Huygens, Treatise on Light

8/3/2019 Huygens, Treatise on Light

1/143

TREATISEu N LIGHTIn which are explainedThe causes of that which occursIn REFLEXK)N,&in REFRACTION.And particularly

In the strange REFRACTIONOF ICELAND CRYSTALBy CHRISTIAAN HUYGENS.

Rendered into EnglishBy SILVANUS P. THOMPSON.

MACMILLAN AND CO., LIMITEDST. MARTIN'S STREET, LONDON

MCMXII.


2/143

CHISWICK PRESS : CHARLES WHITTINGHAM AND CO,TOOKS COURT, CHANCERY LANE, LONDON.


3/143

PREFACEWROTE this Treatise during my sojournin France twelve years ago, and I com-municated it in the year 1 678 to the learnedpersons who then composed the RoyalAcademy of Science, to the membershipofwhich the King had done me the honourof calling me. Several of that body who are still alive willremember having been present when I read it, and abovethe rest those amongst them who applied themselves par-

ticularly to the study of Mathematics ; of whom I cannotcite more than the celebrated gentlemen Cassini, Romer,and De la Hire. And although I have since corrected andchanged some parts, the copies which I had made of it atthat time may serve for proof that I have yet added no-thing to it save some conjectures touching the formation ofIceland Crystal, and a novel observation on the refractionof Rock Crystal. I have desired to relate these particularsto make known how long I have meditated the thingswhich now I publish, and not for the purpose of detraCt-ing from the merit of those who, without having seen any-thing that I have written, may be found to have treatedof


4/143

vi PREFACEof like matters : as has in fa


5/143

PREFACE viithem, and further, principally, when one can imagine andforesee new phenomena which ought to follow from thehypotheses which one employs, and when one finds thattherein the fad: corresponds to our prevision. But if allthese proofs of probability are met with in that which Ipropose to discuss, as it seems to me they are, this oughtto be a very strong confirmation of the success of my in-quiry; and it must be ill if the fa


6/143


7/143

NOTE BY THE TRANSLATORONSIDERING the great influence whichthis Treatise has exercised in the develop-ment of the Science of Optics, it seemsstrange that two centuries should havepassed before an English edition of thework appeared. Perhaps the circumstance

is due to the mistaken zeal with which formerly every-thing that conflicted with the cherished ideas of Newtonwas denounced by his followers. The Treatise on Lightof Huygens has, however, withstood the test of time: andeven now the exquisite skill with which he applied hisconception of the propagation of waves of light to unravelthe intricacies of the phenomena of the double refraftionof crystals, and of the refra6tion of the atmosphere, willexcite the admiration of the student of Optics. It is truethat his wave theory was far from the complete doctrineas subsequently developed by Thomas Young and AugustinFresnel, and belonged rather to geometrical than to physicalOptics. IfHuygens had no conception of transverse vibra-tions, of the principle of interference, or of the existenceof the ordered sequence of waves in trains, he neverthelessattained to a remarkably clear understanding of the prin-b ciples


8/143

x NOTE BY THE TRANSLATORciples of wave-propagation; and his exposition of the sub-jeCt marks an epoch in the treatment of Optical problems.It has been needful in preparing this translation to exer-cise care lest one should import into the author's textideas of subsequent date, by using words that have cometo imply modern conceptions. Hence the adoption of asliteral a rendering as possible. A few of the author's termsneed explanation, He uses the word " refraction," forexample, both for the phenomenon or process usually sodenoted, and for the result of that process: thus the re-fraCted ray he habitually terms

" the refraction " of theincident ray. When a wave-front, or, as he terms it, au wave," has passed from some initial position to a subse-quent one, he terms the wave-front in its subsequentposition " the continuation " of the wave. He also speaksof the envelope of a set of elementary waves, formed bycoalescence of those elementary wave-fronts, as " the ter-mination" of the wave; and the elementary wave-frontshe terms " particular " waves. Owing to the circumstancethat the French word rayon possesses the double signifi-cation of ray of light and radius of a circle, he avoids itsuse in the latter sense and speaks always of the semi-diameter, not of the radius. His speculations as to theether, his suggestive views of the structure of crystallinebodies, and his explanation of opacity, slight as they are,will possibly surprise the reader by their seeming modern-ness. And none can read his investigation ofthe phenomenafound in Iceland spar without marvelling at his insightand sagacity.

S. P. T.June, 1912.


9/143

TABLE OF MATTERSContained in this 'Treatise

CHAP. I. On Rays Propagated inStraight Lines.That Light is produced by a certainmovement. p. 3That no substance passesfrom the lumin-ous objeft to the eyes. p. 3That Light spreads spherically^ almostas Sound does. p. 4Whether Light takes time to spread.

P-*Experience seeming toprove that it passesinstantaneously. p. 5

Experience proving that it takes time.p. 8How much its speed is greater than that

of Sound. p. 10In what the emission of Light differsfrom that of Sound. p. 10That it is not the same medium whichserves for Light and Sound, p. 1 1How Sound is propagated. p. 12How Light is propagated. p. 14Detailed Remarks on the propagationof Light. p. 15Why Rays are propagated only instraight lines. p. 2OHow Light coming in different directionscan cross itself. p. 22CHAP. II. On Reflexion.

Demonstration of equality of angles ofincidence and reflexion. p. 23Why the incident and reflected rays arein the same plane perpendicular to thereflecting surface. p. 25That it is not needfulfor the reflectingsurface to be perfectly flat to attainequality of the angles of incidence andreflexion. p. 27

CHAP. III. On Refradlion.That bodies may be transparent withoutany substance passing through them.

p. 29Proof that the ethereal matter passes

through transparent bodies. p. 30How this matter passing through canrender them transparent. p. 31That the most solid bodies in appearanceare of a very loose texture. p. 31That Light spreads more slowly in waterand in glass than in air. p. 32Third hypothesis to explain transpar-ency^ and the retardation which Lightsuffers. .A32On that which makes bodies opaque.

P- 34Demonstration why Refraction obeys theknownproportion of Sines. p. 35Why the incident and refrafted Rays

produce one another reciprocally, p. 39Why Reflexion within a triangularglass prism is suddenly augmentedwhen the Light can no longer pene-trate, p. 40That bodies which cause greater Refrac-tion also cause stronger Reflexion.

p. 42Demonstration of the Theorem of Mr.Fermat. p. 43CHAP. IV. On the Refradion of

the Air.That the emanations of Light in the airare not spherical. p t 45How consequently some objects appear

higher than they are. p. 47How the Sun may appear on the Hori-zon before he has risen. p. 49


10/143

xii TABLE OFThat the rays of light become curved in

the Air of the Atmosphere, and whateffects this produces. p. 50

CHAP. V. On the Strange Refrac-tion of Iceland Crystal.That this Crystal grows also in other

countries. p. 52Wlw first wrote about it. ^'53Description of Iceland Crystal; its sub-

stance, shape, and properties, p. 53That it has two different Refractions.P- 54That the ray perpendicular to the surface

suffers refraction, and that some raysinclined to the surface pass withoutsuffering refraction. p. 55

Observation of the refractions in thisCrystal. p. 56That there is a Regular and an Ir-regular Refraction. P- 57The way of measuring the two Refrac-tions of Iceland Crystal. P* 57Remarkable properties of the IrregularRefraction. p. 60

Hypothesis to explain the double Refrac-tion, p. 6 1That Rock Crystal has also a doubleRefraction, p. 62

Hypothesis ofemanations ofLight, with-in Iceland Crystal, ofspheroidalform^for the Irregular Refraction, p. 63How a perpendicular ray can sufferRefraction. p. 64How the position andform of the spher-oidal emanations in this Crystal canbe defined. p. 65

Explanation ofthe Irregular Refractionby these spheroidal emanations, p. 67

Easy way to find the Irregular Re-fraction of each incident ray. p. 70Demonstration of the oblique ray which

MATTERStraverses the Crystal without beingrefracted. p. 73Other irregularities of Refraction ex-plained. />. 76That an objeft placed beneath the Crystalappears double^in two images ofdiffer-ent heights, p. SiWhy the apparent heights of one of theimages change on changing the positionof the eyes above the Crystal, p. 85Of the different sections of this Crystalwhich produce yet other refractions^and confirm all this Theory, p. 88

Particular way ofpolishing the surfacesafter it has been cut. p. 9 1

Surprisingphenomenon touching the rayswhich pass through two separatedpieces; the cause of which is not ex-plained, p. 92Probable conjecture on the internalcom-position of Iceland Crystal^ and ofwhat figure its particles are. p. 95

Tests to confirm this conjecture, p. 97Calculations which have been supposedin this Chapter. p. 99

CHAP. VI. On the Figures oftransparent bodies which servefor Refractionand forReflexion.

