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REESE LIBRARY

UNIVERSITY OF CALIFORNIA.
Co

^Accession No .

o o 5 9 . Class No .

SCIENTIFIC MEMOIRS
EDITED BY
J. S. AMES, PH.D.
PROFESSOR OF PHYSICS IN JOHNS HOPKINS UNIVERSITY
X.
THE WAVE-THEORY OF LIGHT

THE
WAVE THEORY OF LIGHT
MEMOIRS BY HUYGENS, YOUNG AND FRESNEL
EDITED BY
HENRY CREW, Pn.D. \N
PROFKSSOR OK PHYSICS, NORTHWESTERN UNIVERSITY
NEW YORK : CINCINNATI .: CHICAGO
AMERICAN BOOK COMPANY

to *i<&
COPYRIGHT, 1900, HY
AMERICAN BOOK COMPANY
Crew, Light.
W. P. I

PKEFACE

THANKS to the labors of Kirchhoff, Kelvin, Huxley, and

others, there is now a widespread opinion that any physical

phenomenon

" is explained" only

when some

one

has

devised a

dynamical model which will duplicate the phenomenon. The

completeness of the explanation is to be measured by the com-

pleteness with which the model will duplicate the phenomenon.

Thus, for instance, a refraction model which, like that of

Airy, describes only the path of the refracted ray when the

incident ray is given, does not in any true sense explain how

the refracted ray comes to take one path rather than another.

Such a model illustrates Suell's law, but does not explain the

phenomenon.

If, however, we take a large and shallow tank of water, the

floor of the tank being partly covered with a false bottom, so

as to give two, and only two, different depths of water, we shall

find that the speed of the waves in the deeper portion of the

tank bears to the speed in the shallower portion a constant

ratio ;

hence,

in

passing

from

one

depth

to

the

other,

these

waves are refracted according to the sine law.
Such a model may be said to be a " partial explanation" of

refraction in so far as it refers the phenomenon to change of

speed which accompanies change of medium. It represents,

however, only the kinematics of refraction.

If, now, we could go one step further, and make a model in

which the wave -producing forces were duplicated in other

words, if we could make a model of the medium and of the

disturbing forces we should have a fairly complete "expla-

nation" of refraction ; in fact, the dynamics of refraction would

be understood. This would imply not only that we knew the

substance disturbed, but also that we were acquainted with

the laws according to which it is disturbed.

83059

PREFACE
A theory of light may be considered either from a kinemat-
ical or from a dynamical point of view. To assume, on exper-
imental grounds, that a ray of light has a certain speed in one
medium and a different speed in a different medium, and that it consists in a particular kind of motion, and thence to infer
the laws of refraction, rectilinear propagation, and diffraction, is to construct a kinematical theory of light. But to assume a certain structure for the luminous body and for the medium, and thence to derive the motions and the different speeds assumed in the kinematical case, is to offer a dynamical ex-
planation of light.
The wave-theory of light is used, nearly always, in the former and narrower sense to mean the kinematical explanation of
light; it leaves entirely to one side the dynamical questions hinted at above. It assumes, not without strong experimental evidence, the existence of waves travelling with different speeds in different media, and proposes to explain the cardinal phe-
nomena of optics. To illustrate its limitations, we may cite the instance of the
ordinary and extraordinary ray in crystals. How it happens
that there are two rays is a problem in the dynamics of light ; but, assuming these two rays, their subsequent behavior, their inability to interfere, etc., must be accounted for in a general way, at least by the kinematical theory of light.
It is in this narrow sense that the wave-theory of light is employed in the memoirs translated in this volume.
The first clear and unmistakable suggestion that light consists in a vibratory motion appears to be due to that brilliant but unfortunate genius, Robert Hooke (1635-1703), who, in
his Micrograpliia (London, 1665), describes the three characteristic features of the motion which he believes to constitute
light.
Since it has not been deemed advisable to reprint Hooke's paper in this volume, it may not be out of place here to quote what few paragraphs are necessary fairly to present his point of view. This will, perhaps, be accomplished by the follow-
ing selections :
' ' It would be somewhat too long a work for this place Zetetically to examine, and positively to prove, what particular kind of motion it is that must be the efficient of Light; for though it be a motion, yet 'tis not every motion that produces
vi

PREFACE

it, since we find there are many bodies very violently mov'd,

which

yet

afford

not

such

an

effect ;

and

there

are

other

bodies,

which to our senses, seem not mov'd so much, which yet shine.

Thus Water and quick-silver, and most other liquors heated, shine not; and several hard bodies, as Iron, Silver, Brass, Cop-

per, Wood, &c., though very often struck with a hammer, shine not presently, though they will all of them grow exceeding

hot; whereas rotten Wood, rotten Fish, Sea Water, Gloworms, &G. have nothing of tangible heat in them, and yet (where

there is no stronger light to affect the Sensory) they shine some of them so Vividly, that one may make a shift to read by them.

"It would be too long, I say, here to insert the discursive

progress by which I inquir'd after the proprieties of the motion of Light, and therefore I shall only add the result.

"And, First, I found it ought to be exceeding quick, such as those motions of fermentation and putrefaction, whereby, certainly, the parts are exceeding nimbly and violently mov'd; and that, because we find those motions are able more mi-

nutely to shatter and divide the body, then the most violent heats or menstruums we yet know. And that fire is nothing else but such a dissolution of the Burning body, made by the most universal menstruum of all sulphureous bodies, namely, the Air, we shall in an other place of this Tractate endeavour
to make probable. 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 bodyes are dissolv'd.
"Next, it must be a Vibrative motion. And for this the

newly mentioned Diamond affords us a good argument; since

if the motion of the parts did not return, the Diamond must

after many rubbings

decay and be

wasted ;

but we

have

no

reason to suspect the latter, especially if we consider the ex-

ceeding difficulty that is found in cutting or wearing away a
Diamond. And a Circular motion of the parts is much more
improbable, since, if that were granted, and they be suppos'd irregular and Angular parts, I see not how the parts of the Diamond should hold so firmly together, or remain in the same

sensible dimensions, which yet they do. Next, if they be Glob-
ular, and mov'd only with a turbinated motion, I know not any

cause that can impress that motion upon the pellucid medium,

which yet is done. Thirdly, any other irregular motion of the

vii

PREFACE
parts one amongst another, must necessarily make the body of a fluid consistence, from which- it is far enough. It must
therefore be a Vibrating motion.
" And Thirdly, That is a very short vibrating motion, I think the instances drawn from the shining of Diamonds will also make probable. For a Diamond being the hardest body we yet know in the World, and consequently the least apt to yield or
bend, must consequently also have its vibrations exceeding
short.
"And these, I think, are the three principal proprieties of
a motion, requisite to produce the effect call'd Light in the
Object." [Micrographia, pp. 54-56.]
The total absence of experimental evidence from the above statement of the case stands in such marked contrast with the
method of modern physics as initiated by Galileo, that we cannot for a moment reckon Hooke among the founders of the
wave-theory. So important, on the contrary, have been the contributions
of Huygens, Newton, Young, and Fresnel, that each has in turn been considered the founder of the modern science of
optics. What justification there is for each of these views will
be clearer from a brief consideration of optical theory before and after it had been modified by the work of each of these four men.
Two questions naturally arise in the consideration of any theory, viz., (1) What phenomena does it explain? and (2) How does it explain them ? The answers which have been
given to these two questions at various periods in the develop-
ment of the wave-theory may be outlined as follows: At the time when Huygens and Newton began their work
on light, the following phenomena were demanding explana-
tion :
1. The existence of rays and shadows, known from the ear-
liest times.
2. The phenomenon of reflection, known from the earliest
times.
3. The phenomenon of refraction, as described by Snell's law. 4. The rainbow and the production of color by the prism. 5. The colors of thin plates Newton's rings.
6. Diffraction bands outside the geometrical shadow, de-
scribed by Grimaldi, 1665.

PREFACE

To these might be added the two following phenomena which
were discovered before the final publication of Newton's Opticks (1704) or Huygens's Traite dela Lumiere (1690).
7. The polarization of light by crystals (Bartholinus, 1670). 8. The finite speed of light (Romer, 1675). Of these eight cardinal facts, the second, the third, and the eighth,, were explained by Huygens on the assumption (a) That a luminous disturbance consists of a wave-motion

in the ether.

(b) That this wave-disturbance travels with a uniform finite

speed through the ether in any homogeneous medium.

(c) That in different media it travels with speeds which are

related inversely as the refractive indices of those media.

But the wave-disturbance as pictured by Huygens was a

single longitudinal pulse, or blow, imparted to an elastic fluid.

Since he did not have in mind either a train of waves or trans-

verse

waves, or

the

idea

of

"
phase,"

or

waves

of

different

lengths, it is evident that he was unable to explain any of the

remaining five facts.
Turning now to that portion of the work of Newton which contributed to the wave-theory, we find that the fourth phenomenon prismatic colors was explained by him in 1666, when

he demonstrated that a single ray of white light contains all the colors of the spectrum, and that color is not produced at the surface of the prism, as had been hitherto supposed. This
discovery made possible, for the first time, the correct explana-
tion of the rainbow.

In Newton's ingenious, though, as we now know, incorrect explanation of the fifth phenomenon colors of thin plates we meet the earliest measurement of the wave-length of light,
viz., the distance traversed by a ray of light during the inter-
val between two successive "fits" of the same kind. We meet

here, also, the first evidence that, in these fits, or, as we now say, waves, there is a regular periodicity. From this point on we must consider light as travelling not only in waves, but in

trains of waves.

At the close of the period of Huygens and Newton, we have then the following facts still demanding explanation :
1. The existence of rays and shadows. 5. The colors of thin plates. .6. The existence of diffraction fringes.

PREFACE

7. The polarization of light by crystals. To these must now be added

9. The phenomenon of stellar aberration, discovered by Brad-
ley in 1727.
Considering next the work of Young, we find that he first
suggested the correct explanation for the colors of thin plates,
having shown by experiment that two rays of light can interfere to produce alternately bright and dark bands. From this experiment and the dark centre in Newton's rings, he concludes that light consists of series of waves which, like other wave - motions, change phase by 180 on reflection from a denser medium.

Young, at this period (1802-3), was still laboring under the

impression that light-waves were longitudinal and were propa-

gated in a fluid

medium ;

fortunately, neither of these assump-

tions affects the validity of his reasoning concerning the colors

of thin plates.
When Fresnel began his optical studies (1814) the following

facts, viz., (1) existence of rays, (6) diffraction fringes, (7)

polarization, and (9) aberration, were still to be accounted for

on the wave-theory. By the union of Huygens's principle with

the principle of interference, Fresnel gave the first satisfac-

tory explanation of the rectilinear propagation of light, and

of the existence of diffraction fringes outside the geometrical

shadow.

FresneFs tematically

memoir, in which these set forth, and which was

discoveries
" crowned"

are most sysby the French

Academy in 1819, is translated in the following pages. For

the purpose of offering an elementary geometrical explanation

of rays and diffraction bands, Fresnel invented the idea of

dividing the wave-front into a certain series of zones, which in

nearly

all

text - books

are

wrongly

referred

to

as

" Huygens's

Zones." That this is not only unfair, but also misleading, has

been pointed out by Professor Schuster. Phil. Mag. vol. xxxi.,

p. 77 (1891). The first mention of these Fresnel Zones, as

they should be called, will be found on p. Ill of the present

volume.

It was in order to explain the phenomenon of polarization
that Fresnel introduced the idea of transverse vibrations in the

ether. The boldness of this now universally accepted hypothesis, which was then practically equivalent to supposing the

PREFACE
ether an elastic solid, can be fully appreciated only after one has carefully studied the views of Fresnel's contemporaries.
The evidence for the transversality of light vibrations rests .pon the inability of two oppositely polarized rays to interfere. The memoir of Arago and Fresnel upon this subject is trans-
lated in the present volume.
Of the nine phenomena which we have more or less arbi-
trarily selected as the principal facts of optics, all, save only the last aberration had received a fairly complete explana-
tion at the close of the labors of Young and Fresnel. This
discovery of Bradley's, which he so easily disposed of on the
corpuscular theory, has received many explanations in terms of the wave -theory; but none of these can be considered as thoroughly satisfactory. Young imagines the ether to pass through ordinary matter "as freely, perhaps, as the wind passes through a grove of trees." On this view, however, it is difficult to see how the speed of light in glass, say, should differ from its speed in a vacuum, or how the aberration constant can remain unchanged when the tube of the telescope
is filled with water, as in Airy's experiment. Proc. Roy. Soc., vol. xx., p. 35 (1872).
For it will be remembered that the aberration constant is
vl V radians, where
#=speed of earth in its orbit, and F^speed of light between the objective and eye-piece of
telescope employed. Fresnel, accordingly, modified Young's hypothesis by assuming that, in their motion through space, refracting bodies carry
with them only so much ether as is required to increase the
density of free ether from unity to p, where p at any point in
the medium is defined by the following equation:
H being the refractive index at the same point in the body. This is really equivalent to saying that et the luminiferous
ether is entirely unaffected by the motion of the matter which
it permeates." [Amer. Jour. Sci., vol. cxxxi., p. 386.] And
that this is the fact of nature is exactly the conclusion at which Fizeau and Michelson and Morley arrive from their experi-
ments upon the effect of motion of the medium upon the speed
of light. LOG dt., p. 377.
xi

PREFACE
When, however, Michelsou and Morley attempt to detect this relative motion of the earth and the ether as the earth
proceeds in its orbital motion, they do not succeed in certainly finding that there is any [Phil. Mag., December, 1887]; and they accordingly conclude that this relative motion is "quite small enough to refute FresnePs explanation of aberration."
Of the two experimental facts just cited, one apparently confirms FresnePs view, and makes possible an explanation of aberration in terms of the wave-theory; while the other leads us to think that the ether moves with the refracting medium, in which case the wave-theory appears incompetent to explain
stellar aberration.
It was in the year 1850 that Fizeau and Foucault measured directly the speed of light in air and in water, and found the ratio of these speeds numerically equal to the ratio of their refractive indices. This experiment has sometimes been called the experimentum crucis of the wave-theory; but with scant justice we venture to think, inasmuch as no great doctrine in physics can be said to rest upon any single fact, though mod-
ification may be demanded by a single fact.
We have now followed, in merest outline, the general ex-
planations which Huygens, Newton, Young, and Fresnel have offered for all, save one, of this group of nine cardinal facts. It is needless to remind the reader that this enumeration forms
but a small fraction of the phenomena which optical science has brought to light within the last two centuries, or, indeed, since the labors of these four men were ended.
No outline of the wave-theory would be complete without
mention of the important addition which was made to it in .the year 1849 by Sir George Stokes. For he it was who first completely justified Huygens's principle by showing that if the primary wave be resolved as proposed by Huygens, no "back wave" will be produced provided we adopt the proper law of disturbance for the secondary wave. The discovery of this law was announced in his memoir on the Dynamical Theory of Diffraction. [Trans. Oamb. Phil. Soc.,vo\. ix., p. 1; Math.
andPhys. Papers, vol. ii., p. 243.] Mathematically speaking, this contribution amounts to the introduction of the factor
1 -f- cos into the equation [Eq. 46, loc. cU.~\, which describes the disturbance in a secondary wave proceeding from an element of the primary wave.
xii

PRE F AC K

While, as has been said above, the following memoirs concern themselves only with the kinematics of light-waves and not at all with the question of what is vibrating, it may not
be out of place to indicate that principally during the last half of the present century at least four more cardinal facts have
presented themselves and demanded explanation. 10. The speed of light in free space is numerically equal
to the ratio of the electrostatic and electromagnetic units of

quantity. 11. In refracting media, the speed of light varies inversely
as the square root of the product of the electric and magnetic
inductivities.
12-. " Most transparent solid bodies are good insulators, and
all good conductors are very opaque." MAXWELL, Treatise, vol.
ii.,art. 799.
13. The plane of polarization is rotated in a magnetic field.

(Faraday.) It was to

"
explain"

these

additional

phenomena

that

Max-

well proposed, in 1865, to modify the wave-theory of light by

replacing the mechanical shear of the ether by an electric dis-
placement. How thoroughly justified Maxwell was in this

move has been amply proved mathematically by the analogy

of his equations with those of the elastic solid theory, and

experimentally by Hertz (1888).

Within the last decade the wave -theory has shown itself

capable of explaining an entirely new group of phenomena,

viz., the color photography discovered by Lippmann. Wiener

has shown that we have here merely two rays of light the

direct and reflected travelling in opposite directions and inter-

fering to produce stationary light waves.
The flexibility of the wave - theory has still more recently

been exemplified by the beautiful discovery of Zeeman; and

Larmor and Preston have shown that by assuming a particular

kind of electrical displacement, viz., an orbital motion of an

ion, the wave-theory is competent to predict not only the trip-

lets and even the sextet, but also the polarization produced by

placing the source of radiation in a magnetic field. Phil Mag.,

February, 1899.

Striking as the resemblance appears between the kinematics

of wave-motion considered in this volume and the phenomena

of optics, it must never be forgotten that in all probability the

PREFACE
vibrating atom is a structure whose motion is vastly complicated as compared with the few simple motions which the' experiments of Huygens, Newton, Young, Fresnel, Maxwell, and Michelson have assigned to it.
H. 0. EVANSTON, 111., November, 1899.
xiv

GENEBAL CONTENTS

PAGE

Preface

v

Treatise on Light. By Christiaan Huygens. (First three chapters).. . 1

Biographical Sketch of Huygens

42

On the Theory of Light and Colors. By Dr. Thomas Young

45

An Account of Some Cases of the Production of Colors not Hitherto

Described. By Dr. Thomas Young

62

Experiments and Calculations relative to Physical Optics. By Dr.

