,,harper',s ,,library of ,,living ,,thought ,illustration3 ,,harper',s ,,library of ,,living ,,thought ,wie ,alles sich zum ,ganzen webt ,eins in dem andern wirkt und lebt6 ,,the ,,ether ,,of ,,space ,,by ,,sir ,,oliver ,,lodge1 ,f4,r4,s4 ,,harper ,,brothers ,,london ,,new ,,york ,illustration3 ,,fig4 #ae4 ,view of ,ether machine complete and in action4 7,see ,chapter ,v1 and figs4 #ab and #ac47 ,frontispiece ,,the ,,ether ,,of ,,space ,,by ,,sir ,,oliver ,,lodge1 ,f4,r4,s4 ,d4 ,sc4 ,lond41 ,hon4 ,d4 ,sc4 ,oxon4 et ,vict4 ,,ll4,d4 ,st4 ,andrews1 ,glasgow1 and ,aberdeen ,vice-,president of the ,institution of ,electrical ,engineers ,rumford ,medallist of the ,royal ,society ,ex-,president of the ,physical ,society of ,london ,late ,professor of ,physics in the ,university ,college of ,liverpool ,honorary ,member of the ,american ,philosophical ,society of ,philadelphia2 of the ,manchester ,philosophical ,society2 of the ,batavian ,society of ,rotterdam2 and of the ,academy of ,sciences of ,bologna ,principal of the ,university of ,birmingham ,,illustrated ,,london ,,and ,,new ,,york ,,harper ,,brothers #de ,,albemarle ,,street1 ,w4 #aiji ,copyright1 #aiji1 by ,harper ,brothers ,all rights reserved ,,preface ,investigation of the nature and properties of the ,ether of ,space has long been for me the most fascinating branch of ,physics1 and ,i welcome the opportunity of attempting to make generally known the conclusions to which ,i have so far been led on this great and perhaps inexhaustible subject4 ,,oliver ,,lodge4 ,,university ,,of ,,birmingham1 ,march1 #aiji4 ,,to ,,the ,,founders ,,of ,,university ,,college1 ,,liverpool1 ,,especially ,,to ,,those ,,bearing ,,the ,,names ,,of ,,rathbone ,,and ,,of ,,holt ,,this ,,book ,,is ,,inscribed ,,contents ,,chapter ,,page ,,introduction4 ,,general ,,and ,,historical xi ,i4 ,,the ,,luminiferous ,,ether ,,and ,,the ,,modern ,,theory ,,of ,,light #a ,,ii4 ,,the ,,interstellar ,,ether ,,as ,a ,,connecting ,,medium #ac ,,iii4 ,,influence ,,of ,,motion ,,on ,,various ,,phenomena #bi ,,iv4 ,,experiments ,,on ,,the ,,ether #dd ,v4 ,,special ,,experiment ,,on ,,etherial ,,viscosity #fg ,,vi4 ,,etherial ,,density #hj ,,vii4 ,,further ,,explanations ,,concerning ,,the ,,density ,,and ,,energy ,,of ,,the ,,ether #hg ,,viii4 ,,ether ,,and ,,matter #ih ,,ix4 ,,strength ,,of ,,the ,,ether #aae ,x4 ,,general ,,theory ,,of ,,aberration #abg ,,appendix #a4 ,,on ,,gravity ,,and ,,etherial ,,tension #adc ,,appendix #b4 ,,calculations ,,in ,,connexion ,,with ,,ether ,,density #adf ,,appendix #c4 ,,fresnel',s ,,law ,a ,,special ,,case ,,of ,a ,,universal ,,potential ,,function #aeb ,,list ,,of ,,illustrations ,,fig4 ,illustrations of ,aberration4 #a4 ,cannon shots #ce #b4 ,boats or ,waves #cf #c4 ,lighthouse beams #cg #d4 ,ray through a moving stratum #dj #e4 ,wave-fronts in moving medium #da #f4 ,normal reflexion in moving medium #dc ,experiments on ,ether drift4 #g4 ,interference ,kaleidoscope #ea #h4 ,hoek's experiment #ec #i4 ,experiment of ,mascart and ,jamin #ed #aj4 ,diagram of ,michelson's experiment #fa ,illustrations of ,ether ,machine 7,lodge74 #aa4 ,diagram of course of light #fi #ab4 ,general view of whirling part of ,ether ,machine #gb #ac4 ,general view of optical frame #gc #ad4 ,drawing of optical details #gd #ae4 ,view of ,ether ,machine in action ,frontispiece #af4 ,appearance of interference bands and micrometer wires #gf #ag4 ,iron mass for magnetisation #gg #ah4 ,appearance of bands #gf #ai4 ,arrangement for electrification #gh ,,introduction ,ether or ther 7 probably from ,i burn17 a material substance of a more subtle kind than visible bodies1 supposed to exist in those parts of space which are apparently empty4 ,so begins the article ,ether1 written for the ninth edition of the ,encyclopdia ,britannica1 by ,james ,clerk ,maxwell4 ,the derivation of the word seems to indicate some connexion in men's minds with the idea of ,fire3 the other three elements1 ,earth1 ,water1 ,air1 representing the solid1 liquid1 and gaseous conditions of ordinary matter respectively4 ,the name ther suggests a far more subtle or penetrating and ultra-material kind of substance4 ,newton employs the term for the medium which fills space--not only space which appears to be empty1 but space also which appears to be full2 for the luminiferous ether must undoubtedly penetrate between the atoms--must exist in the pores so to speak--of every transparent substance1 else light could not travel through it4 ,the following is an extract from ,newton's surmises concerning this medium3-- ,qu4 #ah4 ,if in two large tall cylindrical ,vessels of ,glass inverted1 two little ,thermometers be suspended so as not to touch the ,vessels1 and the ,air be drawn out of one of these ,vessels1 and these ,vessels thus prepared be carried out of a cold place into a warm one2 the ,thermometer in vacuo will grow warm as much and almost as soon as the ,thermometer which is not in vacuo4 ,and when the vessels are carried back into the cold place1 the ,thermometer in vacuo will grow cold almost as soon as the other ,thermometer4 ,is not the ,heat of the warm ,room conveyed through the ,vacuum by the ,vibrations of a much subtiler ,medium than ,air1 which after the ,air was drawn out remained in the ,vacuum8 ,and is not this ,medium the same with that ,medium by which ,light is transmitted1 and by whose ,vibrations ,light communicates ,heat to ,bodies8444 ,and do not the ,vibrations of this ,medium in hot ,bodies contribute to the intenseness and duration of their ,heat8 ,and do not hot ,bodies communicate their ,heat to contiguous cold ones by the ,vibrations of this ,medium propagated from them into the cold ones8 ,and is not this ,medium exceedingly more rare and subtile than the ,air1 and exceedingly more elastic and active8 ,and doth it not readily pervade all bodies8 ,and is it not 7by its elastic force7 expanded through all the ,heavens8 ,qu4 #bb4 ,may not ,planets and ,comets1 and all gross ,bodies1 perform their motions more freely1 and with less resistance in this thereal ,medium than in any ,fluid1 which fills all ,space adequately without leaving any ,pores1 and by consequence is much denser than ,quick-silver and ,gold8 ,and may not its resistance be so small1 as to be inconsiderable8 ,for instance2 if this ther 7for so ,i will call it7 should be supposed #gjjjjj times more elastic than our ,air1 and above #gjjjjj times more rare2 its resistance would be above #fjjjjjjjj times less than that of ,water4 ,and so small a resistance would scarce make any sensible alteration in the ,motions of the ,planets in ten thousand ,years4 ,that the ether1 if there be such a thing in space1 can pass readily into or through matter is often held proven by tilting a mercury barometer2 when the mercury rises to fill the transparent vacuum4 ,everything points to its universal permeance1 if it exist at all4 ,but these1 after all1 are antique thoughts4 ,electric and ,magnetic information has led us beyond them into a region of greater certainty and knowledge2 so that now ,i am able to advocate a view of the ,ether which makes it not only uniformly present and all-pervading1 but also massive and substantial beyond conception4 ,it is turning out to be by far the most substantial thing--perhaps the only substantial thing--in the material universe4 ,compared to ether the densest matter1 such as lead or gold1 is a filmy gossamer structure2 like a comet's tail or a milky way1 or like a salt in very dilute solution4 ,to lead up to and justify the idea of the reality and substantiality1 and vast though as yet largely unrecognised importance1 of the ,ether of ,space1 the following chapters have been written4 ,some of them represent the expanded notes of lectures which have been given in various places--chiefly the ,royal ,institution2 while the first chapter represents a lecture before the ,ashmolean ,society of the ,university of ,oxford in ,june1 #ahhi4 ,one chapter 7viz4 ,chap4 ,,ii7 has already been printed as part of an appendix to the third edition of ,modern ,views of ,electricity1 as well as in the ,fortnightly and ,north ,american ,reviews2 but no other chapters have yet been published1 though parts appear in more elaborate form in ,proceedings or ,transactions of learned societies4 ,the problem of the constitution of the ,ether1 and of the way in which portions of it are modified to form the atoms or other constituent units of ordinary matter1 has not yet been solved4 ,much work has been done in this direction by various mathematicians1 but much more remains to be done4 ,and until it is done1 some scepticism is reasonable--perhaps laudable4 ,meanwhile there are few physicists who will dissent from ,clerk ,maxwell's penultimate sentence in the article ,ether of which the beginning has already been quoted3-- ,whatever difficulties we may have in forming a consistent idea of the constitution of the ther1 there can be no doubt that the interplanetary and interstellar spaces are not empty1 but are occupied by a material substance or body1 which is certainly the largest1 and probably the most uniform body of which we have any knowledge4 ,,the ,,ether ,,of ,,space ,,chapter ,i ,,the ,,luminiferous ,,ether ,,and ,,the ,,modern ,,theory ,,of ,,light ,the oldest and best known function for an ether is the conveyance of light1 and hence the name luminiferous was applied to it2 though at the present day many more functions are known1 and more will almost certainly be discovered4 ,to begin with it is best to learn what we can1 concerning the properties of the ,interstellar ,ether1 from the phenomena of ,light4 ,for now wellnigh a century we have had a wave theory of light2 and a wave theory of light is quite certainly true4 ,it is directly demonstrable that light consists of waves of some kind or other1 and that these waves travel at a certain well-known velocity1--achieving a distance equal to seven times the circumference of the earth every second2 from ,new ,york to ,london and back in the thirtieth part of a second2 and taking only eight minutes on the journey from the sun to the earth4 ,this propagation