General and easy rule to find theseFigures. p. 106

Invention of the Ovals of Mr. DesCartes for Dioptrics. p. 109How he was able to find these Lines.

p. 114{lass foray offinding the surface of a git

perfeft refracJion, when the othersurface is given. p. 116Remark on what happens to rays re-frafted at a spherical surface, p. 123Remark on the curved line which isformed by reflexion in a spherical con-cave mirror. p. 1 26


11/143

TREATISE ON LIGHTCHAPTER I

ON RAYS PROPAGATED IN STRAIGHT LINESS happens in all the sciences in whichGeometry is applied to matter, the demon-strations concerning Optics are foundedon truths drawn from experience. Suchare that the rays of light are propagatedin straight lines; that the angles of re-flexion and of incidence are equal; and that in refraftionthe ray is bent according to the law of sines, now so wellknown, and which is no less certain than the precedinglaws.The majority of those who have written touching the

various parts of Optics have contented themselves withpresuming these truths. But some, more inquiring, havedesired to investigate the origin and the causes, consideringthese to be in themselves wonderful effe


12/143

2 TREATISEjet, so as to contribute as much as I can to the explanationof this department of Natural Science, which, not withoutreason, is reputed to be one of its most difficult parts. Irecognize myself to be much indebted to those who werethe first to begin to dissipate the strange obscurity in whichthese things were enveloped, and to give us hope that theymight be explained by intelligible reasoning. But, on theother hand I am astonished also that even here these haveoften been willing to offer, as assured and demonstrative,reasonings which were far from conclusive. For I do notfind that any one has yet given a probable explanation ofthefirst and most notable phenomena of light, namely why it isnot propagated except in straight lines, and how visiblerays, coming from an infinitude of diverse places, cross oneanother without hindering one another in any way.

I shall therefore essay in this book, to give, in accordancewith the principles accepted in the Philosophy of the pre-sent day, some clearer and more probable reasons, firstly ofthese properties of light propagated re&ilinearly ; secondlyof light which is reflected on meeting other bodies. ThenI shall explain the phenomena of those rays which are saidto suffer refraftion on passing through transparent bodiesof different sorts; and in this part I shall also explain theeffects of the refradlion of the air by the different densitiesof the Atmosphere.Thereafter I shall examine the causes of the strange re-fra6tion of a certain kind of Crystal which is brought fromIceland. And finally I shall treat of the various shapes oftransparent and refle6ting bodies bywhich rays are collectedat a point or are turned aside in various ways. Fromthis it will be seen with what facility, following our newTheory, we find not only the Ellipses, Hyperbolas, andother


13/143

ON LIGHT. CHAP. I 3other curves which Mr. Des Cartes has ingeniously in-vented for this purpose; but also those which the surfaceof a glass lens ought to possess when its other surface isgiven as spherical or plane, or of any other figure thatmay be.

It is inconceivable to doubt that light consists in themotion of some sort of matter. For whether one considersits produ


14/143

4 TREATISEin the way in which a shot or an arrow traverses the air ;for assuredly that would too greatly impugn these twoproperties of light, especially the second of them. It isthen in some other way that light spreads ; and that whichcan lead us to comprehend it is the knowledge which wehave of the spreading of Sound in the air.We know that by means of the air, which is an invisibleand impalpable body, Sound spreads around the spot whereit has been produced, by a movement which is passed onsuccessively from one part of the air to another ; and thatthe spreading of this movement, taking place equallyrapidly on all sides, ought to form spherical surfaces everenlarging and which 'strike our ears. Now there is nodoubt at all that light also comes from the luminous bodyto our eyes by some movement impressed on the matterwhich is between the two; since, as we have already seen, itcannot be by the transport of a body which passes fromone to the other. If, in addition, light takes time for itspassage which we are now going to examine it willfollow that this movement, impressed on the interveningmatter, is successive ; and consequently it spreads, as Sounddoes, by spherical surfaces and waves: for I call themwaves from their resemblance to those which are seen tobe formed in water when a stone is thrown into it, andwhich present a successive spreading as circles, thoughthese arise from another cause, and are only in a flat surface.To see then whether the spreading of light takes time,let us consider first whether there are any fadls of experiencewhich can convince us to the contrary. As to those whichcan be made here on the Earth, by striking lights at greatdistances, although they prove that light takes no sensibletime to pass over these distances, one may say with goodreason


15/143

ON LIGHT. CHAP. I 5reason that they are too small, and that the only conclusionto be drawn from them is that the passage of light is ex-tremely rapid. Mr. Des Cartes, who was of opinion thatit is instantaneous, founded his views, not without reason,upon a better basis of experience, drawn from the Eclipsesof the Moon; which, nevertheless, as I shall show, is notat all convincing. I will set it forth, in a way a littledifferent from his, in order to make the conclusion morecomprehensible.Let A be the place of the sun, BD a part of the orbit or

annual path of the Earth: ABC a straight line which Isuppose to meet the orbit of the Moon, which is representedby the circle CD, at C.Now if light requires time, for example one hour, to

traverse the space which is between the Earth and theMoon, it will follow that the Earth having arrived at B,the shadow which it casts, or the interruption of the light,will not yet have arrived at the point C, but will onlyarrive there an hour after. It will then be one hour after,reckoning from the moment when the Earth was at B,that


16/143

6 TREATISEthat the Moon, arriving at C, will be obscured : but thisobscuration or interruption of the light will not reach theEarth till after another hour. Let us suppose that the Earthin these two hours will have arrived at E. The Earththen, being at E, will see the Eclipsed Moon at C, whichit left an hour before, and at the same time will see thesun at A. For it being immovable, as I suppose withCopernicus, and the light moving always in straight lines,it must always appear where it is. But one has alwaysobserved, we are told, that the eclipsed Moon appears atthe point ofthe Ecliptic opposite to the Sun; and yet here itwould appear in arrear of that point by an amount equal tothe angle GEC, the supplement of AEC. This, however,is contrary to experience, since the angle GEC would bevery sensible, and about 33 degrees. Now according toour computation, which is given in the Treatise on thecauses of the phenomena of Saturn, the distance BA be-tween the Earth and the Sun is about twelve thousanddiameters of the Earth, and hence four hundred timesgreater than BC the distance of the Moon, which is 30diameters. Then the angle ECB will be nearly fourhundred times greater than BAE, which is five minutes;namely, the path which the earth travels in two hoursalong its orbit; and thus the angle BCE will be nearly 33degrees; and likewise the angle CEG, which is greater byfive minutes.

But it must be noted that the speed of light in thisargument has been assufned such that it takes a time ofone hour to make the passage from here to the Moon. Ifone supposes that for this it requires only one minute oftime, then it is manifest that the angle CEG will only be33 minutes; and if it requires only ten seconds of time,the


17/143

ON LIGHT. CHAP. I 7the angle will be less than six minutes. And then it will notbe easy to perceive anything of it in observations of theEclipse; nor, consequently, will it be permissible to deducefrom it that the movement of light is instantaneous.

It is true that we are here supposing a strange velocitythat would be a hundred thousand times greater than thatof Sound. For Sound, according to what I have observed,travels about 180 Toises in the time of one Second, or inabout one beat of the pulse. But this supposition oughtnot to seem to be an impossibility; since it is not a questionof the transport of a body with so great a speed, but of asuccessive movement which is passed on from some bodiesto others. I have then made no difficulty, in meditatingon these things, in supposing that the emanation of lightis accomplished with time, seeing that in this way all itsphenomena can be explained, and that in following thecontrary opinion everything is incomprehensible. For ithas always seemed to me that even Mr. Des Cartes, whoseaim has been to treat all the subje6ts of Physics intelligibly,and who assuredly has succeeded in this better than any onebefore him, has said nothing that is not full of difficulties,or even inconceivable, in dealing with Light and its pro-perties.But that which I employed only as a hypothesis, hasrecently received great seemingness as an established truthby the ingenious proof of Mr. Romer which I am goinghere to relate, expecting him himself to give all that isneeded for its confirmation. It is founded as is the precedingargument upon celestial observations, and proves not onlythat Light takes time for its passage, but also demonstrateshow much time it takes, and that its velocity is even atleast six times greater than that which I have just stated.For


18/143

8 TREATISEFor this he makes use of the Eclipses suffered by the

little planets which revolve around Jupiter, and whichoften enter his shadow : and see what is his reasoning.Let A be the Sun, BCDE the annual orbit of the Earth,F Jupiter, GN the orbit of the nearest of his Satellites, for it

is this one which is more apt for thisinvestigation than any of the otherthree, because of the quickness of itsrevolution. Let G be this Satelliteentering into the shadow of Jupiter,H the same Satellite emerging fromthe shadow.