Thomas Young

68

Biographical Sketch of Young

77

Memoir on the Diffraction of Light, crowned by the [French] Acad-

emy of Sciences. By A. J. Fresnel

79

On the Action of Rays of Polarized Light upon Each Other. By

Arago and Fresnel

145

Biographical Sketch of Fresnel

156

Bibliography

161

Index

165

xv

TBEATISE ON LIGHT
CONTAINING
THE EXPLANATION OF REFLECTION AND OF REFRACTION AND ESPECIALLY OF THE REMARKABLE REFRACTION WHICH
OCCURS IN ICELAND SPAR
BY
CHRISTIAAN HUYGENS
(Leyden, 1690)

CONTENTS

rAGE

Preface

3

Table of Contents

7

The Rectilinear Propagation of Rays and some General Considerations

concerning the Nature of Light

9

Explanation of the Laws of Reflection

25

Explanation of the Laws of Refraction

30

TREATISE ON LIGHT
BY
CHRISTIAAN HUYGENS

PKEFACE

THIS treatise was written during my stay in Paris twelve
years ago, and in the year 1678 was presented to the Eoyal Academy of Sciences, to which the king had. been pleased to call me. Several of this body who are still living, especially those who have devoted themselves to the study of mathematics, will remember having been at the meeting at which I present-
ed the paper; of these I recall only those distinguished gentle-
men Messrs. Cassini, Homer, and De la Hire. Although since
then I have corrected and changed several passages, the copies which I had made at that time will show that I have added noth-

ing except some conjectures concerning the structure of Iceland spar and an additional remark concerning refraction in rockcrystal. I mention these details to show how long I have been
thinking about these matters which I am only just now publish-
ing, and not at all to detract from the merit of those who, with-
out having seen what I have written, may have investigated
similar subjects : as, indeed, happened in the case of two distinguished mathematicians., Newton and Leibnitz, regarding

the question of the proper figure for a converging lens, one

surface being given.

It may be asked why I have so long delayed the publication of this work. The reason is that I wrote it rather carelessly in

French, expecting to translate it into Latin, and, in the mean-

time, to give the subject still further attention.
3

Later I

PREFACE

thought of publishing this volume together with another on

dioptrics in which I discuss the theory of the telescope and the

phenomena associated with it. But soon the subject was no longer new and was therefore less interesting. Accordingly I kept putting off the work from time to time, and now I do

not know when I shall be able to finish it, for my time is large-

ly occupied either by business or by some new investigation.

In view of these facts I have thought wise to publish this

manuscript in its present state rather than to wait longer and run the risk of its being lost.

One finds in this subject a kind of demonstration which does

not carry with it so high a degree of certainty as that employed

in geometry ; and which differs distinctly from the method

employed by geometers in that they prove their propositions

by well-established and incontrovertible principles, while here

principles are tested by the inferences which are derivable

from them. The nature of the subject permits of no other

treatment. It is possible, however, in this way to establish a

probability which is little short of certainty. This is the case

when the consequences of the assumed principles are in perfect

accord with the observed phenomena, and especially when

these verifications are numerous ; but above all when one

employs the hypothesis to predict new phenomena and finds

his expectations realized.

If in the following treatise all these evidences of probability

are present, as, it seems to me, they are, the correctness of my

conclusions will

be confirmed ;

and, indeed,

it is scarcely pos-

sible that these matters differ very widely from the picture

which I have drawn of them. I venture to hope that those who enjoy finding out causes and who appreciate the wonders

of light will be interested in these various speculations arid in
the new explanation of that remarkable property upon which the structure of the human eye depends and upon which are

based those instruments which so powerfully aid the eye. I

trust also there will be some who, -from such beginnings, will

push these investigations far in advance of what I have been

able

to

do ;

for

the

subject

is

not

one

which

is

easily

exhausted.

This will be evident especially from those parts of the subject

which I have indicated as too difficult for solution; and still

more evident from those matters upon which I have not

touched at all, such as the various kinds of luminous bodies

4

PREFACE
and the whole question of color, which no one can yet boast of having explained.
Finally, there is much more to be learned by investigation
concerning the nature of light than I have yet discovered ; and I shall be greatly indebted to those who, in the future, shall
furnish what is needed to complete my imperfect knowledge.
THE HAGUE, 8th of January, 1690.

TABLE OF CONTENTS

CHAPTER I

ON THE RECTILINEAR PROPAGATION OF RAYS

PAGE

Light is produced by a certain motion

10

Particles do not pass from the luminous object to the eye

10

Light is propagated radially very much after the manner of Sound ... 11

[As to] whether Light requires time for its propagation

11

An experiment which apparently shows that its transmission is in-

stantaneous

11

An experiment which shows that it requires time

13

Comparison of the Speeds of Light and Sound

15

How the propagation of Light differs from that of Sound

15

They are not each transmitted by the same medium.

15

The propagation of Sound

16

The propagation of Light

17

Details concerning the propagation of Light

19

Why rays travel only in straight lines

22

How rays coming from different directions cross each other without

interference

23

CHAPTER II

ON REFLECTION

Proof that the angles of incidence and reflection are equal to each

other

25

Why the incident and reflected rays lie in one and the same plane

perpendicular to the reflecting surface

27

Equality between the angles of incidence and reflection does not de-

mand that the reflecting surface be perfectly plane

28

CHAPTER III ON REFRACTION

Bodies may be transparent without any matter passing through them 30

Proof that the ether can penetrate transparent bodies

31

How the ether renders bodies transparent by passing through them. . 32

Bodies, even the most solid ones, have a very porous structure

32

7

TABLE OF CONTENTS

PAGJ?

The speed of light is less in water and in glass than in air

32

A third hypothesis for the explanation of transparency and of the

retardation which light undergoes in bodies

33

Concerning a possible cause of opacity

34

Proof that refraction follows the Law of Sines

34

Why the incident and the refracted rays are each capable of produc-

ing the other

35

Why reflection inside a triangular glass prism suddenly increases

when the light is no longer able to emerge

38

Bodies in which refraction is greatest are also those in which reflec-

tion is strongest

40

Demonstration of a theorem due to Fermat . .

40

CHAPTER IV
ON ATMOSPHERIC REFRACTION
[Not translated.]
CHAPTER V ON THE PECULIAR REFRACTION OF ICELAND SPAR
[Not translated.]
CHAPTER VI ON FIGURES OF TRANSPARENT BODIES ADAPTED FOR REFRAC-
TION AND REFLECTION
[Not translated.] 8

CHAPTER I
ON THE RECTILINEAR PROPAGATION OF RAYS
DEMONSTRATIONS in optics, as in every science where geometry is applied to matter, are based upon experimental facts; as,
for instance, that light travels in straight lines, that the angles
of incidence and reflection are equal, and that rays of light are refracted according to the law of sines. For this last fact is
now as widely known and as certainly known as either of the
preceding.
Most writers upon optical subjects have been satisfied to assume these facts. But others, of a more investigating turn of mind, have tried to find the origin and the cause of these facts, considering them in themselves interesting natural phe-
nomena. And although they have advanced some ingenious
ideas, these are not such that the more intelligent readers do not still want further explanation in order to be thoroughly
satisfied.
Accordingly, I here submit some considerations on this subject with the hope of elucidating, as best I may, this department of natural science, which not undeservedly has gained the reputation of being exceedingly difficult. I feel myself especially indebted to those who first began to make clear these deeply obscure matters, and to lead us to hope that they were
capable of simple explanations. But, on the other hand, I have been astonished to find these
same writers accepting arguments which are far from evi-
dent as if they were conclusive and demonstrative. No one
has yet given even a probable explanation of the fundamental
and remarkable phenomena of light, viz*, why it travels in straight lines and how rays coining from an infinitude of dif-
ferent directions cross one another without disturbing one an-
other.
I shall attempt, in this volume, to present in accordance with
9

M KM 01 US ON
the principles of modern philosophy, some clearer ;i,nd more probable reasons, first, for the rectilinear propagation of light, and, secondly, for its reflection when it meets .other bodies. Later 1 shall explain the phenomenon of rays which art! said to undergo refraction in passing through transparent, bodies of dilTerenl, kinds. Here 1 shall treat, also of refraction efl'i-ets due
to the. varying density of the earth's atmosphere. Afterwards I shall examine the causes of that peculiar refraction occur-
ring in a certain crystal which comes from Iceland. And last I y,
I shall consider the dill'crenl, shapes required in transparent and in rellecting bodies to converge! rays upon a single point or to deflect them in various ways. Hero we shall see with what ease are determined, by our new theory, not only the ellipses, hyperbolas, and Other Curves which M. Descartes has so ingeniously devised for this purpose, but also the curve which one surface of a lens must, have when the other surface is given, as
spherical, plane, or of any figure whatever.
We cannot, help believing that light, consists in the motion
of a certain material. lA>r when we consider its production we find that here on the earth it is generally produced by fire and llame which, beyond doubt, contain bodies in a state of rapid motion, since they are able to dissolve and melt numerous other more solid bodies. And if we consider its effects, we see
that when light is converged, as, for instance, by concave mirrors, it is able to produce combustion just as fire does ; i.e., it.
is able to tear bodies apart ; a property that surely indicates motion, at least in the true philosophy whore one believes all
natural phenomena to be mechanical effects. And, in my opin-
ion, we must admit this, or else give up all hope of ever under-
standing anything in physics. Since, according to this philosophy, it is considered certain
thai, the sensation of sight is caused only by the impulse of some form of matter upon tin* nerves at the base of the eye, we have here still another reason for thinking that light consists in a motion of the matter situated between us and the lumi-
nous body.
When we consider, further, the very great speed with which light is propagated in all directions, and the fact that when rays come from different directions, even those directly op-
posite, they cross without disturbing each other, it must be
evident that we do not see luminous objects by means of matter
10

TIIH \\AYK-TIIKOHY OF LIGHT

translated from the <>l)jcct to us, as a shot or MM arrow travels

through the air. For certainly this would be in contradiction

to the two properties of light which wo have just mentioned,
and especially to the hitter. Light is then propagated in some other manner, an understanding of which we may obtain from our knowledge of the manner in which sound travels through the air.

\\ < know that through the medium of the air, an invisible

and impalpable body, sound is propagated in all directions, from the point where it is produced, by means of a motion which is communicated successively from one part of the air to another ; and since this motion travels with the same speed in all directions, it must, form spherical surfaces which contin-
ually enlarge until linally they strike our ear. Now there can

be no doubt that, light also comes from the luminous body to us by means of some motion impressed upon the matter which
lies in the intervening space; for we have already seen that

this cannot occur through the translation of matter from out-

point to the other.

If. in addition, light requires time for its passage a point
we shall presently consider it will then follow that this motion

is impressed upon the matter gradually, and hence is propagated, as that of sound, by surfaces and spherical waves. I

call these 'irdrrti because of their resemblance to those 'which

are formed when one throws a pebble into water and which

represent gradual propagation in circles, although produced by a different cause and confined <<> ;t plane surface.

As

to

the

nest ion
')

of

light

requiring

time for

its

propaga-

tion, let us consider first whether there is any experimental

evidence to the contrary.

What we can do here on the earth with sources of light placed

at great, distanc.es (alt hough showing that light does not occupy

:i sensible time in passing over these distances) may be objected to on the ground that these distances are still too srnaM, and

thai, therefore, we can conclude only that the propagation of
light is exceedingly rapid. M. Descartes thought it instanta-
neous, and based his opinion upon much better evidence, fur-

nished by the eclipse of the moon. Nevertheless, as I shall

show, even this evidence is not conclusive. I shall state the

matter in a manner slightly different from his in order that we may more easily arrive at all the consequences.

11

MEMOIRS ON

A BD Let

be

the

position

of

the

sun ;

a part of the orbit or

ABC annual

path

of the

earth ;

a straight line intersecting in

C the orbit of the moon, which is represented by the circle CD.

If, now, light requires time say one hour to trav-

erse the space be-
tween the earth

and the moon, it follows that when

the earth has

reached the point

fig j

B, its shadow, or the interruption

of light, will not yet have reached the point C, and will not

reach it until one hour later. Counting from the time when

the earth occupies the position B, it will be one hour later that

the moon arrives at the point C

and

is there obscured ;

but this

eclipse or interruption of light will not be visible at the earth until the end of still another hour. Let us suppose that during

these two hours the earth has moved to the position E. From this point the moon will appear to be eclipsed at C, a position

which it occupied one hour before, while the sun will be seen

at A. -For I assume with Copernicus that the sun is fixed and,

since light travels in straight lines, must always be seen in its

true position. But it is a matter of universal observation, we are told, that the eclipsed moon appears in that part of the

ecliptic directly opposite

the sun ;

while

according to our view

its position ought to be behind this by the angle GEC, the
supplement of the angle AEC. But this is contrary to the fact,
for the angle GEC will be quite easily observed, amounting to about 33. Now according to our computation, which will be

found in the memoir on the causes of the phenomena of Sat-

urn,- the distance, BA, between the earth and the sun is about

12,000 times the diameter of the earth, and consequently 400

times the distance of the moon, which is 30 diameters. The

ECB angle

will, therefore, be almost 400 times as great as

BAE, which is 5', viz., the angular distance traversed by the

earth in its orbit during an interval of two hours. Thus the
angle BCE amounts to almost 33, and likewise the angle

CEG, which is 5' greater.

12

f^"

^^ THE

WAVE-THEORY

OF

(
LI'GHT

But it must be noted that in this argument the speed of light is assumed to be such that the time required for it to pass from here to the moon is one hour. If, however, we suppose that it
requires only a minute of time, then evidently the angle CEG
will amount to only 33' ; and if it requires only ten seconds of time, this angle will amount to less than 6'. But so small a
quantity is not easily observed in a lunar eclipse, and conse-
quently it is not allowable to infer the instantaneous propaga-

tion of light.
It is somewhat unusual, we must 'confess, to assume a speed one hundred thousand times as great as that of sound, which,
according to my observations, travels about 180 toises [1151
feet] in a second, or during a pulse-beat; but this supposition appears by no means impossible, for it is not a question of carrying a body with such speed, but of a motion passing successively from one point to another.
I do not therefore, in thinking of these matters, hesitate to

suppose that the propagation of light occupies time, for on this view all the phenomena can be explained, while on the contrary view none of them can be explained. Indeed, it seems to
me, and to many others also, that M. Descartes, whose object has been to discuss all physical subjects in a clear way, and who
has certainly succeeded better than any one, before him, has written nothing on light and its properties which is not either
full of difficulty or even inconceivable. But this idea which I have advanced only as a hypothesis has
recently been almost established as a fact by the ingenious method of Komer, whose work I propose here to describe, expecting that he himself will later give a complete confirmation
of this view.

His method, like the one we have just discussed, is astro-

nomical. He proves not only that light requires time for its

propagation, but shows also how much time it requires and that

its speed must be at least six times greater than the estimate

which I have just given.

For this demonstration, he uses the eclipses of the small plan-

ets which revolve about Jupiter, and which very often pass

A into its shadow. His reasoning is as follows : Let

denote

the sun; BODE, the annual orbit of the earth; F, Jupiter;

and GN, the orbit of the innermost satellite, for this one, on

account of its short period, is better adapted to this investi-

13

MEMOIRS ON

Cation than is either of the other three. Let G represent the

H point of the satellite's entrance into, and

the point of its

emergence from, Jupiter's shadow.

Let us suppose that an emergence of this

satellite has been observed while the earth

occupies the position B, at some time before

the last quarter. If the earth remained in

this position, 42J hours would elapse before the next emergence would occur. For this

is the time required for the satellite to make one revolution in its orbit and return to op-
position with the sun. If, for instance, the
earth remained at the point B during 30 rev-
olutions, then, after an interval of 30 times

42-J hours, the satellite would again be observed to emerge. But if meanwhile the earth has moved to a point 0, more distant from Jupiter, it is evident that, provided light requires time for its propagation, the

emergence of the little planet will be recorded later at than it would have been at B.

For it will be necessary to add to this in-

terval, 30 times 42 \ hours, the time occupied by ligh't in passing

CH over a distance MC, the difference of the distances

and BH.

In like manner, in the other quarter, while the earth travels

D from

to E, approaching Jupiter, the eclipses will occur

earlier when the earth is at E than if it had remained at D.

Now by means of a large number of these eclipse observations,
covering a period of ten years, it is shown that these inequalities are very considerable, amounting to as much as ten minutes or more; whence it is concluded that, for traversing the whole diameter of the earth's orbit KL, twice the distance from

here to the sun, light requires about 22 minutes.
The motion of Jupiter in its orbit, while the earth passes
from B to C or from D to E, has been taken into account in

the computation, where it is also shown that these inequalities cannot be due either to an irregularity in the motion of the

satellite or to its eccentricity.
If we consider the enormous size of this diameter, KL,

which I have found to be about 24 thousand times that of the

earth, we get some idea of the extraordinary speed of light.
14

THE WAVE-THEORY OF LIGHT

KL Even if we Suppose that

were only 22 thousand diameters

of the earth, a speed covering this distance in 22 minutes would

be equivalent to the rate of one thousand diameters per minute,

i.e., 16f diameters a second (or a pulse-beat), which makes more

than eleven hundred times one hundred thousand toises [212,222

kilometres], since one terrestrial diameter contains 2865 leagues,

of which there are 5 to the degree, and since, according to the

exact determination made by Mr. Picard in 1669 under orders

from the king, each league contains 2282 toises.