in time of an undulatory disturbance necessarily involves a medium4 ,if waves setting out from the sun exist in space eight minutes before striking our eyes1 there must necessarily be in space some medium in which they exist and which conveys them4 ,waves we cannot have1 unless they be waves in something4 ,no ordinary matter is competent to transmit waves at anything like the speed of light3 the rate at which matter conveys waves is the velocity of sound1--a speed comparable to one-millionth of the speed of light4 ,hence the luminiferous medium must be a special kind of substance2 and it is called the ether4 ,the luminiferous ether it used to be called1 because the conveyance of light was all it was then known to be capable of2 but now that it is known to do a variety of other things also1 the qualifying adjective may be dropped4 ,but1 inasmuch as the term 'ether' is also applied to a familiar organic compound1 we may distinguish the ultra-material luminiferous medium by calling it the ,ether of ,space4 ,wave-motion in ether1 light certainly is2 but what does one mean by the term wave8 ,the popular notion is1 ,i suppose1 of something heaving up and down1 or perhaps of something breaking on a shore4 ,but if you ask a mathematician what he means by a wave1 he will probably reply that the most general wave is such a function of x and y and t as to satisfy the differential equation dy_/dt v dy_/dx2 while the simplest wave is y a sin 7x-vt74 ,and he might possibly refuse to give any other answer4 ,and in refusing to give any other answer than this1 or its equivalent in ordinary words1 he is entirely justified2 that is what is meant by the term wave1 and nothing less general would be all-inclusive4 ,translated into ordinary ,english the phrase signifies1 with accuracy and comprehensive completeness1 the full details of a disturbance periodic both in space and time4 ,anything thus doubly periodic is a wave2 and all waves--whether in air as sound waves1 or in ether as light waves1 or on the surface of water as ocean waves--can be comprehended in the definition4 ,what properties are essential to a medium capable of transmitting wave-motion8 ,roughly we may say two3 elasticity and inertia4 ,elasticity in some form1 or some equivalent of it1--in order to be able to store up energy and effect recoil2 inertia1--in order to enable the disturbed substance to overshoot the mark and oscillate beyond its place of equilibrium to and fro4 ,any medium possessing these two properties can transmit waves1 and unless a medium possesses these properties in some form or other1 or some equivalent for them1 it may be said with moderate security to be incompetent to transmit waves4 ,but if we make this latter statement one must be prepared to extend to the terms elasticity and inertia their very largest and broadest signification1 so as to include any possible kind of restoring force1 and any possible kind of persistence of motion1 respectively4 ,these matters may be illustrated in many ways1 but perhaps a simple loaded lath1 or spring1 in a vice will serve well enough4 ,pull it to one side1 and its elasticity tends to make it recoil2 let it go1 and its inertia causes it to overshoot its normal position4 ,that is what inertia is1--power of overshooting a mark1 or1 more accurately1 power of moving for a time even against driving force1--power to rush uphill4 ,both causes together make it swing to and fro till its energy is exhausted4 ,this is a disturbance simply periodic in time4 ,a regular series of such springs1 set at equal intervals and started vibrating at regular intervals of time one after the other1 would be periodic in space too2 and so they would1 in disconnected fashion1 typify a wave4 ,a series of pendulums will do just as well1 and if set swinging in orderly fashion will furnish at once an example and an appearance of wave motion1 which the most casual observer must recognise as such4 ,the row of springs obviously possesses elasticity and inertia2 and any wave-transmitting medium must similarly possess some form of elasticity and some form of inertia4 ,but now proceed to ask what is this ,ether which in the case of light is thus vibrating8 ,what corresponds to the elastic displacement and recoil of the spring or pendulum8 ,what corresponds to the inertia whereby it overshoots its mark8 ,do we know these properties in the ether in any other way8 ,the answer1 given first by ,clerk ,maxwell1 and now reiterated and insisted on by experiments performed in every important laboratory in the world1 is3-- ,the elastic displacement corresponds to electrostatic charge1--roughly speaking1 to electricity4 ,the inertia corresponds to magnetism4 ,this is the basis of the modern electromagnetic theory of light4 ,let me attempt to illustrate the meaning of this statement1 by reviewing some fundamental electrical facts in the light of these analogies3-- ,the old and familiar operation of charging a ,leyden jar--the storing up of energy in a strained dielectric--any electrostatic charging whatever is quite analogous to the drawing aside of our flexible spring4 ,it is making use of the elasticity of the ether to produce a tendency to recoil4 ,letting go the spring is analogous to permitting a discharge of the jar--permitting the strained dielectric to recover itself--the electrostatic disturbance to subside4 ,in nearly all the experiments of electrostatics etherial elasticity is manifest4 ,next consider inertia4 ,how would one illustrate the fact that water1 for instance1 possesses inertia--the power of persisting in motion against obstacles--the power of possessing kinetic energy8 ,the most direct way would be1 to take a stream of water and try suddenly to stop it4 ,open a water tap freely and then suddenly shut it4 ,the impetus or momentum of the stopped water makes itself manifest by a violent shock to the pipe1 with which everybody must be familiar4 ,this momentum of water is utilised by engineers in the water-ram4 ,a precisely analogous experiment in ,electricity is what ,faraday called the extra current4 ,send a current through a coil of wire round a piece of iron1 or take any other arrangement for developing powerful magnetism1 and then suddenly stop the current by breaking the circuit4 ,a violent flash occurs1 if the stoppage is sudden enough1 a flash which means the bursting of the insulating air partition by the accumulated electromagnetic momentum4 ,the scientific name for this electrical inertia is self-induction4 ,briefly we may say that nearly all electromagnetic experiments illustrate the fact of etherial inertia4 ,now return to consider what happens when a charged conductor 7say a ,leyden jar7 is discharged4 ,the recoil of the strained dielectric causes a current1 the inertia of this current causes it to overshoot the mark1 and for an instant the charge of the jar is reversed2 the current now flows backwards and charges the jar up as at first2 back again flows the current2 and so on1 charging and reversing the charge1 with rapid oscillations1 until the energy is all dissipated into heat4 ,the operation is precisely analogous to the release of a strained spring1 or to the plucking of a stretched string4 ,but the discharging body1 thus thrown into strong electrical vibration1 is imbedded in the all-pervading ether2 and we have just seen that the ether possesses the two properties requisite for the generation and transmission of waves1 viz43 elasticity1 and inertia or density2 hence just as a tuning fork vibrating in air excites arial waves1 or sound1 so a discharging ,leyden jar in ether excites etherial waves1 or light4 ,etherial waves can therefore be actually produced by direct electrical means4 ,i discharge here a jar1 and the room is for an instant filled with light4 ,with light1 ,i say1 though you can see nothing4 ,you can see and hear the spark indeed--but that is a mere secondary disturbance we can for the present ignore--,i do not mean any secondary disturbance4 ,i mean the true etherial waves emitted by the electric oscillation going on in the neighbourhood of the recoiling dielectric4 ,you pull aside the prong of a tuning fork and let it go3 vibration follows and sound is produced4 ,you charge a ,leyden jar and let it discharge3 vibration follows and light is excited4 ,it is light1 just as good as any other light4 ,it travels at the same pace1 it is reflected and refracted according to the same laws2 every experiment known to optics can be performed with this etherial radiation electrically produced1--and yet you cannot see it4 ,why not8 ,for no fault of the light1 the fault 7if there be a fault7 is in the eye4 ,the retina is incompetent to respond to these vibrations--they are too slow4 ,the vibrations set up when this large jar is discharged are from a hundred thousand to a million per second1 but that is too slow for the retina4 ,it responds only to vibrations between #djj billion and #gjj billion per second4 ,the vibrations are too quick for the ear1 which responds only to vibrations between #dj and #dj1jjj per second4 ,between the highest audible and the lowest visible vibrations there has been hitherto a great gap1 which these electric oscillations go far to fill up4 ,there has been a great gap simply because we have no intermediate sense organ to detect rates of vibration between #dj1jjj and #djj1jjj1jjj1jjj1jjj per second4 ,it was therefore an unexplored territory4 ,waves have been there all the time in any quantity1 but we have not thought about them nor attended to them4 ,it happens that ,i have myself succeeded in getting electric oscillations so slow as to be audible1--the lowest ,i had got in #ahhi were #abe per second1 and for some way above this the sparks emit a musical note2 but no one has yet succeeded in directly making electric oscillations which are visible1--though indirectly every one does it when they light a candle4 ,it is easy1 however1 to have an electric oscillator which vibrates #cjj million times a second1 and emits etherial waves a yard long4 ,the whole range of vibrations between musical tones and some thousand million per second1 is now filled up4 ,with the large condensers and self-inductances employed in modern cable telegraphy1 it is easy to get a series of beautifully regular and gradually damped electric oscillations1 with a period of two or three seconds1 recorded by an ordinary signalling instrument or siphon recorder4 ,these electromagnetic waves in space have been known on the side of theory ever since #ahfe1 but interest in them was immensely quickened by the discovery of a receiver or detector for them4 ,the great though simple discovery by ,hertz1 in #ahhh1 of an electric eye1 as ,lord ,kelvin called it1 made experiments on these waves for the first time easy or even possible4 ,from that time onward we possessed a sort of artificial sense organ for their appreciation1--an electric arrangement which can virtually see these intermediate rates of vibration4 ,since then ,branly discovered that metallic powder could be used as an extraordinarily sensitive detector2 and on the basis of this discovery1 the 'coherer' was employed by me for distant signalling by means of electric or etheric waves2 until now when many other detectors are available in the various systems of wireless telegraphy4 ,with these ,hertzian waves all manner of optical experiments can be performed4 ,they can be reflected by plain sheets of metal1 concentrated by parabolic reflectors1 refracted by prisms1 and concentrated by lenses4 ,i have made1 for instance1 a large lens of pitch1 weighing over three hundredweight1 for concentrating them to a focus4#a ,they can be made to show the phenomenon of interference1 and thus have their wave-length accurately measured4 ,they are stopped by all conductors1 and transmitted by all insulators4 ,metals are opaque2 but even imperfect insulators1 such as wood or stone1 are strikingly transparent2 and waves may be received in one room from a source in another1 the door between the two being shut4 ,the real nature of metallic opacity and of transparency has long been clear in ,maxwell's theory of light1 and these electrically produced waves only illustrate and bring home the well-known facts4 ,the experiments of ,hertz are1 in fact1 the apotheosis of ,maxwell's theory4 99 99 99 99 99 ,thus1 then1 in every way1 ,clerk ,maxwell's brilliant perception or mathematical deduction1 in #ahfe1 of the real nature of light is abundantly justified2 and for the first time we have a true theory of light1--no longer based upon analogy with sound1 nor upon the supposed properties of some hypothetical jelly or elastic solid1 but capable of being treated upon a substantial basis of its own1 in alliance with the sciences of ,electricity and of ,magnetism4 ,light is an electromagnetic disturbance of the ether4 ,optics is a branch of electricity4 ,outstanding problems in optics are being rapidly solved1 now that we have the means of definitely exciting light with a full perception of what we are doing1 and of the precise mode of its vibration4 ,it remains to find out how to shorten down the waves--to hurry up the vibration until the light becomes visible4 ,nothing is wanted but quicker modes of vibration4 ,smaller oscillators must be used--very much smaller--oscillators not much bigger than molecules4 ,in all probability--one may almost say certainly--ordinary light is the result of electric oscillation in the molecules or atoms of hot bodies1 or sometimes of bodies not hot--as in the phenomenon of phosphorescence4 ,the direct generation of visible light by electric means1 so soon as we have learnt how to attain the necessary frequency of vibration1 will have most important practical consequences2 and that matter is initially dealt with in a section on the ,manufacture of ,light1 #adi1 in ,chapter ,,xiv of ,modern ,views of ,electricity4 ,but here we abandon further consideration of this aspect of our great subject4 ,,footnote3 #a ,see ,lodge and ,howard1 ,philosophical ,magazine for ,july1 #ahhi4 ,see also ,phil4 ,mag41 ,august1 #ahhh1 page #bbi4 ,,chapter ,,ii ,,the ,,interstellar ,,ether ,,as ,a ,,connecting ,,medium ,so far ,i have given a general idea of the present condition of the wave theory of light1 both from its theoretical and from its experimental sides4 ,the waves of light are not anything mechanical or material1 but are something electrical and magnetic--they are in fact electrical disturbances periodic in space and time1 and travelling with a known and tremendous speed through the ether of space4 ,their very existence depends upon the ether1 and their speed of propagation is its best known and most certain quantitative property4 ,a statement of this kind does not even initially express a tithe of our knowledge on the subject2 nor does our knowledge exhaust any large part of the region of discoverable fact2 but the statement above made may be regarded as certain1 although the absence of mechanics or ordinary dynamics about it removes it1 or seems to remove it1 from the category of the historically soundest and best worked department of ,physical ,science1 viz4 that explored by the ,newtonian method4 ,though in truth there is every reason to suppose that we should have had ,newton with us in these modern developments4 ,there is1 ,i believe1 a general tendency to underrate the certainty of some of the convictions to which natural philosophers have gradually1 in the course of their study of nature1 been impelled2 more especially when those convictions have reference to something intangible and occult4 ,the existence of a continuous space-filling medium1 for instance1 is probably regarded by most educated people as a more or less fanciful hypothesis1 a figment of the scientific imagination1--a mode of collating and welding together a certain number of observed facts1 but not in any physical sense a reality1 as water and air are realities4 ,i am speaking purely physically4 ,there may be another point of view from which all material reality can be denied1 but with those questions physics proper has nothing to do2 it accepts the evidence of the senses1 regarding them as the tools or instruments wherewith man may hope to understand one definite aspect of the universe2 and it leaves to philosophers1 equipped from a different armoury1 the other aspects which the material universe may--nay1 must--possess4 ,by a physical explanation is meant a clear statement of a fact or law in terms of something with which daily life has made us familiar4 ,we are all chiefly familiar1 from our youth up1 with two apparently simple things1 motion and force4 ,we have a direct sense for both these things4 ,we do not understand them in any deep way1 probably we do not understand them at all1 but we are accustomed to them4 ,motion and force are our primary objects of experience and consciousness2 and in terms of them all other less familiar occurrences may conceivably be stated and grasped4 ,whenever a thing can be so clearly and definitely stated1 it is said to be explained1 or understood2 we are said to have a dynamical theory of it4 ,anything short of this may be a provisional or partial theory1 an explanation of the less known in terms of the more known1 but ,motion and ,force are postulated in physics as the completely known3 and no attempt is made to press the terms of an explanation further than that4 ,a dynamical theory is recognised as being at once necessary and sufficient4 ,now1 it must be admitted at once that of very few things have we at present such a dynamical explanation4 ,we have no such explanation of matter1 for instance1 or of gravitation1 or of electricity1 or ether1 or light4 ,it is always conceivable that of some such things no purely dynamical explanation will ever be forthcoming1 because something more than motion and force may perhaps be essentially involved4 ,still1 physics is bound to push the search for an explanation to its furthest limits2 and so long as it does not hoodwink itself by vagueness and mere phrases--a feebleness against which its leaders are mightily and sometimes cruelly on their guard1 preferring to risk the rejection of worthy ideas rather than permit a semi-acceptance of anything fanciful and obscure--so long as it vigorously probes all phenomena within its reach1 seeking to reduce the physical aspect of them to terms of motion and force1--so long it must be upon a safe track4 ,and1 by its failure to deal with certain phenomena1 it will learn--it already begins to suspect1 its leaders must long have surmised--the existence of some third1 as yet unknown1 category1 by incorporating which the physics of the future may rise to higher flights and an enlarged scope4 ,i have said that the things of which we are permanently conscious are motion and force1 but there is a third thing which we have likewise been all our lives in contact with1 and which we know even more primarily1 though perhaps we are so immersed in it that our knowledge realises itself later1--viz4 life and mind4 ,i do not now pretend to define these terms1 or to speculate as to whether the things they denote are essentially one and not two4 ,they exist1 in the sense in which we permit ourselves to use that word1 and they are not yet incorporated into physics4 ,till they are1 they may remain more or less vague2 but how or when they can be incorporated1 is not for me even to conjecture4 ,still1 it is open to a physicist to state how the universe appears to him1 in its broad character and physical aspect4 ,if ,i were to make the attempt ,i should find it necessary for the sake of clearness to begin with the simplest and most fundamental ideas2 in order to illustrate1 by facts and notions in universal knowledge1 the kind of process which essentially occurs in connection with the formation of higher and less familiar conceptions1--in regions where the common information of the race is so slight as to be useless4 ,primary ,acquaintance with the ,external ,world4 ,beginning with our most fundamental sense ,i should sketch the matter thus3-- ,we have muscles and can move4 ,i cannot analyse motion1--,i doubt if the attempt is wise1--it is a simple immediate act of perception1 a direct sense of free unresisted muscular action4 ,we may indeed