becomes more complex, for then the needles are not only acted on by
the magnet, but they act upon each other. And if we pass to smaller
masses of iron--to iron filings, for example--we find that they act
substantially as the needles, arranging themselves in definite forms,
in obedience to the magnetic action.
Placing a sheet of paper or glass over a bar magnet and showering iron
filings upon the paper, I notice a tendency of the filings to arrange
themselves in determinate lines. They cannot freely follow this
tendency, for they are hampered by the friction against the paper.
They are helped by tapping the paper; each tap releasing them for a
moment, and enabling them to follow their tendencies. But this is an
experiment which can only be seen by myself. To enable you all to see
it, I take a pair of small magnets and by a simple optical arrangement
throw the magnified images of the magnets upon the screen. Scattering
iron filings over the glass plate to which the small magnets are
attached, and tapping the plate, you see the arrangement of the iron
filings in those magnetic curves which have been so long familiar to
scientific men (fig. 23).
[Illustration: Fig. 23.
N is the nozzle of the lamp; M a plane mirror, reflecting the beam
upwards. At P the magnets and iron filings are placed; L is a lens
which forms an image of the magnets and filings; and R is a totally
reflecting prism, which casts the image G upon the screen.]
(By a very ingenious device, Professor Mayer, of Hoboken, has
succeeded in fixing and photographing the magnetic curves. I am
indebted to his kindness for the annexed beautiful illustration, fig.
24.)
The aspect of these curves so fascinated Faraday that the greater
portion of his intellectual life was devoted to pondering over them.
He invested the space through which they run with a kind of
materiality; and the probability is that the progress of science, by
connecting the phenomena of magnetism with the luminiferous ether,
will prove these 'lines of force,' as Faraday loved to call them, to
represent a condition of this mysterious substratum of all radiant
action.
It is not, however, the magnetic curves, as such, but their
relationship to theoretic conceptions, that we have now to consider.
By the action of the bar magnet upon the needle we obtain the notion
of a polar force; by the breaking of the strip of magnetized steel we
attain the notion that polarity can attach itself to the ultimate
particles of matter. The experiment with the iron filings introduces a
new idea into the mind; the idea, namely, of _structural arrangement_.
Every pair of filings possesses four poles, two of which are
attractive and two repulsive. The attractive poles approach, the
repulsive poles retreat; the consequence being a certain definite
arrangement of the particles with reference to each other.
§ 2. _Theory of Crystallization._
Now this idea of structure, as produced by polar force, opens a way
for the intellect into an entirely new region, and the reason you
are asked to accompany me into this region is, that our next inquiry
relates to the action of crystals upon light. Prior to speaking of
this action, I wish you to realise intellectually the process of
crystalline architecture. Look then into a granite quarry, and spend a
few minutes in examining the rock. It is not of perfectly uniform
texture. It is rather an agglomeration of pieces, which, on
examination, present curiously defined forms. You have there what
mineralogists call quartz, you have felspar, you have mica. In a
mineralogical cabinet, where these substances are preserved
separately, you will obtain some notion of their forms. You will see
there, also, specimens of beryl, topaz, emerald, tourmaline, heavy
spar, fluor-spar, Iceland spar--possibly a full-formed diamond, as it
quitted the hand of Nature, not yet having got into the hands of the
lapidary.
[Illustration: Fig. 24.]
These crystals, you will observe, are put together according to law;
they are not chance productions; and, if you care to examine them more
minutely, you will find their architecture capable of being to some
extent revealed. They often split in certain directions before a
knife-edge, exposing smooth and shining surfaces, which are called
planes of cleavage; and by following these planes you sometimes reach
an internal form, disguised beneath the external form of the crystal.
Ponder these beautiful edifices of a hidden builder. You cannot help
asking yourself how they were built; and familiar as you now are with
the notion of a polar force, and the ability of that force to produce
structural arrangement, your inevitable answer will be, that those
crystals are built by the play of polar forces with which their
molecules are endowed. In virtue of these forces, molecule lays
itself to molecule in a perfectly definite way, the final visible form
of the crystal depending upon this play of its ultimate particles.
Everywhere in Nature we observe this tendency to run into definite
forms, and nothing is easier than to give scope to this tendency by
artificial arrangements. Dissolve nitre in water, and allow the water
slowly to evaporate; the nitre remains and the solution soon becomes
so concentrated that the liquid condition can no longer be preserved.
The nitre-molecules approach each other, and come at length within the
range of their polar forces. They arrange themselves in obedience to
these forces, a minute crystal of nitre being at first produced. On
this crystal the molecules continue to deposit themselves from the
surrounding liquid. The crystal grows, and finally we have large
prisms of nitre, each of a perfectly definite shape. Alum crystallizes
with the utmost ease in this fashion. The resultant crystal is,
however, different in shape from that of nitre, because the poles of
the molecules are differently disposed. When they are _nursed_ with
proper care, crystals of these substances may be caused to grow to a
great size.
