light as it does to the waves of water and the waves of sound. And the
conditions of interference are the same in all three. If two series of
light-waves of the same length start at the same moment from a common
origin (say A, fig. 11), crest coincides with crest, sinus with sinus,
and the two systems blend together to a single system (A _m_ _n_) of
double amplitude. If both series start at the same moment, one of them
being, at starting, a whole wavelength in advance of the other, they
also add themselves together, and we have an augmented luminous
effect. The same occurs when the one system of waves is any _even_
number of semi-undulations in advance of the other. But if the one
system be half a wave-length (as at A' _a_', fig. 12), or any _odd_
number of half wavelengths, in advance, then the crests of the one
fall upon the sinuses of the other; the one system, in fact, tends to
_lift_ the particles of ether at the precise places where the other
tends to _depress_ them; hence, through the joint action of these
opposing forces (indicated by the arrows) the light-ether remains
perfectly still. This stillness of the ether is what we call darkness,
which corresponds with a dead level in the case of water.
[Illustration: Fig. 12.]
It was said in our first lecture, with reference to the colours
produced by absorption, that the function of natural bodies is
selective, not creative; that they extinguish certain constituents of
the white solar light, and appear in the colours of the unextinguished
light. It must at once occur to you that, inasmuch as we have in
interference an agency by which light may be self-extinguished, we may
have in it the conditions for the production of colour. But this would
imply that certain constituents are quenched by interference, while
others are permitted to remain. This is the fact; and it is entirely
due to the difference in the lengths of the waves of light.
§ 7. _Colours of thin Films. Observations of Boyle and Hooke_.
This subject may be illustrated by the phenomena which first suggested
the undulatory theory to the mind of Hooke. These are the colours of
thin transparent films of all kinds, known as the _colours of thin
plates_. In this relation no object in the world possesses a deeper
scientific interest than a common soap-bubble. And here let me say
emerges one of the difficulties which the student of pure science
encounters in the presence of 'practical' communities like those of
America and England; it is not to be expected that such communities
can entertain any profound sympathy with labours which seem so far
removed from the domain of practice as are many of the labours of the
man of science. Imagine Dr. Draper spending his days in blowing
soap-bubbles and in studying their colours! Would you show him the
necessary patience, or grant him the necessary support? And yet be it
remembered it was thus that minds like those of Boyle, Newton and
Hooke were occupied; and that on such experiments has been founded a
theory, the issues of which are incalculable. I see no other way for
you, laymen, than to trust the scientific man with the choice of his
inquiries; he stands before the tribunal of his peers, and by their
verdict on his labours you ought to abide.
Whence, then, are derived the colours of the soap-bubble? Imagine a
beam of white light impinging on the bubble. When it reaches the first
surface of the film, a known fraction of the light is reflected back.
But a large portion of the beam enters the film, reaches its second
surface, and is again in part reflected. The waves from the second
surface thus turn back and hotly pursue the waves from the first
surface. And, if the thickness of the film be such as to cause the
necessary retardation, the two systems of waves interfere with each
other, producing augmented or diminished light, as the case may be.
But, inasmuch as the waves of light are of different lengths, it is
plain that, to produce extinction in the case of the longer waves, a
greater thickness of film is necessary than in the case of the shorter
ones. Different colours, therefore, must appear at different
thicknesses of the film.
Take with you a little bottle of spirit of turpentine, and pour it
into one of your country ponds. You will then see the glowing of those
colours over the surface of the water. On a small scale we produce
them thus: A common tea-tray is filled with water, beneath the surface
of which dips the end of a pipette. A beam of light falls upon the
water, and is reflected by it to the screen. Spirit of turpentine is
poured into the pipette; it descends, issues from the end in minute
drops, which rise in succession to the surface. On reaching it, each
drop spreads suddenly out as a film, and glowing colours immediately
flash forth upon the screen. The colours change as the thickness of
the film changes by evaporation. They are also arranged in zones, in
consequence of the gradual diminution of thickness from the centre
outwards.