move without feeling it1 and that teaches us nothing1 but we may move so as to feel it1 and this teaches us much1 and leads to our first scientific inference1 viz4 space2 that is1 simply1 room to move about4 ,we might have had a sense of being jammed into a full or tight-packed universe2 but we have not3 we feel it to be a spacious one4 ,of course we do not stop at this baldness of inference3 our educated faculty leads us to realise the existence of space far beyond the possibility of direct sensation2 and1 further1 by means of the direct appreciation of speed in connection with motion1--of uniform and variable speed1--we become able to formulate the idea of time1 or uniformity of sequence2 and we attain other more complex notions--acceleration and the like--upon a consideration of which we need not now enter4 ,but our muscular sense is not limited to the perception of free motion3 we constantly find it restricted or forcibly resisted4 ,this muscular action impeded is another direct sense1 that of force2 and attempts to analyse it into anything simpler than itself have hitherto resulted only in confusion4 ,by force is meant primarily muscular action not accompanied by motion4 ,our sense of this teaches us that space1 though roomy1 is not empty3 it gives us our second scientific inference--what we call matter4 ,again we do not stop at this bare inference4 ,by another sense1 that of pain1 or mere sensation1 we discriminate between masses of matter in apparently intimate relation with ourselves1 and other or foreign lumps of matter2 and we use the first portion as a measure of the extent of the second4 ,the human body is our standard of size4 ,we proceed also to subdivide our idea of matter1--according to the varieties of resistance with which it appeals to our muscular sense1--into four different states1 or elements as the ancients called them2 viz4 the solid1 the liquid1 the gaseous1 and the etherial4 ,the resistance experienced when we encounter one or other of these forms of material existence varies from something very impressive--the solid1--through something nearly impalpable--the gaseous1--up to something entirely imaginative1 fanciful1 or inferential1 viz4 the ether4 ,the ether does not in any way affect our sense of touch 7i4e4 of force72 it does not resist motion in the slightest degree4 ,not only can our bodies move through it1 but much larger bodies1 planets and comets1 can rush through it at what we are pleased to call a prodigious speed 7being far greater than that of an athlete7 without showing the least sign of friction4 ,i myself1 indeed1 have designed and carried out a series of delicate experiments to see whether a whirling mass of iron could to the smallest extent grip the ether and carry it round1 with so much as a thousandth part of its own velocity4 ,these shall be described further on1 but meanwhile the result arrived at is distinct4 ,the answer is1 no2 ,i cannot find a trace of mechanical connection between matter and ether1 of the kind known as viscosity or friction4 ,why1 then1 if it is so impalpable1 should we assert its existence8 ,may it not be a mere fanciful speculation1 to be extruded from physics as soon as possible8 ,if we were limited for our knowledge of matter to our sense of touch1 the question would never even have presented itself2 we should have been simply ignorant of the ether1 as ignorant as we are of any life or mind in the universe not associated with some kind of material body4 ,but our senses have attained a higher stage of development than that4 ,we are conscious of matter by means other than its resisting force4 ,matter acts on one small portion of our body in a totally different way1 and we are said to taste it4 ,even from a distance it is able to fling off small particles of itself sufficient to affect another delicate sense4 ,or again1 if it is vibrating with an appropriate frequency1 another part of our body responds2 and the universe is discovered to be not silent but eloquent to those who have ears to hear4 ,are there any more discoveries to be made8 ,yes2 and already some have been made4 ,all the senses hitherto mentioned speak to us of the presence of ordinary matter1--gross matter1 as it is sometimes called1--though when appealing to our sense of smell1 and more especially to a dog's sense of smell1 it is not very gross2 still1 with the senses hitherto enumerated we should never have become aware of the ether4 ,a stroke of lightning might have smitten our bodies back into their inorganic constituents1 or a torpedo-fish might have inflicted on us a strange kind of torment2 but from these violent tutors we should have learnt little more than a schoolboy learns from the once ever-ready cane4 ,but it so happens that the whole surface of our skin is sensitive in yet another way1 and a small portion of it is astoundingly and beautifully sensitive1 to an impression of an altogether different character--one not necessarily associated with any form of ordinary matter--one that will occur equally well through space from which all solid1 liquid1 or gaseous matter has been removed4 ,hold your hand near a fire1 put your face in the sunshine1 and what is it you feel8 ,you are now conscious of something not arriving by ordinary matter at all4 ,you are now as directly conscious as you can be of the etherial medium4 ,true the process is not very direct4 ,you cannot apprehend the ether as you can matter1 by touching or tasting or even smelling it2 but the process is analogous to the kind of perception we might get of ordinary matter if we had the sense of hearing alone4 ,it is something akin to vibrations in the ether that our skin and our eyes feel4 ,it may be rightly asserted that it is not the etherial disturbances themselves1 but other disturbances excited by them in our tissues1 that our heat nerves feel2 and the same assertion can be made for our more highly-developed and specialised sight nerves4 ,all nerves must feel what is occurring next door to them1 and can directly feel nothing else2 but the radiation1 the cause which excited these disturbances1 travelled through the ether1--not through any otherwise known material substance4 ,it should be a commonplace to rehearse how we know this4 ,briefly1 thus3 ,radiation conspicuously comes to us from the sun4 ,if any free or ordinary matter exists in the intervening space1 it must be an exceedingly rare gas4 ,in other words1 it must consist of scattered particles of matter1 some big enough to be called lumps1 some so small as to be merely atoms1 but each with a considerable gap between it and its neighbour4 ,such isolated particles are absolutely incompetent to transmit light4 ,and1 parenthetically1 ,i may say that no form of ordinary matter1 solid1 liquid1 or gaseous1 is competent to transmit a thing travelling with the speed and subject to the known laws of light4 ,for the conveyance of radiation or light all ordinary matter is not only incompetent1 but hopelessly and absurdly incompetent4 ,if this radiation is a thing transmitted by anything at all1 it must be by something sui generis4 ,but it is transmitted1--for it takes time on the journey1 travelling at a well-known and definite speed2 and it is a quivering or periodic disturbance1 falling under the general category of wave-motion4 ,nothing is more certain than that4 ,no physicist disputes it4 ,newton himself1 who is commonly and truly asserted to have promulgated a rival theory1 felt the necessity of an etherial medium1 and knew that light consisted essentially of waves4 ,sight4 ,a small digression here1 to avoid any possible confusion due to the fact that ,i have purposely associated together temperature nerves and sight nerves4 ,they are admittedly not the same1 but they are alike in this1 that they both afford evidence of radiation2 and1 were we blind1 we might still know a good deal about the sun1 and if our temperature nerves were immensely increased in delicacy 7not all over1 for that would be merely painful1 but in some protected region71 we might even learn about the moon1 planets1 and stars4 ,in fact1 an eye1 consisting of a pupil 7preferably a lens7 and a sunken cavity lined with a surface sensitive to heat1 could readily be imagined1 and might be somewhat singularly effective4 ,it would be more than a light recorder1 it could detect all the etherial quiverings caused by surrounding objects1 and hence would see perfectly well in what we call the dark4 ,but it would probably see far too much for convenience1 since it would necessarily be affected by every kind of radiation in simple proportion to its energy2 unless1 indeed1 it were provided with a supply of screens with suitably selected absorbing powers4 ,but whatever might be the advantage or disadvantage of such a sense-organ1 we as yet do not possess one4 ,our eye does not act by detecting heat2 in other words1 it is not affected by the whole range of etherial quiverings1 but only by a very minute and apparently insignificant portion4 ,it wholly ignores the ether waves whose frequency is comparable with that of sound2 and1 for thirty or forty octaves above this1 nothing about us responds2 but high up1 in a range of vibration of the inconceivably high pitch of four to seven hundred million million per second--a range which extremely few accessible bodies are able to emit1 and which it requires some knowledge and skill artificially to produce--to those waves the eye is acutely1 surpassingly1 and most intelligently sensitive4 ,this little fragment of total radiation is in itself trivial and negligible4 ,were it not for men1 and glow-worms1 and a few other forms of life1 hardly any of it would ever occur1 on such a moderate-sized lump of matter as the earth4 ,except for an occasional volcano1 or a flash of lightning1 only gigantic bodies like the sun and stars have energy enough to produce these higher flute-like notes2 and they do it by sheer main force and violence--the violence of their gravitative energy--producing not only these1 but every other kind of radiation also4 ,glow-worms1 so far as ,i know1 alone have learnt the secret of emitting the physiologically