The condition of perfect crystallization is, that the crystallizing
force shall act with deliberation. There should be no hurry in its
operations; but every molecule ought to be permitted, without
disturbance from its neighbours, to exercise its own rights. If the
crystallization be too sudden, the regularity disappears. Water may be
saturated with sulphate of soda, dissolved when the water is hot, and
afterwards permitted to cool. When cold the solution is
supersaturated; that is to say, more solid matter is contained in it
than corresponds to its temperature. Still the molecules show no sign
of building themselves together.
This is a very remarkable, though a very common fact. The molecules in
the centre of the liquid are so hampered by the action of their
neighbours that freedom to follow their own tendencies is denied to
them. Fix your mind's eye upon a molecule within the mass. It wishes
to unite with its neighbour to the right, but it wishes equally to
unite with its neighbour to the left; the one tendency neutralizes the
other and it unites with neither. But, if a crystal of sulphate of
soda be dropped into the solution, the molecular indecision ceases. On
the crystal the adjacent molecules will immediately precipitate
themselves; on these again others will be precipitated, and this act
of precipitation will continue from the top of the flask to the
bottom, until the solution has, as far as possible, assumed the solid
form. The crystals here produced are small, and confusedly arranged.
The process has been too hasty to admit of the pure and orderly action
of the crystallizing force. It typifies the state of a nation in which
natural and healthy change is resisted, until society becomes, as it
were, supersaturated with the desire for change, the change being then
effected through confusion and revolution.
Let me illustrate the action of the crystallizing force by two
examples of it: Nitre might be employed, but another well-known
substance enables me to make the experiment in a better form. The
substance is common sal-ammoniac, or chloride of ammonium, dissolved
in water. Cleansing perfectly a glass plate, the solution of the
chloride is poured over the glass, to which when the plate is set on
edge, a thin film of the liquid adheres. Warming the glass slightly,
evaporation is promoted, but by evaporation the water only is removed.
The plate is then placed in a solar microscope, and an image of the
film is thrown upon a white screen. The warmth of the illuminating
beam adds itself to that already imparted to the glass plate, so that
after a moment or two the dissolved salt can no longer exist in the
liquid condition. Molecule then closes with molecule, and you have a
most impressive display of crystallizing energy overspreading the
whole screen. You may produce something similar if you breathe upon
the frost ferns which overspread your window-panes in winter, and then
observe through a pocket lens the subsequent recongelation of the
film.
In this case the crystallizing force is hampered by the adhesion of
the film to the glass; nevertheless, the play of power is strikingly
beautiful. Sometimes the crystals start from the edge of the film and
run through it from that edge; for, the crystallization being once
started, the molecules throw themselves by preference on the crystals
already formed. Sometimes the crystals start from definite nuclei in
the centre of the film, every small crystalline particle which rests
in the film furnishing a starting-point. Throughout the process you
notice one feature which is perfectly unalterable, and that is,
angular magnitude. The spiculæ branch from the trunk, and from these
branches others shoot; but the angles enclosed by the spiculæ are
unalterable. In like manner you may find alum-crystals,
quartz-crystals, and all other crystals, distorted in shape. They are
thus far at the mercy of the accidents of crystallization; but in one
particular they assert their superiority over all such
accidents--_angular magnitude_ is always rigidly preserved.
My second example of the action of crystallizing force is this: By
sending a voltaic current through a liquid, you know that we decompose
the liquid, and if it contains a metal, we liberate this metal by
electrolysis. This small cell contains a solution of acetate of lead,
which is chosen for our present purpose, because lead lends itself
freely to this crystallizing power. Into the cell are dipped two very
thin platinum wires, and these are connected by other wires with a
small voltaic battery. On sending the voltaic current through the
solution, the lead will be slowly severed from the atoms with which it
is now combined; it will be liberated upon one of the wires, and at
the moment of its liberation it will obey the polar forces of its
atoms, and produce crystalline forms of exquisite beauty. They are now
before you, sprouting like ferns from the wire, appearing indeed like
vegetable growths rendered so rapid as to be plainly visible to the
naked eye. On reversing the current, these wonderful lead-fronds will
dissolve, while from the other wire filaments of lead dart through the
liquid. In a moment or two the growth of the lead-trees recommences,
but they now cover the other wire.
In the process of crystallization, Nature first reveals herself as a
builder. Where do her operations stop? Does she continue by the play
of the same forces to form the vegetable, and afterwards the animal?
Whatever the answer to these questions may be, trust me that the
notions of the coming generations regarding this mysterious thing,
which some have called 'brute matter,' will be very different from
those of the generations past.
