, who, taking the
results tabulated by his predecessors, applied his amazing industry
to extract from them their meaning--that is to say, to discover
the physical principles which lay at their root. In this attempt
he was less successful than in his astronomical labors. In 1604,
Kepler published his _Supplement to Vitellio_, in which he virtually
acknowledged his defeat by enunciating an approximate rule, instead
of an all-satisfying natural law. The discovery of such a law, which
constitutes one of the chief corner-stones of optical science, was
made by Willebrod Snell, about 1621.
A ray of light may, for our purposes, be presented to the mind as a
luminous straight line. Let such a ray be supposed to fall vertically
upon a perfectly calm water-surface. The incidence, as it is called,
is then perpendicular, and the ray goes through the water without
deviation to the right or left. In other words, the ray in the air
and the ray in the water form one continuous straight line. But the
least deviation from the perpendicular causes the ray to be broken,
or “refracted,” at the point of incidence. What, then, is the law
of refraction discovered by Snell? It is this, that no matter how
the angle of incidence and with it the angle of refraction may vary,
the relative magnitude of two lines, dependent on these angles,
and called their sines, remains, for the same medium, perfectly
unchanged. Measure, in other words, for various angles, each of these
two lines with a scale, and divide the length of the longer one by
that of the shorter; then, however the lines individually vary in
length, the quotient yielded by this division remains absolutely the
same. It is, in fact, what is called “the index of refraction” of the
medium.
Science is an organic growth, and accurate measurements give
coherence to the scientific organism. Were it not for the antecedent
discovery of the law of sines, founded as it was on exact
measurements, the rainbow could not have been explained. Again and
again, moreover, the angular distance of the rainbow from the sun
had been determined and found constant. In this divine remembrancer
there was no variableness. A line drawn from the sun to the rainbow,
and another drawn from the rainbow to the observer’s eye, always
inclosed an angle of 41°. Whence this steadfastness of position--this
inflexible adherence to a particular angle? Newton gave to De
Dominis[4] the credit of the answer; but we really owe it to the
genius of Descartes. He followed with his mind’s eye the rays of
light impinging on a raindrop. He saw them in part reflected from
the outside surface of the drop. He saw them refracted on entering
the drop, reflected from its back, and again refracted on their
emergence. Descartes was acquainted with the law of Snell, and taking
up his pen, he calculated, by means of that law, the whole course
of the rays. He proved that the vast majority of them escaped from
the drop as _divergent_ rays, and, on this account, soon became
so enfeebled as to produce no sensible effect upon the eye of an
observer. At one particular angle, however--namely, the angle 41°
aforesaid--they emerged in a practically _parallel sheaf_. In their
union was strength, for it was this particular sheaf which carried
the light of the “primary” rainbow to the eye.
There is a certain form of emotion called intellectual pleasure which
may be excited by poetry, literature, nature, or art. But I doubt
whether among the pleasures of the intellect there is any more pure
and concentrated than that experienced by the scientific man when a
difficulty which has challenged the human mind for ages melts before
his eyes, and re-crystallizes as an illustration of natural law. This
pleasure was doubtless experienced by Descartes when he succeeded in
placing upon its true physical basis the most splendid meteor of our
atmosphere. Descartes showed, moreover, that the “secondary bow” was
produced when the rays of light underwent two reflections within the
drop, and two refractions at the points of incidence and emergence.
Descartes proved that, according to the principles of refraction, a
circular band of light must appear in the heavens exactly where the
rainbow is seen. But how are the colors of the bow to be accounted
for? Here his penetrative mind came to the very verge of the
solution, but the limits of knowledge at the time barred his further
progress. He connected the colors of the rainbow with those produced
by a prism; but then these latter needed explanation just as much as
the colors of the bow itself. The solution, indeed, was not possible
until the composite nature of white light had been demonstrated by
Newton. Applying the law of Snell to the different colors of the
spectrum, Newton proved that the primary bow must consist of a series
of concentric circular bands, the largest of which is red and the
smallest violet; while in the secondary bow these colors must be
reversed. The main secret of the rainbow, if I may use such language,
was thus revealed.