But, as I have said above, sound travels at the rate of only

180 toises [350 metres] per second. Accordingly, the speed of

light is more than 600,000 times as great as that of sound,

which, however, is a very different thing from being instanta-

neous, the difference being exactly that between a finite quantity

and infinity. The idea that luminous disturbances are handed

on from point to point in a gradual manner being thus con-

firmed, it follows, as I have already said, that light is propa-

gated by spherical waves, as is the case with sound.

But if they resemble each other in this, respect, they differ in

several others viz., in the original production of the motion

which causes them, in the medium through which they travel, and in the manner in which they are transmitted in this

medium.

Sound, we know, is produced by the rapid disturbance of some body (either as a whole or in part) ; this disturbance setting in motion the contiguous air. But luminous disturbances must
arise at each point of the luminous object, else all the different parts of this object would not be visible. This fact will be more evident in what follows.

In my opinion, this motion of luminous bodies cannot be bet-
ter explained than by supposing that those which are fluid, such as a flame, and apparently the sun and stars, are composed
of particles that float about in a much more subtle medium, which sets them in rapid motion, causing them to strike against the still smaller particles of the surrounding ether. But in the case of luminous solids, such as red-hot metal or carbon, we
may suppose this motion to be caused by the violent disturb-
ance of the particles of the metal or of the wood, those which lie on the surface exciting the ether. Thus the motion which produces light must also be more sudden and more rapid than that which causes sound, since we do not observe that sonorous

15

MEMOIRS ON

disturbances give rise to light any more than that the motion

of the hand through the air gives rise to sound.

The question next arises as to the nature of the medium in

which is propagated this motion produced by luminous bodies.

I

have

called

it

ether ;

but

it

is

evidently

something

different

from the medium through which sound travels. For this lat-

ter is simply the air which we feel and breathe, and which,

when removed from any region, leaves behind the luminiferous

medium. This fact is shown by enclosing a sounding body in a

glass vessel and removing the atmosphere by means of the air-

pump which Mr. Boyle has devised, and with which he has per-

formed so many beautiful experiments. But in trying this it

is well to place the sounding body on cotton or feathers in such

a way that it cannot communicate its vibrations either to the

glass receiver or to the air-pump, a point which has hitherto

been neglected. Then, when all the air has been removed, one

hears no sound from the metal even when it is struck.

From this we infer not only that our atmosphere, which is unable to penetrate glass, is the medium through which sound
travels, but also that it is different from that which carries

luminous disturbances for when the vessel is exhausted of ;

air, light traverses it as freely as before.
This last point is demonstrated even more clearly by the celebrated experiment of Torricelli. That part of the glass tube which the mercury does not fill contains a high vacuum, but transmits light the same as when filled with air. This shows that there is within the tube some form of matter which

is different from air, and which penetrates either glass or mercury, or both, although both the glass and the mercury are im-
pervious to air. And if the same experiment is repeated, ex-
cept that a little water be placed on top of the mercury, it becomes equally evident that the form of matter in question passes either through the glass or through the water or through

both.

As to the different modes of transmission of Sound and light,
it is easy to understand what happens in the case of sound when one recalls that air can be compressed and reduced to
a much smaller volume than it ordinarily occupies, and that
just in proportion as its volume is diminished it tends to regain its original size. This property, taken in conjunction with its penetrability, which it retains in spite of compression,
16

THE WAVE-THEORY OF LIGHT

appears to show that it is composed of small particles which

float about, in rapid motion, in an ether composed of still finer

particles. Sound, then, is propagated by the effort of these
air particles to escape when at any point in the path of the wave

they are more compressed than at some other point.

But the enormous speed of light, together with its other

properties, hardly allows us to believe that it is propagated in
the same way. Accordingly, I propose to explain the manner

in which I think it must occur. It will be necessary first, how-

ever, to describe that property of hard bodies in virtue of which

they transmit motion from one to another.

If one takes a large number of spheres of equal size, made of

any hard material, and arranges them in contact in a straight

line, he will find that, on allowing a sphere of the same size to

roll against one end of the line, the motion is transmitted in an

instant to the other end of the line* The last sphere in the

row flies off while the intermediate ones are apparently undis-

turbed ;

the

sphere

which

originally produced

the

disturbance

also remains at rest. Here we have a motion which is trans-

mitted with high speed, which varies directly as the hardness
of the spheres. Nevertheless, it is certain that this motion is not instantane-

ous, but is gradual, requiring time. For if the motion, or, if you please, the tendency to motion, did not pass successively from one sphere to another, they would all be affected at the same instant, and would all move forward together. So far from this being the case, it is the last one only which leaves the row, and it acquires the speed of the sphere which gave the blow. Besides this experiment there are others which show that all bodies, even those which are considered hardest, such as tempered steel, glass, and agate, are really elastic, and bend to some extent whether they are made into rods, spheres, or bodies

of any other shape; that is, they yield slightly at the point

where they are struck, and immediately regain their original

figure. For I have found that in allowing a glass or agate

sphere to strike upon a large, thick, flat piece of the same ma-

terial, whose surface has been dulled by the breath, the point

of contact is marked by a circular disk which varies in size

directly as the strength of the blow. This shows that during

the encounter these materials yield and then fly back, a proc-

ess which must require time.

B

17

MEMOIRS ON
Now to apply this kind of motion to the explanation of
light, nothing prevents our imagining the particles of the ether as endowed with a hardness almost perfect and with an elasticity as great as we please. It is not necessary here to discuss the cause either of this hardness or of this elasticity, for such a consideration would lead us too far from the subject. I will, however, remark in passing that these ether particles, in spite of their small size, are in turn composed of parts, and that their elasticity consists in a very rapid motion of a subtle material
which traverses them in all directions and compels them to assume a structure which offers an easy and open passage to this fluid. This accords with the theory of M. Descartes, except that I do not agree with him in assigning to the pores the form of hollow circular canals. So far from there being any-
thing absurd or impossible in all this, it is quite credible that nature employs an infinite series of different-sized molecules, endowed with different velocities, to produce her marvellous
effects.
But although we do not understand the cause of elasticity? we cannot fail to observe that most bodies possess this property : it is not unnatural, therefore, to suppose that it is a char-
acteristic also of the small, invisible' particles of the ether. If,
indeed, one looks for some other mode of accounting for the
gradual propagation of light, he will have difficulty in finding one better adapted than elasticity to explain the fact of uniform
speed. And this appears to be necessary; for if the motion slowed
up as it became distributed through a larger mass of matter, and receded farther from the source of light, then its high speed would be lost at great distances. But we suppose the
elasticity to be a property of the ether so that its particles regain their shape with equal rapidity whether they are struck with a hard or a gentle blow; and thus the rate at which the
light moves remains the same [at all distances from the source]. Nor is it necessary that the ether particles should be arranged
in straight lines, as was the ease with our row of spheres. The most irregular configuration, provided the particles are in con-
tact with each other, will not prevent their transmitting the motion and handing it on to the regions in front. It is to be
noted that we have here a law of motion which governs this kind of propagation, and which is verified by experiment, viz., when a sphere such as A, touching several other smaller ones,
18

THE WAVE-THEORY OF LIGHT

CCC, is struck by another sphere, B, in such a way as to make an impression upon each of its neighbors, it transfers its motion to them and remains at rest, as does also the sphere B. Now, without supposing that ether particles are
spherical (for I do not see that this is necessary), we can nevertheless understand that this
Jaw of impulses plays a part in the propagation of the motion.

Equality of size would appear to be a more necessary assumption, since otherwise we should expect the motion to be reflected on passing from a smaller to a larger particle, following the laws of percussion which I published some

Fig. 3

years ago. Yet, as will appear later, this equal-
ity is necessary not so much to make the propagation of light possible as to make it easy and intense. Nor does it appear improbable that the ether particles were made equal for a pur-
pose so important as the transmission of light. This may be
true, at least, in the vast region lying beyond our atmosphere and serving only to transmit the light of the sun and the
stars.

I have now shown how we may consider light as propagated, in time, by spherical waves, arid how it is possible that the speed of propagation should be as great as that demanded by
experiment and by astronomical observation. It must, however, be added that although the ether particles are supposed
to be in continual motion (and there is much evidence for this
view), the gradual transmission of the waves
is not thus interfered with. For it does not

consist in a translation of these particles, but merely in a small vibration, which they are

compelled to transmit to their neighbors in spite of their proper motion and their change
of relative position.
But we must consider, in greater detail, the origin of these waves and the manner of their propagation from one point to another. And, first, it follows from what has already been said concerning the production of light that each point of a luminous body, such as the sun, a candle, or a piece of burning car-
19

MEMOIRS ON

bon, gives rise to its own waves, and is the centre of these waves. Thus if A, B, and C represent different points in a
candle flame, concentric circles described about each of these
points will represent the waves to which they give rise. And
the same is true for all the points on the surface and within the flame. But since the disturbances at the centre of these

waves do not follow each other in regular succession, we need
not imagine the waves to follow one another at equal intervals; and if, in the figure, these waves are equally spaced, it is rather
to indicate the progress which one and the same wave has made

during equal intervals of time than to represent several waves having their origin at the same point.*
Nor does this enormous number of waves, crossing one another without confusion and without disturbing one another, appear unreasonable, for it is well known that one and the same particle of matter is able to transmit several waves coming from different, and even opposite, directions. And this is true not only in the case where the displacements follow one

another in succession, but also where they are simultaneous. This is because the motion is propagated gradually. It is shown by the row of hard and equal spheres above mentioned.
A If we allow two equal spheres, and D, to strike against the
opposite sides of this row at the same instant, they will be observed to rebound each with the same speed that it had before

collision, while all the other spheres remain at rest, although

the motion has twice traversed the entire row. [This evidently

A D implies that the spheres

and have equal speeds justi before

OOO00OO

collision.] If these two oppositely directed motions happen to meet at the middle sphere, B, or at any other sphere, say 0, it will yield and spring back from both sides, thus transmitting both motions at the same instant.
* [From this paragraph it would appear that Huygens had no conception of trains of light-waves. The experimental evidence for thinking that light-
waves travel in trains seems first to have been furnished by Young. See pp. 60, 61 below. If, however, one prefers to interpret the colored rings of Newton
in terms of the wave-theory, this experimental evidence may be ascribed to
Newton.'] 30

THE WAVE-THEORY OF LIGHT

Bnt what is strangest and most astonishing of all is that waves produced by displacements and particles so minute should spread to distances so immense, as, for instance, from the sun or from

the stars to the earth. For the intensity of these waves must diminish in proportion to their distance from the origin until finally each individual wave is of itself unable to produce the sensation of light. Our astonishment, however, diminishes when we consider that in the great distance which separates us from the luminous body there is an infinitude of waves which, although coming from different parts of the [luminous] body, are practically compounded into a single wave which thus acquires sufficient intensity to affect our senses. Thus the infinitely great number of waves which at any one instant leave a fixed star, as large possibly as our sun, unite to form what
is equivalent to one single wave* of intensity sufficient to affect
the eye. Not only so, but each luminous point may send us
thousands of waves in the shortest imaginable time, on account of r! e rapidity of the blows with which the particles of the
luminous body strike the ether at these points. The effect of the waves would thus be rendered still more sensible.

In considering the propagation of waves, we must remember that each particle of the medium through which the wave spreads doe not communicate its motion only to that neighbor which lies in the straight line drawn from the luminous point, but shares it with all the particles which touch it and resist its motion. Each particle is thus to be considered as the centre
of a wave. Thus if DCF is a wave whose centre and origin
is the luminous point A, a parti-
cle at B, inside the sphere DCF, will give rise to its own individual
[secondary] wave, KCL, which will
touch the wave DCF in the point
C, at the same instant in which the

principal wave, originating at A,

reaches the position DCF. And it

is clear that there will be only one D
point of the wave KCL which will

touch the wave DCF, viz., the point
A which lies in the straight line from

Fig. 6

drawn through B. In like manner, each of the other particles,

bbbb, etc., lying within the sphere DCF, gives rise to its

21

MEMOIRS ON

own wave. The intensity of each of these waves may, however, be infinitesimal compared with that of DCF, which is
the resultant of all those parts of the other waves which are at
a maximum distance from the centre A.
We see, moreover, that the wave DCF is determined by the
extreme limit to which the motion has travelled from the point
A within a certain interval of time. For there is no motion

beyond this wave, whatever may have been produced inside by
those parts of the secondary waves which do not touch the
sphere DCF. Let no one think this discussion mere hair-

splitting. For, as the sequel will show, this principle, so far from being an ultra-refinement, is the chief element in the ex-

planation of all the properties of light, including the phe-
nomena of reflection and refraction. This is exactly the point which seems to have escaped the attention of those who first
took up the study of light-waves, among whom are Mr. Hooke,
in his Miorographia, and Father Pardies, who had undertaken to explain reflection and refraction on the wave -theory, as I know from his having shown me a part of a memoir which he was unable to finish before his death. But the most important fundamental idea, which consists in the principle I have just stated, is wanting in his demonstrations. On other points also his view is different from mine, as will some day appear in case
his writings have been preserved.
Passing now to the properties of light, we observe first that
each part of the wave is propagated in such a way that its extremities lie always between the same straight lines drawn from the lumi-
nous point. For instance, that part of the wave
BGr, whose centre is the luminous

point A, develops into the arc CE,
ABO limited by the straight lines,
and AGE. For although the sec-

ondary waves produced by the par-
CAE ticles lying within the space

Rff.fi

may spread to the region outside,
nevertheless they do not combine at

the same instant to produce one single wave limiting the
motion and lying in the circumference CE which is their common tangent. This explains the fact that light, pro-
22

THE WAVE-THEORY OF LIGHT

vided its rays are not reflected or refracted, always travels in straight lines, so that no body is illuminated by it unless the straight -line path from the source to this body is unob-

structed.

Let us, for instance, consider the aperture BG- as limited by

the

opaque

bodies

BH,

GI ;

then, as

we

have

just

indicated,

the light- waves will always be limited by the straight lines

AC, AE. The secondary waves which spread into the region

ACE outside of

have not sufficient intensity to produce the

sensation of light.

Now, however small we may make the opening BG, the cir-

cumstances which compel the light to travel in straight lines

still remain the same ;

for

this

aperture

is

always

sufficiently

large to contain a great number of these exceedingly minute

ether particles. It is thus evident that each particular part of

any wave can advance only along the straight line drawn to it
from the luminous point. And this justifies us in considering

rays of light as straight lines.
From what has been said concerning the small intensity of
the secondary waves, it would appear not to be necessary that all the ether particles be equal, although such an equality would favor the propagation of the motion. The effect of inequality would be to make a particle, in colliding with a
larger one, use up a part of its momentum in an effort to recover. The secondary waves thus sent backward towards
the luminous point would be unable to produce the sensation of light, and would not result in a primary wave similar to CE.

Another and more remarkable property of light is that when rays come from different, or even opposite, directions each produces its effect without disturbance from the other. Thus several observers are able, all at the same time, to
look at different objects through one single opening ; and two individuals can look into each other's eyes at the same

instant.

If we now recall our explanation of the action of light and of
waves crossing without destroying or interrupting each other, these effects which we have just described are readily understood, though they are not so easily explained from Descartes' point of view, viz., that light consists in a continuous [hydrostatic] pressure which produces only a tendency to motion.
23

MEMOIRS ON THE WAVE-THEORY OF LIGHT
For such a pressure cannot, at the same instant, affect bodies from two opposite sides unless these bodies have some tendency to approach each other. It is, therefore, impossible to understand how two persons can look each other in the eye or how one torch can illuminate another.
24

CHAPTER II ON REFLECTION

HAVING explained the effects produced by light-waves in a
homogeneous medium, we shall next consider what happens when they impinge upon other bodies. First of all we shall see how reflection is explained by these same waves and how
the equality of angles follows as a consequence.
Let AB represent a plane
polished surface of some
metal, glass, or other sub-
stance, which, for the present, we shall consider as

perfectly smooth (concerning irregularities which are unavoidable we shall

have something to say at the close of this demon-

stration) ; and let the line
AC, inclined to AB, represent a part of a light-wave whose centre is so far away that this
part AC may be considered as a straight line. It may be men-
tioned here, once for all, that we shall limit our consideration

to a single plane, viz., the plane of the figure, which passes

through the centre of the spherical wave and cuts the plane
AB at right angles.

The region immediately about C on the wave AC will, after

a certain interval of time, reach the point B in the plane AB,

travelling along the straight line CB, which we may think of

as drawn from the source of light and hence drawn perpen-
dicular to AC. Now in this same interval of time the ^egion A about on the same wave is unable to transmit its entire

AB motion beyond the plane

; it must, therefore, continue its

25

MEMOIRS ON

motion on this side of the plane to a distance equal to CB,

sending out a secondary spherical wave in the manner described

above. This secondary wave is here represented by the circle

A AN SNR, drawn with its centre at and with its radius

equal

to CB.

H So, also, if we consider in turn the remaining parts of the

wave AC, it will be seen that they not only reach the surface

AB HK along the straight lines

parallel to CB, but they will

produce, at the centres K, their own spherical waves in the

transparent medium. These secondary waves are here repre-

KM sented by circles whose radii are equal to

that is, equal

HK to the prolongations of

BG to the straight line

which

is drawn parallel to AC. But, as is easily seen, all these cir-

cles have a common tangent in the straight line BN, viz., the same line which passes through B and is tangent to
the first circle having A as centre and AN, equal to BC, as

radius.

