F. (François) Arago.

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angles, and one retarded by one fourth of a wave-length behind the
other; these being superimposed will, by mathematical consequence,
give rise to vibrations, no longer plane, but performed in circles; or in
ellipses, if the retardation be any other fraction of a wave-length.
Such a piece of glass is called Fresnel's Rhomb. The course of the
ray will be apparent by inspection of the annexed diagram, which
needs no further explanation.



CIRCULAR POLARIZATION.



227



other means by which to produce circular polarization ;
and, as usual, a remarkable discovery was the reward of
these efforts. This discovery may be announced in two
words ; there is a partmdar kind of double refraction
which communicates to rays circular polarization, as the
double refraction of Iceland spar communicates the com-

The mechanical conception of two rectilinear vibrations at right




angles compounded, giving an elliptical or circiilar vibration, may be
illustrated by a very simple contrivance, which may be described as
follows : —

On any convenient support, there projects an arm terminating in



22^ FRESNEL.

mon polarization of Huygliens. This special double re-
fraction, results not from the nature of the crystal, but
two branches, on which, by the pivots g g', a smah frame swings. In




D ii

this frame, by the pivots h h^, whose axis is at right angles to g g', a
pendulum p vibrates. (The upper end is light, and carries a white
ball or disk, carried up to such a height as to be conspicuous for lec-
ture illustrations.)

Now, by the pivots h h/ the pendulum can only vibrate in the plane
of c D, and by the pivots o gi it can only vibrate in the plane of a b
at right angles to c d. If now motion be given it in one of these planes,
and at an instant after in the other, the result will be a revolution in
the ellipse e e/, which will be a circle if the interval be exactly one
fourth of a vibration.

Or mathematically thus : —

Let the waves in planes at right angles, with a difference of retarda-
tion d, be expressed by

z = a sin (nt — kx) y = 13 sin (nt — kx -{- d)

Hence, — = sin (nt — kx) and / \ ^2

" ■%/ — = cos (n< — kx),

or expanding ?/ and substituting

Whence transposing and squaring

-TT, + ^ — ^ cos rf = sin 2(i
/3^ a2 ap

The equation to an ellipse : which becomes a circle if fl = /3 and
d = 90°.— Translator.



CIRCULAR POLARIZATIOX.



229



from certain sections of it which Fresnel pointed out.
The properties of rays circularlj polarized also led our
colleague to new and very curious means of producing
coloured polarization.*

* The author must be supposed here to allude to that remarkable
instance of circular polarization which is produced by transmitting a
plane polarized ray along the axis of quartz or rock crystal, and which
depends, as he says, not on the nature of the crystal, but on the section
of it, that is to say, on the thickness: the effect continually changing
as slices are cut from the crystal perpendicular to its axis of increas-
ing thickness. This statement is somewhat remarkable, as he here
unequivocally ascribes the discovery to Fresnel, which has been
usually by English writers ascribed to himself.

The term " rotatory " polarization has been since appropriated to
describe this phenomenon. Yet the student must be careful to dis-
tinguish the application of this term from that of " circular" polar-
ization. The light is in fact circularly polarized: but the effect
called "rotation" is quite distinct from the '• circularity." It may
be desirable to add a brief explanation. Let a ray, r, polarized in a



K






p






^


\






/


\




230 FRESNEL.

In all times and all countries, we find morose disposi-
tions, who, though ready enough to proclaim the glories
of the dead, do not treat' their contemporaries with any
thing like the same favour. As soon as a discovery is
announced, they deny its truth : they contest its novelty,
and pretend to detect it in some passage of an ancient
writer, obscure and forgotten ; or, lastly, they maintain
that it was only the result of chance.

I do not know whether the men of our age are better
than their predecessors : but certainly no doubt has been
raised either as to the accuracy, or the novelty, or the
importance of the discovei-ies of which I have just given
an account. As to the effect of chance, the blindest envy

plane p, pass along the axis of rock crystal c, of the thickness x: it
emerges polarized in a new plane p', inclined to p, by a certain angle.
If the crystal were of a greater thickness i', the plane would be turned
still further into the position p//, at t' into v"/^ and so on. Thus the
successive planes of polarization formed a twisted surface like a cork-
screw staircase. In some crystals this twisting takes place towards
the right, in others towards the left. The change of plane is also dif-
ferent for each of the different primary coloured rays. Thus exam-
ined by an analyzer, the transmitted ray always presents a succession
of colours.