Let it be then supposed, the Earthbeing at B some time before thelast quadrature, that one has seenthe said Satellite emerge from theshadow; it must needs be, if theEarth remains at the same place,that, after 42^ hours, one wouldagain see a similar emergence, be-cause that is the time in which itmakes the round of its orbit, andwhen it would come again into op-position to the Sun. And if theEarth, for instance, were to remain

always at B during 30 revolutions of this Satellite, onewould see it again emerge from the shadow after 30 times42-^ hours. But the Earth having been carried along duringthis time to C, increasing thus its distance from Jupiter,it follows that if Light requires time for its passage theillumination of the little planet will be perceived later atC


19/143

ONLIGHT. CHAP. I 9C than it would have been at B, and that there must beadded to this time of 30 times 42^ hours that whichthe Light has required to traverse the space MC, thedifference of the spaces CH, BH. , Similarly at the otherquadrature when the earth has come to E from D whileapproaching toward Jupiter, the immersions of the Satelliteought to be observed at E earlier than they would havebeen seen if the Earth had remained at D.Now in quantities ofobservations ofthese Eclipses, madeduring ten consecutive years, these differences have beenfound to be very considerable, such as ten minutes andmore; and from them it has been concluded that in orderto traverse the whole diameter of the annual orbit KL,which is double the distance from here to the sun, Lightrequires about 22 minutes of time.The movement of Jupiter in his orbit while the Earthpassed from B to C, or from D to E, is included in thiscalculation; and this makes it evident that one cannotattribute the retardation of these illuminations or theanticipation of the eclipses, either to any irregularityoccurring in the movement of the little planet or to itseccentricity.

If one considers the vast size of the diameter KL, whichaccording to me is some 24 thousand diameters of theEarth, one will acknowledge the extreme velocity of Light.For, supposing that KL is no more than 22 thousand ofthese diameters, it appears that being traversed in 22minutes this makes the speed a thousand diameters in oneminute, that is i6j- diameters in one second or in one beatof the pulse, which makes more than 1 1 hundred times ahundred thousand toises; since the diameter of the Earthcontains 2,865 leagues, reckoned at 25 to the degree, andc each


20/143

io TREATISEeach league is 2,282 Toises, according to the exa6t measure-ment which Mr. Picard made by order ofthe King in 1 669.But Sound, as I have said above, only travels 180 toises inthe same time of one second : hence the velocity of Lightis more than six hundred thousand times greater than thatof Sound. This, however, is quite another thing frombeing instantaneous, since there is all the difference be-tween a finite thing and an infinite. Now the successivemovement of Light being confirmed in this way, it follows,as I have said, that it spreads by spherical waves, like themovement of Sound. -But if the one resembles the other in this respe


21/143

ON LIGHT. CHAP. I nagitation of the particles of the metal or of the wood ;those of them which are on the surface striking similarlyagainst the ethereal matter. The agitation, moreover, ofthe particles which engender the light ought to be muchmore prompt and more rapid than is that of the bodieswhich cause sound, since we do not see that the tremorsofa body which is giving out a sound are capable ofgivingrise to Light, even as the movement of the hand in the airis not capable of producing Sound.Now if one examines what this matter may be inwhich the movement coming from the luminous body ispropagated, which I call Ethereal matter, one will seethat it is not the same that serves for the propagationof Sound. For one finds that the latter is really that whichwe feel and which we breathe, and which being removedfrom any place still leaves there the other kind of matterthat serves to convey Light. This may be proved byshutting up a sounding body in a glass vessel from whichthe air is withdrawn by the machine which Mr. Boylehas given us, and with which he has performed so manybeautiful experiments. But in doing this of which Ispeak, care must be taken to place the sounding body oncotton or on feathers, in such a way that it cannot commu-nicate its tremors either to the glass vessel which enclosesit, or to the machine; a precaution which has hithertobeen negle&ed. For then after having exhausted all theair one hears no Sound from the metal, though it isstruck.One sees here not only that our air, which does notpenetrate through glass, is the matter by which Soundspreads; but also that it is not the same air but anotherkind of matter in which Light spreads; since if the air isremoved


22/143

12 TREATISEremoved from the vessel the Light does not cease to traverseit as before.And this last point is demonstrated even more clearly bythe celebrated experiment of Torricelli, in which the tubeof glass from which the quicksilver has withdrawn itself,remaining void of air, transmits Light just the same aswhen air is in it. For this proves that a matter differentfrom air exists in this tube, and that this matter musthave penetrated the glass or the quicksilver, either one orthe other, though they are both impenetrable to the air.And when, in the same experiment, one makes the vacuumafter putting a little water above the quicksilver, one con-cludes equally that the said matter passes through glass orwater, or through both.As regards the different modes in which I have said themovements of Sound and of Light are communicated, onemay sufficiently comprehend how this occurs in the caseof Sound if one considers that the air is of such a naturethat it can be compressed and reduced to a much smallerspace than that which it ordinarily occupies. And in pro-portion as it is compressed the more does it exert an effortto regain its volume; for this property along with itspenetrability, which remains notwithstanding its com-pression, seems to prove that it is made up of small bodieswhich float about and which are agitated very rapidly inthe ethereal matter composed of much smaller parts. Sothat the cause of the spreading of Sound is the effort whichthese little bodies make in collisions with one another, toregain freedom whe^n they are a little more squeezed to-gether in the circuit of these waves than elsewhere.But the extreme velocity of Light, and other propertieswhich it has, cannot admit of such a propagation of motion,and


23/143

ON LIGHT. CHAP. I 13and I am about to show here the way in which I conceiveit must occur. For this, it is needful to explain the pro-perty which hard bodies must possess to transmit move-ment from one to another. .When one takes a number of spheres of equal size, madeof some very hard substance, and arranges them in a straightline, so that they touch one another, one finds, on strikingwith a similar sphere against the first of these spheres, thatthe motion passes as in an instant to the last of them,which separates itself from the row, without one's beingable to perceive that the others have been stirred. Andeven that one which was used to strike remains motionlesswith them. Whence one sees that the movement passeswith an extreme velocity which is the greater, the greaterthe hardness of the substance of the spheres.But it is still certain that this progression of motion isnot instantaneous, but successive, and therefore must taketime. For if the movement, or the disposition to move-ment, if you will have it so, did not pass successivelythrough all these spheres, they would all acquire themovement at the same time, and hence would all advancetogether; which does not happen. For the last one leavesthe whole row and acquires the speed of the one which waspushed. Moreover there are experiments which demon-strate that all the bodies which we reckon of the hardestkind, such as quenched steel, glass, and agate, aft assprings and bend somehow, not only when extended asrods but also when they are in the form of spheres or ofother shapes. That is to say they yield a little in them-selves at the place where they are struck, and immediatelyregain their former figute. For I have found that on strik-ing with a ball of glass or of agate against a large and quitethick


24/143

i 4 TREATISEthick piece of the same substance whicn nau a flat surface,slightly soiled with breath or in some other way, thereremained round marks, of smaller or larger size accordingas the blow had been weak or strong. This makes itevident that these substances yield where they meet, andspring back: and for this time must be required.Now in applying this kind of movement to that whichproduces Light there is nothing to hinder us from estimat-ing the particles of the ether to be of a substance as nearlyapproaching to perfeft hardness and possessing a springi-ness as prompt as we choose. It is not necessary to examinehere the causes of this hardness, or of that springiness,the consideration of which would lead us too far fromour subjeft. I will say, however, in passing that we mayconceive that the particles of the ether, notwithstandingtheir smallness, are in turn composed of other parts and thattheir springiness consists in the very rapid movement ofa subtle matter which penetrates them from every sideand constrains their structure to assume such a disposition asto give to this fluid matter the most overt and easy pass-age possible. This accords with the explanation whichMr. Des Cartes gives for the spring, though I do not, likehim, suppose the pores to be in the form of round hollowcanals. And it must not be thought that in this there isanything absurd or impossible, it being on the contraryquite credible^ that it is this infinite series of differentsizes of corpuscles, having different degrees of velocity,ofwhich Nature makes use to produce so many marvellouseffefts.

But though we shall ignore the true cause of springinesswe still see that there are many bodies which possess thisproperty; and thus there is nothing strange in supposingthat


25/143

ON LIGHT. CHAP. I 15that it exists also in little invisible bodies like the particlesof the Ether. Also if one wishes to seek for any other wayin which the movement of Light is successively com-municated, one will find none which agrees better, withuniform progression, as seems to be necessary, than the pro-perty of springiness; because if this movement should growslower in proportion as it is shared over a greater quantityof matter, in moving away from the source of the light, itcould not conserve this great velocity over great distances.But by supposing springiness in the ethereal matter, itsparticles will have the property of equally rapid restitutionwhether they are pushed strongly or feebly; and thus thepropagation of Light will always go on with an equalvelocity.^And it must be known that although the particles ofthe ether are not ranged thus in straight lines, as in ourrow of spheres, but confusedly, so that one of them touchesseveral others, this does not hinder them from transmittingtheirmovement and from spreading it always forward. As tothis it is to be remarked that there is a law ^-^ofmotion serving for this propagation, and ( B )verifiable by experiment. It is that when ^ 'a sphere, such as A here, touches severalother similar spheres CCC, if it is struckby another sphere B in such a way as toexert an impulse against all the spheresCCC which touch it, it transmits to themthe whole of its movement, and remainsafter that motionless like the sphere B. And without sup-posing that the ethereal particles are of spherical form (forI see indeed no need to suppose them so) one may wellunderstand that this property of communicating an im-pulse


26/143

16 TREATISEpulse does not fail to contribute to the aforesaid propaga-tion of movement.

Equality of size seems* to be more necessary, because

otherwise there ought to be some reflexion of movementbackwards when it passes from a smaller particle to alarger one, according to the Laws of Percussion which Ipublished some years ago.However, one will see hereafter that we have to supposesuch an equality not so much as a necessity for the propaga-tion of light as for rendering that propagation easier andmore powerful ; for it is not beyond the limits of prob-ability that the particles of the ether have been madeequal for a purpose so important as that of light, at leastin that vast space which is beyond the region of atmo-sphere and which seems to serve only to transmit thelight of the Sun and the Stars.