BN This line

(lying between B and the point N, the foot of

the perpendicular let fall from A) is the envelope of all these

circles, and marks the limit of the motion produced by the

reflection of the wave AC. It is here that the motion is more

intense than at any other

point, because, as has been

BN explained,

is the new

position which the wave
AC has assumed at the in-

stant when the point C has reached B. For there is

no other line which, like
BN, is a common tangent
to these circles, unless it

be BG, on the other side of the plane AB. And BGr

Fig. 7

will represent the trans-
mitted wave onlv in case

the motion occurs in a medium which is homogeneous with

that above the plane. If, however, one wishes to see just how

the wave AC has gradually passed into the wave BN, he has

KO only to use the same figure and draw the straight lines

KL parallel to BN, and the straight lines

parallel to AC. It is

thus seen that the wave AC, from being a straight line, passes

26

THE WAVE-THEORY OF LIGH

successively into all the broken lines OKL, and reassumes the

form of a single straight line NB.

It is now evident that the angle of reflection is equal to the

BNA ABC angle of incidence. For the right-angled triangles

and

have the side AB in common, and the side OB equal to the side

NA, whence it follows that the angles opposite these sides are
equal, and hence also the angles CBA and NAB. But .CB,

perpendicular to CA, is the direction of the incident ray, while AN, perpendicular to the wave BN, has the direction of the

reflected ray. These rays are, therefore, equally inclined to the plane AB.
BN Against this demonstration it may he urged that while
is the common tangent of the circular waves in the plane of

this figure, the fact is that these waves are really spherical and
have an infinitely great number of similar tangents, viz., all
straight lines drawn through the point B and lying in the sur-

face of a cone generated by the revolution of a straight line

BN BA about

as axis. It remains to be shown, therefore, that

this objection presents no difficulty ; and, incidentally, we shall see that the incident and reflected rays each lie in one plane

perpendicular to the reflecting plane.

I remark, then, that the wave AC, so long as it is considered

merely a line, can produce no light. For a ray of light, however slender, must have a finite thickness in order to be visible.

In order, therefore, to represent a wave whose path is along

AC this ray, it is necessary to replace the straight line

by a

HC plane area, as, for instance, by the circle

in the following

figure, where the luminous point is supposed to be infinitely
distant. From the preceding proof it is easily seen that each

element of area on the wave HC, having reached the plane AB,

will

there

give

rise

to

its

own

secondary

wave ;

and

when C

reaches the point B, these will all have a common tangent

BN plane, viz.. the circle

equal to CH. This circle will be cut

through the centre and at right angles by the same plane which

CH thus cuts the circle

and the ellipse AB.

It is thus seen that the spherical secondary waves can have
no common tangent plane other than BN. In this plane will

be located more of the reflected motion than in any other, and it will therefore receive the light transmitted from the wave CH.

I have noted in the preceding explanation that the motion of
A the wave incident at is not transmitted beyond the plane AB,

27

MEMOIRS ON
at least not entirely. And here it is necessary to remark that, although the motion of. the ether may be partly communicated
to the reflecting body, this cannot in the slightest alter the speed of the propagation of the waves, which determines the angle of reflection. For, in any one medium, a slight disturbance produces waves which travel with the same speed as those
Fig. 8
due to a very great disturbance, a consequence of that property of elastic bodies concerning which we have spoken above, viz., the time occupied in recovery is the same whether the compression be large or small. In every case of reflection of light from the surface of any substance whatever the angles of incidence and reflection are therefore equal, even though the body be of such a nature as to absorb a part of the motion delivered .by the incident wave. And, indeed, experiment shows
that among polished bodies there is no exception to this law
of reflection.
"We must emphasize the fact that in our demonstration there is no need that the reflecting surface be considered a perfectly smooth plane, as has been assumed by all those who have attempted to explain the phenomena of reflection. All that is called for is a degree of smoothness such as would be produced by the particles of the reflecting medium being placed one near another. These particles are much larger than those of the ether, as will be shown later when we come to treat of the transparency and opacity of bodies. Since, now, the surface consists thus of particles assembled together, the ether particles being above and smaller, it is evident that one cannot demonstrate the equality of the angles of incidence and reflection from the time-worn analogy with that which happens when
28

THE WAVE-THEORY OF LIGHT
a ball is thrown against a wall. By our method, on the other
hand, the fact is explained without difficulty. Take particles of mercury, for instance, for they are so
small that we must think of the least visible portion of surface as containing millions, arranged like the grains in a heap of
sand which one has smoothed out as much as possible; this
surface for our purpose is equal to polished glass. And, though such a surface may be always rough compared with ether particles, it is evident that the centres of all the secondary waves of reflection which we have described above lie practically in one plane. Accordingly, a single tangent comes as near touch-
ing them all as is necessary for the production of light. And
this is all that is required in our demonstration to explain the equality of angles without allowing the rest of the motion, reflected in various directions, to produce any disturbing elfect.

CHAPTER III
OK REFRACTION

IK the same manner that reflection has been explained by

light-waves reflected at the surface of polished bodies, we pro-

pose now to explain transparency and the phenomena of refrac-

tion by means of waves propagated into and through transpar-

ent bodies, whether solids, such as glass, or liquids, such as

water and oils. But, lest the passage of waves into these

bodies appear an unwarranted assumption, I will first show that

this is possible in more ways than one.

Let us imagine that the ether does penetrate any transparent

body, its particles will still be able to transmit the motion of

the waves just as do those of the ether, supposing them each to

be elastic. And this we can easily believe to be the case with

water and other transparent liquids, since they are composed

of discrete particles. But it may appear more difficult in the

case of glass and other bodies that are transparent and hard,

because their solidity would hardly allow that they should take

up any motion except that of their mass as a whole. This,

however, is not necessary, since this solidity is not what it ap-

pears to us to be, for it is more probable that these bodies are

composed of particles which are placed near one another and

bound together by an external pressure due to some other kind

of matter and by irregularity of their own configurations. For

their looseness of structure is seen in the facility with which

they are penetrated by the medium of magnetic vortices and

those which cause gravitation. One cannot go further than to

say that these bodies have a structure similar to that of a sponge,

or of light bread, because heat will melt them and change the

We relative positions of their particles.

infer, then, as has

been indicated above, that they are assemblages of particles

touching one another but not forming a continuous' solid.

This being the case, the motion which these particles receive

30

MEMOIRS ON THE WAVE-THEORY OF LIGHT
in the transmission of light is simply communicated from one to another, while the particles themselves remain tethered in their own positions and do not become disarranged among themselves. It is easily possible for this to occur without in any way affecting the solidity of the structure as seen by us.
By the external pressure of which I have spoken is not to be
understood that of -'the air, which would be quite insufficient, but that of another and more subtle medium, whose pressure is exhibited by an experiment which I chanced upon a long while ago, namely, that water from which the air has been removed remains suspended in a glass tube open at the lower end, even
though the air may have been exhausted from a vessel enclosing
this tube.
We may thus explain transparency without assuming that
bodies are penetrated by the luminiferous ether or that they
contain pores through which the ether can pass. The fact, however, is not only that this medium penetrates ordinary
bodies, but that it does so with the utmost ease, as indeed has
already been shown by the experiment of Torricelli which we
have cited above. When the mercury or the water leaves the
upper part of the glass tube, the ether appears at once to take its place and transmit light. But following is still another argument for thinking that bodies, not only those which are transparent, but others also, are easily penetrable.
When light traverses a hollow glass sphere which is com-
pletely closed, it is evident that the sphere is filled with ether,
just as is the space outside the sphere. And this ether, as we
have shown above, consists of particles lying in close contact with each other. If, now, it were enclosed in the sphere in such a way that it could not escape through the pores of the glass, it would be compelled to partake of any motion which one might impress upon the sphere ; ^consequently nearly the same force would be required to impress a given speed upon this sphere, lying upon a horizontal plane, as if it were filled with water, or possibly mercury. For the resistance which a body offers to any velocity one may wish to impart to it varies directly as the quantity of matter which the body contains and which is compelled to acquire velocity. But the fact is that the sphere resists the motion only in proportion to the amount of glass in it. Whence it follows that the ether within is not
enclosed, but flows through the glass with perfect freedom.
31

MEMOIRS ON

Later we shall show, by this same process, that penetrability

may be inferred for opaque bodies also.
A second and more probable explanation of transparency

is to say that the light-waves continue on in the ether which

always fills the interstices, or pores, of transparent bodies.

For since it passes continuously and with ease, it follows that

these pores are always full. Indeed, it may be shown that these

interstices occupy more space than the particles which make

up the body.
Now if it be true, as we have said, that the force required

to impart a given horizontal velocity to a body is proportional

to the mass of the body, and if this force be also proportional
to the weight of the body, as we know by experiment that it

is,

then

the

mass

of any body

must

be
^also

proportional

to

its weight. Now we know that water weighs only -fa part as

much as an equal volume of mercury, therefore the substance

of the water occupies only -fa part of the space that encloses

its mass. Indeed, it must occupy even a smaller fraction than

this, "because mercury is not so heavy as gold, and gold is a
substance which is not very dense, since the medium of mag-

netic vortices and that which causes gravitation penetrate it

with the utmost ease.

But it may be objected that if water be a substance of such
small density, and if its particles occupy so small a portion of
its apparent volume, it is very remarkable that it should offer such stubborn resistance to compression ; for it has not been condensed by any force hitherto employed, and remains perfectly liquid while under pressure.
This is, indeed, no small difficulty. But it may nevertheless
be explained by supposing that the very violent and rapid
motion of the subtle medium which keeps water liquid also
sets in motion the particles of which it is composed, and maintains this liquid state in spite of any pressure which has hitherto
been applied. If, now, the structure of transparent bodies be as loose as we
have indicated, we may easily imagine waves penetrating the ether which fills the interstices between the particles. Not
only so, but we can easily believe that the speed of these waves inside the body must be a little less on account of the small detours necessitated by these same particles. I propose to show
that in this varying velocity of light lies the cause of refraction.
32

THE WAVE-THEORY OF LIGHT

I will first indicate a third and last method by which we may

explain transparency, namely, by supposing that the motion of

the light-waves is transmitted equally well by the ether particles

which fill the interstices of the body, and by the particles which

compose the body, the motion being handed on from one to the

A other.

little later we shall see how beautifully this hypothesis

explains the double'refraction of certain transparent substances.
Should one object that the particles of ether are much smaller

than those of the transparent body, since the former pass

through the intervals between the latter, and that consequent-

ly they would be able to communicate only a small portion of

their momentum, we may reply that the particles of the body

are composed of other still smaller particles, and that it is these
secondary particles that take up the momentum from those of

the ether.

Moreover, if the particles- of the transparent body are slight-
ly less elastic than are the ether particles, which we may

reasonably suppose, it would still follow that the speed of

the light waves is less inside the body than outside in the

ether.

We have here, what appears to me, the manner in which

light-waves are probably transmitted by transparent bodies. But there still remains the consideration of opaque bodies and

the difference between these and transparent bodies, a question all the more interesting in view of the ease with which ether

penetrates all bodies, a fact to which attention has already been directed, and which might lead one to think that all bodies

should be transparent. For considering the hollow sphere, by which I have shown the open structure of glass and the ease

with which ether passes through it, one would naturally infer the same penetrability as a property of metals and all other

substances. Imagine the sphere to be of silver; it would then

certainly contain luminiferous ether, because this substance,

as well as air, would be present in it when the opening in the sphere was closed up. But when closed and placed upon a horizontal plane it would resist motion only in proportion to the amount of silver in it, showing as above that the enclosed

ether does not acquire the motion of the sphere. Silver, there-

fore, like glass, is easily penetrated by ether. In between the"

particles of silver and of all other opaque bodies this substance

is distributed continuously and abundantly ; and, since it can

c

33

MEMOIRS ON

transmit light, we are led to expect that these bodies should be

as transparent as glass, which, however, is not the fact.

How, then, shall we explain their opacity? Are their con-

stituent particles soft and built up of still smaller particles, and thus able to change shape when they are struck by ether
particles ? Do they thus damp out the motion and stop the

propagation of the light-waves ? This seems hardly possible ;
for if the particles of a metal were soft, how could polished silver and mercury reflect light so well ? What seems to me

more probable is that metallic bodies, which are almost the

only ones that are really opaque, have interspersed among their

hard particles some which are soft, the former producing reflec-

tion, the latter destroying transparency ; while, on the other

hand, transparent bodies are made up of only hard and elastic

particles, which, together with the ether, propagate light- waves

in the manner already indicated.
We pass now to the explanation of refraction, assuming, as

above, that light-waves pass through transparent substances

arid in them undergo diminution of speed.

The fundamental phenomenon in refraction is the follow-

ing, viz., when any ray of light, AB, travelling in air, strikes

obliquely upon the polished surface of a transparent body, PGy

it undergoes a sudden change of direction at the point of inci-

dence,

B ;

and

this change occurs in such

a way that the angle

CBE, which the ray makes with the normal to the surface, is less than the angle ABD, which the ray in air made with the same normal. To determine the numerical value of these

angles, describe about the point B a circle cutting the rays AB, BC. Then the perpendiculars, AD, CE,

let fall from these points of intersection

upon the normal, DE, viz., the sines of

the angles ABD, CBE, bear to one an-

other a certain ratio which, for any

one transparent body, is constant for

all directions of the incident ray. For

glass this ratio is almost exactly f,

while for water it is very nearly f , thus

varying from one transparent body to

another.

Another property, not unlike the preceding, is that the refractions of rays entering and of rays emerging from a transpar-
34

THE WAVE-THEORY OF LIGHT

ent body are reciprocal. That is to say, if an incident ray, AB,

be refracted by a transparent body into the ray BO, so also will

a ray, CB, in the interior of the body be refracted, on emer-

gence, into the ray BA.

In order to explain these phenomena on our theory, let the

AB straight line

Fig. 10, represent the plane surface bounding a

transparentbodyextendingin
a direction between C and N.

By the use of the word plane we do not mean to

imply a perfectly smooth sur-

face, but merely such a one

as was employed in treating

of reflection, and for the

same reason. Let the line

M

AC represent a part of a

light- wave whose source is

so distant that this part may

be treated as a straight line.

The region 0, on the wave

Fig. 10

AC, will, after a certain in-

terval of time, arrive at the plane AB, along the straight line

CB, which we must think of #s drawn /from the source of

AC light, and which will, therefore, intersect

at right angles.

A But during this same interval of time the region about would

have arrived at G, along the straight line AG, equal and parallel
to CB, and, indeed, the whole of the wave AC would have

reached the position GB, provided the transparent body were capable of transmitting waves as rapidly as the ether. But
suppose that the rate of transmission is less rapid, say one-third
A less. Then the motion from the point will extend into the
transparent body to a distance which is only two-thirds of CB, while producing its secondary spherical wave as described above. This wave is represented by the circle SNR, whose cen-
A tre is at and whose radius is equal to f CB. If we consider,
H in like manner, the other points of the wave AC, it will be
seen that, during the same time which C employs in going to B, these points will not only have reached the surface AB, along the straight lines HK, parallel to CB, but they will have start-
ed secondary waves into the transparent body from the points
K as centres. These secondary waves are represented by cir-
35

MEMOIRS ON

KM HK cles whose radii are respectively equal to f of the distances

that is, f of the prolongations of

to the straight line

BG. If the two transparent media had the same ability to

transmit light, these radii would equal the whole lengths of

the various lines KM.

But all these circles have a common tangent in the line BN,

viz., the same line which we drew from the point B tangent to

SNR the circle

first considered. For it is easy to see that all

the other circles from B up to the point of contact, N, touch,

N in the same manner, the line BN, where

is also the foot of

the perpendicular let fall from A upon BN.

BN We may, therefore, say that

is made up of small arcs of

these circles, and that it marks the limits which the motion
from the wave AC has reached in the transparent medium, and
the region where this motion is much greater than anywhere

else. And, furthermore, that this line, as already indicated, is
the position assumed by the wave AC at the instant when the

region C has reached the point B. For there is no other line

below the plane AB, which, like BN, is a common tangent to

all these secondary waves.

Accordingly, if one wishes to discover through what in-

termediate steps the wave AC reached the position BN, he has

KO only to draw, in the same figure, the straight lines

KL parallel to BN, and all the lines

parallel to ,AC. He will

CA thus see that the wave

passes from a straight line into the

successive broken lines LKO, reassuming the form of a straight line in the position BN. From what has preceded this will be

so evident as to need no further explanation.

If, now, using the same

C

figure, we draw EAF nor-

mal to the plane AB at the

point A, and draw DA at

right angles to the wave AC,

the incident ray of light will

then be represented by DA;

and AN, which is drawn per-

pendicular to BN, will be

the refracted ray; for these

rays are merely the straight

ffiff- 10

lines along which the parts of the waves travel.

36

THE WAVE-THEORY OF LIGHT

From the foregoing it is easy to deduce the principal law of

DAE refraction, viz., that the sine of the angle

always bears a

constant ratio of the sine of the angle NAF, whatever may be

the direction of the incident ray, and that the ratio is the

same as that which the speed of the waves in the medium on

AE the side

bears to their speed on the side AF.

AB For if we consider

as the radius of a circle, the sine

ABN of the angle BAG is BC, and the sine of the angle

_is

AN.

DAE But the angles BAG and

are equal; for each is

the complement of CAE.