Sir J. Herschel showed that the right or left handed character of
the polarization agreed with the like inclination of the small facets of
the complete crystal round the summit. Biot and Seebeck discovered
the same property to exist in certain liquids such as oil of turpentine,
and even in some vapours.

The phenomenon is explained theoreticallj^ by supposing two rays,
each circularly polarized in opposite directions, traversing the axis
together, but with unequal velocities. In this case it is shown me-
chanically that the resultant of such vibrations will be a plane
vibration in a continually changing direction, proportional to the
retardation which one of the rays has undergone, behind the other,
in traversing successive thicknesses. This was the discovery of
Fresnel. For raj's deviating a little from the direction of the axis,
Mr. Airy showed that a similar theory would apply with eUipiicaRy
polarized light.



THKORIES OP LIGHT. 231

could not dare to appeal to it, so complicated, so minute,
and so directly designed for the purpose proposed were
the experimental means employed by Fresnel in the study
of circular polarization. Perhaps it may be proper to
observe that the greater part of them were suggested by
theoretical ideas ; for Avithout that, most of the experi-
ments of our colleague offer combinations, of which, so to
speak, it would seem impossible that any one would have
thought. If, in writing the history of the sciences, it is
just to put in their full light the discoveries of those who
have cultivated them with distinction, it is important also,
— it seems to me right, — though freely stating the truth,
yet not to put it in such a light as might render it a source
of discouragement to any who might be engaged in the
same pursuits.

PRINCIPAL CHARACTERISTICS OF THE SYSTEM OF EMIS-
SION AND OF THAT OF WAVES. GROUNDS ON WHICH

FRESNEL WAS LED TO REJECT UNRESERVEDLY THE
SYSTEM OF EMISSION.

After having studied with so much care the properties
of luminous rays, it was natui-al to inquire of what light
consists ? This scientific question, one of the grandest,
without contradiction, on which men have ever occupied
themselves, has given occasion for the most animated dis-
cussion. Fresnel took an active part in it. I will therefore
endeavour to point out precisely the nature of the ques-
tion, and give a concise analysis of the experiments to
which it has given rise.

The senses of hearing and smell enable us to discover
the existence of bodies at a distance by totally different
means. Every odorous substance undergoes a species of
evaporation: minute particles are sent off from it inces-



232 FRESNEL.

santly, they mix with the air, which becomes a vehicle
for them, and diffuses them in every direction. A grain
of musk, whose subtle emanations penetrate through all
parts of a vast surrounding circuit loses its power from
day to day ; it ends by being entirely dissipated and
totally disappearing.

It is not the same with a sounding body. Eveiy one
knows that a distant bell, whose sound strikes faintly on
our ear, nevertheless does not send to us a single mole-
cule of metal ; that it can resound without interruption
for successive centuries without losing any of its weight.
When the clapper strikes it, its sides vibrate, they undergo
an oscillatory motion which communicates itself immedi-
ately to the neighbouring portions of the air, and thence
by degrees to the whole atmosphere. These atmospheric
vibrations constitute sound.

Our organs, whatever may be their nature, cannot be
put in relation with distant bodies, except in one or the
other of these two ways : thus either the sun emits inces-
santly, as odorous bodies do, material particles from all
points of his surface with a velocity of 77,000 leagues in
a second, and these are minute solar fragments which by
penetrating into the eye produce vision ; — or else that
luminary, in this respect like a bell, excites simply an
undulatory movement in a medium extremely elastic, fill-
ing all space, and these vibrations proceed to agitate our
retinas as the sonorous undulations affect the membrane
of the tympanum.