I have then shown in what manner one may conceiveLight to spread successively, by spherical waves, and howit is possible that this spreading is accomplished with asgreat a velocity as that which experiments and celestialobservations demand. Whence it may be further remarkedthat although the particles are supposed to be in con-tinual movement (for there are many reasons for this) thesuccessive propagation of the waves cannot be hindered bythis; because the propagation consists nowise in the trans-port ofthose particles but merely in a small agitation whichthey cannot help communicating to those surrounding,notwithstanding any movement which may aft on themcausing them to be changing positions amongst themselves.But we must consider still more particularly the originof these waves, and the manner in which they spread.And, first, it follows from what has been said on the pro-duftion


27/143

ON LIGHT. CHAP. I 17du6Hon of Light, that each little region of a luminous body,such as the Sun, a candle, or a burning coal, generates itsown waves of which that region is thecentre. Thus in the flame of a candle,having distinguished the points A, B, C,concentric circles described about eachof these points represent the waveswhich come from them. And one mustimagine the same about every pointof the surface and of the part withinthe flame.But as the percussions at the centresof these waves possess no regular suc-cession, it must not be supposed thatthewavesthemselves followone anotherat equal distances: and if the distances marked in the figureappear to be such, it is rather to mark the progression ofone and the same wave at equal intervals of time than torepresent several of them issuing from one and the samecentre.

After all, this prodigious quantity of waves whichtraverse one another without confusion and without effac-ing one another must not be deemed inconceivable; itbeing certain that one and the same particle of matter canserve for many waves coming from different sides or evenfrom contrary dire


28/143

i8 TREATISED,one will see each ofthem rebound with the same velocitywhich it had in striking, yet the whole row will remain in

.

its place, although the movement has passed along its wholelength twice over. And ifthese contrarymovements happento meet one another at the middle sphere, B, or at someother such as C, that sphere will yield and at as a springat both sides, and so will serve at the same instant to trans-mit these two movements.But what may at first appear full strange and even in-credible is that the undulations produced by such smallmovements and corpuscles, should spread to such immensedistances; as for example from the Sun or from the Starsto us. For the force of these waves must grow feeble inproportion as they move away from their origin, so thatthe aftion of each one in particular will without doubt be-come incapable of making itself felt to our sight. But onewill cease to be astonished by considering how at a greatdistance from the luminous body an infinitude of waves,though they have issued from different points of this body,unite together in such a way that they sensibly composeone single wave only, which, consequently, ought to haveenough force to make itself felt. Thus this infinite numberof waves which originate at the same instant from allpoints of a fixed star, big it may be as the Sun, makepractically only one single wave which may well haveforce enough to produce an impression on our eyes. More-over from each luminous point there may come manythousands of waves in the smallest imaginable time, bythe frequent percussion of the corpuscles which strike theEther


29/143

ON LIGHT. CHAP. I 19Ether at these points: which further contributes to render-ing their aftion more sensible.There is the further consideration in the emanation ofthese waves, that each particle of matter in which a wavespreads, ought not to communicate its motion only to thenext particle which is in the straight line drawn from theluminous point, but that it also imparts some of itnecessarily to all the others which touch it and whichoppose themselves to its movement. So it arises that aroundeach particle there ismadea wave of which thatparticle is the centre.Thus if DCF is a waveemanating from the lu-minous point A, whichis its centre, the particleB, one ofthose comprisedwithin the sphere DCF,will have made its par-ticular or partial waveKCL, which will touchthe wave DCF at C atthe same moment that the principal wave emanating fromthe point A has arrived at DCF ; and it is clear that itwill be only the region C of the wave KCL which willtouch the wave DCF, to wit, that which is in the straightline drawn through AB. Similarly the other particles ofthe sphere DCF, such as bb> dd^ etc., will each make itsown wave. But each of these waves can be infinitelyfeeble only as compared with the wave DCF, to the com-position of which all the others contribute by the part oftheir surface which is most distant from the centre A.One

B


30/143

20 TREATISEOne sees, in addition, that the wave DCF is determined

by the distance attained in a certain space of time by themovement which started from the point A; there being nomovement beyond this wave, though there will be in thespace which it encloses, namely in parts of the particularwaves, those parts which do not touch the sphere DCF.And all this ought not to seem fraught with too muchminuteness or subtlety, since we shall see in the sequelthat all the properties of Light, and everything pertain-ing to its reflexion and its refra6lion, can be explainedin principle by this means. This is a matter which hasbeen quite unknown to those who hitherto have begunto consider the waves of light, amongst whom are Mr*Hooke in his Micrographia^ and Father Pardies, who,in a treatise of which he let me see a portion, and whichhe was unable to complete as he died shortly afterward,had undertaken to prove by these waves the effefts ofreflexion and refra&ion. But the chief foundation, whichconsists in the remark I have just made, was lacking inhis demonstrations; and for the rest he had opinions verydifferent from mine, as may be will appear some day if hiswriting has been preserved.To come to the properties of Light. We remark firstthat each portion of a wave ought to spread in such a waythat its extremities lie always between the same straightlines drawn from the luminous point. Thus the portionBG of the wave, having the luminous point A as its centre,will spread into the arc CE bounded by the straightlines ABC, AGE. For although the particular waves pro-duced by the particles comprised within the space CAEspread also outside this space, they yet do not concur at thesame instant to compose a wave which terminates themovement


31/143

ON LIGHT. CHAP. I 21movement, as they do precisely at the circumference CE,which is their common tangent.And hence one sees the reason why light, at least if itsrays are not reflefted or broken, spreads only by straightlines, so that it illuminates no object except when the pathfrom its source to that obje6l is open along such lines.For if, for example, there were an opening BG, limitedby opaque bodies BH, GI, the wave of light which issuesfrom the point A will always be terminated by the straightlines AC, AE, as has just been shown ; the parts of the par-tial waves which spread outside the space ACE being toofeeble to produce light there.Now, however small we make the opening BG, thereis always the same reason causing the light there to passbetween straight lines ; since this opening is always largeenough to contain a great number of particles of theethereal matter, which are of an inconceivable smallness ;so that it appears that each little portion of the wavenecessarily advances following the straight line whichcomes from the luminous point. Thus then we may takethe rays of light as if they were straight lines.

It appears, moreover, by what has been remarked touch-ing the feebleness of the particular waves, that it is notneedful that all the .particles of the Ether should be equalamongst themselves, though equality is more apt for thepropagation of the movement. For it is true that inequalitywill cause a particle by pushing against another larger oneto strive to recoil with a part of its movement; but it willthereby merely generate backwards towards the luminouspoint some partial waves incapable of causing light, andnot a wave compounded of many as CE was.

Another property of waves of light, and one of the mostmarvellous.


32/143

22 TREATISEmarvellous, is that when some of them come from differentor even from opposing sides, they produce their effeft acrossone another without any hindrance. Whence also it comesabout that a number ofspectators may view different objeftsat the same time through the same opening, and that twopersons can at the same time see one another's eyes. Nowaccording to the explanation which has been given of theaction of light, how the waves do not destroy nor interruptone another when they cross one another, these effectswhich I have just mentioned are easily conceived. But inmy judgement they are not at all easy to explain accord-ing to the views of Mr. Des Cartes, who makes Light toconsist in a continuous pressure merely tending to move-ment. For this pressure not being able to aft from twoopposite sides at the same time, against bodies whichhave no inclination to approach one another, it is im-possible so to understand what I have been saying abouttwo persons mutually seeing one another's eyes, or howtwo torches can illuminate one another.