ABN And the angle

is equal to

NAF, since each is the complement of BAN". Hence the sine

NAF DAE of the angle

is to the sine

as BC is to AN. But

AN the ratio of BO to

is the same as that of the speeds of

AE light in the media on the side towards

and the side tow-

DAE ards AF, respectively ; hence, also, the sine of the angle

NAF bears to the sine of the angle

the same ratio as these two

speeds of light.
In order to follow the refracted ray when the light-waves en-
ter a body which transmits them .more rapidly than the body from which they emerge (say in the ratio of 3 to 2), it is necessary only to repeat the same construction and the same demonstration which we have just been

using, substituting, however,
f in place of f . And we find,
by the same logical process,
employing this other figure, that when the region of
the wave AO reaches the

point B of the surface AB, the whole wave AC will have

advanced to the position BN,

such that the ratio of BC, per-

pendicular to AC, is to AN,

perpendicular to BN, as 2 is to 3. The same ratio will

Fig. 11

EAD also hold between the sine of the angle

and the sine of

the angle FAN.

The reciprocal relations between the refractions of a ray

on entering and on emerging from one and the same me-

NA dium is thus made evident. If the ray

is incident upon

the exterior surface AB, and is refracted into AD, then

37

MEMOIRS ON

DA the ray

on emerging from the medium will be refracted

into AN".

We are now able to explain a remarkable phenomenon which

DA occurs in this refraction. When the incident ray

exceeds

a certain inclination it loses its ability to pass into the other

DAQ medium. Because if the angle

OBA or

is such that, in

the triangle AOB, OB is equal to or greater than f of AB, then

AN, being equal to or greater than AB, can no longer form one

BN side of the triangle ANB. ' Therefore the wave

does not

AN exist, and consequently there can be no line

drawn at right

DA angles to it. And thus the incident ray

cannot penetrate

the surface AB.

When the wave-speeds are in the ratio of % to 3, as in the

case of glass and air, which we have considered, the angle

DAQ DA must exceed 48 11' if the ray

is to emerge. And

when the ratio of speeds is that of 3 to 4, as is almost exactly

DAQ the case in water and air, this angle

must be greater than

41 24'. And this agrees perfectly with experiment.

But one may here ask why no light penetrates the surface,
since the encounter of the wave AC against the surface AB
must produce some motion in the medium on the other side. The answer is simple, if we recall what has already been said. For although an infinite number of secondary waves may be started into the medium on the other side of AB, these waves

at no time have a common tangent* line, either straight or
curved. There is thus no line which marks the limit to which

the wave AC has been transmitted beyond the plane, AB, nor is

there any line in which the motion has been sufficiently con-

centrated to produce light.
In the following manner one may easily recognize the fact
that, when OB is greater than f AB, the waves beyond the
K plane AB have no common tangent. About the centres
describe circles having radii respectively equal to f LB. These
circles will enclose one another and will each pass beyond the

point B.

DAQ It is to be noted that just as soon as the angle

becomes

DA too small to allow the refracted ray

to pass into, the other

AB medium, the internal reflection which occurs at the surface

increases rapidly in brilliancy, as may be easily shown by means

of a triangular prism. In terms of our theory, we may thus

DAQ explain this phenomenon : While the angle

is still large

38

THE WAVE-THEORY OF LIGHT

DA enough for the ray

to be transmitted, it is evident that the

light from the wave-front AC will be concentrated into a much

shorter line when it reaches the position BN. It will be seen

BN also that the wave-front

grows shorter in proportion as the

DAQ angle CBA or

becomes smaller, until finally, when the

BN limit indicated above is reached,

is reduced to a point.

That is to say, when the region about C, on the wave AC,
reaches B, the wave BN", which is the wave AC after trans-

mission, is entirely compressed into this same point B ; and, in

H K like manner, when the region about has reached the point

AH the part

is completely reduced to this same point K. It

follows, therefore, that in proportion as the direction of propa-
gation of the wave AC happens to coincide with the surface AB,

so will be the quantity of motion along this surface.
Now this motion must necessarily spread into the transparent

body and also greatly reinforce the secondary waves which pro-

duce internal reflection at the face AB, according to the laws

of this reflection explained above.

And since a small diminution in the angle of incidence is

BN sufficient to reduce the wave -front

from a fairly large

quantity to zero (for if this angle in the case of glass be

BAN 49 11', the angle

amounts to as much as 11 21'; but if

DAQ this same angle

be diminished by one degree only, the

angle BAN becomes zero and the wave-front BN is reduced to

a point), it follows that the internal reflection occurs suddenly,

passing from comparative darkness to brilliancy at the instant when the angle of incidence assumes a value which no longer

permits refraction.

Now as to ordinary external reflection, i. e., reflection which

DAQ occurs when the angle of incidence

is still large enough

to allow the refracted ray to pass through the face AB, this

reflection must be from the particles which bound the trans-

parent body on the outside, apparently from particles of air

and from others which are mixed with, but are larger than, the

ether particles.
On the other hand, external reflection from bodies is pro-

duced by the particles which compose these bodies, and which

are larger than those of the ether, since the ether flows through

the interstices of the body.

It must be confessed that we here find difficulty in explain-

ing the experimental fact that internal reflection occurs even

39

MEMOIRS ON

where the particles of air can cut no figure, as, for instance, in vessels and tubes from which the air has been exhausted.

Experiment shows further that these two reflections are of

almost equal intensity, and that in various transparent bodies

this intensity increases directly as the refractive index. Thus

we see that reflection from glass is stronger than that from

water, while in turn that from diamond is stronger than that

from glass.

I shall conclude this theory of refraction by demonstrating a

remarkable proposition depending upon it, namely, that when

a ray of light passes from one point to another, the two points

lying in different media, refraction at the bounding surface

occurs in such a way as to make the time required the least

possible ; and exactly the same thing occurs in reflection at a

plane surface. M. Fermat discovered this property of refrac-

tion, believing with us and in opposition to M. Descartes that

light travels more slowly through glass than through air.

But, besides this, he assumed what we have just proved from

the fact that the velocities in the two media are different, viz.,

that

the ratio

of

the

sines is

a

constant ;

or,

what

amounts

to

the same thing, he assumed, besides the different velocities,

that

the

time

employed

was

a

minimum ;

and from this he

derived the constancy of the sine ratio.

His* demonstration, which may be found in his works and in

the correspondence of M. Descartes, is very long. It is for this

reason that I here offer a simpler and easier one.

KF A Let

represent a plane surface ; imagine the point in

the medium through which the light travels more rapidly, say

air ;

the

point C lies

in

anoth-

er, say water, in which the speed

of light is less. Let us sup-

pose that a ray passes from A,

through B, to 0, suffering re-

fraction at B, according to the

law above demonstrated ;

or,

what is the same thing, having

drawn PBQ perpendicular to

the surface, the sine of the

ABP angle

is to the sine of the

angle CBQ in the same ratio as

the speed of light in the medium

40

THE WAVE-THEORY OF LIGHT

A containing is to the speed in the medium containing C. It

remains to show that the time required for the light to traverse
AB and BC taken together is the least possible. Let us assume

that the light takes some other path, say AF, FC, where F, the

point at which refraction occurs, is more distant than B from A.

Draw

AO

perpendicular

to

AB,

and

FO

BA parallel to

;

BH

perpendicular to FO, and FG perpendicular to BC. Since, now,

the angle HBF is equal to PBA, and the angle BFG is equal to

HBF QBC, it follows that the sine of the angle

will bear to the

sine of BFG the same ratio as the speed of light in the medium

A bears to the speed in the medium 0. But if we consider BF

the radius of a circle, then sines are represented by the lines

HF, BG.

BG Accordingly, the lines HF,

are in the ratio of

these speeds. If, therefore, we imagine OF to be the incident
H ray, the time of passage from to F will be the same as the

time of passage from B to G in the medium C.

But the time from A to B is equal to the time from to H.

A Hence the time from to F is the same as the time from to

G, via B. Again, the time along FC is greater than the time

along

GC ;

and

hence

the

time

along

the

route

OFC

is greater

than that along the path ABC. But AF is greater than OF;

AFC hence, a fortiorij the time along

is greater than that

along ABC.

Let us now assume that the ray passes from A to C by the

A route AK, KC, the point of refraction, K, being nearer to

CN than is B. Draw

perpendicular to

BC ;

KN" parallel

to BC ;

BM KN perpendicular to

KL and
;

perpendicular to BA.

KM Here BL and

BKL represent the sines of the angles

and

KBM that is, the angles PBA and QBC ; and hence they are

A in the same ratio as the speeds of light in the media and C

respectively. The time, therefore, from L to B is equal to the
K M time from to ; and, since the time from B to C is equal to M the time from to N, the time by the path LBC is the same K as the time via KMN. But the time from A to is greater

A than the time from to L, and, therefore, the time by the

AKN route

is greater than the route ABC.

KC Not only so, but since

is greater than KN, the time by

AKC the path

will be so much the greater than by the path

ABC. Hence follows that which was to be proved, namely,

ABC that the time along the path

is the least possible.

41

MEMOIRS ON

BIOGRAPHICAL SKETCH

WHILE there are no sharp lines in nature, there is a very
true sense in which the year 1642, marking the death of

Galileo and the birth of Newton, serves as a line of demar-

cation between the foundation and the superstructure of mod-

ern physics.

Galileo, by his careful study of gravitation, by his clear grasp

of force as determining acceleration, by his careful search after

causes and their respective effects, by his profound faith in experiment, had more than cleared the ground for the builders of modern physics. The rapid rise of this structure at the hands of Newton and his brilliant contemporaries, Boyle,
Leibnitz, Bonier, Du Fay, Bradley, and Hooke, marks a dis-
tinctly modern era compared with that of Galileo.

The work of Christiaan Huygens, the "Dutch Archimedes,"

occupies, as regards both time and character, a position inter-

mediate between these two periods. He was born at The

A Hague in 1629, and died there in 1695.

splendid ancestry,

three years of university training at Leyden and Breda, much

travel, and a rare group of associates, combined to give him

an education which left little to be desired. Most of his life

was spent in Holland, but for the fifteen years following 1666 he lived and worked in Paris, where he was the guest of Louis
XIV. and the then recently founded French Academy of Sciences. This was for him a happy period of great activity, and
it was only in anticipation of the revocation of the Edict of
Nantes, in 1685, that he returned to his own country, where in private retirement and study he spent most of his remain-

ing years. His intellectual achievements fall into three not very dis-

tinct departments of science namely, mathematics, physics, and physical astronomy. In mathematics, his chief accom-

plishments refer to
(a) The quadrature of conies. (#) The theory of probabilities.
A (c) discussion of the evolutes and involutes of curves and
the introduction of the idea of the envelope of a moving

straight line. 42

THE WAVE-THEORY OF LIGHT
In physics he gave
(a) A general solution of the problem of the Compound Pen-
dulum, and in the demonstration enunciated the very general principle that in any mechanical system acting under gravity the centre of gravity can never rise to a point higher than that from which it fell a principle which we now recognize as a special case of the law that the potential energy of any mechanical system tends to a minimum. (b) The invention of the pendulum clock and its application to the measurement of gravity at various points on the
earth's surface.
(c) An accurate description of the behavior of bodies in
collision.
(d) The laws governing centrifugal forces. (e) The undulatory theory of light arid its application to
the explanation of reflection, ordinary refraction, and double refraction.
Among his contributions to physical astronomy are
(a) The construction of the first powerful telescope of the
refracting kind.
(b) The discovery of the rings of Saturn and its sixth
satellite.
(c) Improvements in the methods of grinding lenses and the addition of a tube to the object-glass and another to
the eye-piece of the aerial telescope. All his mechanical inventions are characterized by practica-
bility, and all his intellectual work by clearness and elegance. Those who wish a more detailed account of his activity will
find it in the superb edition of his works* recently published by the Societe Hollandaise des Sciences, while that delightful sketch of his life and work given 'by Dr. Bosschaf should be read by every one.
* (Euvres Computes de Christiaan Huygens (La Haye : Martin us Nijhoff, 1888 to 19).
f Bosscha : Christiaan Huygens, Rede am 200sten Ged^chtnistage seines
Lebensende. Ubersetzt von Engelmann. (Eugelmann : Leipzig, 1895),
pp. 77. 43
LIBRA >*-' ov
Oc

ON THE THEORY OF LIGHT AND
COLOES
From the Philosophical Transactions for 1802, p. 12.
AN ACCOUNT OF SOME CASES OF THE
PRODUCTION OF COLORS NOT HITHERTO DESCRIBED
From the Philosophical Transactions for 1802. p. 387.
EXPERIMENTS AND CALCULATIONS
RELATIVE TO PHYSICAL OPTICS
From the Philosophical Transactions for 1804.
.BY
THOMAS YOUNG.
These three papers are reprinted in Young's Miscellaneous Works, vol. i., and also in his Lectures on Natural Philosophy and Mechanical Arts.
45

CONTENTS

PAGE

General Statement of Wave - Theory, including the Principle of Inter-

ference

47

Diffraction in che Shadow of a Narrow Obstacle

,

62

Observations on the Interference Bands in the Shadow of a Narrow

Obstacle. . .

68

46

ON THE THEORY OF LIGHT AND
COLORS*
A BAKERIAN LECTURE
Read November 12, 1801.

ALTHOUGH the invention of plausible hypotheses, indepen-

dent of any connection with experimental observations, can be of

very little use in the promotion of natural knowledge, yet the discovery of simple and uniform principles, by .which a great

number of apparently heterogeneous phenomena are reduced to coherent and universal laws, must ever be allowed to be of

considerable importance towards the improvement of the hu-
man intellect.

The object of the present dissertation is not so much to pro-

pose any opinions which are absolutely new, as to refer some

theories, which have been already advanced, to their original
inventors, to support them by additional evidence, and to apply them to a great number of diversified facts, which have hitherto been buried in obscurity. Nor is it absolutely necessary in this instance to produce a single new experiment ; for of experiments there is already an ample store, which are so much

the more unexceptionable as they must have been conducted

without the least partiality for the system by which they will be explained ; yet some facts, hitherto unobserved, will be brought forward, in order to show the perfect agreement of

that system with the multifarious phenomena of nature.

The

optical

observations

of Newton are yet

unrivalled ;

and,

excepting some casual inaccuracies, they only rise in our estimation as we compare them with later attempts to improve on

* From the Philosophical Transactions for 1802, p. 12
47

MEMOIRS ON

A them.

further consideration of the colors of thin plates, as

they are described in the second book of Newton's Optics, has

converted that prepossession which I before entertained for the

undulatory system of light into a very strong conviction of its

truth and sufficiency, a conviction which has been since most

strikingly confirmed by an analysis of the colors of striated

substances. The phenomena of thin plates are indeed so sin-

gular that their general complexion is not without great diffi-

culty reconcilable to any theory, however complicated, that

has

hitherto

been

applied

to

them ;

and

some

of

the

principal

circumstances have never been explained by the most gratui-

tous assumptions; but it will appear that the minutest particu-

lars of these phenomena are not only perfectly consistent with

the theory which will now be detailed, but that they are all the

necessary consequences of that theory, without any auxiliary suppositions ; and this by inferences so simple that they become particular corollaries, which scarcely require a distinct

enumeration.

A more extensive examination of Newton's various writings

has shown me that he was in reality the first that suggested

such a theory

as

I

shall

endeavor

to

maintain ;

that

his

own

opinions varied less from this theory than is now almost univer-

sally supposed ; and that a variety of arguments have been ad-

vanced, as if to confute him, which may be found nearly in a

similar

form

in his

own

works ;

and

this

by

no

less

a

math-

ematician than Leonard Euler, whose system of light, as

far as it is worthy of notice, either was, or might have been,

wholly borrowed from Newton, Hooke, Hnygens, and Male-

branche.

Those who are attached, as they may be with the greatest justice, to every doctrine which is stamped with the Newtonian
approbation, will probably be disposed to bestow on these con-
siderations so much the more of their attention, as they appear to coincide more nearly with Newton's own opinions. For
this reason, after having briefly stated each particular po-
sition of my theory, I shall collect, from Newton's various
writings, such passages as seem to be the most favorable to its admission; and although I shall quote some papers which may
be thought to have been partly retracted at the publication of the Optics, yet I shall borrow nothing from them that can be
supposed to militate against his rnaturer judgment.
48

THE WAVE-THEORY OF LIGHT

HYPOTHESIS I

A luminiferous ether pervades the universe, rare and elastic
in a high degree.

PASSAGES FROM KEWTOtf

"The hypothesis
his own/' that is,

certainly has Dr. Hooke's,

a
"

much greater affinity with
hypothesis than he seems

to be aware of; the vibrations of the ether being as useful and

necessary in this as in his." Phil. Trans., vol. vii., p. 5087.