Of these two explanations of tlie phenomena of light,
one is called the theory of emission, the other is known
under the name of the system of waves.* We find long

* To assist the general conception of tlie mode of propagation of
waves by transverse vibrations, perhaps it may be desirable to refer



EMISSION THEORY,



233



ago traces of the former in the writings of Empedocles.
Among tlie moderns I can cite among its adherents, Kep-
ler, Newton, and Laplace. The system of waves does
not reckon less illustrious partisans ; Aristotle, Descartes,
Hooke, Huyghens, Euler, adopted it. Such names on
either side render a choice difficult, if in a matter of sci-

the reader to a very simple machine, represented in the annexed figure
contrived by the translator, which exhibits a set of white balls, repre-




senting the molecules of ether: these are attached to rods, which are
moved on turning the handle by cranks at their lower end, so ai-ranged
that each bull is in succession raised or lowered nearly in a straight
line; so that they follow each other in the form of a wave. When the
bar supporting the rings through which the rods pass, is lowered, the
balls no longer move up and down in straight lines, but describe each a
kind of oval curve, which becomes more rounded the lower the bar is
placed. In the former case the machine represents a wave with plain
vibrations, in the latter, with elliptic or circular vibrations.



234 fresneL.

ence the most illustrious names could be authorities capa-
ble of determhiing the point.

If, liowever, it astonish us to see men of such great
genius thus divided, I would say that in their times the
question in dispute could not be resolved ; that the neces-
sary experiments were wanting ; and that then the two
different theories of light were not logical deductions
from facts, but, if I may so express myself, simple mat-
ters of persuasion ; and that, in a word, the gift of infal-
libility is not granted even to the most skilful, if they
transgress the bounds of observation, and, abandoning
themselves to conjecture, desert the strict and sure path-
by which science advances in our age on reasonable prin-
ciples, and by which it has been enabled to make such
incontestable progress. Before we review the great in-
roads which have been recently made on the theory of
emission, it will be perhaps convenient to cast a glance
over the vigorous attacks of which it was the object, in
the writings of Euler, of Franklin, and others ; and to
show that the partisans of Newton might then, without
looking forward too much, have considered the solution
as adjourned for a long period. Tlie effects which a
cannon ball can produce depend so directly on its mass
and its velocity jointly, that we can, without altering
them, change at pleasure one of these elements, provided
we make the others change in an inverse ratio. Thus a
ball of two kilogrammes may overthrow a wall ; a ball of
one kilogramme will also overthrow it, provided we im-
press on it a velocity double of the former. If the weight
of the ball were reduced to -^i^ih or xoiyth of its original
amount, to produce the same effect we must give a veloc-
ity ten times or one hundred times as great. Now we
know that the velocity of a cannon ball is the 640,000th



EMISSION THEORY. 235

of that of light ; if the weight of a luminous molecule
were the 640,000th part of that of the cannon ball, it
would in like manner overthrow a wall.

These deductions are certain : but let us look at the
facts. A luminous molecule not only cannot overthrow a
wall, but it even penetrates into an organ so delicate as
the eye without occasioning the least pain, without even
producing any sensible dynamic effect. We can say
more : in experiments undertaken with the view of ren-
dering sensible the impulsions of light, physicists have
not been content to use an isolated agent, they have
brought to act simultaneously the immense quantity of
light which can be condensed at the focus of a large lens ;
they have not opposed to the shock of the rays very re-
sisting objects, but bodies so delicately suspended that a
breath could derange them enormously ; they have ope-
rated for example, on the extremity of a very light lever
suspended horizontally by -a spider's thread. The sole
obstacle to the rotatory movement of such an apparatus
would be the force of reaction, which the thread would
acquire in twisting. But this force might be consid-
ered as nothing, since from its nature it always increases
rapidly with the degree of torsion ; and, in this instance,
one of the observers whose experiments I am analyzing,
found no perceptible force of this kind, after having had
the patience to give the thread 14,000 turns, by turning
the lever round on its centre. It is then well established
that, in spite of their excessive velocity, myriads of lumi-
nous rays acting simultaneously produce no jjerceptible
force. But we should be going beyond the legitimate
consequences which this interesting experiment author-
izes, if we concluded that a ray is not composed of mate-
rial elements endowed with a rapid motion of translation.