Any film whatever will produce these colours. The film of air between
two plates of glass squeezed together, exhibits, as shown by Hooke,
rich fringes of colour. A particularly fine example of these fringes
is now before you. Nor is even air necessary; the rupture of optical
continuity suffices. Smite with an axe the black, transparent
ice--black, because it is pure and of great depth--under the moraine
of a glacier; you readily produce in the interior flaws which no air
can reach, and from these flaws the colours of thin plates sometimes
break like fire. But the source of most historic interest is, as
already stated, the soap-bubble. With one of the mixtures employed by
the eminent blind philosopher, Plateau, in his researches on the
cohesion figures of thin films, we obtain in still air a bubble ten or
twelve inches in diameter. You may look at the bubble itself, or you
may look at its projection upon the screen; rich colours arranged in
zones are, in both cases, exhibited. Rendering the beam parallel, and
permitting it to impinge upon the sides, bottom, and top of the
bubble, gorgeous fans of colour, reflected from the bubble, overspread
the screen, rotating as the beam is carried round. By this experiment
the internal motions of the film are also strikingly displayed.
Not in a moment are great theories elaborated: the facts which demand
them become first prominent; then, to the period of observation
succeeds a period of pondering and of tentative explanation. By such
efforts the human mind is gradually prepared for the final theoretic
illumination. The colours of thin plates, for example, occupied the
attention of Robert Boyle. In his 'Experimental History of Colours' he
contends against the schools which affirmed that colour was 'a
penetrative quality that reaches to the innermost parts of the
object,' adducing opposing facts. 'To give you a first instance,' he
says, 'I shall need but to remind you of what I told you a little
after the beginning of this essay, touching the blue and red and
yellow that may be produced upon a piece of tempered steel; for these
colours, though they be very vivid, yet if you break the steel they
adorn, they will appear to be but superficial.' He then describes, in
phraseology which shows the delight he took in his work, the following
beautiful experiment:--
'We took a quantity of clean lead, and melted it with a strong fire,
and then immediately pouring it out into a clean vessel of convenient
shape and matter (we used one of iron, that the great and sudden heat
might not injure it), and then carefully and nimbly taking off the
scum that floated on the top, we perceived, as we expected, the smooth
and glossy surface of the melted matter to be adorned with a very
glorious colour, which, being as transitory as delightful, did almost
immediately give place to another vivid colour, and that was as
quickly succeeded by a third, and this, as it were, chased away by a
fourth; and so these wonderfully vivid colours successively appeared
and vanished till the metal ceasing to be hot enough to hold any
longer this pleasing spectacle, the colours that chanced to adorn the
surface when the lead thus began to cool remained upon it, but were so
superficial that how little soever we scraped off the surface of the
lead, we did, in such places, scrape off all the colour.' 'These
things,' he adds, 'suggested to me some thoughts or ravings which I
have not now time to acquaint you with.'[13]
He extends his observations to essential oils and spirits of wine,
'which being shaken till they have good store of bubbles, those
bubbles will (if attentively considered) appear adorned with various
and lovely colours, which all immediately vanish upon the
retrogressing of the liquid which affords these bubbles their skins
into the rest of the oil.' He also refers to the colour of glass
films. 'I have seen one that was skilled in fashioning glasses by the
help of a lamp blowing some of them so strongly as to burst them;
whereupon it was found that the tenacity of the metal was such that
before it broke it suffered itself to be reduced into films so
extremely thin that they constantly showed upon their surface the
varying colours of the rainbow.'[14]
Subsequent to Boyle the colours of thin plates occupied the attention
of Robert Hooke, in whose writings we find a dawning of the undulatory
theory of light. He describes with great distinctness the colours
obtained with thin flakes of 'Muscovy glass' (talc), also those
surrounding flaws in crystals where optical continuity is destroyed.