Abr., vol. i., p. 145. Nov., 1672.
" To proceed to the hypothesis : first, it is to be supposed therein that there is an ethereal medium, much of the same

constitution with air, but far rarer, subtler, and more strongly

elastic. It is not to be supposed that this medium is one uni-

form matter, but compounded, partly of the main phlegmatic

body of ether, partly of other various ethereal spirits, much after the manner that air is compounded of the phlegmatic

body of air, intermixed with various vapors and exhalations :

for the electric and magnetic effluvia and gravitating princi-

ple seem to argue such variety." BIRCH, Hist, of R. 8., vol.

iii., p. 249, Dec., 1675.
" Is not the heat (of the warm room) conveyed through the vacuum by the vibrations of a much subtler medium than air ? And is not this medium the same with that medium by
which light is refracted and reflected, and by whose vibrations
light communicates heat to bodies, and is put into fits of easy
reflection and easy transmission ? And do not the vibrations of this medium in hot bodies contribute to the intenseness and

duration of their heat ? And do not hot bodies communicate

their heat to contiguous cold ones by the vibrations of this me-

dium propagated from them into the cold ones ? And is not this

medium exceedingly more rare and subtle than the air, and ex-

ceedingly more elastic and active ? And doth it not readily pervade all bodies ? And is it not, by its elastic force, expanded

through all the heavens ? May not planets and comets, and

all the gross bodies, perform their motions in this ethereal me-

dium ? And may not its resistance be so small as to be incon-

siderable ? For instance, if this ether (for so I will call it)

should be supposed 700,000 times more elastic than our air,

and above 700,000 times more rare, its resistance would be

D

49

MEMOIRS ON

about 600,000,000 times less than that of water. And so small a resistance would scarce make any sensible alteration in the
motions of the planets in ten thousand years. If any one
would ask how a medium can be so rare, let him tell me how
an electric body can by friction emit an exhalation so rare and
subtle, and yet so potent? And how the effluvia of a mag-
net can pass through a plate of glass without resistance, and yet turn a magnetic needle beyond the glass ?" Optics, Qu. 18, 22.
HYPOTHESIS II

Undulations are excited in this ether 'whenever a body becomes luminous.

Scholium. I use the word undulation in preference to vibration, because vibration is generally understood as implying a motion which is continued alternately backward and for-
ward by a combination of the momentum of the body with an
accelerating force, and which is naturally more or less permanent; but an undulation is supposed to consist in vibratory motion transmitted successively through different parts of a medium without any tendency in each particle to continue its motion, except in consequence of the transmission of succeeding undulations from a distinct vibrating body; as in the air the vibrations of a chord produce the undulations constituting
sound.
PASSAGES FROM NEWT02ST

" Were I to assume an hypothesis, it should be this, if pro-

pounded more generally, so as not to determine what light is

further than that it is something or other capable of e-xciting

vibrations in the ether ;

for

thus

it will

become so general

and

comprehensive of other hypotheses as to leave little room for

new ones to be invented." BIRCH, Hist, of R. S., vol. iii., p.

249. Dec., 1675.
" In the second place, it is to be supposed that the ether is a

vibrating medium like air, only the vibrations far more swift

and

minute ;

those

of

air,

made

by

a

man's

ordinary

voice,

succeeding one another at more than half a foot or a foot dis-

tance, but those of ether at a less distance than the hundred-
thousandth part of an inch. And as in air the vibrations are

50

THE WAVE-THEORY OF LI
some larger than others, but yet all equally swift (for in a ring of bells the sound of every tone is heard at two or three miles distance in the same order that the bells are struck), so, I suppose, the ethereal vibrations differ in bigness, but not in swiftness. Kow, these vibrations, besides their use in reflection and
refraction, may be supposed the chief means by which the parts
of fermenting or putrefying substances, fluid liquors, or melted, burning, or other hot bodies, continue in motion." BIRCH, Hist, of R. S., vol. iii., p. 251, Dec., 1675.
"When a ray of light falls upon the surface of any pellucid body, and is there refracted or reflected, may not waves of
vibrations, or tremors, be thereby excited in the refracting or
reflecting medium ? And are not these vibrations propagated from the point of incidence to great distances ? And do they
not overtake the rays of light, and by overtaking them successively, do not they put them into the fits of easy reflection and easy transmission described above ?" Optics, Qu. 17.
"Light is in fits of easy reflection and easy transmission
before its incidence on transparent bodies. And probably it is
put into such fits at its first emission from luminous bodies, and continues in them during all its progress/' Optics, Book ii.,
part iii., prop. 13.
HYPOTHESIS III
The sensation of different colors depends on the different frequency of vibrations excited by light in the retina.
PASSAGES FROM NEWTON
"The objector's hypothesis, as to the fundamental part of it,
is not against me. That fundamental supposition is, that the parts of bodies, when briskly agitated, do excite vibrations in the ether, which are propagated every way from those bodies in straight lines, and cause a sensation of light by beating and dashing against the bottom of the eye, something after the manner that vibrations in the air cause a sensation of sound
by beating against the organs of hearing. Now, the most free and natural application of this hypothesis to the solution of phenomena I take to be this that the agitated parts of bodies, according to their several sizes, figures, and motions, do excite
vibrations in the ether of various depths or bignesses, which,
51

MEMOIRS ON

being promiscuously propagated through that medium to our

eyes, effect in us a sensation of light of a white color; but if

by any means those of unequal bignesses be separated from one

another, the largest beget a sensation of a red color; the least,

or shortest, of a deep violet, and the intermediate ones of inter-

mediate

colors ;

much

after

the

manner

that

bodies,

according

to their several sizes, shapes, and motions, excite vibrations in

the air of various bignesses, which, according to those bignesses,
make several tones in sound : that the largest vibrations are

best able to overcome the resistance of a refracting superficies,

and

so break

through

it

with

least

refraction ;

whence

the vi-

brations of several bignesses that is, the rays of several colors,

which are blended together in light must be parted from one

another by refraction, and so cause the phenomena of prisms

and

other

refracting

substances ;

and

that it depends on the

thickness of a thin transparent plate or bubble whether a vi-

bration shall be reflected at its further superficies or transmit-

ted ;

so

that,

according

to

the

number of

vibrations

interced-

ing the two superficies, they may be reflected or transmitted for many successive thicknesses. And since the vibrations which

make blue and violet are supposed shorter than those which

make red and yellow, they must be reflected at a less thickness

of the plate, which is sufficient to explicate all the ordinary

phenomena of those plates or bubbles, and also of all natural

bodies, whose parts are like so many fragments of such plates.

These seem to be the most plain, genuine, and necessary con-

ditions of this hypothesis; and they agree so justly with my

theory that if the animadversor think fit to apply them, he

need

not,

on

that

account,

apprehend

a

divorce

from

it ;

but

yet, how he will defend it from other difficulties I know not."-

Phil Trans., vol. vii., p. 5088. Abr., vol. i., p. 145. Nov., 1672.
"To explain colors, I suppose that as bodies of various

sizes, densities, or sensations do by percussion or other action

excite sounds of various tones, and consequently vibrations in

the air of different bigness, so the rays of light, by impinging

on the stiff refracting superficies, excite vibrations in the

ether of various bigness, the biggest, strongest, or most po-

tent rays, the largest

vibrations ;

and

others

shorter, according

to their bigness, strength, or power : and therefore the ends of

the capillamenta of the optic nerve, which pave or face the retina, being such refracting superficies, when the rays impinge

52

THE WAVE-THEORY OF LIGHT

upon them, they must there excite these vibrations, which vi-

brations (like those of sound in a trunk or trumpet) will run

along the aqueous pores or crystalline pith of the capillamenta,

through

the

optic

nerves, into

the

sensorium ;

and

there, I

suppose, affect the sense with various colors, according to their

bigness

and

mixture ;

the

biggest

with

the

strongest colors,

reds and yellows ; the least with the weakest

blues and violets ;

the middle with green, and a confusion of all with white
much after the manner that, in the sense of hearing, nature

makes use of aerial vibrations of several bignesses to generate

sounds of divers tones, for the analogy of nature is to be ob-

served." BIRCH, Hist, of R. 8., vol. iii., p. 262, Dec., 1675.

' ' Considering the lastingness of the motions excited in the bot-
tom of the eye by light, are they not of a vibrating nature ? Do

not the most refrangible rays excite the shortest vibrations, the

least refrangible the largest ? May not the harmony and dis-

cord of colors arise from the proportions of the vibrations

propagated through the fibres of the optic nerve into the brain,

as the harmony and discord of sounds arise from the propor-

tions of the vibrations of the air ?" Optics, Qu. 16, 13, 14.

[Scholium omitted.]

HYPOTHESIS IV

All material bodies have an attraction for the ethereal medium, by means of which it is accumulated within their substance, and for a small distance around them, in a state of greater
density but not of greater elasticity.

It has been shown that the three former hypotheses, which

may be called essential, are literally parts of the more compli-

cated Newtonian system. This fourth hypothesis differs per-

haps, in some degree from any that have been proposed by

former authors, and is diametrically opposite to that of New-

ton ;

but

both

being

in

themselves

equally

probable, the op-

position is merely accidental, and it is only to be inquired

which is the best capable of explaining the phenomena. Other

suppositions might perhaps be substituted for this, and there-

fore I do not consider it as fundamental, yet it appears to be

the simplest and best of any that have occurred to me.

53

OK THli
UNIVERSIT

MEMOIRS ON
PROPOSITION I
All impulses are propagated in a homogeneous elastic medium with an equable velocity.
Every experiment relative to sound coincides with the observation already quoted from Newton, that all undulations are propagated through the air with equal velocity ; and this is further confirmed by calculations. (LAGRANGE, Misc. Taur.,
vol. i., p. 91. Also, -much more concisely, in my syllabus of
a course of lectures on Natural and Experimental Philosophy, about to be published. Art. 289.) If the impulse be so great as materially to disturb the density of the medium, it will be no longer homogeneous; but, as far as concerns our
senses, the quantity of motion may be considered as infinitely
small. It is surprising that Euler, although aware of the matter of fact, should still have maintained that the more frequent undulations are more rapidly propagated. (Tlieor. mus. and Conject. phys.} It is possible that the actual velocity of the
particles of the luminiferous ether may bear a much less pro-
portion to the velocity of the undulations than in sound, for
light maybe excited by the motion of a body moving at the rate
of only one mile in the time that light moves a hundred millions. Scholium 1. It has been demonstrated that in different me-
diums the velocity varies in the snbduplicate ratio of the force directly and of the density inversely. (Misc. Taur., vol. L, p. 91. Young's Syllabus. Art. 294.)
Scholium 2. It is obvious, from the phenomena of elastic bodies and of sounds, that the undulations may cross each other without interruption ; but there is no necessity that the
various colors of white light should intermix their undulations, for, supposing the vibrations of the retina to continue but a five-hundredth of a second after their excitement, a mill-
ion undulations of each of a million colors may arrive in dis-
tinct succession within this interval of time, and produce the same sensible effect as if all the colors arrived precisely at the same instant.
PROPOSITION II
An undulation conceived to originate from the vibration of a
single particle must expand through a homogeneous medium
54

THE WAVE-THEORY OF LIGHT

in a spherical form, but with different quantities of motion in different parts.

For, since every impulse, considered as positive or negative,

is propagated with a constant velocity, each part of the undula-

tion must in equal times have passed through equal distances

from the vibrating-point. And, supposing the vibrating particle,

in the course of its motion, to proceed forward to a small dis-

tance in a given direction, the principal strength of the undula-

tion will naturally be

straight

before it ;

behind

it the motion

will be equal in a contrary direction ; and at right angles to

the line of vibration the undulation will be evanescent.

Now, in order that such an undulation may continue its

progress to any considerable distance, there must be in each

part of it a tendency to preserve its own motion in a right line

from

the

centre ;

for

if

the

excess

of

force

at

any part

were

communicated to the neighboring particles, there can be no

reason why it should not very soon be equalized throughout,

or, in other words, become wholly extinct, since the motions in

contrary directions would naturally destroy each other. The

origin of sound from the vibration of a chord is evidently of

this nature ;

on the contrary, in a circular wave

of water every

part is at the same instant either elevated or depressed. It may be difficult to show mathematically the mode in which this in-

equality of force is preserved, but the inference from the mat-

ter of fact

appears to be

unavoidable ;

and

while the science

of

hydrodynamics is so imperfect that we cannot even solve the

simple problem of the time required to empty a vessel by ;i

given aperture, it cannot be expected that we should be able

to account perfectly for so complicated a series of phenomena

as those of elastic fluids. The theory of Huygens, indeed, ex-

plains the circumstance in a manner tolerably satisfactory. He supposes every particle of the medium to propagate a distinct

undulation in all directions, and that the general effect is only

perceptible where a portion of each undulation conspires in

direction at the same instant ;

and it is easy to

show that

sucli

a general undulation would in all cases proceed rectilinearly,

with proportionate force ; but, upon this supposition, it seems

to follow that a greater quantity of force must be lost by the

divergence of the partial undulations than appears to be con-

sistent with the propagation of the effect to any considerable

55

MEMOIRS ON

distance ;

yet it

is

obvious

that

some

such

limitation

of the

motion must naturally be expected to take place, for if the in-

tensity of the motion of any particular part, instead of co^itinu-

ing to be propagated straight forward, were supposed to affect

the intensity of a neighboring part of the undulation, an im-

pulse must then have travelled from an internal to an external circle in an oblique direction, in the same time as in the direc-

tion of the radius, and consequently with a greater velocity,

against the first proposition. In the case of water the velocity is by no means so rigidly limited as in that of an elastic medium.

Yet it is not necessary to suppose, nor is it indeed probable, that

there is absolutely not the least lateral communication of the

force of the undulation, but that, in highly elastic mediums,

this communication is almost insensible. In the air, if a chord

be perfectly insulated so as to propagate exactly such vibra-
tions as have been described, they will, in fact, be much less

forcible than if the chord be placed in the neighborhood of a

sounding-board, and probably in some measure because of this

lateral communication of motions of an opposite tendency.
And the different intensity of different parts of the same circular undulation may be observed by holding a common tun-

ing-fork at arm's-length, while sounding, and turning it, from

a plane directed to the ear, into a position perpendicular to

that plane.

PROPOSITION III
A portion of a spherical undulation, admitted through an
aperture into a quiescent medium, toill proceed to be further propagated rectilinearly in concentric superficies, terminated laterally by weak and irregular portions of newly diverging
undulations.

At the instant of admission the circumference of each of

the undulations may be supposed to generate a partial undula-

tion, filling up the nascent angle between the radii and the sur-

face

terminating

the medium ;

but

no

sensible addition

will

be

made to its strength by a divergence of motion from any other

parts of the undulation, for want of a coincidence in time, as

has already been explained with respect to the various force of

a spherical undulation. If, indeed, the aperture bear but a small

proportion to the breadth of an undulation, the newly gener-

56

THE WAVE-THEORY OF LIGHT

ated undulation may nearly absorb the whole force of the por-

tion admitted ;

and

this

is

the

case

considered

by Newton

in

the Principia. But no experiment can be made under these

circumstanced with light, on account of the minuteness of its

undulations and the interference of inflection; and yet some

faint radiations do actually diverge beyond any probable lim-

its of inflection, rendering the margin of the aperture distinctly

visible in all directions. These are attributed by Newton to

some unknown cause, distinct from inflection (Optics, Book

iii., obs. 5)/and they fully answer the description of this

proposition.

Let the concentric lines in Fig. 13 represent the con-

temporaneous situation of similar parts of a number of succes-

sive undulations diverging from the point A; they will also

represent the successive situations of each individual undula-

tion: let the force of each undulation be represented by the

ABO breadth of the line, and let the cone of light

be admitted

through the aperture BO; then the principal undulations will proceed in a rectilinear direction towards GrH, and the faint
radiations on each side will diverge from B

and as centres, without receiving any ad-

ditional force from any intermediate point
D of the undulation, on account of the in-

DE equality of the lines

and DF. But if

we allow some little lateral divergence from

the extremities of the undulations, it must

diminish their force, without adding materi-

ally to that of the dissipated light ; and their -

termination, instead of the right line BG,

will assume the form OH, since the loss of

force must be more considerable near to

than at greater distances. This line corre-

sponds with the boundary of the shadow

in

Newton's first

observation,

Fig.

13 ;

and

it is much more probable that such a dissi-

pation of light was the cause of the increase

of the shadow in that observation than that

it was owing to the action of the inflecting

atmosphere, which must have extended a

thirtieth of an inch each way in order to pro-

duce it ;

especially when it

is

considered

that

57

Fig. 13

MEMOIRS ON

the shadow was not diminished by surrounding the hair with a denser medium than air, which must in all probability have weakened and contracted its inflecting atmosphere. In other

circumstances the lateral divergence might appear to increase, instead of diminishing, the breadth of the beam.
As the subject of this proposition has always been esteemed the most difficult part of the undulatory system, it will be proper to examine here the objections which Newton has

grounded upon it.
''To me the fundamental supposition itself seems impossi-
ble namely, that the waves or vibrations of any fluid can, like
the rays of light, be propagated in straight lines, without a continual and very extravagant spreading and bending every way into the quiescent medium, where they are terminated by it. I mistake if there be not both experiment and demonstra-

tion to the contrary." Phil. Trans., vol. vii., p. 5089. Abr., vol. L, p. 146. Nov. 1672.
" Motus omnis per flu id urn. propagatus divergit a recto

tramite in spatia immota.",
"Quoniam medium ibi," in the middle of an undulation admitted, " densius est, quam in spatiis hinc inde, dilatabit sese

tarn versus spatia utrinque sita, quam versus pulsum rariora

intervalla ;

eoque

pacto

pulsns eadem fere celeritate sese in

medii partes

quiescentes

hinc

inde

relaxare

debent ;

ideoqne

spatium totum occupabunt Hoc experimur in sonis." Prin-

cip., lib. ii., prop. 42.
"Are not all hypotheses erroneous in which light is sup-
posed to consist in pression or motion propagated through a
fluid medium ? If it consisted in pression or motion, propa-
gated either in an instant, or in time, it would bend into the shadow. For pression or motion cannot be propagated in a fluid in right lines beyond an obstacle which stops part of the motion, but will bend and spread every way into the quiescent
medium which lies beyond the obstacle. The waves on the

surface of stagnating water passing by the sides of a broad obstacle which stops part of them, bend afterwards, and dilate themselves gradually into the quiet water behind the obstacle. The waves, pulses, or vibrations of the air, wherein sounds
consist, bend manifestly, though not so much as the waves of water. For a bell or a cannon may be heard beyond a hill
which intercepts the sight of the sounding body ; and sounds
58

THE WAVE-THEORY OF LIGHT

are propagated as readily through crooked pipes as straight

ones. Bat light is never known to follow crooked passages

nor to bend into the shadow. For the fixed stars, by the inter-

position of any of the planets, cease to be seen. And so do

the parts of the sun by the interposition of the moon, Mer-

cury, or Venus. The rays which pass very near to the edges

of any body are bent a little by the action of the body ; but

this bending is not towards but from the shadow, and is per-

formed only in the passage of the ray by the body, and at a

very small distance from it. So soon as the ray is past the

body it goes right on." Optics, Qu. 28.
Now the proposition quoted from the Principia does not di-

rectly contradict this proposition ; for it does not assert that

such

a motion

must diverge

equally in

all

directions ;

neither

can it with truth be maintained that the parts of an elastic

medium communicating any motion must propagate that mo-

tion equally in all directions. All that can be inferred by rea-

soning is that the marginal parts of the undulation must be

somewhat weakened and that there must be a faint divergence

in

every

direction ;

but

whether

either

of these

effects

might

be of sufficient magnitude to be sensible could not have been

inferred from argument, if the affirmative had not been ren-

dered probable by experiment.