I have said that each color of the rainbow is carried to the eye by
a sheaf of approximately parallel rays. But what determines this
parallelism? Here our real difficulties begin. Let us endeavor to
follow the course of the solar rays before and after they impinge
upon a spherical drop of water. Take, first of all, the ray that
passes through the centre of the drop. This particular ray strikes
the back of the drop as a perpendicular, its reflected portion
returning along its own course. Take another ray close to this
central one and parallel to it--for the sun’s rays when they reach
the earth are parallel. When this second ray enters the drop it is
refracted; on reaching the back of the drop it is there reflected,
being a second time refracted on its emergence from the drop. Here
the incident and the emergent rays inclose a small angle with each
other. Take, again, a third ray a little further from the central
one than the last. The drop will act upon it as it acted upon its
neighbor, the incident and the emergent rays inclosing in this
instance a larger angle than before. As we retreat further from the
central ray the enlargement of this angle continues up to a certain
point, where it reaches a maximum, after which further retreat
from the central ray diminishes the angle. Now, a maximum resembles
the ridge of a hill, or a watershed, from which the land falls in a
slope at each side. In the case before us the divergence of the rays
when they quit the raindrop would be represented by the steepness
of the slope. On the top of the watershed--that is to say, in the
neighborhood of our maximum--is a kind of summit-level, where the
slope for some distance almost disappears. But the disappearance of
the slope indicates, as in the case of our raindrop, the absence of
divergence. Hence we find that at our maximum, and close to it, there
issues from the drop a sheaf of rays which are nearly, if not quite,
parallel to each other. They are the so-called “effective rays” of
the rainbow.
But though the step here taken by Descartes and Newton was a great
one, it left the theory of the bow incomplete. Within the rainbow
proper, in certain conditions of the atmosphere, are seen a series of
richly colored zones, which were not explained by either Descartes
or Newton. They are said to have been first described by Mariotte,
and they long challenged explanation. At this point our difficulties
thicken, but, as before, they are to be overcome by attention. It
belongs to the very essence of a maximum, approached continuously
on both sides, that on the two sides of it pairs of equal value may
be found. The maximum density of water, for example, is 39° Fahr.
Its density, when 5° colder and when 5° warmer than this maximum, is
the same. So also with regard to the slopes of a watershed. A series
of pairs of points of the same elevation can be found upon the two
sides of the ridge; and, in the case of the rainbow, on the two
sides of the maximum deviation we have a succession of pairs of rays
having the same deflection. Such rays travel along the same line,
and add their forces together after they quit the drop. But light,
thus reinforced by the coalescence of non-divergent rays, ought to
reach the eye. It does so; and were light what it was once supposed
to be--a flight of minute particles sent by luminous bodies through
space--then these pairs of equally deflected rays would diffuse
brightness over a large portion of the area within the primary bow.
But inasmuch as light consists of _waves_, and not of particles, the
principle of interference comes into play, in virtue of which waves
alternately reinforce and destroy each other. Were the distance
passed over by the two corresponding rays within the drop the same,
they would emerge as they entered. But in no case are the distances
the same. The consequence is that when the rays emerge from the drop
they are in a condition either to support or to destroy each other.
By such alternate reinforcement and destruction, which occur at
different places for different colors, the colored zones are produced
within the primary bow. They are called “supernumerary bows,” and
are seen, not only within the primary, but sometimes also outside
the secondary bow. The condition requisite for their production is
that the drops which constitute the shower shall all be of nearly the
same size. When the drops are of different sizes, we have a confused
superposition of the different colors, an approximation to white
light being the consequence. This second step in the explanation of
the rainbow was taken by a man the quality of whose genius resembled
that of Descartes or Newton, and who in 1801 was appointed Professor
of Natural Philosophy in the Royal Institution. I refer, of course,
to the illustrious Thomas Young.