236 FRESNEL.

We may, indeed, faii-ly deduce from the absence of all
rotation in tlie lever suspended by tiie spider's thread,
under the action of an enormous quantity of hght, that
the elementary particles of the luminous rays have not
dimensions comparable to the millionth part of the finest
molecules possessing any weight. But as there is nothing
to shovF any absurdity in supposing them a million, or a
myriad, times less than this, this kind of experiment and
argument (the first idea of which is due to Franklin)
cannot furnish any decisive conclusion.

Among the objections whicli Euler has presented in
his works against the theory of emission, I will point out
two, on which he has particularly insisted, and which
seem to him irresistible. "• If tlie sun," (said this great
geometer,) "continually darts out particles of his own
substance in every direction, and with enormous velocity,
he must end by exhausting himself: and during the many
ages which elapsed since the historical period, some dimi-
nution ought already to have become sensible."

But is it not evident that this diminution depends on
the magnitude of the particulars ? Now there is nothing
to hinder our supposing them of such small diameters
that, after millions of years' continual emission, the mass
of the sun should not be sensibly altered. And, besides,
there is no accurate observation to prove that this lumi-
nary does not waste, or that its diameter is really as great
as it was even in the time of Hipparchus.

No one is ignorant of the fact, that millions of rays can
penetrate together into a dark room through a pin-hole,
and there form distinct images of external objects. In
crossing each other in that minute space, the material
elements of which we suppose this multitude of rays to
consist ought, nevertheless, to encounter and clash against



OBJECTIONS TO EMISSION. 237

each other with great violence, to change each other's
directions in a thousand ways, and to mingle together
without any order. This difficulty is no doubt specious,
but it does not appear insurmountable.

The chance that two molecules setting out from the
same hole should encounter each other, depends both on
the absolute diameter of the molecules, and on the inter-
vals which separate them. We might then by suitably
diminishing the diameters reduce the chances of encoun-
ter to nothing. But we have here also in the intervals
of the molecules another element, which alone would in
a great degree lead to the same conclusion. In fact
every sensation of light lasts for a certain time ; the
luminous object which has darted its rays into the eye
still remains visible (as experiment has proved) at least
for an hundredth of a second after the object has dis-
appeared. Now, in an hundredth of a second, light has
gone through 770 leagues. Thus the luminous mole-
cules which form each ray may be at 770 leagues inter-
val from one another, and nevertheless produce a con-
tinuous sensation of light. With such distances what
becomes of the repeated clashings spoken of by Euler,
and which in any circumstances ought to put a stop to
the regular propagation of the rays ? It is almost hu-
miliating to" see a geometer of so rare a genius believe
himself authorized by such futile objections to call the
system of emission a mistake of Newton, — a gross error,
— the belief of which, he says, can only be accounted for
by recollecting the remark of Cicero, " There is nothing
so absurd but that it has been maintained by some phi-
losopher." *

* It has been too common a practice, both with the advocates and
the opponents of the wave theory, to rest its defence or its refutation



238 FKESNEL.

However, the system of emission has few partisans ;
but it is not under the blows dealt by Euler that it has

on single points ; to uphold a solitary experimental fact as decisive one
way or the other. A single favourable fact will not prove the theory ;
and, on the other hand, the only real conclusion in cases where a
single fact appears to stand out as an objection is, that (granting the
fact incapable of being otherwise interpreted) the theory requires re-
modelling; and that some undue assumption has crept into it. Such
reconstruction has always been the process by which it has been suc-
cessively fouud to adapt itself to nev/ phenomena, even when at first
sight they appeared most opposed to it. But even were it otherwise,
the theory is one which is not to be staked on single facts; it rests its
claim (in the first instance) in being that which connects by a common
principle, and tlms explains the greatest number of facts. Many of the
old theories, as of inflexion, attractions, &c., each explained a certain
small number of facts; but the real argument against them was, that
they did not explain each other. Every new partial explanation of
the wave theory, on the contrary, not only explains a certain class of
facts, but connects these with some other class similarly explained.
Newton had proposed one idea (that of fits of easy reflexion and trans-
mission) to account for the altei'nations in the colours of thin plates;
another totally unconnected theorj"- of inflexion, or bending in and
out in passing the edge of a body, to explain the phenomena of dif-
fraction: a third idea of polarity, for double refraction; besides other
occasional references to waves, or even a combination of vibrations
with molecular emission in some cases; but all unconnected with, and
indejjendeni of, each other, and each confessedly a mere arbitrary as-
sumption, not pretending to stand on any other ground than that it
explained in a certain way the particular phenomenon in relation to
which it was adduced.