As to the analogy with other fluids, the most natural infer-

ence from it is this : "The waves of the air, wherein sounds

consist, bend manifestly, though not so much as the waves of

water "; water being an inelastic and air a moderately elastic

medium ;

but

ether

being

most

highly elastic,

its

waves

bend

very far less than those of the air, and therefore almost imper-

ceptibly. Sounds are propagated through crooked passages,

because their sides are capable of reflecting sound, just as light

would be propagated through a bent tube, if perfectly polished

within.

The light of a star is by far too weak to produce, by its faint

divergence, any visible illumination of the margin of a planet

eclipsing

it ;

and

the

interception

of

the

sun's

light

by

the

moon is as foreign to the question as the statement of inflec-

tion is inaccurate.

To the argument adduced by Huygens in favor of the rectilinear propagation of undulations Newton has made no reply; perhaps because of his own misconception of the nature of the
59

MEMOIRS ON

motions of elastic mediums, as dependent on a peculiar law of vibration, which has been corrected by later mathematicians.
On the whole, it is presumed that this proposition may be
safely admitted as perfectly consistent with analogy and with
experiment.

PROPOSITION IV
When an undulation arrives at a surface which is the limit of mediums of different densities, a partial reflection takes
place proportionate in force to the difference of the densities.

This may be illustrated, if not demonstrated, by the analogy
of elastic bodies of different sizes. " If a smaller elastic body
strikes against a larger one, it is well known that the smaller is

reflected more or less powerfully, according to the difference of

their magnitudes : thus, there is always a reflection when the

rays

of

light pass

from a

rarer

to

a

denser

stratum

of

ether ;

and frequently an echo when a sound strikes against a cloud.

A greater body striking a smaller one propels it, without losing

all its motion : thus, the particles of a denser stratum of ether

do not impart the whole of their motion to a rarer, but, in their

effort to proceed, they are recalled by the attraction of the

refracting

substance

with

equal

force ;

and

thus a reflection is

always secondarily produced when the rays of light pass from

a denser to a rarer stratum." But it is not absolutely necessary to suppose an attraction in the latter case, since the effort

to proceed would be propagated backward without it, and the

undulation would be reversed, a rarefaction returning in place

of a condensation ;

and

this

will

perhaps

be

found

most

con-

sistent with the phenomena.

[Propositions F., VI., and VII. omitted.]

PROPOSITION VIII
When two undulations, from different origins, coincide
either perfectly or very nearly in direction, their joint effect is a combination of the motions belonging to each.

Since every particle of the medium is affected by each undu-
lation, wherever the directions coincide, the undulations can
proceed no otherwise than by uniting their motions, so that
the joint motion may be the sum or difference of the separate
60

THE WAVE-THEORY OF LIGHT
motions, accordingly as similar or dissimilar parts of the undu-
lations are coincident.
I have, on a former occasion,, insisted at large on the application of this principle to harmonics ; and it will appear to be of still more extensive utility in explaining the phenomena of
colors. The undulations which are now to be compared are those of equal frequency. When the two series coincide ex-
actly in point of time, it is obvious that the united velocity of
the particular motions must be greatest, and, in effect at least, double the separate velocities ; and also that it must be smallest,
and, if the undulations are of equal strength, totally destroyed
when the time of the greatest direct motion belonging to one undulation coincides with that of the greatest retrograde motion
of the other. In intermediate states the joint undulation will be of intermediate strength ; but by what laws this intermediate strength must vary cannot be determined without further data.
It is well known that a similar cause produces in sound that
effect which is called a beat ; two series of undulations of nearly equal magnitude co-operating and destroying each other alternately, as they coincide more or less perfectly in the times of performing their respective motions.
[Proposition IX. and five corollaries to Proposition VIII.
are here omitted.] 61

AN ACCOUNT OF SOME CASES OF THE
PRODUCTION OF COLORS NOT HITHERTO DESCRIBED*
READ JULY 1, 1802
WHATEVER opinion maybe entertained of the theory o
and colors which I have lately had the honor of submitting to the Royal Society, it must at any rate be allowed that it has given birth to the discovery of a simple and general law capable of explaining a number of the phenomena of colored light, which, without this law, would remain insulated and unintelligible. The law is, that " wherever two portions of the same light arrive at the eye by different routes, either exactly or very nearly in the same direction, the light becomes most intense when the difference of the routes is any multiple of a certain length, and least intense in the intermediate state of the interfering portions ; and this length is different for
light of different colors."
I have already shown in detail the sufficiency of this law for explaining all the phenomena described in the second and third books of Newton's Optics, as well as some others not mentioned by Newton. But it is still more satisfactory to observe its conformity to other facts, which constitute new and distinct classes of phenomena, and which could scarcely have agreed so well with any anterior law, if that law had been erroneous or imaginary : these are the colors of fibres and the colors of mixed plates.
As I was observing the appearance of the fine parallel lines' of light which are seen upon the margin of an object held near
*From the Philosophical Transactions for 1802, p. 387.

ERSITY
MEMOIRS OK THE WAVE-THEORY OF LIGHT

the eye, so as to intercept the greater part of the light of a
distant luminous object, and which are produced by the fringes caused by the inflection of light already known, I observed

that they were sometimes accompanied by colored fringes,
much broader and more distinct and I soon found that ;

these broader fringes were occasioned by the accidental inter-

position of a hair. . In order to make them more distinct, I

employed a horse-hair, but they were then no longer visible.

r \\

ith

a

fibre of

wool,

on

the

contrary,

they

became

very large

ard conspicuous; and, with a single silk -worm's thread,

their magnitude was so much increased that two or three of

them seemed to occupy the whole field of view. They appeared to extend on each side of the candle, in the same order

as the colors of thin plates seen by transmitted light. It oc-
curred to me that their cause must be sought in the interfer-

ence of two portions of light, one reflected from the fibre, the other bending round its opposite side, and at last coinciding

nearly in direction with the former portion ; that, accordingly, as both portions deviated more from a rectilinear direction, the difference of the length of their paths would become gradual-

ly greater and greater, and would consequently produce the

appearances

of

color

usual

in

such

cases ;

that

supposing

them to be inflected at right angles, the difference would

amount nearly to the diameter of the fibre, and that this dif-

ference must consequently be smaller as the fibre became

smaller ;

and, the

number

of fringes

in a right angle

becoming

smaller, that their angular distances would consequently be-

come greater, and the whole appearance would be dilated. It

was easy to calculate that for the light least inflected the

difference of the paths would be to the diameter of the fibre

very nearly as the deviation of the ray at any point from the rectilinear direction to its distance from the fibre.

I therefore made a rectangular hole in a card, and bent its

ends so as

to support

a

hair parallel

to

the

sides of the

hole ;

then, upon applying the eye near the hole, the hair, of course, appeared dilated by indistinct vision into a surface, of which

the breadth was determined by the distance of the hair and

the magnitude of the hole, independently of the temporary
aperture of the pupil. When the hair approached so near to
the direction of the margin of a candle that the inflected light was sufficiently copious to produce a sensible effect, the fringes
63

M E M O I R S ON

began to appear ; and it was easy to estimate the proportion

of their breadth to the apparent breadth of the hair across the

image of which they extended. I found that six of the bright-

est red fringes, nearly at equal distances, occupied the whole

of that image. The breadth of the aperture was T{Hb-> and its

distance from the hair -f$ of an inch ; the diameter of the hair

was

less

than

of

-g-J-g-

an

inch ;

as

nearly

as

I

could

ascertain

it was ^. Hence, we have y-j-J^ for the deviation of the

^ ^ first red fringe at the distance

and as
;

T^-Q :

::

-g-g-g-

rro O-OTT* or OTST f r tne difference of the routes of the rea

light where it was most intense. The measure deduced from

Newton's experiments is 36 | 00 . I thought this coincidence,

with only an error of one-ninth of so minute a quantity, suffi-

ciently perfect to warrant completely the explanation of the

phenomenon, and even to render a repetition of the experi-

ment unnecessary ; for there are several circumstances whicft

make it difficult to calculate much more precisely what ought

to be the result of the measurement.

When- a number of fibres of the same kind for instance, a

uniform lock of wool are held near to the eye, we see an ap-

pearance

of

halos

surrounding

a

distant

candle ;

but

their

brilliancy, and even their existence, depends on the uniformity

of the

dimensions

of

the

fibres ;

and

they

are

larger

as

the

fibres are smaller. It is obvious that they are the immediate

consequences of the coincidence of a number of fringes of the

same size, which, as the fibres are arranged in all imaginable

directions, must necessarily surround the luminous object at

equal distances on all sides, and constitute circular fringes.

There can be little doubt that the colored atmospherical

halos are of the

same kind ;

their

appearance

must

depend on

the existence of a number of particles of water of equal dimen-

sions, and in a proper position with respect to the luminary

and to the eye. As there is no natural limit to the magnitude

of the spherules of water, we may expect these halos to vary

without limit in their diameters, and accordingly Mr. Jordan

has observed that their dimensions are exceedingly various,

and has remarked that they frequently change during the time

of observation.

I first noticed the colors of mixed plates in looking at a candle through two pieces of plate-glass with a little moisture between them. I observed an appearance of fringes resembling

64:

THE WAVE-THEORY OF LIGHT

the common colors of thin plates ; and, upon looking for the

fringes by reflection, I found that these new fringes were

always in the same direction as the other fringes, but many

times larger. By examining the glasses with a magnifier, I

perceived that wherever these fringes were visible the moist-

ure was intermixed with portions of air, producing an appear-

ance similar to dew. I then supposed that the origin of the

colors

was

the

same

as

that

of

the

colors

of

halos ;

but, on

a more minute examination, I found that the magnitude of the

portions of air and water was by no means uniform, and that

the explanation was, therefore, inadmissible. It was, however,

easy to find two portions of light sufficient for the production

of these fringes ; for the light transmitted through the water,

moving in it with a velocity different from that of the light

passing through the interstices filled only with air, the two

portions would interfere with each other and produce effects of color according to the general law. The ratio of the

velocities

in

water

and

in

air

is

that of

3

to

4 ;

the

fringes

ought, therefore, to appear where the thickness is six times as

great as that which corresponds to the same color in the com-
mon case of thin plates ; and, upon making the experiment

with a plane glass and a lens slightly convex, I found the sixtli

dark circle actually of the same diameter as the first in the

new fringes. The colors are also very easily produced when

butter or tallow is substituted for water; and the rings then

become smaller, on account of the greater refractive density

of

the

oils ;

but when water is

added,

so

as

to

fill

up

the

in-

terstices of the oil, the rings are very much enlarged ; for here

the difference only of the velocities in water and in oil is to

be considered, and this is much smaller than the difference

between air and water. All these circumstances are sufficient

to satisfy us with respect to the truth of the explanation ; and

it is still more confirmed by the effect of inclining the plates

to the direction of the light; for then, instead of dilating, like

the colors of thin plates, these rings contract: and this is the

obvious consequence of an increase of the length of the paths

of light, which now traverse both mediums obliquely ; and the

effect is everywhere the same as that of a thicker plate.

It must, however, be observed that the colors are not pro-

duced in the whole light that is transmitted through the

mediums : a small portion only of each pencil, passing through

E

65

MEMOIRS ON

the water contiguous to the edges of the particle, is sufficient-

ly coincident with the light transmitted by the neighboring

portions

of

air

to

produce

the

necessary

interference ;

and

it

is easy to show that, on account of the natural concavity of the

surface of each portion of the fluid adhering to the two pieces

of glass, a considerable portion of the light which is beginning

to pass through the water will be dissipated laterally by re-
flection at its entrance, and that much of the light passing

through the air will be scattered by refraction at the second
surface. For these reasons the fringes are seen when the

plates are not directly interposed between the eye and the
luminous object; and on account of the absence of foreign light, even more distinctly than when they are in the same
right line with that object. And if we remove the plates to a

considerable distance out of this line, the rings are still visible

and

become

larger

than

before ;

for here

the

actual

route

of

the light passing through the air is longer than that of the

light passing more obliquely through the water, and the differ-

ence in the times of passage is lessened.

It is however, im?<

possible to be quite confident with respect to the causes of

these minute variations, without some means of ascertaining

accurately the forms of the dissipating surfaces.

In applying the general law of interference to these colors, as well as to those of thin plates already known, I must confess that it is impossible to avoid another supposition, which is

a part of the undulatory theory that is, that the velocity of

light

is

the

greater

the

rarer

the

medium ;

and

that

there

is

also a condition annexed to the explanation of the colors of thin plates which involves another part of the same theory that is, that where one of the portions of light has been reflected at the surface of a rarer medium, it must be supposed

to be retarded one-half of the appropriate interval for instance, in the central black spot of a soap-bubble, where the

actual lengths of the paths very nearly coincide, but the effect is the same as if one of the portions had been so retarded as to
destroy the other. From considering the nature of this cir-
cumstance,- I ventured to predict that if the two reflections

were of the same kind, made at the surfaces of a thin plate of a density intermediate between the densities of the mediums

containing it, the effect would be reversed, and the central

spot,

instead

of

black,

would

become

white ;

and

I

have

now

66

THE WAVE-THEORY OF LIGHT
the pleasure of stating that I have fully verified this prediction by interposing a drop of oil of sassafras between a prism of fiint-glass and a lens of crown-glass ; the central spot seen by reflected light was white and surrounded by a dark ring. It was, however, necessary to use some force in order to produce a contact sufficiently intimate ; and the white spot differed, even at last, in the same degree from perfect whiteness as the black spot usually does from perfect blackness.
[Three pages of speculation concerning dispersion are here
omitted.] 67

EXPEEIMENTS AND CALCULATIONS REL-
ATIVE TO PHYSICAL OPTICS*
A BAKEKIAN LECTUEE
Read Noveniber 24, 1803
I. EXPERIMENTAL DEMONSTRATION OF THE GENERAL LAW OF THE INTERFERENCE OF LIGHT.
IN making some experiments on the fringes of colors accompanying shadows, I have found so simple and so demonstrative a proof of the general law of the interference of two portions of light, which I have already endeavored to estab-
lish, that I think it right to lay before the Royal Society a
short statement of the facts which appear to me so decisive. The proposition on which I mean to insist at present is simply
this that fringes of colors are produced by the interference of two portions of light ; and I think it will not be defied by the most prejudiced that the assertion is proved by the ex-
periments I am about to relate, which may be repeated with
great ease whenever the sun shines, and without any other apparatus than is at hand to every one.
Experiment 1. I made a small hole in a window-shutter, and covered it with a piece of thick paper, which I perforated with a fine needle. For greater convenience of observation I placed
a small looking-glass without the window-shutter, in such a position as to reflect the sun's light in a direction nearly horizontal upon the opposite wall, and to cause the cone of diverging light to pass over a table on which were several little screens of card-paper. I brought into the sunbeam a slip of
*From the Philosophical Transactions for 1804.

MEMOIRS ON THE WAVE-THEORY OF LIGHT

card about one-thirtieth of an inch in breadth, and observed

its shadow, either on the wall or on other cards held at differ-

ent distances. Besides the fringes of color on each side of

the shadow, the shadow itself was divided by similar parallel
fringes of smaller dimensions, differing in number according
to the distance at which the shadow was observed, but leaving
the middle of the-' shadow always white. Now these fringes

were the joint effects of the portions of light passing on each

side of the slip of card, and inflected, or rather diffracted, into

the shadow ;

for

a

little screen being

placed

a few inches

from the card so as to receive either edge of the shadow on

its margin, all the fringes which had before been observed in

the shadow on the wall immediately disappeared, although the

light inflected on the other side was allowed to retain its course,

and although this light must have undergone any modification

that the proximity of the other edge of the slip of card might
have been capable of occasioning. When the interposed screen
was more remote from the narrow card, it was necessary to plunge it more deeply into the shadow, in order to extinguish

the parallel lines ; for here the light diffracted from the edge of the object had entered farther into the shadow in its way towards the fringes. Nor was it for want of a sufficient in-

tensity of light that one of the two portions was incapable of

producing the

fringes

alone ;

for

when they were

both

unin-

terrupted, the lines appeared, even if the intensity was reduced

to one- tenth or one-twentieth.