CHAPTER IION REFLEXION

AVING explained the effefts of waves oflight which spread in a homogeneousmatter, we will examine next that whichhappens to them on encountering otherbodies. We will first make evident howthe Reflexion of light is explained by these

same waves, and why it preserves equality of angles. Let


33/143

ON LIGHT. CHAP. II 23Let there be a surface AB, plane and polished, of some

metal, glass, or other body, which at first I will consideras perfeftly uniform (reserving to myself to deal at the endof this demonstration with the inequalities from which itcannot be exempt), and let a line AC, inclined to A&,represent a portion of a wave of light, the centre of whichis so distant that this portion AC may be considered as astraight line; forI consider all thisas in one plane,imagining to my-self that the planein which this fig-ure is, cuts thesphere ofthe wavethrough its centreand intersects theplane AB at rightangles. This ex-planation will suf-fice once for all.The piece C ofthe wave AC, willin a certain space of time advance as far as the plane ABat B, following the straight line CB, which may be sup-posed to come from the luminous centre, and which inconsequence is perpendicular to AC. Now in this samespace of time the portion A of the same wave, which hasbeen hindered from communicating its movement beyondthe plane AB, or at least partly so, ought to have con-tinued its movement in the matter which is above thisplane, and this along a distance equal to CB, making itsown


34/143

24 TREATISEown partial spherical wave, according to what has beensaid above. Which wave is here represented by the cir-cumference SNR, the centre of which is A, and its semi-diameter AN equal to CB.If one considers further the other pieces H of the waveAC, it appears that they will not only have reached thesurface AB by straight lines HK parallel to CB, but thatin addition they will have generated in the transparent air,from the centres K, K, K, particular spherical waves, re-presented here by circumferences the semi-diameters ofwhich are equal to KM, that is to say to the continuationsof HK as far as the line, BG parallel to AC. But all thesecircumferences have as a common tangent the straight lineBN, namely the same which is drawn from B as a tangentto the first of the circles, of which A is the centre, and ANthe semi-diameter equal to BC, as is easy to see.

It is then the line BN (comprised between B and thepoint N where the perpendicular from the point A falls)which is as it were formed by all these circumferences, andwhich terminates the movement which is made by thereflexion of the wave AC ; and it is also the place wherethe movement occurs in much greater quantity than any-where else. Wherefore, according to that which has beenexplained, BN is the propagation of the wave AC at themoment when the piece C of it has arrived at B. For thereis no other line which like BN is a common tangent to allthe aforesaid circles, except BG below the plane AB;which line BG would be the propagation of the wave ifthe movement could have spread in a medium homogene-ous with that which is above the plane. And if one wishesto see how the wave AC has come successively to BN, onehas only to draw in the same figure the straight lines KOparallel


35/143

ON LIGHT. CHAP. II 25parallel to BN, and the straight lines KL parallel to AC.Thus one will see that the straight wave AC has becomebroken up into all the OKL parts successively, and that ithas become straight again at NB.Now it is apparent here that the angle of reflexion ismade equal to the angle of incidence. For the trianglesACB, BNA being re6tangular and having the side ABcommon, and the side CB equal to NA, it follows that theangles opposite to these sides will be equal, and thereforealso the angles CBA, NAB. But as CB, perpendicular toCA, marks the direction of the incident ray, so AN, per-pendicular to the wave BN, marks the direftion of thereflected ray ; hence these rays are equally inclined to theplane AB.But in considering the preceding demonstration, onemight aver that it is indeed true that BN is the commontangent of the circular waves in the plane of this figure,but that these waves, being in truth spherical, have still aninfinitude of similar tangents, namely all the straight lineswhich are drawn from the point B in the surface generatedby the straight line BN about the axis BA. It remains,therefore, to demonstrate that there is no difficulty herein :and by the same argument one will see why the incidentray and the reflected ray are always in one and the sameplane perpendicular to the reflecting plane. I say then thatthe wave AC, being regarded only as a line, produces nolight. For a visible ray of light, however narrow it may be,has always some width, and consequently it is necessary,in representing the wave whose progression constitutes theray, to put instead of a line AC some plane figure such asthe circle HC in the following figure, by supposing, as wehave done, the luminous point to be infinitely distant.E Now


36/143

26 TREATISENow it is easy to see, following the preceding demonstra-tion, that each small piece of this wave HC having arrivedat the plane AB, and there generating each one its parti-cular wave, these will all have, when C arrives at B, a com-mon plane which will touch them, namely a circle BNsimilar to CH; and this will be intersected at its middleand at right angles by the same plane which likewise in-tersedts the circle CH and the ellipse AB.One sees also that the said spheres of the partial wavescannot have any common tangent plane other than the

circle BN; so that it will be this plane where there willbe more reflected movement than anywhere else, andwhich will therefore carry on the light in continuance fromthe wave CH.I have also stated in the preceding demonstration that themovement of the piece A of the incident wave is not ableto communicate itself beyond the plane AB, or at least notwholly. Whence it is to be remarked that though themovement of the ethereal matter might communicate itselfpartly to that of the reflecting body, this could in nothingalter the velocity of progression of the waves, on whichthe


37/143

ON LIGHT. CHAP. II 27the angle of reflexion depends. For a slight percussionought to generate waves as rapid as strong percussion inthe same matter. This comes about from the property ofbodies which aft as springs, ofwhich we have spoken above;namely that whether compressed little or much they recoilin equal times. Equally so in every reflexion of the light,against whatever body it may be, the angles of reflexionand incidence ought to be equal notwithstanding that thebody might be of such a nature that it takes away a portionof the movement made by the incident light. And experi-ment shows that in fa6t there is no polished body the re-flexion of which does not follow this rule.

But the thing to be above all remarked in our demon-stration is that it does not require that the reflecting surfaceshould be considered as a uniform plane, as has been sup-posed by all those who have tried to explain the effects ofreflexion ; but only an evenness such as may be attained bythe particles of the matter of the reflecting body being setnear to one another; which particles are larger than those ofthe ethereal matter, as will appear by what we shall say intreating of the transparency and opacity of bodies. Forthe surface consisting thus of particles put together, andthe ethereal particles being above, and smaller, it is evidentthat one could not demonstrate the equality of the anglesof incidence and reflexion by similitude to that whichhappens to a ball thrown against a wall, of which writershave always made use. In our way, on the other hand,the thing is explained without difficulty. For the smallnessof the particles of quicksilver, for example, being such thatone must conceive millions of them, in the smallest visiblesurface proposed, arranged like a heap of grains of sandwhich has been flattened as much as it is capable of being,this


38/143

28 TREATISEthis surface then becomes for our purpose as even as apolished glass is : and, although it always remains roughwith respeft to the particles of the Ether it is evident thatthe centres of all the particular spheres of reflexion, ofwhichwe have spoken, are almost in one uniform plane, and thatthus the common tangent can fit to them as perfectly as isrequisite for the production of light. And this alone is re-quisite, in our method of demonstration, to cause equalityof the said angles without the remainder of the movementrefle&ed from all parts being able to produce any contraryeffeft.

CHAPTER IIION REFRACTION

N the same way as the effects of Reflexionhave been explained by waves of light re-fledled at the surface of polished bodies, wewillexplain transparencyandthephenomenaof refraction by waves which spread withinand across diaphanous bodies, both solids,such as glass, and liquids, such as water, oils, etc. But inorder that it may not seem strange to suppose this passageof waves in the interior of these bodies, I will firstshow that one may conceive it possible in more thanone mode.

First, then, if the ethereal matter cannot penetratetransparent bodies at all, their own particles would be ableto communicate successively the movement of the waves,the same as do those of the Ether, supposing that, likethose, they are of a nature to aft as a spring. And this iseasy


39/143

ON LIGHT. CHAP. Ill 29easy to conceive as regards water and other transparentliquids, they being composed of detached particles. Butit may seem more difficult as regards glass and other trans-parent and hard bodies, because their solidity does not seemto permit them to receive movement except in their wholemass at the same time. This, however, is not necessarybecause this solidity is not such as it appears to us, it beingprobable rather that these bodies are composed of particlesmerely placed close to one another and held together bysome pressure from without of some other matter, and bythe irregularity of their shapes. For primarily their rarityis shown by the facility with which there passes throughthem the matter of the vortices of the magnet, and thatwhich causes gravity. Further, one cannot say that thesebodies are of a texture similar to that of a sponge or of lightbread, because the heat of the fire makes them flow andthereby changes the situation of the particles amongstthemselves. It remains then that they are, as has been said,assemblages of particles which touch one another withoutconstituting a continuous solid. This being so, the move-ment which these particles receive to carry on the waves oflight, being merely communicated from some of them toothers, without their going for that purpose out of theirplaces or without derangement, it may very well produceits effe6l without prejudicing in any way the apparentsolidity of the compound.By pressure from without, of which I have spoken,must not be understood that of the air, which would not

be sufficient, but that of some other more subtle matter, apressure which I chanced upon by experiment long ago,namely in the case of water freed from air, which remainssuspended in a tube open at its lower end, notwithstandingthat