useful waves1 and none others4 ,why these waves are physiologically useful--why they are what is called light1 while other kinds of radiation are dark1 is a question to be asked1 but1 at present1 only tentatively answered4 ,the answer must ultimately be given by the ,physiologist2 for the distinction between light and non-light can only be stated in terms of the eye1 and its peculiar specialised sensitiveness2 but a hint may be given him by the ,physicist4 ,the etherial waves which affect the eye and the photographic plate are of a size not wholly incomparable with that of the atoms of matter4 ,when a physical phenomenon is concerned with the ultimate atoms of matter1 it is often relegated at present to the field of knowledge summarised under the head of ,chemistry4 ,sight is probably a chemical sense4 ,the retina may contain complex aggregations of atoms1 shaken asunder by the incident light vibrations1 and rapidly built up again by the living tissues in which they live2 the nerve-endings meanwhile appreciating them in their temporarily dissociated condition4 ,a vague speculation6 ,not to be further countenanced except as a working hypothesis leading to examination of fact2 but1 nevertheless1 the direction in which the thoughts of some physicists are tending--a direction towards which many recently discovered experimental facts point4#b ,gravitation and ,cohesion4 ,it would take too long to do more than suggest some other functions for which a continuous medium of communication is necessary4 ,we shall argue in ,chapter ,,viii that technical action at a distance is impossible4 ,a body can only act immediately on what it is in contact with2 it must be by the action of contiguous particles1--that is1 practically1 through a continuous medium1 that force can be transmitted across space4 ,radiation is not the only thing the earth feels from the sun2 there is in addition its gigantic gravitative pull1 a force or tension more than what a million million steel rods1 each seventeen feet in diameter1 could stand 7see ,chap4 ,,ix74 ,what mechanism transmits this gigantic force8 ,again1 take a steel bar itself3 when violently stretched1 with how great tenacity its parts cling together6 ,yet its particles are not in absolute contact1 they are only virtually attached to each other by means of the universal connecting medium--the ether1--a medium that must be competent to transmit the greatest stresses which our knowledge of gravitation and of cohesion shows us to exist4 ,electricity and ,magnetism4 ,hitherto ,i have mainly confined myself to the perception of the ether by our ancient sense of radiation1 whereby we detect its subtle and delicate quiverings4 ,but we are growing a new sense2 not perhaps an actual sense-organ1 though not so very unlike a new sense-organ1 though the portions of matter which go to make the organ are not associated with our bodies by the usual links of pain and disease2 they are more analogous to artificial teeth or mechanical limbs1 and can be bought at an instrument-maker's4 ,electroscopes1 galvanometers1 telephones--delicate instruments these2 not yet eclipsing our sense-organs of flesh1 but in a few cases coming within measurable distance of their surprising sensitiveness4 ,and with these what do we do8 ,can we smell the ether1 or touch it1 or what is the closest analogy8 ,perhaps there is no useful analogy2 but nevertheless we deal with it1 and that closely4 ,not yet do we fully realise what we are doing4 ,not yet have we any dynamical theory of electric currents1 of static charges1 and of magnetism4 ,not yet1 indeed1 have we any dynamical theory of light4 ,in fact1 the ether has not yet been brought under the domain of simple mechanics--it has not yet been reduced to motion and force3 and that probably because the force aspect of it has been so singularly elusive that it is a question whether we ought to think of it as material at all4 ,no1 it is apart from mechanics at present4 ,conceivably it may remain apart2 and our first additional category1 wherewith the foundations of physics must some day be enlarged1 may turn out to be an etherial one4 ,and some such inclusion may have to be made before we can attempt to annex vital or mental processes4 ,perhaps they will all come in together4 ,howsoever these things be1 this is the kind of meaning lurking in the phrase that we do not yet know what electricity or what the ether is4 ,we have as yet no dynamical explanation of either of them2 but the past century has taught us what seems to their student an overwhelming quantity of facts about them4 ,and when the present century1 or the century after1 lets us deeper into their secrets1 and into the secrets of some other phenomena now in course of being rationally investigated1 ,i feel as if it would be no merely material prospect that will be opening on our view1 but some glimpse into a region of the universe which ,science has never entered yet1 but which has been sought from far1 and perhaps blindly apprehended1 by painter and poet1 by philosopher and saint4 ,note on the ,spelling of ,ethereal4 ,the usual word ethereal suggests something unsubstantial1 and is so used in poetry2 but for the prosaic treatment of ,physics it is unsuitable1 and etheric has occasionally been used instead4 ,no just derivation can be given for such an adjective1 however2 and ,i have been accustomed simply to spell etherial with an i when no poetic meaning was intended4 ,this alternative spelling is not incorrect2 but ,milton uses the variant ethereous1 in a sense suggestive of something strong and substantial 7,par4 ,lost1 vi1 #dgc74 ,either word1 therefore1 can be employed to replace ethereal in physics3 and in succeeding chapters one or other of these is for the most part employed4 ,,footnote3 #b ,cf4 sections #aeg;,a1 #adc1 #ahg1 and chap4 xvi41 of my ,modern ,views of ,electricity4 ,,chapter ,,iii ,,influence ,,of ,,motion ,,on ,,various ,,phenomena ,notwithstanding its genuine physical nature and properties1 the ether is singularly intangible and inaccessible to our senses1 and accordingly is a subject on which it is extremely difficult to try experiments4 ,many have been the attempts to detect some phenomena depending on its motion relative to the earth4 ,the earth is travelling round the sun at the rate of #ai miles a second1 and although this is slow compared with light--being in fact just about #a_/aj1jjjth of the speed of light1--yet it would seem feasible to observe some modification of optical phenomena due to this motion through the ether4 ,and one such phenomenon is indeed known1 namely1 the stellar aberration discovered by ,bradley in #agbi4 ,the position of objects not on the earth1 and not connected with the solar system1 is apparently altered by an amount comparable to one part in ten thousand1 by the earth's motion2 that is to say1 the apparent place of a star is shifted from its true place by an angle #a_/aj1jjjth of a radian1#c or about #bj seconds of arc4 ,this is called ,astronomical ,aberration1 and is extremely well known4 ,but a number of other problems open out in connexion with it1 and on these it is desirable to enter into detail4 ,for if the ether is stationary while the earth is flying through it--at a speed vastly faster than any cannon ball1 as much faster than a cannon ball as an express train is faster than a saunter on foot--it is for all practical purposes the same as if the earth were stationary and the ether streaming past it with this immense velocity1 in the opposite direction4 ,and some consequence of such a drift might at first sight certainly be expected4 ,it might1 for instance1 seem doubtful whether terrestrial surveying operations can be conducted1 with the extreme accuracy expected of them1 without some allowance for the violent rush of the light-conveying medium past and through the theodolite of the observer4 ,let us therefore consider the whole subject further4 ,,aberration4 ,everybody knows that to shoot a bird on the wing you must aim in front of it4 ,every one will readily admit that to hit a squatting rabbit from a moving train you must aim behind it4 ,these are examples of what may be called aberration from the sender's point of view1 from the point of view of the source4 ,and the aberration1 or needful divergence between the point aimed at and the thing hit has opposite sign in the two cases--the case when receiver is moving1 and the case when source is moving4 ,hence1 if both be moving1 it is possible for the two aberrations to neutralise each other4 ,so to hit a rabbit running alongside the train you must aim straight at it4 ,if there were no air that is all simple enough4 ,but every rifleman knows to his cost that though he fixes both himself and his target tightly to the ground1 so as to destroy all aberration proper1 yet a current of air is very competent to introduce a kind of spurious aberration of its own1 which may be called windage2 and that he must not aim at the target if he wants to hit it1 but must aim a little in the eye of the wind4 ,so much from the shooter's point of view4 ,now attend to the point of view of the target4 ,consider it made of soft enough material to be completely penetrated by the bullet1 leaving a longish hole wherever struck4 ,a person behind the target1 whom we may call a marker1 by applying his eye to the hole immediately after the hit1 may be able to look through it at the shooter1 and thereby to spot the successful man4 ,i know that this is not precisely the function of an ordinary marker1 but it is more complete than his ordinary function4 ,all he does usually is to signal an impersonal hit2 some one else has to record the identity of the shooter4 ,i am rather assuming a volley of shots1 and that the marker has to allocate the hits to their respective sources by means of the holes made in the target4 ,well1 will he do it correctly8 ,assuming1 of course1 that he can do so if everything is stationary1 and ignoring all curvature of path1 whether vertical or horizontal curvature4 ,if you think it over you will perceive that a wind will not prevent his doing it correctly2 the line of hole