But our task is not, even now, complete. The finishing touch to
the explanation of the rainbow was given by the eminent Astronomer
Royal, Sir George Airy. Bringing the knowledge possessed by the
founders of the undulatory theory, and that gained by subsequent
workers, to bear upon the question, Sir George Airy showed that,
though Young’s general principles were unassailable, his calculations
were sometimes wide of the mark. It was proved by Airy that the
curve of maximum illumination in the rainbow does not quite
coincide with the geometric curve of Descartes and Newton. He also
extended our knowledge of the supernumerary bows, and corrected
the positions which Young had assigned to them. Finally, Professor
Miller of Cambridge and Dr. Galle of Berlin illustrated with careful
measurements with the theodolite the agreement which exists between
the theory of Airy and the facts of observation. Thus, from Descartes
to Airy, the intellectual force expended in the elucidation of the
rainbow, though broken up into distinct personalities, might be
regarded as that of an individual artist, engaged throughout this
time in lovingly contemplating, revising, and perfecting his work.
The white rainbow (_l’arc-en-ciel blanc_) was first described by the
Spanish Don Antonio de Ulloa, lieutenant of the Company of Gentleman
Guards of the Marine. By order of the King of Spain, Don Jorge Juan
and Ulloa made an expedition to South America, an account of which
is given in two amply illustrated quarto volumes to be found in the
library of the Royal Institution. The bow was observed from the
summit of the mountain Pambamarca, in Peru. The angle subtended by
its radius was 33° 30′, which is considerably less than the angle
subtended by the radius of the ordinary bow.
The white rainbow has been explained in various ways. The genius of
Thomas Young throws light upon this subject, as upon so many others.
He showed that the whiteness of the bow was a direct consequence of
the smallness of the drops which produce it. The smaller the drops,
the broader are the zones of the supernumerary bows, and Young proved
by calculation that when the drops have a diameter of 1-3000th or
1-4000th of an inch, the bands overlap each other, and produce white
light by their mixture.
SNOW, HAIL, AND DEW
--ALEXANDER BUCHAN
Snow is the frozen moisture which falls from the atmosphere when the
temperature is 32° or lower. It is composed of crystals, usually in
the form of six-pointed stars, of which about 1,000 different kinds
have been already observed, and many of them figured, by Scoresby,
Glaisher, and others. These numerous forms have been reduced to
five principal varieties: Thin plates, the most numerous class,
containing several hundred forms of the rarest and most exquisite
beauty; spherical nucleus or plane figure studded with needle-shaped
crystals; six or more rarely three-sided prismatic crystals; pyramids
of six sides; prismatic crystals, having at the ends and middle thin
plates perpendicular to their length. The forms of the crystals
in the same fall of snow are generally similar to each other. The
crystals of hoar-frost being formed on leaves and other bodies
disturbing the temperature are often irregular and opaque; and it has
been observed that each tree or shrub has its own peculiar crystals.
Snowflakes vary from an inch to 7-100ths of an inch in diameter, the
largest occurring when the temperature is near 32°, and the smallest
at very low temperatures. As air has a smaller capacity for retaining
its vapor as the temperature sinks, it follows that the aqueous
precipitation, snow or rain, is much less in polar than in temperate
regions. The white color of snow is the result of the combination of
the different prismatic rays issuing from the _minute_ snow-crystals.
Pounded glass and foam are analogous cases of the prismatic colors
blending together and forming the white light out of which they had
been originally formed. It may be added that the air contained in
the crystals intensifies the whiteness of the snow. The limit of
the fall of snow coincides nearly with 30° N. lat., which includes
nearly the whole of Europe; on traversing the Atlantic, it rises to
45°, but on nearing America descends to near Charleston; rises on
the west of America to 47°, and again falls to 40° in the Pacific.
It corresponds nearly with the winter isothermal of 52° Fahr. Snow
is unknown at Gibraltar; at Paris, it falls 12 days on an average
annually, and at St. Petersburg 170 days. It is from 10 to 12 times
lighter than an equal bulk of water. From its loose texture, and its
containing about 10 times its bulk of air, it is a very bad conductor
of heat, and thus forms an admirable covering for the earth from
the effects of radiation--it not infrequently happening, in times
of great cold, that the soil is 40° warmer than the surface of the
overlying snow. The flooding of rivers from the melting of the snow
on mountains in summer carries fertility into regions which would
otherwise remain barren wastes.
The word hail in English is unfortunately used to denote two
phenomena of apparently different origin. In French, we have the
terms _grèle_ and _grésil_--the former of which is hail proper; the
latter denotes the fine grains, like small shot, which often fall
in winter, much more rarely in summer, and generally precede snow.