40/143

3o TREATISEthat the air has been removed from the vessel in whichthis tube is enclosed.One can then in this way conceive of transparency in asolid without any necessity that the ethereal matter whichserves for light should pass through it, or that it shouldfind pores in which to insinuate itself. But the truth isthat this matter not only passes through solids, but does soeven with great facility ; of which the experiment ofTorricelli, above cited, is already a proof. Because onthe quicksilver and the water quitting the upper part ofthe glass tube, it appears that it is immediately filled withethereal matter, since light passes across it. But here isanother argument which proves this ready penetrability,not only in transparent bodies but also in all others.When light passes across a hollow sphere of glass, closedon all sides, it is certain that it is full of ethereal matter,as much as the spaces outside the sphere. And this etherealmatter, as has been shown above, consists of particles whichjust touch one another. If then it were enclosed in thesphere in such a way that it could not get out throughthe pores of the glass, it would be obliged to follow themovement of the sphere when one changes its place : andit would require consequently almost the same force toimpress a certain velocity on this sphere, when placed ona horizontal plane, as if it were full of water or perhapsof quicksilver : because every body resists the velocity ofthe motion which one would give to it, in proportion tothe quantity of matter which it contains, and which isobliged to follow this motion. But on the contrary onefinds that the sphere resists the impress ofmovement only inproportion to the quantity of matter of the glass of whichit is made. Then it must be that the ethereal matter whichis


41/143

ON LIGHT. CHAP. Ill 31is inside is not shut up, but flows through it with verygreat freedom. We shall demonstrate hereafter that bythis process the same penetrability may be inferred also asrelating to opaque bodies.The second mode then of explaining transparency, andone which appears more probably true, is by saying that thewaves of light are carried on in the ethereal matter, whichcontinuously occupies the interstices or pores of transpar-ent bodies. For since it passes through them continuouslyand freely, it follows that they are always full of it. Andone may even show that these interstices occupy muchmore space than the coherent particles which constitutethe bodies. For if what we have just said is true : that forceis required to impress a certain horizontal velocity on bodiesin proportion as they contain coherent matter; and if theproportion of this force follows the law of weights, as isconfirmed by experiment, then the quantity of the con-stituent matter of bodies also follows the proportion oftheir weights. Now we see that water weighs only onefourteenth part as much as an equal portion of quicksilver :therefore the matter of the water does not occupy thefourteenth part of the space which its mass obtains. Itmust even occupy much less of it, since quicksilver is lessheavy than gold, and the matter of gold is by no meansdense, as follows from the fa6l that the matter of thevortices of the magnet and of that which is the cause ofgravity pass very freely through it.But it may be objedled here that if water is a body ofso great rarity, and if its particles occupy so small aportion of the space of its apparent bulk, it is very strangehow it yet resists Compression so strongly without per-mitting itself to be condensed by any force which one hashitherto


42/143

32 TREATISEhitherto essayed to employ, preserving even its entireliquidity while subjeded to this pressure.This is no small difficulty. It may, however, be resolvedby saying that the very violent and rapid motion of thesubtle matter which renders water liquid, by agitating theparticles of which it is composed, maintains this liquidityin spite of the pressure which hitherto any one has beenminded to apply to it.The rarity of transparent bodies being then such as wehave said, one easily conceives that the waves might becarried on in the ethereal matter which fills the inter-stices of the particles. And, moreover, one may believethat the progression of these waves ought to be a littleslower in the interior of bodies, by reason of the smalldetours which the same particles cause. In which differ-ent velocity of light I shall show the cause of refraftionto consist.

Before doing so, I will indicate the third and last modein which transparency may be conceived; which is bysupposing that the movement of the waves of light istransmitted indifferently both in the particles of theethereal matter which occupy the interstices of bodies,and in the particles which compose them, so that themovement passes from one to the other. And it will beseen hereafter that this hypothesis serves excellently toexplain the double refra6tion of certain transparent bodies.Should it be objected that if the particles of the etherare smaller than those of transparent bodies (since theypass through their intervals), it would follow that theycan communicate to them but little of their movement, itmay be replied that the particles of these bodies are inturn composed of still smaller particles, and so it will bethese


43/143

ON LIGHT. CHAP. Ill 33these secondary particles which will receive the movementfrom those of the ether.

Furthermore, if the particles of transparent bodies havea recoil a little less prompt than that of the etherealparticles, which nothing hinders us from supposing, itwill again follow that the progression of the waves of lightwill be slower in the interior of such bodies than it isoutside in the ethereal matter.

All this I have found as most probable for the mode inwhich the waves of light pass across transparent bodies.To which it must further be added in what respe


44/143

34 TREATISEbodies: and since it serves for the propagation of light itwould seem that these bodies ought also to be transparent,which however is not the case.Whence then, one will say, does their opacity come?

Is it because the particles which compose them are soft;that is to say, these particles being composed of othersthat are smaller, are they capable of changing their figureon receiving the pressure of the ethereal particles, the mo-tion of which they thereby damp, and so hinder the con-tinuance of the waves of light? That cannot be: for if theparticles of the metals are soft, how is it that polishedsilver and mercury refleft light so strongly? What I findto be most probable herein, is to say that metallic bodies,which are almost the only really opaque ones, have mixedamongst their hard particles some soft ones; so that someserve to cause reflexion and the others to hinder trans-parency; while, on the other hand, transparent bodies con-tain only hard particles which have the faculty of recoil,and serve together with those of the ethereal matter forthe propagation of the waves of

light, as has been said.Let us pass now to the ex-planation of the effects of Re-fraction, assuming, as we havedone, the passage of waves oflight through transparentbodies, and the diminution ofvelocity which these same wavessuffer in them.The chief property of Refraction is that a ray of light,such as AB, being in the air, and falling obliquely uponthe polished surface of a transparent body, such as FG, isbroken


45/143

ON LIGHT. CHAP. Ill 35broken at the point of incidence B, in such a way thatwith the straight line DBE which cuts the surface per-pendicularly it makes an angle CBE less than ABD whichit made with the same perpendicular when in the air. Andthe measure of these angles is found by describing, aboutthe point B, a circle which cuts the radii AB, BC. Forthe perpendiculars AD, CE, let fall from the points ofintersection upon the straight line DE, which are calledthe Sines of the angles ABD, CBE, have a certain ratiobetween themselves; which ratio is always the same for allinclinations of the incident ray, at least for a given trans-parent body. This ratio is, in glass, very nearly as 3 to 2;and in water very nearly as 4 to 3; and is likewise differentin other diaphanous bodies.Another property, similar to this, is that the refra6lionsare reciprocal between the rays entering into a transparentbody and those which are leaving it. That is to say thatif the ray ABin entering thet r ansp arentbody is refradtedinto BC, thenlikewise CBbeing taken asa ray in theinterior of thisbody will berefrafted, onpassing out, in-to BA.To explain then the reasons of these phenomena accord-ing to our principles, let AB be the straight line whichrepresents


46/143

36 TREATISErepresents a plane surface bounding the transparent sub-stances which lie towards C and towards N. When I sayplane, that does not signify a perfeft evenness, but suchas has been understood in treating of reflexion, and for thesame reason. Let the line AC represent a portion of awave of light, the centre of which is supposed so distantthat this portion may be considered as a straight line.The piece C, then, of the wave AC, will in a certain spaceof time have advanced as far as the plane AB followingthe straight line CB, which may be imagined as comingfrom the luminous centre, and which consequently willcut AC at right angles. Now in the same time the pieceA would have come to G along the straight line AG,equal and parallel to CB; and all the portion of wave ACwould be at GB if the matter of the transparent bodytransmitted the movement of the wave as quickly as thematter of the Ether. But let us suppose that it transmitsthis movement less quickly, by one-third, for instance.Movement will then be spread from the point A, in thematter of the transparent body through a distance equalto two-thirds of CB, making its own particular sphericalwave according to what has been said before. This waveis then represented by the circumference SNR, the centreof which is A, and its semi-diameter equal to two-thirds ofCB. Then if one considers in order the other pieces H ofthe wave AC, it appears that in the same time that the pieceC reaches B they will not only have arrived at the surfaceAB along the straight lines HK parallel to CB, but that,in addition, they will have generated in the diaphanoussubstance from the centres K, partial waves, representedhere by circumferences the semi-diameters of which areequal to two-thirds of the lines KM, that is to say, totwo-thirds