will point to the shooter along the path of his bullet1 though it will not point along his line of aim4 ,also1 if the shots are fired from a moving ship1 the line of hole in a stationary target will point to the position the gun occupied at the instant the shot was fired1 though it may have moved since then4 ,in neither of these cases 7moving medium and moving source7 will there be any error4 ,but if the target is in motion1 on an armoured train for instance1 then the marker will be at fault4 ,the hole will not point to the man who fired the shot1 but to an individual ahead of him4 ,the source will appear to be displaced in the direction of the observer's motion4 ,this is common aberration4 ,it is the simplest thing in the world4 ,the easiest illustration of it is that when you run through a vertical shower1 you tilt your umbrella forward2 or1 if you have not got one1 the drops hit you in the face2 more accurately1 your face as you run forward hits the drops4 ,so the shower appears to come from a cloud ahead of you1 instead of from one overhead4 ,we have thus three motions to consider1 that of the source1 of the receiver1 and of the medium2 and1 of these1 only motion of receiver is able to cause an aberrational error in fixing the position of the source4 ,so far we have attended to the case of projectiles1 with the object of leading up to light4 ,but light does not consist of projectiles1 it consists of waves2 and with waves matters are a little different4 ,waves crawl through a medium at their own definite pace2 they cannot be flung forwards or sideways by a moving source2 they do not move by reason of an initial momentum which they are gradually expending1 as shots do2 their motion is more analogous to that of a bird or other self-propelling animal1 than it is to that of a shot4 ,the motion of a wave in a moving medium may be likened to that of a rowing-boat on a river4 ,it crawls forward with the water1 and it drifts with the water2 its resultant motion is compounded of the two1 but it has nothing to do with the motion of its source4 ,a shot from a passing steamer retains the motion of the steamer as well as that given it by the powder4 ,it is projected therefore in a slant direction4 ,but a boat lowered from the side of a passing steamer1 and rowing off1 retains none of the motion of its source2 it is not projected1 it is self-propelled4 ,that is like the case of a wave4 ,the diagram illustrates the difference4 ,fig4 #a shows a moving cannon or machine-gun1 moving with the arrow1 and firing a succession of shots which share the motion of the cannon as well as their own1 and so travel slant4 ,the shot fired from position #a has reached ,a1 that fired from position #b has reached ,b1 and that fired from position #c has reached ,c1 by the time the fourth shot is fired at ,d4 ,the line ,a ,b ,c ,d is a prolongation of the axis of the gun2 it is the line of aim1 but it is not the line of fire2 all the shots are travelling aslant this line1 as shown by the arrows4 ,there are thus two directions to be distinguished4 ,there is the row of successive shots1 and there is the path of any one shot4 ,these two directions enclose an angle4 ,it may be called an aberration angle1 because it is due to the motion of the source1 but it need not give rise to any aberration4 ,true direction may still be perceived from the point of view of the receiver4 ,to prove this let us attend to what is happening at the target4 ,the first shot is supposed to be entering at ,a1 and if the target is stationary will leave it at ,y4 ,a marker looking along ,y ,a will see the position whence the shot was fired4 ,this may be likened to a stationary observer looking at a moving star4 ,he sees it where and as it was when the light started on its long journey4 ,he does not see its present position1 but there is no reason why he should4 ,he does not see its physical state or anything as it is now4 ,he sees it as it was when it sent the information which he has just received4 ,there is no aberration caused by motion of source4 ,illustration3 ,,fig4 #a4 ,shots or ,disturbances with ,momentum from a ,moving ,gun4 ,but now let the receiver be moving at same pace as the gun1 as when two grappled ships are firing into each other4 ,the motion of the target carries the point ,y forward1 and the shot ,a leaves it at ,z1 because ,z is carried to where ,y was4 ,so in that case the marker looking along ,z ,a will see the gun1 not as it was when firing1 but as it is at the present moment2 and he will see likewise the row of shots making straight for him4 ,this is like an observer looking at a terrestrial object4 ,motion of the earth does not disturb ordinary vision4 ,fig4 #b shows as nearly the same sort of thing as possible for the case of emitted waves4 ,the tube is a source emitting a succession of disturbances without momentum4 ,a ,b ,c ,d may be thought of as horizontally flying birds1 or as crests of waves1 or as self-swimming torpedoes2 or they may even be thought of as bullets1 if the gun stands still every time it fires1 and only moves between whiles4 ,illustration3 ,,fig4 #b4 ,waves or ,disturbances without ,momentum from a ,moving ,source4 ,the line ,a ,b ,c ,d is now neither the line of fire nor the line of aim3 it is simply the locus of disturbances emitted from the successive positions #a #b #c #d4 ,a stationary target will be penetrated in the direction ,a ,y1 and this line will point out the correct position of the source when the received disturbance started4 ,if the target moves1 a disturbance entering at ,a may leave it at ,z1 or at any other point according to its rate of motion2 the line ,z ,a does not point to the original position of the source1 and so there will be aberration when the target moves4 ,otherwise there would be none4 ,illustration3 ,,fig4 #c4 ,beam from a ,revolving ,lighthouse4 ,now ,fig4 #b also represents a parallel beam of light travelling from a moving source1 and entering a telescope or the eye of an observer4 ,the beam lies along ,a ,b ,c ,d1 but this is not the direction of vision4 ,the direction of vision1 to a stationary observer1 is determined not by the locus of successive waves1 but by the path of each wave4 ,a ray may be defined as the path of a labelled disturbance4 ,the line of vision is ,y ,a #a1 and coincides with the line of aim2 which in the projectile case 7,fig4 #a7 it did not4 ,the case of a revolving lighthouse1 emitting long parallel beams of light and brandishing them rapidly round1 is rather interesting4 ,fig4 #c may assist the thinking out of this case4 ,successive disturbances ,a1 ,b1 ,c1 ,d1 lie along a spiral curve1 the spiral of ,archimedes2 and this is the shape of the beams1 as seen illuminating the dust particles1 though the pitch of the spiral is too gigantic to be distinguished from a straight line4 ,at first sight it might seem as if an eye looking along those curved beams would see the lighthouse slightly out of its true position2 but it is not so4 ,the true rays or actual paths of each disturbance are truly radial2 they do not coincide with the apparent beam4 ,an eye looking at the source will not look tangentially along the beam1 but will look along ,a ,s1 and will see the source in its true position4 ,it would be otherwise for the case of projectiles from a revolving turret4 ,thus1 neither translation of star nor rotation of sun can affect direction4 ,there is no aberration so long as the receiver is stationary4 ,but what about a wind1 or streaming of the medium past source and receiver1 both stationary8 ,look at ,fig4 #a again4 ,suppose a row of stationary cannon firing shots1 which get blown by a cross wind along the slant #a ,a ,y 7neglecting the curvature of path which would really exist73 still the hole in the target fixes the gun's true position1 the marker looking along ,y ,a sees the gun which fired the shot4 ,there is no true deviation from the point of view of the receiver1 provided the drift is uniform everywhere1 although the shots are blown aside and the target is not hit by the particular gun aimed at it4 ,with a moving cannon combined with an opposing wind1 ,fig4 #a would become very like ,fig4 #b4 7,n4,b4--,the actual case1 even without complication of spinning1 etc41 but merely with the curved path caused by steady wind-pressure1 is not so simple1 and there would really be an aberration or apparent displacement of the source towards the wind's eye3 an apparent exaggeration of the effect of wind shown in the diagram47 ,in ,fig4 #b the result of a wind is much the same1 though the details are rather different4 ,the medium is supposed to be drifting downwards1 across the field4 ,the source may be taken as stationary at ,s4 ,the horizontal arrows show the direction of waves in the medium2 the dotted slant line shows their resultant direction4 ,a wave centre drifts from ,d to #a in the same time as the disturbance reaches ,a1 travelling down the slant line ,d ,a4 ,the angle between dotted and full lines is the angle between ray and wave-normal4 ,now1 if the motion of the medium inside the receiver is the same as it is outside1 the wave will pass straight on along the slant to ,z1 and the true direction of the source is fixed4 ,but if the medium inside the target or telescope is stationary1 the wave will cease to drift as soon as it gets inside1 under cover as it were2 it will proceed along the path it has been really pursuing in the medium all the time1 and make its exit at ,y4 ,in this latter case--of different motion of the medium inside and outside the telescope--the apparent direction1 such as ,y ,a1 is not the true direction of the source4 ,the ray is in fact bent where it enters the differently-moving medium 7as shown in ,fig4 #d74 ,illustration3 ,,fig4 #d4 ,ray through a ,moving ,stratum4 ,a slower moving stratum bends an oblique ray1 slanting with the motion1 in the same direction as if it were a denser medium4 ,a quicker stratum bends it oppositely4 ,if a medium is both denser and quicker moving1 it is possible for the two bendings to be equal and opposite1 and thus for a ray to go on straight4 ,parenthetically ,i may say that