velocity to light in glass and water than in air or stellar space; and
that on this point it was at direct issue with the theory of
undulation, which makes the velocity in air or stellar space greater
than in glass or water. By an experiment proposed by Arago, and
executed with consummate skill by Foucault and Fizeau, this question
was brought to a crucial test, and decided in favour of the theory of
undulation.
In the present instance also the two theories are at variance. Newton
assumed that the action which produces the alternate bright and dark
rings took place at a _single surface_; that is, the second surface of
the film. The undulatory theory affirms that the rings are caused by
the interference of waves reflected from both surfaces. This also has
been demonstrated by experiment. By a proper arrangement, as we shall
afterwards learn, we may abolish reflection from one of the surfaces
of the film, and when this is done the rings vanish altogether.
Rings of feeble intensity are also formed by _transmitted_ light.
These are referred by the undulatory theory to the interference of
waves which have passed _directly_ through the film, with others which
have suffered _two_ reflections within the film, and are thus
completely accounted for.
§ 10. _The Diffraction of Light_.
Newton's espousal of the Emission Theory is said to have retarded
scientific discovery. It might, however, be questioned whether, in the
long run, the errors of great men have not really their effect in
rendering intellectual progress rhythmical, instead of permitting it
to remain uniform, the 'retardation' in each case being the prelude to
a more impetuous advance. It is confusion and stagnation, rather than
error, that we ought to avoid. Thus, though the undulatory theory was
held back for a time, it gathered strength in the interval, and its
development within the last half century has been so rapid and
triumphant as to leave no rival in the field. We have now to turn to
the investigation of new classes of phenomena, of which it alone can
render a satisfactory account.
Newton, who was familiar with the idea of an ether, and who introduced
it in some of his speculations, objected, as already stated, that if
light consisted of waves shadows could not exist; for that the waves
would bend round the edges of opaque bodies and agitate the ether
behind them. He was right in affirming that this bending ought to
occur, but wrong in supposing that it does not occur. The bending is
real, though in all ordinary cases it is masked by the action of
interference. This inflection of the light receives the name of
_Diffraction_.
To study the phenomena of diffraction it is necessary that our source
of light should be a physical point, or a fine line; for when a
luminous surface is employed, the waves issuing from different points
of the surface obscure and neutralize each other. A _point_ of light
of high intensity is obtained by admitting the parallel rays of the
sun through an aperture in a window-shutter, and concentrating the
beam by a lens of short focus. The small solar image at the focus
constitutes a suitable point of light. The image of the sun formed on
the convex surface of a glass bead, or of a watch-glass blackened
within, though less intense, will also answer. An intense _line_ of
light is obtained by admitting the sunlight through a slit and sending
it through a strong cylindrical lens. The slice of light is contracted
to a physical line at the focus of the lens. A glass tube blackened
within and placed in the light, reflects from its surface a luminous
line which, though less intense, also answers the purpose.
In the experiment now to be described a vertical slit of variable
width is placed in front of the electric lamp, and this slit is looked
at from a distance through another vertical slit, also of variable
aperture, and held in the hand.
The light of the lamp being, in the first place, rendered
monochromatic by placing a pure red glass in front of the slit, when
the eye is placed in the straight line drawn through both slits an
extraordinary appearance (shown in fig. 15) is observed. Firstly, the
slit in front of the lamp is seen as a vivid rectangle of light; but
right and left of it is a long series of rectangles, decreasing in
vividness, and separated from each other by intervals of absolute
darkness.
The breadth of these bands is seen to vary with the width of the slit
held before the eye. When the slit is widened the bands become
narrower, and crowd more losely together; when the slit is narrowed,
the individual bands widen and also retreat from each other, leaving
between them wider spaces of darkness than before.
[Illustration: Fig. 15.]
Leaving everything else unchanged, let a blue glass or a solution of
ammonia-sulphate of copper, which gives a very pure blue, be placed in
the path of the light. A series of blue bands is thus obtained,
exactly like the former in all respects save one; the blue rectangles
are _narrower_, and they are _closer together_ than the red ones.