47/143

ON LIGHT. CHAP. Ill 37two-thirds of the prolongations ofHK down to the straightline BG; for these semi-diameters would have been equalto entire lengths of KM if the two transparent substanceshad been of the same penetrability.Now all these circumferences have for a common tangentthe straight line BN; namely the same line which is drawnas a tangent from the point B to the circumference SNRwhich we considered first. For it is easy to see that allthe other circumferences will touch the same BN, fromB up to the point of contact N, which is the same pointwhere AN falls perpendicularly on BN.It is then BN, which is formed by small arcs of these cir-cumferences,which terminates the movement that the waveAC has communicated within the transparent body, andwhere this movement occurs in much greater amount thananywhere else. And for that reason this line, in accordancewith what has been said more than once, is the propaga-tion of the wave AC at the moment when its piece C hasreached B. For there is no other line below the planeAB which is, like BN, a common tangent to all thesepartial waves. And if one would know how the wave AChas come progressively to BN, it is necessary only to drawin the same figure the straight lines KO parallel to BN,and all the lines KL parallel to AC. Thus one will seethat the wave CA, from being a straight line, has becomebroken in all the positions LKO successively, and that ithas again become a straight line at BN. This beingevident by what has already been demonstrated, there isno need to explain it further.Now, in the same figure, if one draws EAF, which cutsthe plane AB at right angles at the point A, since AD isperpendicular to the wave AC, it will be DA which willmark


48/143

38 TREATISEmark the ray of incident light, and AN which was per-pendicular to BN, the refra6led ray: since the rays arenothing else than the straight lines along which theportions of the waves advance.Whence it is easy to recognize this chief property of re-fradtion, namely that the Sine ofthe angle DAE has alwaysthe same ratio to the Sine of the angle NAF, whatever bethe inclination of the ray DA: and that this ratio is thesame as that of the velocity of the waves in the transparentsubstance which is towards AE to their velocity in thetransparent substance towards AF. For, considering ABas the radius of a circle, the Sine of the angle BAG is BC,and the Sine of the angle ABN is AN. But the angleBAG is equal to DAE, since each of them added to CAEmakes a right angle. And the angle ABN is equal toNAF, since each of them with BAN makes a right angle.Then also the Sine of the angle DAE is to the Sine ofNAF as BC is to AN. But the ratio of BC to AN was thesame as that of the velocities of light in the substancewhich is towards AE and in that which is towards AF;therefore also the Sine of the angle DAE will be to theSine of the angle NAF the same as the said velocitiesof light.To see, consequently, what the refradtion will be whenthe waves of light pass into a substance in which themovement travels more quickly than in that from whichthey emerge (let us again assume the ratio of 3 to 2), itis only necessary to repeat all the same construction anddemonstration which we have just used, merely substitut-ing everywhere f instead off. And it will be found by thesame reasoning, in this other figure, that when the pieceC of the wave AC shall have reached the surface AB at B,all


49/143

ON LIGHT. CHAP. Ill 39all the portions of the wave AC will have advanced as faras BN, so that BC the perpendicular on AC is to AN theperpendicular on BN as 2 to 3. And there will finally bethis same ratio of 2 to 3 between the Sine of the angleBAD and the Sine of the angle FAN.Hence one sees the reciprocal relation of the refra6tionsof the ray on entering and on leaving one and the sametransparent body: namely that if NA falling on the ex-ternal surface ABis refradted into thedirection AD, sothe ray AD will berefrafted on leavingthe transparentbody into the direc-tion AN.One sees alsothe reason for anoteworthy acci-dent which hap-pens in this re-fraftion : which isthis, that after a certain obliquity of the incident ray DA,it begins to be quite unable to penetrate into the othertransparent substance. For if the angle DAQj>r CBA issuch that in the triangle ACB, CB is equal to f of AB,or is greater, then AN cannot form one side of the triangleANB, since it becomes equal to or greater than AB: sothat the portion of wave BN cannot be found anywhere,neither consequently can AN, which ought to be per-pendicular to it. And thus the incident ray DA does notthen pierce the surface AB. When


50/143

40 TREATISEWhen the ratio of the velocities of the waves is as twoto three, as in our example, which is that which obtainsfor glass and air, the angle DAQ^jrnust be more than48 degrees 1 1 minutes in order that the ray DA may beable to pass by refra


51/143

ON LIGHT. CHAP. Ill 41is easy to realize by experiment with a triangular prism;and for this our theory can afford this reason. Whenthe angle DAQ_is still large enough to enable the rayDA to pass, it is evident that the light from the portionAC of the wave is colle6ted in a minimum space whenit reaches BN. It appears also that the wave BN be-comes so much the smaller as the angle CBA or DAQis made less, until when the latter is diminished tothe limit indicated a little previously, this wave BN iscollected together always at one point. That is to say,that when the piece C of the wave AC has then arrivedat B, the wave BN which is the propagation of AC isentirely reduced to the same point B. Similarly whenthe piece H has reached K, the part AH is entirely reducedto the same point K. This makes it evident that in pro-portion as the wave CA comes to meet the surface AB,there occurs a great quantity of movement along thatsurface; which movement ought also to spread withinthe transparent body and ought to have much re-enforcedthe partial waves which produce the interior reflexionagainst the surface AB, according to the laws of reflexionpreviously explained.And because a slight diminution of the angle of incid-ence DAQ^causes the wave BN, however great it was,to be reduced to zero, (for this angle being 49 degrees 1 1minutes in the glass, the angle BAN is still 1 1 degrees 21minutes, and the same angle being reduced by one degreeonly the angle BAN is reduced to zero, and so the waveBN reduced to a point) thence it comes about that theinterior reflexion from being obscure becomes suddenlybright, so soon as the angle of incidence is such that it nolonger gives passage to the refra6tion.G Now


52/143

42 TREATISENow as concerns ordinary external reflexion, that is tosay which occurs when the angle of incidence DAQjsstill large enough to enable the refrafted ray to penetratebeyond the surface AB, this reflexion should occur againstthe particles of the substance which touches the trans-parent body on its outside. And it apparently occurs againstthe particles of the air or others mingled with the etherealparticles and larger than they. So on the other hand theexternal reflexion of these bodies occurs against the par-ticles which compose them, and which are also largerthan those of the ethereal matter, since the latter flowsin their interstices. It is true that there remains heresome difficulty in those experiments in which this interiorreflexion occurs without the particles of air being able tocontribute to it, as in vessels or tubes from which the airhas been extracted.

Experience, moreover, teaches us that these two re-flexions are of nearly equal force, and that in differenttransparent bodies they are so much the stronger as therefra&ion of these bodies is the greater. Thus one seesmanifestly that the reflexion of glass is stronger than thatof water, and that of diamond stronger than that of glass.

I will finish this theory of refraction by demonstratinga remarkable proposition which depends on it; namely,that a ray of light in order to go from one point toanother, when these points are in different media, is re-fradled in such wise at the plane surface which joins thesetwo media that it employs the least possible time: andexactly the same happens in the case of reflexion against aplane surface. Mr. Fermat was the first to propound thisproperty of refraction, holding with us, and directlycounter to the opinion of Mr, Des Cartes, that light passesmore


53/143

ON LIGHT. CHAP. Ill 43more slowly through glass and water than through air.But he assumed besides this a constant ratio of Sines,which we have just proved by these different degrees ofvelocity alone: or rather, what is equivalent, he assumednot only that the velocities were different but that the lighttook the least time possible for its passage, and thencededuced the constant ratio of the Sines. His demonstra-tion, which may be seen in his printed works, and in thevolume of letters of Mr. Des Cartes, is very long ; where-fore I give here anotherwhich is simpler andeasier.

Let KF be the planesurface; A the point inthe medium which the -light traverses moreeasily, as the air ; C thepoint in the other whichis more difficult to pene-trate, as water. And sup-pose that a ray has comefrom A, by B, to C, hav-ing been refraded at B according to the law demon-strated a little before; that is to say that, having drawnPBQ, which cuts the plane at right angles, let the sineof the angle ABP have to the sine of the angle CBQthe same ratio as the velocity of light in the mediumwhere A is to the velocity of light in the mediumwhere C is. It is to be shown that the time of passageof light along AB and BC taken together, is the shortestthat can be. Let us assume that it may have come byother lines, and, in the first place, along AF, FC, sothat


54/143

44 TREATISEthat the point of refradtion F may be further from Bthan the point A; and let AO be a line perpendicularto AB, and FO parallel to AB ; BH perpendicular toFO, and FG to BC.Since then the angle HBF is equal to PBA, and theangle BFG equal to QBC, it follows that the sine of theangle HBF will also have the same ratio to the sine ofBFG, as the velocity of light in the medium A is to itsvelocity in the medium C. But these sines are the straightlines HF, BG, if we take BF as the semi-diameter of acircle. Then these lines HF, BG, will bear to one anotherthe said ratio of the velocities. And, therefore, the time ofthe light along HF, supposing that the ray had been OF,would be equal to the time along BG in the interior ofthe medium C. But the time along AB is equal to thetime along OH ; therefore the time along OF is equal tothe time along AB, BG. Again the time along FC isgreater than that along GC ; then the time along OFC willbe longer than that along ABC. But AF is longer thanOF, then the time along AFC will by just so muchmore exceed the time along ABC.Now let us assume that the ray has come from A to Calong AK, KC ; the point of refraction K being nearerto A than the point B is; and let CN be the perpendi-cular upon BC, KN parallel to BC : BM perpendicularupon KN, and KL upon BA.Here BL and KM are the sines of angles BKL, KBM;that is to say, of the angles PBA, QBC ; and thereforethey are to one another as the velocity of light in themedium A is to the velocity in the medium C. Thenthe time along LB is equal to the time along KM ; andsince the time along BC is equal to the time along MN, thetime


55/143

ON LIGHT. CHAP. IV 45time along LBC will be equal to the time along KMN.But the time along AK is longer than that along AL :hence the time along AKN is longer than that alongABC. And KC being longer than KN, the time alongAKC will exceed, by as much more, the time along ABC.Hence it appears that the time along ABC is the shortestpossible; which was to be proven.