this is precisely what happens1 on ,fresnel's theory1 down the axis of a water-filled telescope exposed to the general terrestrial ether drift4 ,in a moving medium waves do not advance in their normal direction1 they advance slantways4 ,the direction of their advance is properly called a ray4 ,the ray does not coincide with the wave-normal in a moving medium4 ,illustration3 ,,fig4 #e4 ,successive ,wave ,fronts in a ,moving ,medium4 ,all this is well shown in ,fig4 #e4 ,s is a stationary source emitting successive waves1 which drift as spheres to the right4 ,the wave which has reached ,m has its centre at ,c1 and ,c ,m is its normal2 but the disturbance1 ,m1 has really travelled along ,s ,m1 which is therefore the ray4 ,it has advanced as a wave from ,s to ,p1 and has drifted from ,p to ,m4 ,disturbances subsequently emitted are found along the ray1 precisely as in ,fig4 #b4 ,a stationary telescope receiving the light will point straight at ,s4 ,a mirror1 ,m1 intended to reflect the light straight back must be set normal to the ray1 not tangential to the wave front4 ,the diagram also equally represents the case of a moving source in a stationary medium4 ,the source1 starting at ,c1 has moved to ,s1 emitting waves as it went2 which waves1 as emitted1 spread out as simple spheres from the then position of source as centre4 ,wave-normal and ray now coincide3 ,s ,m is not a ray1 but only the locus of successive disturbances4 ,a stationary telescope would look not at ,s1 but along ,m ,c to a point where the source was when it emitted the wave ,m2 a moving telescope1 if moving at same rate as source1 will look at ,s4 ,hence ,s ,m is sometimes called the apparent ray4 ,the angle ,s ,m ,c is the aberration angle1 which in ,chap4 ,x we denote by 4 ,fig4 #f shows normal reflexion for the case of a moving medium4 ,the mirror ,m reflects light received from ,s1 to a point ,s1--just in time to catch the source there if that is moving with the medium4 ,parenthetically ,i may say that the time taken on the double journey1 ,s ,m ,s1 when the medium is moving1 is not quite the same as the double journey ,s ,m ,s1 when all is stationary2 and that this is the principle of ,michelson's great experiment2 which must be referred to later4 ,illustration3 ,,fig4 #f4 ,normal ,reflexion in ,moving ,medium4 ,the angle ,m ,s ,x is the angle in the theory of ,michelson's experiment described in ,chapter ,,iv4 ,the ether stream we speak of is always to be considered merely as one relative to matter4 ,absolute velocity of matter means velocity through the ether--which is stationary4 ,if there were no such physical standard of rest as the ether--if all motion were relative to matter alone--then the contention of ,copernicus and ,galileo would have had no real meaning4 ,,footnote3 #c ,radian is the name given by ,prof4 ,james ,thomson to a unit angle of circular measure1 an angle whose arc equals its radius1 or about #eg4 ,,chapter ,,iv ,,experiments ,,on ,,the ,,ether ,we have arrived at this3 that a uniform ether stream all through space causes no aberration1 no error in fixing direction4 ,it blows the waves along1 but it does not disturb the line of vision4 ,stellar aberration exists1 but it depends on motion of observer1 and on motion of observer only4 ,etherial motion has no effect upon it2 and when the observer is stationary with respect to object1 as he is when using a terrestrial telescope1 there is no aberration at all4 ,surveying operations are not rendered the least inaccurate by the existence of a universal etherial drift2 and they therefore afford no means of detecting it4 ,but observe that everything depends on the ether's motion being uniform everywhere1 inside as well as outside the telescope1 and along the whole path of the ray4 ,if stationary anywhere it must be stationary altogether3 there must be no boundary between stationary and moving ether1 no plane of slip1 no quicker motion even in some regions than in others4 ,for 7referring back to the remarks preceding ,fig4 #d7 if the ether in receiver is stagnant while outside it is moving1 a wave which has advanced and drifted as far as the telescope will cease to drift as soon as it gets inside1 but will advance simply along the wave-normal4 ,and in general1 at the boundary of any such change of motion a ray will be bent1 and an observer looking along the ray will see the source not in its true position1 not even in the apparent position appropriate to his own motion1 but lagging behind that position4 ,such an aberration as this1 a lag or negative aberration1 has never yet been observed2 but if there is any slip between layers of ether1 if the earth carries any ether with it1 or if the ether1 being in motion at all1 is not equally in motion everywhere throughout every transparent substance1 then such a lag or negative aberration must occur1 in precise proportion to the amount of the carriage of ether by moving bodies 7cf4 p4 #fa74 ,on the other hand1 if the ether behaves as a perfectly frictionless inviscid fluid1 or if for any other reason there is no rub between it and moving matter1 so that the earth carries no ether with it at all1 then all rays will be straight1 aberration will have its simple and well-known value1 and we shall be living in a virtual ether stream of nineteen miles a second1 by reason of the orbital motion of the earth4 ,it may be difficult to imagine that a great mass like the earth can rush at this tremendous pace through a medium without disturbing it4 ,it is not possible for an ordinary sphere in an ordinary fluid4 ,at the surface of such a sphere there is a viscous drag1 and a spinning motion diffuses out thence through the fluid1 so that the energy of the moving body is gradually dissipated4 ,the persistence of terrestrial and planetary motions shows that etherial viscosity1 if existent1 is small2 or at least that the amount of energy thus got rid of is a very small fraction of the whole4 ,but there is nothing to show that an appreciable layer of ether may not adhere to the earth and travel with it1 even though the force acting on it be but small4 ,this1 then1 is the question before us3-- ,does the earth drag some ether with it8 or does it slip through the ether with perfect freedom8 7,never mind the earth's atmosphere2 the part it plays is known and not important47 ,in other words1 is the ether wholly or partially stagnant near the earth1 or is it streaming past us with the opposite of the full terrestrial velocity of nineteen miles a second8 ,surely if we are living in an ether stream of this rapidity we ought to be able to detect some evidence of its existence4#d ,it is not so easy a thing to detect as you would imagine4 ,we have seen that it produces no deviation or error in direction4 ,neither does it cause any change of colour or ,doppler effect2 that is1 no shift of lines in spectrum4 ,no steady wind can affect pitch1 simply because it cannot blow waves to your ear more quickly than they are emitted4 ,it hurries them along1 but it lengthens them in the same proportion1 and the result is that they arrive at the proper frequency4 ,the precise effects of motion on pitch are summarised in the following table3-- ,changes of ,frequency due to ,motion4 ,source approaching shortens waves4 ,receiver approaching alters relative velocity4 ,medium flowing alters both wave-length and velocity in exactly compensatory manner4 99 99 99 99 99 ,what other phenomena may possibly result from motion8 ,here is a list3-- ,phenomena resulting from ,motion4 7#a7 ,change or apparent change in direction2 observed by telescope1 and called aberration4 7#b7 ,change or apparent change in frequency2 observed by spectroscope1 and called ,doppler effect4 7#c7 ,change or apparent change in time of journey2 observed by lag of phase or shift of interference fringes4 7#d7 ,change or apparent change in intensity2 observed by energy received by thermopile4 99 99 99 99 99 ,what we have arrived at so far is the following3-- ,motion of either source or receiver can alter frequency2 motion of receiver can alter apparent direction2 motion of the medium can do neither4 ,but the question must be asked1 can it not hurry a wave so as to make it arrive out of phase with another wave arriving by a different path1 and thus produce or modify interference effects8 ,or again1 may it not carry the waves down stream more plentifully than up stream1 and thus act on a pair of thermopiles1 arranged fore and aft at equal distances from a source1 with unequal intensity8 ,and once more1 perhaps the laws of reflection and refraction in a moving medium are not the same as they are if it be at rest4 ,then1 moreover1 there is double refraction1 colours of thin plates and thick plates1 polarisation angle1 rotation of the plane of polarisation2 all sorts of optical phenomena that need consideration4 ,it may have to be admitted1 perhaps1 that in empty space the effect of an ether drift is difficult to detect1 but will not the presence of dense matter--especially the passage through dense transparent matter--make the detection easier8 ,so a great number of questions arise1 all of which have been1 from time to time1 seriously discussed4 ,interference4 ,as an instance of such discussion1 consider ,no4 #c of the phenomena tabulated above4 ,i expect that every reader understands interference1 but ,i may just briefly say that two similar sets of waves interfere whenever and wherever the crests of one set coincide with and obliterate the troughs of the other set4 ,light advances in any given direction when crests in that direction are able to remain crests1 and troughs to remain troughs4 ,but if we contrive to split a beam of light into two halves1 to send them round by different paths1 and make them meet again1 there is no guarantee that crest will meet crest and trough trough2 it may be just the other way in some places1 and wherever that opposition of phase occurs there1 there will be local obliteration or interference4 ,two reunited half-beams of light may thus produce local stripes of darkness1 and these stripes are called interference bands4 ,it is not to be supposed that