Experiment 2. The crested fringes described by the ingenious

and accurate Grimaldi afford an elegant variation of the pre-
ceding experiment and an interesting example of a calcula-
tion grounded on it. When a shadow is formed by an object

which has a rectangular termination besides the usual external

fringes there are two or three alternations of colors, beginning from the line which bisects the angle, disposed on each side of it in curves, which are convex towards the bisecting line, and which converge in some degree towards it as they become more remote from the angular point. These fringes are also the joint effect of the light which is inflected directly towards the shadow from each of the two outlines of the object ; for if a screen be placed within a few inches of the object, so as to receive only one of the edges of the shadow, the whole of the fringes disappear ; if, on the contrary, the rectangular point

MEM OIKS ON

of the screen be opposed to the point of the shadow so as barely to receive the angle of the shadow on its extremity, the fringes will remain undisturbed.

II. COMPARISON OF MEASURES DEDUCED FROM VARIOUS EX-
PERIMENTS.

If we now proceed to examine the dimensions of the fringes under different circumstances, we may calculate the differences

of the lengths of the paths described by the portions of light which have thus been proved to be concerned in producing
those fringes ; and we shall find that where the lengths are

equal

the

light always

remains white ;

but

that where

either

the brightest light or the light of any given color disappears and reappears a first, a second, or a third time, the differences

of the lengths of the paths of the two portions are in arithmet-

ical progression, as nearly as we, can expect experiments of this

kind to agree with each other. I shall compare, in this point of view, the measures deduced from several experiments of
Newton and from some of my own.

In the eighth and ninth observations of the third book of

Newton's Optics some experiments are related which, together

with the third observation, will furnish us with the data neces-
sary for the calculation. Two knives were placed, with their
edges meeting at a very acute angle, in a beam of the sun's light, admitted through a small aperture, and the point of concourse of the two first dark lines bordering the shadows of the re-

spective knives was observed at various distances. The results

of six observations are expressed in the first three lines of the
first table. On the supposition that the dark line is produced
by the first interference of the light reflected from the edges of

the knives, with the light passing in a straight line between
them, we may assign, by calculating the difference of the two

paths, the interval for the first disappearance of the brightest
light, as it is expressed in the fourth line. The second table
contains the results of a similar calculation from Newton's ob-

servations

on the

shadow

of

a

hair ;

and

the

third,

from

some

experiments of

my own of the

same

nature ;

the

second

bright

line being supposed to correspond to a double interval, the sec-
ond dark line to a triple interval, and the succeeding lines to depend on a continuation of the progression. The unit of all

,the tables is an inch.

70

THE WAVE-THEORY OF LIGHT

TABLE I. Observation 9. N.

Distance of the knives from the aperture

101

Distance of the

paper from the knives
Distance b e -

1

^

&t

32

96

131

tween the

edges of the knives o p-
posite to the
point of concourse

012

.020

.034

.057

.081

.087

Interval of dis-

appearance

0000122 .0000155 .0000182 .0000167 .0000166 .0000166

TABLE II. Observation 3. N.

Breadth of the hair

Distance of the hair from the aperture Distances of the scale from the aperture (Breadths of the shadow Breadth between ihe second pair of bright lines
Interval of disappearance, or half the difference of the

paths

Breadth between the third pair of bright lines

. ..

Interval of disappearance, one-fourth of the difference..

^

144

150

252

^

)

4

-g?

TT

0000151 .0000173

^

3
T

.0000130 .0000143

TABLE III. Experiment 3.
Breadth of the object Distance of the object from the aperture Distance of the wall from the aperture Distance of the second pair of dark lines from each other Interval of disappearance, one-third of the difference

434 125 250 1.167 0000149

Experiment 4.

Breadth of the wire

083

Distance of the wire from the aperture

32

Distance of the wall from the aperture

250

(Breadth of the shadow, by three

measurements

815.

.826, or

.827 ;

mean,

.823)

Distance of the first pair of dark lines 1.165, 1.170, or 1.160; mean, 1.165

Interval of disappearance ..........

0000194

Distance of the second pair of dark

lines

1.402. 1.395, or 1.400; mean. 1.399

Interval of disappearance Distance of the third pair of dark

0000137

lines. ,
Interval of disappearance

1.594,

1.580,

or

1.585 ;

mean,

1.586

0000128

71

MEMOIRS ON

It appears, from five of the six observations of the first

table, in which the distance of the shadow was varied from

about 3 inches to 11 feet, and the breadth of the fringes was

increased in the ratio of 7 to 1, that the difference of the

routes constituting the interval of disappearance varied but

one-eleven tli at most and that in three out of the five it ;

agreed with the mean, either exactly or within y^- part.

Hence we are warranted in inferring that the interval appro-

priate to the extinction of the brightest light is either accu-

rately or very nearly constant.

But it may be inferred from a comparison of all the other

observations that when the obliquity of the reflection is very

great some circumstance takes place which causes the inter-

val thus calculated to be somewhat greater ; thus, in the elev-

enth line of the third table it comes out one-sixth greater than
the mean of the five already mentioned. On the other hand,

the mean of two of Newton's experiments and one of mine is

a result about one-fourth less than the former. With respect

to the nature of this circumstance I cannot at present form a

decided opinion ; but I conjecture that it is a deviation of

some of the light concerned, from the rectilinear direction as-

signed to it, arising either from its natural diffraction, by which

the magnitude of the shadow is also enlarged, or from some

other unknown cause. If we imagined the shadow of the

wire and the fringes nearest it to be so contracted that the

motion of the light bounding the shadow might be rectilinear,

we should thus make a sufficient compensation for this devia-

tion ;

but

it is

difficult to

point

out what

precise track

of

the

light would cause it to require this correction. The mean of the three experiments which appear to have been

least affected by this unknown deviation gives .0000127 for the

interval appropriate to the disappearance of the brightest

light ; and. it may be inferred that if they had been wholly ex-

empted from its effects the measure would have been some-
what smaller. Now the analogous interval, deduced from the

experiments of Newton on this plate, is .0000112, which is

about one-eighth less than the former result ; and this appears

to be a coincidence fully sufficient to authorize us to attribute

these two classes of phenomena to the same cause. It is very

easily shown, with respect to the colors of thin plates, that

each kind of light disappears and reappears where the differ-

72

THE WAVE-THEORY OF LIGHT

ences of the routes of two of its portions are in arithmetical
progression*} and we have seen that the same law may be in general inferred from the phenomena of diffracted light, even
independently of the analogy.
The distribution of the colors is also so similar in both cases

as to point immediately to a similarity in the causes. In the

thirteenth observation of the second part of the first book

Newton relates that the interval of the glasses where the rings

appeared in red light was to the interval where they appeared in

violet light as

14 to

9 ;

and,

in

the

eleventh

observation

of the

third book, that the distances between the fringes, under the

same circumstances, were the twenty-second and the twenty-sev-

enth of an inch. Hence, deducting the breadth of the hair and

taking the squares, in order to find the relation of the difference

of the routes, we have the proportion of 14 to 9, which scarcely

differs from the proportion observed in the colors of the thin

plate.
We may readily determine from this general principle the

form

of

the

crested fringes

of

Grimaldi,

already

described }

for

it will appear that, under the circumstances of the experiment

related, the points in which the differences of the lengths of

the paths described by the two portions of light are equal to

a constant quantity, and in which, therefore, the same kinds

of light ought to appear or disappear, are always found in

equilateral hyperbolas, of which the axes coincide with the

outlines of the shadow, and the asymptotes nearly with the

diagonal line. Such, therefore, must be the direction of the

fringes ; and this conclusion agrees perfectly with the observa-

tion. But it must be remarked that the parts near the out-

lines of the shadow are so much shaded off as to render the

character of the curve somewhat less decidedly marked where it approaches to its axis. These fringes have a slight resemblance to the hyperbolic fringes observed by Newton ; but the
analogy is only distant.
[///. Application to the Supernumerary Rainbows, omitted.]

IV. ARGUMENTATIVE INFERENCE RESPECTING THE NATURE
OF LIGHT.
The experiment of Grimaldi on the crested fringes within
the shadow, together with several others of his observations
73

MEMOIRS ON

equally important, has been left unnoticed by Newton. Those

who are attached to the Newtonian theory of light, or to the

hypothesis of modern opticians founded on views still less

enlarged, would do well to endeavor to imagine anything like

an explanation of these experiments derived from their own

doctrines ;

and if they fail in

the

attempt, to

refrain

at

least

from idle declamation against a system which is founded on

the accuracy of its application to all these facts, and to a thou-

sand others of a similar nature.

From the experiments and calculation which have been premised, we may be allowed to infer that homogeneous light

at certain equal distances in the direction of its motion is pos-

sessed of opposite qualities capable of neutralizing or destroy-
ing each other, and of extinguishing the light where they happen to be united; that these qualities succeed each other

alternately in successive concentric superficies, at distances
which are constant for the same light passing through the
same medium. From the agreement of the measures, and from the similarity of the phenomena, we may conclude that these
intervals are the same as are concerned in the production of the

colors of thin plates ; but these are shown, by the experi-

ments of Newton, to be the smaller the denser the medium;

and since it may be presumed that their number must neces-

sarily remain unaltered in a given quantity of light, it follows, of course, that light moves more slowly in a denser than in a rarer medium'; and this being granted, it must be allowed that

refraction is not the effect of an attractive force directed to a

denser medium. The advocates for the projectile hypothesis
of light must consider which link in this chain of reasoning they may judge to be the most feeble, for hitherto I have advanced in this paper no general hypothesis whatever. But since we know that sound diverges in concentric superficies,

and that musical sounds consist of opposite qualities, capable of neutralizing each other, and succeeding at certain equal

intervals, which are different according to the difference of the note, we are fully authorized to conclude that there must be some strong resemblance between the nature of sound and

that of light. I have not, in the course of these investigations, found any
reason to suppose the presence of such an inflecting medium
in the neighborhood of dense substances as I was formerly
74

THE WAVE-T11EOKY OF LIGHT

inclined

to attribute to them ;

and,

upon considering the

phe-

nomena of the aberration of the stars, I am disposed to believe

that the luminiferous ether pervades the substance of all ma-

terial bodies, with little or no resistance, as freely, perhaps, as

the wind passes through a grove of trees.

The observations on the effects of diffraction and inter-

ference may, perhaps, sometimes be applied to a practical pur-

pose in making us cautious in our conclusions respecting the

appearances of minute bodies viewed in a microscope. The

shadow of a fibre, however opaque, placed in a pencil of light

admitted through a small aperture, is always somewhat less dark
A in the middle of its breadth than in the parts on each side.

similar effect may also take place, in some degree, with respect

to the image on the retina, and impress the sense with an idea

of a transparency which

has

no

real

existence ;

and if a

small

portion of light be really transmitted through the substance,

this may again be destroyed by its interference with the dif-

fracted light, and produce an appearance of partial opacity,

instead of uniform semi-transparency. Thus a central dark spot

and a light spot, surrounded by a darker circle, may respec-

tively be produced in the images of a semi-transparent and

an opaque corpuscle, and impress us with an idea of a com-

plication of structure which does not exist. In order to detect

the fallacy, we make two or three fibres cross each other, and

view a number of globules contiguous to each other; or we

may obtain a still more effectual remedy by changing the mag-

nifying power; and then, if the appearance remain constant in

kind and in degree, we may be assured that it truly represents

the nature of the substance to be examined. It is natural to

inquire whether or not the figures of the globules of blood

delineated by Mr. Hewson in the Phil. Trans., vol. Ixiii., for

1773, might not in some measure have been influenced by a

deception

of

this

kind ;

but,

as

far

as

I have

hitherto

been

able

to examine the globules with a lens of one-fiftieth of an inch

focus, I have found them nearly such as Mr. Hewson has de-

scribed them.

[ V. Remarks on the Colors of Natural Bodies, omitted.]

VI. EXPERIMENT ON THE DARK RAYS OF RITTER
Experiment 6. The existence of solar rays accompanying light, more refrangible than the violet rays and cognizable by
75

MEMOIRS ON

their chemical effects,

was first ascertained by Mr.

Bitter ;

but

Dr. Wollaston made the same experiments a very short time

afterwards without having been informed of what had been

done on the Continent. These rays appear to extend beyond

the violet rays of the prismatic spectrum, through a space

nearly equal to that which is occupied by the violet. In order

to complete the comparison of their properties with those of

visible light, I was desirous of examining the effect of their re-

flection from a thin plate of air, capable of producing the well-

known rings of colors. For this purpose I formed an image

of the rings, by means of the solar microscope, with the appa-

ratus which I have described in the Journals of the Royal

Institution, and I threw this image on paper dipped in a solu-

tion of nitrate of silver, placed at the distance of about nine

inches from the microscope. In the course of an hour portions

of three dark rings were very distinctly visible, much smaller

than the brightest rings of the colored image, and coinciding

very nearly in their dimensions with the rings of violet light

that appeared upon the interposition of violet glass. I thought

the dark rings were a little smaller than the violet rings, but

the difference was not sufficiently great to be accurately ascer-

tained ;

it might

be

as

much

as fa or fa of

the

diameters,

but

not greater. It is the less surprising that the difference should

be so small, as the dimensions of the colored rings do not by

any means vary at the violet end of the spectrum so rapidly as

at the red end. For performing this experiment with very

great accuracy a heliostat would be necessary, since the motion

of the sun causes a slight change in the place of the image ;

and leather impregnated with the muriate of silver would

indicate the effect with greater delicacy. The experiment,

however, in its present state, is sufficient to complete the anal-

ogy of the invisible with the visible rays, and to show that they

are equally liable to the general law which is the principal sub-

ject of this paper. If we had thermometers sufficiently delicate,

it is probable that we might acquire, by similar means, infor-

mation still more interesting with respect to the rays of invis-

ible

heat

discovered

by Dr.

Herschel ;

but

at

present

there is

great reason to doubt of the practicability of such an experi-

ment.

76

THE WAVE-THEORY OF LIGHT
BIOGRAPHICAL SKETCH
THOMAS YOUNG was born at Milverton. England, in 1773,
and died at London in 1829. His education, in respect to the amount of ground it co.vered, is quite as remarkable as his later scientific work. As a lad he showed marked proficiency in
linguistic studies, acquired great mechanical skill, distin-
guished himself in drawing, music, and athletics. As a young man he pursued his university studies at London, Edinburgh, Gb'ttingeu, and Cambridge.
The following programme of his daily work at Gottingen in the autumn of 1795 characterizes at once the lad, the youth, and the mature man:
" At 8, I attend Spittler's course on the History of the Principal States of Europe, exclusive of Germany.
" At 9, Arnemann on Materia Medica. "At 10, Richter on Acute Diseases. " At 11, twice a week, private lessons from Blessman, the academical
dancing-master.
"At 12, I dine at Ruhlander's table d'hote. "At 1, twice a week, lessons on the clavichord from Forkel; and twice a week at home, from Fiorillo on Drawing. " At 2, Lichtenberg on Physics. "At 3, I ride in the academical manege, under the instruction of Ayrer,
four times a week. " At 4, Stromeyer on Diseases. *' At 5, Blumenbach on Natural History.
"At 6, twice Blessman with other pupils, and twice Forkel."
He was born of a well-to-do Quaker family; he inherited
ample money ; he had all that travel, leisure, and good society could do for a man. Only in one particular does his education appear to have been defective viz., in the absence of any training in advanced dynamics or in higher mathematical
analysis.
In 1800 he completed his medical studies at Cambridge, and settled as a practising physician in London. In the year following he was appointed to the professorship of natural philosophy in the then newly founded Royal Institution, a position from which he resigned at the end of two years in order to devote himself more completely to the practice of medicine. It was during his occupancy of this chair that he published the
77

MEMOIRS ON THE WAVE-THEORY OF LIGHT
three papers reprinted in this volume, the first of which is possibly the most important of his contributions to physics. It was during this period also that he wrote his Lectures on Natural Philosophy, which must always be reckoned as a potent factor in the spread of sound physical science in the nineteenth century, while its bibliography of more than four hundred quarto pages is to-day valuable as well as classic.
But nothing short of a catalogue of his papers can give one an adequate idea of the varied activity of this man during the remaining quarter-century of his life. His contributions cover
fields as diverse as the physiology of the human eye, hydro-
dynamics, music, paleography, atmospheric refraction, theory of tides, tables of mortality, theory of structures. His explanation of color-vision as due to the presence of three sets of
nerve fibres in the retina, which, when excited, give respectively sensations of red, green, and violet, has been adopted and modified by Helmholtz, and is to-day perhaps the most widely accepted of the various theories on this subject.
After all, it rnnst^ be confessed, even by his most ardent admirers, that Young's style is, in general, far from clear. Whether this is in any way connected with his lack of mathematical training, or whether it is due to the fact that his own clear intuitions bridged most of the gaps in his written work,
it is difficult to say ; but in any event many of his papers are obscure, and few of them are read. The reader who desires a
full biography will find it in Dr. Peacock's Life of Young (London, 1855). This biographer also edited his Miscellaneous Works, 3 vols. (London, 1855). All his papers, however, which
are of especial interest to the student of physics are contained in the lectures on Natural Philosophy (London, 1807).
78