He shows very clearly the dependence of the colour upon the thickness
of the film, and proves by microscopic observation that plates of a
uniform thickness yield uniform colours. 'If,' he says, 'you take any
small piece of the Muscovy glass, and with a needle, or some other
convenient instrument, cleave it oftentimes into thinner and thinner
laminæ, you shall find that until you come to a determinate thinness
of them they shall appear transparent and colourless; but if you
continue to split and divide them further, you shall find at last that
each plate shall appear most lovely tinged or imbued with a
determinate colour. If, further, by any means you so flaw a pretty
thick piece that one part begins to cleave a little from the other,
and between these two there be gotten some pellucid medium, those
laminated or pellucid bodies that fill that space shall exhibit
several rainbows or coloured lines, the colours of which will be
disposed and ranged according to the various thicknesses of the
several parts of the plate.' He then describes fully and clearly the
experiment with pressed glasses already referred to:--
'Take two small pieces of ground and polished looking-glass plate,
each about the bigness of a shilling: take these two dry, and with
your forefingers and thumbs press them very hard and close together,
and you shall find that when they approach each other very near there
will appear several irises or coloured lines, in the same manner
almost as in the Muscovy glass; and you may very easily change any of
the colours of any part of the interposed body by pressing the plates
closer and harder together, or leaving them more lax--that is, a part
which appeared coloured with a red, may presently be tinged with a
yellow, blue, green, purple, or the like. 'Any substance,' he says,
'provided it be thin and transparent, will show these colours.' Like
Boyle, he obtained them with glass films; he also procured them with
bubbles of pitch, rosin, colophony, turpentine, solutions of several
gums, as gum arabic in water, any glutinous liquor, as wort, wine,
spirit of wine, oyl of turpentine, glare of snails, &c.
Hooke's writings show that even in his day the idea that both light
and heat are modes of motion had taken possession of many minds.
'First,' he says, 'that all kind _of fiery burning bodies_ have their
parts in motion I think will be easily granted me. That the spark
struck from a flint and steel is in rapid agitation I have elsewhere
made probable;... that heat argues a motion of the internal parts is
(as I said before) generally granted;... and that in all extremely hot
shining bodies there is a very quick motion that causes light, as well
as a more robust that causes heat, may be argued from the celerity
wherewith the bodies are dissolved. Next, it must be _a vibrative
motion.'_ His reference to the quick motion of light and the more
robust motion of heat is a remarkable stroke of sagacity; but Hooke's
direct insight is better than his reasoning; for the proofs he adduces
that light is 'a vibrating motion' have no particular bearing upon the
question.
Still the Undulatory Theory had undoubtedly dawned upon the mind of
this remarkable man. In endeavouring to account for the colours of
thin plates, he again refers to the relation of colour to thickness:
he dwells upon the fact that the film which shows these colours must
be transparent, proving this by showing that however thin an opaque
body was rendered no colours were produced. 'This,' he says, 'I have
often tried by pressing a small globule of mercury between two smooth
plates of glass, whereby I have reduced that body to a much greater
thinness than was requisite to exhibit the colours with a transparent
body.' Then follows the sagacious remark that to produce the colours
'there must be a considerable reflecting body adjacent to the under or
further side of the lamina or plate: for this I always found, that the
greater that reflection was the more vivid were the appearing colours.
From which observation,' he continues, 'it is most evident, _that the
reflection from the further or under side of the body is the principal
cause of the production of these colours._'
He draws a diagram, correctly representing the reflection at the two
surfaces of the film; but here his clearness ends. He ascribes the
colours to a coalescence or confusion of the two reflecting pulses;
the principal of interference being unknown to him, he could not go
further in the way of explanation.
§ 8. _Newton's Rings. Relation of Colour to Thickness of Film_.