There is hardly a more beautiful and instructive example of this play
of molecular force than that furnished by water. You have seen the
exquisite fern-like forms produced by the crystallization of a film of
water on a cold window-pane.[15] You have also probably noticed the
beautiful rosettes tied together by the crystallizing force during the
descent of a snow-shower on a very calm day. The slopes and summits of
the Alps are loaded in winter with these blossoms of the frost. They
vary infinitely in detail of beauty, but the same angular magnitude is
preserved throughout: an inflexible power binding spears and spiculæ
to the angle of 60 degrees.
The common ice of our lakes is also ruled in its formation by the same
angle. You may sometimes see in freezing water small crystals of
stellar shapes, each star consisting of six rays, with this angle of
60° between every two of them. This structure may be revealed in
ordinary ice. In a sunbeam, or, failing that, in our electric beam, we
have an instrument delicate enough to unlock the frozen molecules,
without disturbing the order of their architecture. Cutting from
clear, sound, regularly frozen ice, a slab parallel to the planes of
freezing, and sending a sunbeam through such a slab, it liquefies
internally at special points, round each point a six-petalled liquid
flower of exquisite beauty being formed. Crowds of such flowers are
thus produced. From an ice-house we sometimes take blocks of ice
presenting misty spaces in the otherwise continuous mass; and when we
inquire into the cause of this mistiness, we find it to be due to
myriads of small six-petalled flowers, into which the ice has been
resolved by the mere heat of conduction.
A moment's further devotion to the crystallization of water will be
well repaid; for the sum of qualities which renders this substance
fitted to play its part in Nature may well excite wonder and stimulate
thought. Like almost all other substances, water is expanded by heat
and contracted by cold. Let this expansion and contraction be first
illustrated:--
A small flask is filled with coloured water, and stopped with a cork.
Through the cork passes a glass tube water-tight, the liquid standing
at a certain height in the tube. The flask and its tube resemble the
bulb and stem of a thermometer. Applying the heat of a spirit-lamp,
the water rises in the tube, and finally trickles over the top.
Expansion by heat is thus illustrated.
Removing the lamp and piling a freezing mixture round the flask, the
liquid column falls, thus showing the contraction of the water by the
cold. But let the freezing mixture continue to act: the falling of the
column continues to a certain point; it then ceases. The top of the
column remains stationary for some seconds, and afterwards begins to
rise. The contraction has ceased, and _expansion by cold_ sets in. Let
the expansion continue till the liquid trickles a second time over the
top of the tube. The freezing mixture has here produced to all
appearance the same effect as the flame. In the case of water,
contraction by cold ceases, and expansion by cold sets in at the
definite temperature of 39° Fahr. Crystallization has virtually here
commenced, the molecules preparing themselves for the subsequent act
of solidification, which occurs at 32°, and in which the expansion
suddenly culminates. In virtue of this expansion, ice, as you know, is
lighter than water in the proportion of 8 to 9.[16]
A molecular problem of great interest is here involved, and I wish now
to place before you, for the satisfaction of your minds, a possible
solution of the problem:--
Consider, then, the ideal case of a number of magnets deprived of
weight, but retaining their polar forces. If we had a mobile liquid of
the specific gravity of steel, we might, by making the magnets float
in it, realize this state of things, for in such a liquid the magnets
would neither sink nor swim. Now, the principle of gravitation
enunciated by Newton is that every particle of matter, of every kind,
attracts every other particle with a force varying inversely as the
square of the distance. In virtue of the attraction of gravity, then,
the magnets, if perfectly free to move, would slowly approach each
other.
But besides the unpolar force of gravity, which belongs to matter in
general, the magnets are endowed with the polar force of magnetism.
For a time, however, the polar forces do not come sensibly into play.
In this condition the magnets resemble our water-molecules at the
temperature say of 50°. But the magnets come at length sufficiently
near each other to enable their poles to interact. From this point the
action ceases to be solely a general attraction of the masses.
Attractions of special points of the masses and repulsions of other
points now come into play; and it is easy to see that the
rearrangement of the magnets consequent upon the introduction of these
new forces may be such as to require a greater amount of room. This, I
take it, is the case with our water-molecules. Like our ideal magnets,
they approach each other for a time _as wholes_. Previous to reaching
the temperature 39° Fahr., the polar forces had doubtless begun to
act, but it is at this temperature that their claim to more room
exactly balances the contraction due to cold. At lower temperatures,
as regards change of volume, the polar forces predominate. But they
carry on a struggle with the force of contraction until the freezing
temperature is attained. The molecules then close up to form solid
crystals, a considerable augmentation of volume being the immediate
consequence.
§ 3. _Ordinary Refraction of Light explained by the Wave Theory_.
We have now to exhibit the bearings of this act of crystallization
upon optical phenomena. According to the undulatory theory, the
velocity of light in water and glass is less than in air. Consider,
then, a small portion of a wave issuing from a point of light so
distant that the minute area may be regarded as practically plane.