CHAPTER IVON THE REFRACTION OF THE AIRE have shown how the movementwhich constitutes light spreads byspherical waves in any homogeneousmatter. And it is evident that whenthe matter is not homogeneous, butof such a constitution that the move-

ment is communicated in it more rapidly toward one sidethan toward another, these waves cannot be spherical : butthat they must acquire their figure according to the differ-ent distances over which the successive movement passesin equal times.

It is thus that we shall in the first place explain therefractions which occur in the air, which extends fromhere to the clouds and beyond. The effefts of which re-fradions are very remarkable; for by them we often seeobjects which the rotundity of the Earth ought otherwiseto hide; such as Islands, and the tops of mountains whenone is at sea. Because also of them the Sun and the Moonappear as risen before in fa


56/143

46 TREATISElater: so that at times the Moon has been seen eclipsedwhile the Sun appeared still above the horizon. And so alsothe heights ofthe Sun and of the Moon, and those of all theStars always appear a little greater than they are in reality,because of these same refrations, as Astronomers know.But there is one experiment which renders this refraftionvery evident; which is that of fixing a telescope on somespot so that it views an objet, such as a steeple or ahouse, at a distance of half a league or more. If then youlook through it at different hours of the day, leaving italways fixed in the same way, you will see that the samespots of the object will not always appear at the middleof the aperture of the telescope, but that generally in themorning and in the evening, when there are more vapoursnear the Earth, these objefts seem to rise higher, so thatthe half or more of them will no longer be visible ; andso that they seem lower toward mid-day when thesevapours are dissipated.Those who consider refraction to occur only in thesurfaces which separate transparent bodies of differentnature, would find it difficult to give a reason for all thatI have just related; but according to our Theory the thingis quite easy. It is known that the air which surroundsus, besides the particles which are proper to it and whichfloat in the ethereal matter as has been explained, is fullalso of particles of water which are raised by the acftion ofheat; and it has been ascertained further by some verydefinite experiments that as one mounts up higher thedensity of air diminishes in proportion. Now whether theparticles of water and those of air take part, by means ofthe particles of ethereal matter, in the movement whichconstitutes light, but have a less prompt recoil than these,or


57/143

ON LIGHT. CHAP. IV 47or whether the encounter and hindrance which these par-ticles of air and water offer to the propagation of movementof the ethereal progress, retard the progression, it followsthat both kinds of particles flying amidst the etherealparticles, must render the air, from a great height downto the Earth, gradually less easy for the spreading of thewaves of light.Whence the configuration of the waves ought to be-

come nearly such as this figure represents: namely, if A isa light, or the visible point of a steeple, the waves whichstart from it ought to spread more widely upwards andless widely downwards, but in other directions more or lessas they approximate to these two extremes. This beingso, it necessarily follows that every line intersecting oneof these waves at right angles will pass above the point A,always excepting the one line which is perpendicular tothe horizon. Let


58/143

48 TREATISELet BC be the wave which brings the light to the

spe6lator who is at B, and let BD be the straight linewhich intersects this wave at right angles. Now becausethe ray or straight line by which we judge the spot wherethe object appears to us is nothing else than the perpendic-ular to the wave that reaches our eye, as will be under-stood by what was said above, it is manifest that the pointA will be per-

c e i ved asbeing in theline BD, andthereforehigher thanin faft it is.

Similarlyif the Earthbe AB, andthe top of theAtmosphereCD, whichprobably isnot a well de-fined spheri-cal surface

(since we know that the air becomes rare in proportionas one ascends, for above there is so much less of it topress down upon it), the waves of light from the suncoming, for instance, in such a way that so long as theyhave not reached the Atmosphere CD the straight line AEinterse


59/143

ON LIGHT. CHAP. IV 49CA is the wave which brings the light to the speftator atA, its region C will be the furthest advanced ; and thestraight line AF, which intersects this wave at right angles,and which determines the apparent place of the Sun, willpass above the real Sun, which will be seen along the lineAE. And so it may occur that when it ought not to bevisible in the absence of vapours, because the line AEencounters the rotundity of the Earth, it will be perceivedin the line AF by refra6lion. But this angle EAF isscarcely ever more than half a degree because the attenua-tion of the vapours alters the waves of light but little.Furthermore these refraftions are not altogether constantin all weathers, particularly at small elevations of 2 or 3degrees; which results from the different quantity ofaqueous vapours rising above the Earth.And this same thing is the cause why at certain timesa distant obje6t will be hidden behind another less distantone, and yet may at another time be able to be seen,although the spot from which it is viewed is always thesame. But the reason for this effeft will be still moreevident from what we are going to remark touching thecurvature of rays. It appears from the things explainedabove that the progression or propagation of a small partof a wave of light is properly what one calls a ray. Nowthese rays, instead of being straight as they are in homo-geneous media, ought to be curved in an atmosphere ofunequal penetrability. For they necessarily follow fromthe objeft to the eye the line which intersefts at rightangles all the progressions of the waves, as in the firstfigure the line AEB does, as will be shown hereafter ; andit is this line which determines what interposed bodieswould or would not hinder us from seeing the objed. ForH although


60/143

50 TREATISEalthough the point of the steeple A appears raised to D, itwould yet not appear to the eye B if the tower H wasbetween the two, because it crosses the curve AEB. Butthe tower E, which is beneath this curve, does not hinderthe point A from being seen. Now according as the airnear the Earth exceeds in density that which is higher,the curvature of the ray AEB becomes greater: so thatat certain times it passes above the summit E, whichallows the point A tobe perceived by the

eye at B ; and at othertimes it is intercepted: by the same tower Ewhich hides A from

this same eye.: But to demonstrate

this curvature of therays conformably to allour preceding Theory,let us imagine that ABis a small portion of awave of light comingfrom the side C, whichwe may consider as a straight line. Let us also suppose

that it is perpendicular to the Horizon, the portion Bbeing nearer to the Earth than the portion A; and thatbecause the vapours are less hindering at A than at B,the particular wave which comes from the point A spreadsthrough a certain space AD while the particular wavewhich starts from the point B spreads through a shorterspace BE; AD and BE being parallel to the Horizon.Further, supposing the straight lines FG, HI, etc., to bedrawn


61/143

ON LIGHT. CHAP. IV 51drawn from an infinitude of points in the straight line ABand to terminate on the line DE (which is straightor may be considered as such), let the different penetra-bilities at the different heights in the air between A andB be represented by all these lines ; so that the particularwave, originating from the point F, will spread across thespace FG, and that from the point H across the space HI,while that from the point A spreads across the space AD.Now if about the centres A, B, one describes the circlesDK, EL, which represent the spreading ofthe waves whichoriginate from these two points, and if one draws thestraight line KL which touches these two circles, it iseasy to see that this same line will be the common tangentto all the other circles drawn about the centres F, H, etc. ;and that all the points of contact will fall within that partof this line which is comprised between the perpendicularsAK, BL. Then it will be the line KL which will terminatethe movement of the particular waves originating fromthe points of the wave AB ; and this movement will bestronger between the points KL, than anywhere else at thesame instant, since an infinitude of circumferences concurto form this straight line; and consequently KL will bethe propagation of the portion of wave AB, as has beensaid in explaining reflexion and ordinary refraction. Nowit appears that AK and BL dip down toward the sidewhere the air is less easy to penetrate: for AK beinglonger than BL, and parallel to it, it follows that the linesAB and KL, being prolonged, would meet at the side L.But the angle K is a right angle: hence KAB is necessarilyacute, and consequently less than DAB. If one investigatesin the same way the progression of the portion of thewave KL, one will find that after a further time it hasarrived


62/143

52 TREATISEarrived at MN in such a manner that the perpendicularsKM, LN, dip down even more than do AK, BL. Andthis suffices to show that the ray will continue along thecurved line which intersefts all the waves at right angles,as has been said.

CHAPTER VON THE STRANGE REFRACTION OF ICELAND CRYSTAL

IJHERE is brought from Iceland, which isan Island in the North Sea, in the latitudeof 66 degrees, a kind of Crystal or trans-parent stone, very remarkable for its figureand other qualities, but above all for itsstrange refractions. The causes of thishave seemed to me to be worthy of being carefully in-

vestigated, the more so because amon

Documents

Huygens, Treatise on Light