[Illustration: Fig. 13]
In this way, then, by the active operation of different minds, facts
are observed, examined, and the precise conditions of their
appearance determined. All such work in science is the prelude to
other work; and the efforts of Boyle and Hooke cleared the way for the
optical career of Newton. He conquered the difficulty which Hooke had
found insuperable, and determined by accurate measurements the
relation of the thickness of the film to the colour it displays. In
doing this his first care was to obtain a film of variable and
calculable depth. On a plano-convex glass lens (D B E, fig. 13) of
very feeble curvature he laid a plate of glass (A C) with a plane
surface, thus obtaining a film of air of gradually increasing depth
from the point of contact (B) outwards. On looking at the film in
monochromatic light he saw, with the delight attendant on fulfilled
prevision, surrounding the place of contact, a series of bright rings
separated from each other by dark ones, and becoming more closely
packed together as the distance from the point of contact augmented
(as in fig. 14). When he employed red light, his rings had certain
diameters; when he employed blue light, the diameters were less. In
general terms, the more refrangible the light the smaller were the
rings. Causing his glasses to pass through the spectrum from red to
blue, the rings gradually contracted; when the passage was from blue
to red, the rings expanded. This is a beautiful experiment, and
appears to have given Newton the most lively satisfaction. When white
light fell upon, the glasses, inasmuch as the colours were not
superposed, a series _of iris-coloured_ circles was obtained. A
magnified image of _Newton's rings_ is now before you, and, by
employing in succession red, blue, and white light, we obtain all the
effects observed by Newton. You notice that in monochromatic light the
rings run closer and closer together as they recede from the centre.
This is due to the fact that at a distance the film of air thickens
more rapidly than near the centre. When white light is employed, this
closing up of the rings causes the various colours to be superposed,
so that after a certain thickness they are blended together to white
light, the rings then ceasing altogether. It needs but a moment's
reflection to understand that the colours of thin plates, produced by
white light, are never unmixed or monochromatic.
[Illustration: Fig. 14]
Newton compared the tints obtained in this way with the tints of his
soap-bubble, and he calculated the corresponding thickness. How he did
this may be thus made plain to you: Suppose the water of the ocean to
be absolutely smooth; it would then accurately represent the earth's
curved surface. Let a perfectly horizontal plane touch the surface at
any point. Knowing the earth's diameter, any engineer or mathematician
in this room could tell you how far the sea's surface will lie below
this plane, at the distance of a yard, ten yards, a hundred yards, or
a thousand yards from the point of contact of the plane and the sea.
It is common, indeed, in levelling operations, to allow for the
curvature of the earth. Newton's calculation was precisely similar.
His plane glass was a tangent to his curved one. From its refractive
index and focal distance he determined the diameter of the sphere of
which his curved glass formed a segment, he measured the distances of
his rings from the place of contact, and he calculated the depth
between the tangent plane and the curved surface, exactly as the
engineer would calculate the distance between his tangent plane and
the surface of the sea. The wonder is, that, where such infinitesimal
distances are involved, Newton, with the means at his disposal, could
have worked with such marvellous exactitude.
To account for these rings was the greatest optical difficulty that
Newton, ever encountered. He quite appreciated the difficulty. Over
his eagle eye there was no film--no vagueness in his conceptions. At
the very outset his theory was confronted by the question, Why, when a
beam of light is incident on a transparent body, are some of the
light-particles reflected and some transmitted? Is it that there are
two kinds of particles, the one specially fitted for transmission and
the other for reflection? This cannot be the reason; for, if we allow
a beam of light which has been reflected from one piece of glass to
fall upon another, it, as a general rule, is also divided into a
reflected and a transmitted portion. The particles once reflected are
not always reflected, nor are the particles once transmitted always
transmitted. Newton saw all this; he knew he had to explain why it is
that the self-same particle is at one moment reflected and at the next
moment transmitted. It could only he through _some change in the
condition of the particle itself_. The self-same particle, he
affirmed, was affected by 'fits' of easy transmission and reflection.
§ 9. _Theory of 'Fits' applied to Newton's Rings_.