If we employ colours of intermediate refrangibilities, which we may do
by causing the different colours of a spectrum to shine through the
slit, we obtain bands of colour intermediate in width, and occupying
intermediate positions, between those of the red and blue. The aspect
of the bands in red, green, and violet light is represented in fig.
16. When _white light_, therefore, passes through the slit the various
colours are not superposed, and instead of a series of monochromatic
bands, separated from each other by intervals of darkness, we have a
series of coloured spectra placed side by side. When the distant slit
is illuminated by a candle flame, instead of the more intense electric
light, or when a distant platinum wire raised to a white heat by an
electric current is employed, substantially the same effects are
observed.
[Illustration: Fig. 16.]
§ 11. _Application of the Wave-theory to the Phenomena of
Diffraction_.
Of these and of a multitude of similar effects the Emission Theory is
incompetent to offer any satisfactory explanation. Let us see how they
are accounted for by the Theory of Undulation.
And here, with the view of reaching absolute clearness, I must make an
appeal to that faculty the importance of which I have dwelt upon so
earnestly here and elsewhere--the faculty of imagination. Figure
yourself upon the sea-shore, with a well-formed wave advancing. Take a
line of particles along the front of the wave, all at the same
distance below the crest; they are all rising in the same manner and
at the same rate. Take a similar line of particles on the back of the
wave, they are all falling in the same manner and at the same rate.
Take a line of particles along the crest, they are all in the same
condition as regards the motion of the wave. The same is true for a
line of particles along the furrow of the wave.
The particles referred to in each of these cases respectively, being
in the same condition as regards the motion of the wave, are said to
be in the same _phase_ of vibration. But if you compare a particle on
the front of the wave with one at the back; or, more generally, if you
compare together any two particles not occupying the same position in
the wave, their conditions of motion not being the same, they are said
to be in different phases of vibration. If one of the particles lie
upon the crest, and the other on the furrow of the wave, then, as one
is about to rise and the other about to fall, they are said to be in
_opposite_ phases of vibration.
There is still another point to be cleared up--and it is one of the
utmost importance as regards our present subject. Let O (fig. 17) be a
spot in still water which, when disturbed, produces a series of
circular waves: the disturbance necessary to produce these waves is
simply an oscillation up and down of the water at O. Let _m_ _n_ be
the position of the ridge of one of the waves at any moment, and _m'_
_n'_ its position a second or two afterwards. Now every particle of
water, as the wave passes it, oscillates, as we have learned, up and
down. If, then, this oscillation be a sufficient origin of
wave-motion, each distinct particle of the wave _m_ _n_ ought to give
birth, to a series of circular waves. This is the important point up
to which I wish to lead you. Every particle of the wave _m_ _n_ _does_
act in this way. Taking each particle as a centre, and surrounding it
by a circular wave with a radius equal to the distance between _m_ _n_
and _m'_ _n'_, the coalescence of all these little waves would build
up the large ridge _m'_ _n'_ exactly as we find it built up in nature.
Here, in fact, we resolve the wave-motion into its elements, and
having succeeded in doing this we shall have no great difficulty in
applying our knowledge to optical phenomena.
[Illustration: Fig. 17.]
Now let us return to our slit, and, for the sake of simplicity, we
will first consider the case of monochromatic light. Conceive a series
of waves of ether advancing from the first slit towards the second,
and finally filling the second slit. When each wave passes through the
latter it not only pursues its direct course to the retina, but
diverges right and left, tending to throw into motion the entire mass
of the ether behind the slit. In fact, as already explained, _every
point of the wave which fills the slit is itself a centre of a new
wave system which is transmitted in all directions through the ether
behind the slit_. This is the celebrated principle of Huyghens: we
have now to examine how these secondary waves act upon each other.
[Illustration: Fig. 18.]
Let us first regard the central band of the series. Let AP (fig. 18)
be the width of the aperture held before the eye, grossly exaggerated
of course, and let the dots across the aperture represent ether
particles, all in the same phase of vibration. Let E T represent a
portion of the retina. From O, in the centre of the slit, let a
perpendicular O R be imagined drawn upon the retina. The motion
communicated to the point R will then be the sum of all the motions
emanating in this direction from the ether particles in the slit.