On the undulatory view, on the contrary, every subordinate law
successively established, and every class of phenomena explained,
has become directly connected with all the others. Everj' part is in
intimate relation with every other part, and the progressive improve-
ment and enlargement of the theory has regularly kept pace with the
advance of experimental discovery; every new modification, as it
were, has grown out of the simple principles at first laid down by a
natural sequence, without anj' new hypothesis, or forced and arbi-
trary changes. It is a theory of which an eminent philosopher, by no
means unduly biased in its favour, and at a time when it had by no
means reached its present point of perfection, emphatically said, " It



VELOCITY OF LIGHT. 239

fallen. Insurmountable objections have been found in
various phenomena of whose very existence that philos-
opher was necessarily ignorant. This great advance in
the science belongs to the physicists of our own day, and
is due in a great measure to tlie labours of Fresnel.
This consideration alone obliges me to point them out in
detail, eren if the interest of the question did not oblige
me to do so.

If light is a wave, the rays of different colours, similar
in that respect to the sounds employed in music, are
composed of vibrations unequally rapid ; and the red,
green, blue, and violet rays, are transmitted through the
ethereal spaces, as are all the notes of the gamut through
the air, with velocities exactly equal.

If light be an emanation, the rays of different colours
are formed of molecules necessarily different, either as to
their nature, or their mass, and which besides are en-
dowed with different velocities.

An attentive inspection of the borders of the shadows
produced by the satellites of Jupiter in their passage
across the luminous disk of the planet, and better still,
the observations on changeable stars, have proved that
all the rays of light move equally fast. Thus a charac-
teristic feature of the system of waves is found verified.

In each of the two systems of light * the original

is a series of felicities; and if not true, eminently deserves to be true."
And the increasing proof which it continues to receive by its readi-
ness in meeting nearly everj' new experimental case as it arises, aug-
ments in the same proportion our conviction that it will sooner or
later be equally successful in the solution of those few phenomena,
which still appear to stand out as exceptional instances to its appli-
cation. — Translator.

* When the author affirms that in each of the two theories, (dans
I'un et dans I'autrc des deux systemes,) the original velocity of a ray
determines its refraction, there seems to be a certain degree of con-



240 FRESNEL.

velocity of a ray determines the refraction which it must
undergo when it falls obliquely on the surface of a trans-
fusion, which it is difficult to explain. The assertion is clear, and the
whole subsequent argument agrees with that assertion, in rtgard to
the emission theory. Here, undoubtedly, the original velocity with
which a ray enters a new medium, when it is acted upon by the
attractions of a number of surrounding particles, will essentially deter-
mine the velocity with which it will continue to move under the in-
fluence of these attractions, and the path it will take. But on the icave
theory there appears nothing obviously and antecedently to show what
will be the case.

The author proceeds, as if continuinf/ the last topic, to quite another
point, viz: the experimental fact that light from the most different
sources, both terrestrial and celestial, moves with precisely the same
velocity throuyh air or vacuum. He argues that this is a " mathe-
matical consequence" of the wave theory; because, in the parallel
case of sound, tones produced by the most different instruments are
propagated through the air with the same rapidity. It is certainly a
close analogy, but hardly a " mathematical consequence." The re-
mai-k which follows as to the consequence of molecular theory, in
rendering light from different sources unequally rapid in its flight
from their differences of attractive power, presents, no doubt, a formi-
dable difficulty to that theory, as being in contradiction to the experi-
mental result just mentioned.

But when in reference to his own beautiful experiment on observing
the refractions of light when its velocity is respectively increased and
diminished by the whole velocity of the earth, he adds, " such rays



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