If you are willing to follow me in an attempt to reveal the
speculative groundwork of this theory of fits, the intellectual
discipline will, I think, repay you for the necessary effort of
attention. Newton was chary of stating what he considered to be the
cause of the fits, but there can hardly be a doubt that his mind
rested on a physical cause. Nor can there be a doubt that here, as in
all attempts at theorising, he was compelled to fall back upon
experience for the materials of his theory. Let us attempt to restore
his course of thought and observation. A magnet would furnish him with
the notion of attracted and repelled poles; and he who habitually saw
in the visible an image of the invisible would naturally endow his
light-particles with such poles. Turning their attracted poles towards
a transparent substance, the particles would be sucked in and
transmitted; turning their repelled poles, they would be driven away
or reflected. Thus, by the ascription of poles, the transmission and
reflection of the self-same particle at different times might be
accounted for.
Consider these rings of Newton as seen in pure red light: they are
alternately bright and dark. The film of air corresponding to the
outermost of them is not thicker than an ordinary soap-bubble, and it
becomes thinner on approaching the centre; still Newton, as I have
said, measured the thickness corresponding to every ring, and showed
the difference of thickness between ring and ring. Now, mark the
result. For the sake of convenience, let us call the thickness of the
film of air corresponding to the first dark ring _d_; then Newton
found the distance corresponding to the second dark ring 2 _d_; the
thickness corresponding to the third dark ring 3 _d_; the thickness
corresponding to the tenth dark ring 10 _d_, and so on. Surely there
must be some hidden meaning in this little distance, _d_, which turns
up so constantly? One can imagine the intense interest with which
Newton pondered its meaning. Observe the probable outcome of his
thought. He had endowed his light-particles with poles, but now he is
forced to introduce the notion of _periodic recurrence_. Here his
power of transfer from the sensible to the subsensible would render it
easy for him to suppose the light-particles animated, not only with a
motion of translation, but also with a motion of rotation. Newton's
astronomical knowledge rendered all such conceptions familiar to him.
The earth has such a double motion. In the time occupied in passing
over a million and a half of miles of its orbit--that is, in
twenty-four hours--our planet performs a complete rotation; and in the
time required to pass over the distance _d_, Newton's light-particle
might be supposed to perform a complete rotation. True, the
light-particle is smaller than the planet, and the distance _d_,
instead of being a million and a half of miles, is a little over the
ninety thousandth of an inch. But the two conceptions are, in point of
intellectual quality, identical.
Imagine, then, a particle entering the film of air where it possesses
this precise thickness. To enter the film, its attracted end must be
presented. Within the film it is able to turn _once_ completely round;
at the other side of the film its attracted pole will be again
presented; it will, therefore, enter the glass at the opposite side of
the film _and be lost to the eye_. All round the place of contact,
wherever the film possesses this precise thickness, the light will
equally disappear--we shall therefore have a ring of darkness.
And now observe how well this conception falls in with the law of
proportionality discovered by Newton. When the thickness of the film
is 2 _d_, the particle has time to perform, _two_ complete rotations
within the film; when the thickness is 3 _d, three_ complete
rotations; when 10 _d, ten_ complete rotations are performed. It is
manifest that in each of these cases, on arriving at the second
surface of the film, the attracted pole of the particle will be
presented. It will, therefore, be transmitted; and, because no light
is sent to the eye, we shall have a ring of darkness at each of these
places.
The bright rings follow immediately from the same conception. They
occur between the dark rings, the thicknesses to which they correspond
being also intermediate between those of the dark ones. Take the case
of the first bright ring. The thickness of the film is ½_d_; in this
interval the rotating particle can perform only half a rotation. When,
therefore, it reaches the second surface of the film, its repelled
pole is presented; it is, therefore, driven back and reaches the eye.
At all distances round the centre corresponding to this thickness the
same effect is produced, and the consequence is a ring of brightness.
The other bright rings are similarly accounted for. At the second one,
where the thickness is 1½_d_, a rotation and a half is performed; at
the third, two rotations and a half; and at each of these places the
particles present their repelled poles to the lower surface of the
film. They are therefore sent back to the eye, and produce there the
impression of brightness. This analysis, though involving difficulties
when closely scrutinised, enables us to see how the theory of fits may
have grown into consistency in the mind of Newton.