Considering the extreme narrowness of the aperture, we may, without
sensible error, regard all points of the wave A P as equally distant
from R. No one of the partial waves lags sensibly behind the others:
hence, at R, and in its immediate neighbourhood, we have no sensible
reduction of the light by interference. This undiminished light
produces the brilliant central band of the series.
Let us now consider those waves which diverge laterally behind the
second slit. In this case the waves from the two sides of the slit
have, in order to converge upon the retina, to pass over unequal
distances. Let A P (fig. 19) represent, as before, the width of the
second slit. We have now to consider the action of the various parts
of the wave A P upon a point R' of the retina, not situated in the
line joining the two slits.
[Illustration: Fig. 19.]
Let us take the particular case in which the difference of path from
the two marginal points A, P, to the retina is a whole wave-length of
the red light; how must this difference affect the final illumination
of the retina?
Let us fix our attention upon the particular oblique line that passes
through the _centre_ O of the slit to the retina at R'. The difference
of path between the waves which pass along this line and those from
the two margins is, in the case here supposed, half a wavelength. Make
_e_ R' equal to P R', join P and _e_, and draw O _d_ parallel to P e.
A e is then the length of a wave of light, while A _d_ is half a
wave-length. Now the least reflection will make it clear that not only
is there discordance between the central and marginal waves, but that
every line of waves such as _x_ R', on the one side of O R', finds a
line _x_' R' upon the other side of O R', from which its path differs
by half an undulation--with which, therefore, it is in complete
discordance. The consequence is, that the light on the one side of the
central line will completely abolish the light on the other side of
that line, absolute darkness being the result of their coalescence.
The first dark interval of our series of bands is thus accounted for.
It is produced by an obliquity of direction which causes the paths of
the marginal waves to be _a whole wave-length_ different from each
other.
When the difference between the paths of the marginal waves is _half a
wave-length,_ a partial destruction of the light is effected. The
luminous intensity corresponding to this obliquity is a little less
than one-half--accurately 0.4--that of the undiffracted light. If the
paths of the marginal waves be three semi-undulations different from
each other, and if the whole beam be divided into three equal parts,
two of these parts will, for the reasons just given, completely
neutralize each other, the third only being effective. Corresponding,
therefore, to an obliquity which produces a difference of three
semi-undulations in the marginal waves, we have a luminous band, but
one of considerably less intensity than the undiffracted central band.
With a marginal difference of path of four semi-undulations we have a
second extinction of the entire beam, because here the beam can be
divided into four equal parts, every two of which quench each other.
A second space of absolute darkness will therefore correspond to the
obliquity producing this difference. In this way we might proceed
further, the general result being that, whenever the direction of
wave-motion is such as to produce a marginal difference of path of an
_even_ number of semi-undulations, we have complete extinction; while,
when the marginal difference is an _odd_ number of semi-undulations,
we have only partial extinction, a portion of the beam remaining as a
luminous band.
A moment's reflection will make it plain that the wider the slit the
less will be the obliquity of direction needed to produce the
necessary difference of path. With a wide slit, therefore, the bands,
as observed, will be closer together than with a narrow one. It is
also plain that the shorter the wave, the less will be the obliquity
required to produce the necessary retardation. The maxima and minima
of violet light must therefore fall nearer to the centre than the
maxima and minima of red light. The maxima and minima of the other
colours fall between these extremes. In this simple way the undulatory
theory completely accounts for the extraordinary appearance above
referred to.