Moving vertically downwards, and impinging on a horizontal surface of
glass or water, the wave would go through the medium without change of
direction. As, however, the velocity in glass or water is less than
the velocity in air, the wave would be retarded on passing into the
denser medium.
[Illustration: Fig. 25.]
But suppose the wave, before reaching the glass, to be _oblique_ to
the surface; that end of the wave which first reaches the medium will
be the first retarded by it, the other portions as they enter the
glass being retarded in succession. It is easy to see that this
retardation of the one end of the wave must cause it to swing round
and change its front, so that when the wave has fully entered the
glass its course is oblique to its original direction. According to
the undulatory theory, light is thus _refracted_.
With these considerations to guide us, let us follow the course of a
beam of monochromatic light through our glass prism. The velocity in
air is to its velocity in glass as 3: 2. Let A B C (fig. 25) be the
section of our prism, and _a_ _b_ the section of a plane wave
approaching it in the direction of the arrow. When it reaches _c_ _d_,
one end of the wave is on the point of entering the glass. Following
it still further, it is obvious that while the portion of the wave
still in the air passes over the distance _c_ _e_, the wave in the
glass will have passed over only two-thirds of this distance, or _d_
_f_. The line _e_ _f_ now marks the front of the wave. Immersed wholly
in the glass it pursues its way to _g_ _h_, where the end _g_ of the
wave is on the point of escaping into the air. During the time
required by the end _h_ of the wave to pass over the distance _h_ _k_
to the surface of the prism, the other end _g_, moving more rapidly,
will have reached the point _i_. The wave, therefore, has again
changed its front, so that after its emergence from the prism it will
pass on to _l_ _m_, and subsequently in the direction of the arrow.
The refraction of the beam is thus completely accounted for; and it
is, moreover, based upon actual experiment, which proves that the
ratio of the velocity of light in glass to its velocity in air is that
here mentioned. It is plain that if the change of velocity on entering
the glass were greater, the refraction also would be greater.
§ 4. _Double Refraction of Light explained by the Wave Theory_.
The two elements of rapidity of propagation, both of sound and light,
in any substance whatever, are _elasticity_ and _density_, the speed
increasing with the former and diminishing with the latter. The
enormous velocity of light in stellar space is attainable because the
ether is at the same time of infinitesimal density and of enormous
elasticity. Now the ether surrounds the atoms of all bodies, but it is
not independent of them. In ponderable matter it acts as if its
density were increased without a proportionate increase of elasticity;
and this accounts for the diminished velocity of light in refracting
bodies. We here reach a point of cardinal importance. In virtue of the
crystalline architecture that we have been considering, the ether in
many crystals possesses different densities, and different
elasticities, in different directions; the consequence is, that in
such crystals light is transmitted with different velocities. And as
refraction depends wholly upon the change of velocity on entering the
refracting medium, being greatest where the change of velocity is
greatest, we have in many crystals two different refractions. By such
crystals a beam of light is divided into two. This effect is called
_double refraction_.
In ordinary water, for example, there is nothing in the grouping of
the molecules to interfere with the perfect homogeneity of the ether;
but, when water crystallizes to ice, the case is different. In a plate
of ice the elasticity of the ether in a direction perpendicular to the
surface of freezing is different from what it is parallel to the
surface of freezing; ice is, therefore, a double refracting substance.
Double refraction is displayed in a particularly impressive manner by
Iceland spar, which is crystallized carbonate of lime. The difference
of ethereal density in two directions in this crystal is very great,
the separation of the beam into the two halves being, therefore,
particularly striking.
I am unwilling to quit this subject before raising it to unmistakable
clearness in your minds. The vibrations of light being transversal,
the elasticity concerned in the propagation of any ray is the
elasticity at right angles to the direction of propagation. In Iceland
spar there is one direction round which the crystalline molecules are
symmetrically built. This direction is called the axis of the crystal.
In consequence of this symmetry the elasticity is the same in all
directions perpendicular to the axis, and hence a ray transmitted
along the axis suffers no double refraction. But the elasticity along
the axis is greater than the elasticity at right angles to it.
Consider, then, a system of waves crossing the crystal in a direction
perpendicular to the axis. Two directions of vibration are open to
such waves: the ether particles can vibrate parallel to the axis or
perpendicular to it. _They do both_, and hence immediately divide
themselves into two systems propagated with different velocities.
Double refraction is the necessary consequence.
[Illustration: Fig. 26.]
By means of Iceland spar cut in the proper direction, double
refraction is capable of easy illustration. Causing the beam which
builds the image of our carbon-points to pass through the spar, the
single image is instantly divided into two. Projecting (by the lens E,
fig. 26) an image of the aperture (L) through which the light issues
from the electric lamp, and introducing the spar (P), two luminous
disks (E O) appear immediately upon the screen instead of one.