The cause of the latter seems to be simply the freezing of raindrops
as they pass in their fall through a colder region of air than that
where they originated. We know by balloon ascents and various other
methods of observation that even in calm weather different strata
of the atmosphere have extremely different temperatures, a stratum
far under the freezing point being often observed between two others
comparatively warm.
But that true hail, though the process of its formation is not yet
perfectly understood, depends mainly upon the meeting of two nearly
opposite currents of air--one hot and saturated with vapor, the
other very cold--is rendered pretty certain by such facts as the
following. A hailstorm is generally a merely local phenomenon, or at
most, ravages a belt of land of no great breadth, though it may be
of considerable length. Hailstorms occur in the greatest perfection
in the warmest season, and at the warmest period of the day, and
generally are most severe in the most tropical climates. A fall of
hail generally _precedes_, sometimes accompanies, and rarely, if
ever, follows a thunder-shower.
When a mass of air, saturated with vapor, rising to a higher level,
meets a cold one, there is, of course, instant condensation of vapor
into ice by the cold due to expansion; at the same time, there is
generally a rapid production of electricity, the effect of which upon
such light masses as small hailstones is to give them in general
rapid motion in various directions successively. These motions are in
addition to the vortex motions or eddies, caused in the air by the
meeting of the rising and descending currents. The small ice-masses
then moving in all directions impinge upon each other, sometimes with
great force, producing that peculiar rattling sound which almost
invariably precedes a hail-shower. At the same time, by a well-known
property of ice, the impinging masses are frozen together; and this
process continues until the weight of the accumulated mass enables
it to overcome the vortices and the electrical attractions, when it
falls as a larger or smaller hailstone. On examining such hailstones,
which may have any size from that of a pea to that of a walnut, or
even an orange, we at once recognize the composite character which
might be expected from such a mode of aggregation.
A curious instance of the fall of large hail, or rather ice-masses,
occurred on one of her Majesty’s ships off the Cape in January, 1860.
Here the stones were the size of half-bricks, and beat several of
the crew off the rigging, doing serious injury. We may conclude by
a description (taken from _Mem. de l’Acad. des Sciences_, 1790) of
one of the most disastrous hailstorms that has occurred in Europe
for many years back. This storm passed over Holland and France in
July, 1788. It traveled _simultaneously_ along two lines nearly
parallel--the eastern one had a breadth of from half a league to
five leagues, the western of from three to five leagues. The space
between was visited only by heavy rain; its breadth varied from three
to five and a half leagues. At the outer border of each, there was
also heavy rain, but we are not told how far it extended. The length
was at least a hundred leagues; but from other reports it may be
gathered that it really extended to nearly two hundred. It seems to
have originated near the Pyrenees, and to have traveled at a mean
rate of about sixteen and a half leagues per hour toward the Baltic,
where it was lost sight of. The hail only fell for about seven and
a half minutes at any one place. The hailstones were generally of
irregular form, the heaviest weighing about eight French ounces. This
storm devastated 1,039 parishes in France alone, and the damage was
officially placed at 24,690,000 francs.
For any assigned temperature of the atmosphere, there is a certain
quantity of aqueous vapor which it is capable of holding in
suspension at a given pressure. Conversely, for any assigned quantity
of aqueous vapor held in suspension in the atmosphere, there is
a minimum temperature at which it can remain so suspended. This
minimum temperature is called the dew-point. During the daytime,
especially if there has been sunshine, a good deal of aqueous vapor
is taken into suspension in the atmosphere. If the temperature in the
evening now falls below the dew-point, which after a hot and calm
day generally takes place about sunset, the vapor which can be no
longer held in suspension is deposited on the surface of the earth,
sometimes to be seen visibly falling in a fine mist. This is one
form of the phenomenon of dew, but there is another. The surface of
the earth, and all things on it, and especially the smooth surfaces
of vegetable productions, are constantly parting with their heat by
radiation. If the sky is covered with clouds, the radiation sent
back from the clouds nearly supplies an equivalent for the heat thus
parted with; but if the sky be clear, no equivalent is supplied, and
the surface of the earth and things growing on it become colder than
the atmosphere.