When a slit and telescope are used, instead of the slit and naked eye,
the effects are magnified and rendered more brilliant. Looking,
moreover, through a properly adjusted telescope with a small circular
aperture in front of it, at a distant point of light, the point is
seen encircled by a series of coloured bands. If monochromatic light
be used, these bands are simply bright and dark, but with white light
the circles display iris-colours. If a slit be shortened so as to form
a square aperture, we have two series of spectra at right angles to
each other. The effects, indeed, are capable of endless variation by
varying the size, shape, and number of the apertures through which the
point of light is observed. Through two square apertures, with their
corners touching each other as at A, Schwerd observed the appearance
shown in fig. 20. Adding two others to them, as at B, he observed the
appearance represented in fig. 21. The position of every band of light
and shade in such figures has been calculated from theory by Fresnel,
Fraunhofer, Herschel, Schwerd, and others, and completely verified by
experiment. Your eyes could not tell you with greater certainty of the
existence of these bands than the theoretic calculation.
[Illustration: Fig. 20.]
The street-lamps at night, looked at through the meshes of a
handkerchief, show diffraction phenomena. The diffraction effects
obtained in looking through a bird's feathers are, as shown by
Schwerd, very brilliant. The iridescence of certain Alpine clouds is
also an effect of diffraction which may be imitated by the
spores of Lycopodium. When shaken over a glass plate these spores
cause a point of light, looked at through the dusted plate, to be
surrounded by coloured circles, which rise to actual splendour when
the light becomes intense. Shaken in the air the spores produce the
same effect. The diffraction phenomena obtained during the artificial
precipitation of clouds from the vapours of various liquids in an
intensely illuminated tube are, as I have elsewhere shewn, exceedingly
fine.
[Illustration: Fig. 21.]
One of the most interesting cases of diffraction by small particles
that ever came before me was that of an artist whose vision was
disturbed by vividly coloured circles. He was in great dread of losing
his sight; assigning as a cause of his increased fear that the circles
were becoming larger and the colours more vivid. I ascribed the
colours to minute particles in the humours of the eye, and ventured to
encourage him by the assurance that the increase of size and vividness
on the part of the circles indicated that the diffracting particles
were becoming _smaller_, and that they might finally be altogether
absorbed. The prediction was verified. It is needless to say one word
on the necessity of optical knowledge in the case of the practical
oculist.
Without breaking ground on the chromatic phenomena presented by
crystals, two other sources of colour may be mentioned here. By
interference in the earth's atmosphere, the light of a star, as shown
by Arago, is self-extinguished, the twinkling of the star and the
changes of colour which it undergoes being due to this cause. Looking
at such a star through an opera-glass, and shaking the glass so as to
cause the image of the star to pass rapidly over the retina, you
produce a row of coloured beads, the spaces between which correspond
to the periods of extinction. Fine scratches drawn upon glass or
polished metal reflect the waves of light from their sides; and some,
being reflected from the opposite sides of the same scratch, interfere
with and quench each other. But the obliquity of reflection which
extinguishes the shorter waves does not extinguish the longer ones,
hence the phenomena of colours. These are called the colours of
_striated surfaces_. They are beautifully illustrated by
mother-of-pearl. This shell is composed of exceedingly thin layers,
which, when cut across by the polishing of the shell, expose their
edges and furnish the necessary small and regular grooves. The most
conclusive proof that the colours are due to the mechanical state of
the surface is to be found in the fact, established by Brewster, that
by stamping the shell carefully upon black sealing-wax, we transfer
the grooves, and produce upon the wax the colours of mother-of-pearl.
LECTURE III.
RELATION OF THEORIES TO EXPERIENCE
ORIGIN OF THE NOTION OF THE ATTRACTION OF GRAVITATION
NOTION OF POLARITY, HOW GENERATED
ATOMIC POLARITY
STRUCTURAL ARRANGEMENTS DUE TO POLARITY
ARCHITECTURE OF CRYSTALS CONSIDERED AS AN INTRODUCTION
TO THEIR ACTION UPON LIGHT
NOTION OF ATOMIC POLARITY APPLIED TO CRYSTALLINE STRUCTURE
EXPERIMENTAL ILLUSTRATIONS
CRYSTALLIZATION OF WATER
EXPANSION BY HEAT AND BY COLD
DEPORTMENT OF WATER CONSIDERED AND EXPLAINED
BEARINGS OF CRYSTALLIZATION ON OPTICAL PHENOMENA
REFRACTION
DOUBLE REFRACTION
POLARIZATION
ACTION OF TOURMALINE
CHARACTER OF THE BEAMS EMERGENT FROM ICELAND SPAR
POLARIZATION BY ORDINARY REFRACTION AND REFLECTION
DEPOLARIZATION
§ 1. _Derivation of Theoretic Conceptions from Experience._
One of the objects of our last lecture, and that not the least
important, was to illustrate the manner in which scientific theories
are formed. They, in the first place, take their rise in the desire of
the mind to penetrate to the sources of phenomena. From its
infinitesimal beginnings, in ages long past, this desire has grown and
strengthened into an imperious demand of man's intellectual nature. It
long ago prompted Cæsar to say that he would exchange his victories
for a glimpse of the sources of the Nile; it wrought itself into the
atomic theories of Lucretius; it impelled Darwin to those daring
speculations which of late years have so agitated the public mind. But
in no case, while framing theories, does the imagination _create_ its
materials. It expands, diminishes, moulds, and refines, as the case
may be, materials derived from the world of fact and observation.
This is more evidently the case in a theory like that of light, where
the motions of a subsensible medium, the ether, are presented to the
mind. But no theory escapes the condition. Newton took care not to
encumber the idea of gravitation with unnecessary physical
conceptions; but we know that he indulged in them, though he did not
connect them with his theory. But even the theory, as it stands, did
not enter the mind as a revelation dissevered from the world of
experience. The germ of the conception that the sun and planets are
held together by a force of attraction is to be found in the fact that
a magnet had been previously seen to attract iron. The notion of
matter attracting matter came thus from without, not from within. In
our present lecture the magnetic force must serve as the portal into a
new domain; but in the first place we must master its elementary
phenomena.
The general facts of magnetism are most simply illustrated by a
magnetized bar of steel, commonly called a bar magnet. Placing such a
magnet upright upon a table, and bringing a magnetic needle near its
bottom, one end of the needle is observed to retreat from the magnet,
while the other as promptly approaches. The needle is held quivering
there by some invisible influence exerted upon it. Raising the needle
along the magnet, but still avoiding contact, the rapidity of its
oscillations decreases, because the force acting upon it becomes
weaker. At the centre the oscillations cease. Above the centre, the
end of the needle which had been previously drawn towards the magnet
retreats, and the opposite end approaches. As we ascend higher, the
oscillations become more violent, because the force becomes stronger.
At the upper end of the magnet, as at the lower, the force reaches a
maximum; but all the lower half of the magnet, from E to S (fig. 22),
attracts one end of the needle, while all the upper half, from E to N,
attracts the opposite end. This _doubleness_ of the magnetic force is
called _polarity_, and the points near the ends of the magnet in which
the forces seem concentrated are called its _poles_.
[Illustration: Fig. 22.]
What, then, will occur if we break this magnet in two at the centre E?
Shall we obtain two magnets, each with a single pole? No; each half is
in itself a perfect magnet, possessing two poles. This may be proved
by breaking something of less value than the magnet--the steel of a
lady's stays, for example, hardened and magnetized. It acts like the
magnet. When broken, each half acts like the whole; and when these
parts are again broken, we have still the perfect magnet, possessing,
as in the first instance, two poles. Push your breaking to its utmost
sensible limit--you cannot stop there. The bias derived from
observation will infallibly carry you beyond the bourne of the senses,
and compel you to regard this thing that we call magnetic polarity as
resident in the ultimate particles of the steel. You come to the
conclusion that each molecule of the magnet is endowed with this polar
force.
Like all other forces, this force of magnetism is amenable to
mechanical laws; and, knowing the direction and magnitude of the
force, we can predict its action. Placing a small magnetic needle near
a bar magnet, it takes a determinate position. That position might be
deduced theoretically from the mutual action of the poles. Moving the
needle round the magnet, for each point of the surrounding space there
is a definite direction of the needle and no other. A needle of iron
will answer as well as the magnetic needle; for the needle of iron is
magnetized by the magnet, and acts exactly like a steel needle
independently magnetized.