there is any destruction of light1 or any dissipation of energy3 it is merely a case of redistribution4 ,the bright parts are brighter just in proportion as the dark parts are darker4 ,the screen is illuminated in stripes and no longer uniformly1 but its total illumination is the same as if there were no interference4 ,,projection ,,of ,,interference ,,bands4 ,it is not easy to project these interference bands on a screen so as to make them visible to an audience1--partly because the bands or stripes of darkness are exceedingly narrow2 indeed ,i had not previously seen the experiment attempted4 ,but by means of what ,i call an interference kaleidoscope1 consisting of two mirrors set at an angle with a third semi-transparent mirror between them1 it is possible to get the bands remarkably clear and bright1 so that they can readily be projected3 and ,i showed these at a lecture to the ,royal ,institution of ,great ,britain in #ahib4 ,each mirror is mounted on a tripod with adjustable screw feet1 which stand on a thick iron slab1 which again rests on hollow india-rubber balls4 ,looking down on the mirrors the plan is as in the diagram ,fig4 #g1 which indicates sufficiently the geometry of the arrangement1 and shows that the two half-beams1 into which the semi-transparent plate divides the light1 will each travel round the same contour ,a ,b ,c in opposite directions1 and will then reunite and travel together towards the point of the arrow4 ,a parallel beam from an electric lantern1 when thus treated1 depicts bright and broad interference bands on a screen4 ,and the arrangement is very little sensitive to disturbance1 because the paths of the two halves of the beam are identical1 and because of the mounting4 ,a piece of good glass can be interposed without disturbance1 and the table can be struck a heavy blow without confusing the bands4 ,illustration3 ,,fig4 #g4 ,plan of ,interference ,kaleidoscope with three mirrors4 ,the arrow-feather ray is bifurcated at ,a by a semi-transparent mirror of thinly-silvered glass2 and the two halves reunite along the arrow-head after traversing a triangular contour ,a ,b ,c in opposite directions4 ,the simple geometrical relations which permit this are sufficiently indicated in the figure4 ,the arrangement would suit ,fizeau's experiment4 ,the only regular and orderly way of causing a shift of the bands is to accelerate one half of the beam and to retard the other half1 by moving a transparent substance along the contour4 ,for instance1 let the sides of the triangle ,a ,b ,c1 or one of them1 consist of a tube of water in which a rapid stream is maintained2 then the stream has a chance of accelerating one half the beam1 and retarding the other half1 thereby shifting the fringes from their normal position by a measurable amount4 ,this is the experiment made in #ahei by ,fizeau4 7,appendix #c47 ,now that most interesting and important1 and ,i think now well-known1 experiment of ,fizeau proves quite simply and definitely that if light be sent along a stream of water1 travelling inside the water as a transparent medium1 it will go quicker with the current than against it4 ,you may say that is only natural2 a wind assists sound one way and retards it the opposite way4 ,yes1 but then sound travels in air2 and wind is a bodily transfer of air2 hence1 of course1 it gives the sound a ride4 ,whereas light does not really travel in water1 but always in ether2 and it is by no means obvious whether a stream of water can help or hinder it4 ,experiment decides1 however1 and answers in the affirmative4 ,it helps it along with just about half the speed of the water2 not with the whole speed1 which is curious and important1 and really means that the moving water has no effect whatever on the ether of space1 though we must defer explaining how this comes about4 ,suffice for present purposes the fact that the velocity of light inside moving water1 and therefore presumably inside all transparent matter1 is altered to some extent by motion of that matter4 ,illustration3 ,,fig4 #h4 ,hoek's arrangement4 ,the light from source ,s is reflected so as to travel half through stagnant water and half through air on its direct journey1 the path being inverted on the return journey1 after which it enters the eye4 ,does not this fact afford an easy way of detecting a motion of the earth through the ether8 ,every vessel of stagnant water is really travelling along through the ether at the rate of nineteen miles a second4 ,send a beam of light through it one way1 and it will be hurried2 its velocity1 instead of being #adj1jjj miles a second1 will be #adj1jji miles4 ,send a beam of light the other way1 and its velocity will be #aci1iia2 just as much less4 ,bring these two beams together2 surely some of their wave-lengths will interfere4 ,m4 ,hoek1 ,astronomer at ,utrecht1 tried the experiment in this very form2 here is a diagram of his apparatus 7,fig4 #h74 ,babinet had tried another form of the experiment previously4 ,hoek expected to see interference bands1 from the two half-beams which had traversed the water1 one in the direction of the earth's motion and the other against it4 ,but no interference bands were seen4 ,the experiment gave a negative result4 ,illustration3 ,,fig4 #i4 ,arrangement of ,mascart and ,jamin4 ,a modification of ,fig4 #h1 with the beam split definitely into two halves by reflexion from a thick glass plate and reunited before observation4 ,the two half-beams go through stagnant water in opposite directions4 ,an experiment1 however1 in which nothing is seen is never a very satisfactory form of a negative experiment2 it is1 as ,mascart calls it1 doubly negative1 and we require some guarantee that the conditions were right for seeing what might really have been in some sort there4 ,hence ,mascart and ,jamin's modification of the experiment is preferable 7,fig4 #i74 ,the thing now looked for is a shift of already existing interference bands1 when the above apparatus is turned so as to have different aspects with respect to the earth's motion2 but no shift was seen4 ,interference methods all fail to display any trace of relative motion between earth and ether4 ,try other phenomena then4 ,try refraction4 ,the index of refraction of glass is known to depend on the ratio of the speed of light outside1 to the speed inside1 the glass4 ,if then the ether be streaming through glass1 the velocity of light will be different inside according as it travels with the stream or against it1 and so the index of refraction may be different4 ,arago was the first to try this experiment by placing an achromatic prism in front of a telescope on a mural circle1 and observing the deviation it produced on stars4 ,observe that it was an achromatic prism1 treating all wave-lengths alike2 he looked at the deviated image of a star1 not at its dispersed image or spectrum1--else he might have detected the change-of-frequency-effect due to motion of source or receiver first actually seen by ,sir ,w4 ,huggins4 ,i do not think ,arago would have seen it1 because ,i do not suppose his arrangements were delicate enough for that very small effect2 but there is no error in the conception of his experiment1 as ,prof4 ,mascart has inadvertently suggested there was4 ,then ,maxwell repeated the attempt in a much more powerful manner1 a method which could have detected a very minute effect indeed1 and ,mascart has also repeated it in a simple form4 ,all are absolutely negative4 ,well1 then1 what about aberration8 ,if one looks through a moving stratum1 say a spinning glass disk1 there ought to be a shift caused by the motion 7see ,fig4 #d74 ,that particular experiment has not been tried1 but ,i entertain no doubt about its result1 though a high speed and considerable thickness of glass or other medium would be necessary to produce even a microscopic apparent displacement of objects seen through it4 ,but the speed of the earth is available1 and the whole length of a telescope tube may be filled with water2 surely that is enough to displace rays of light appreciably4 ,sir ,george ,airy tried it at ,greenwich on a star1 with an appropriate zenith-sector full of water4 ,stars were seen through the water-telescope precisely as through an air telescope4 ,a negative result again6 7,the theory is fully dealt with in ,chapter ,x and ,appendix #c47 ,stellar observations1 however1 are unnecessarily difficult4 ,fresnel had pointed out that a terrestrial source of light would do just as well4 ,he had also 7being a man of exceeding genius7 predicted that nothing would happen4 ,hoek has now tried it in a perfect manner and nothing did happen4 ,but these facts are not at all disconcerting2 they are just what ought to be anticipated1 in the light of true theory4 ,the absence of all effect caused by stagnant dense matter inserted in the path of a beam of light1 that is of dense transparent matter not artificially moved with reference to the earth--or rather with reference to source and receiver--is explicable on ,fresnel's theory concerning the behaviour of ether inside matter4 ,if the index of refraction of the matter is called 1 that means that the speed of light inside it is #a_/th of the speed outside or in vacuo4 ,and that is only another way of saying that the virtual etherial density inside it is represented by 1 since the velocity of waves is inversely as the square root of the density of the medium which conveys them2--the elasticity being reckoned as constant1 and the same inside as out4 ,but then if the ether is incompressible its density must really be constant1--so how can it be denser inside matter than it is outside8 ,the answer is that presumably the ether is not really extra dense1 but is1 as it were1 loaded by the matter4 ,the atoms of matter1 or the constituent electrons1 must be presumed to be shaken by the passage of the waves of light1 as they obviously are in fluorescent substances2 and accordingly the speed of propagation will be lessened by the extra loading which the waves encounter4 ,it is not a real increase of density1 but a virtual increase1 which is really due to the addition of a certain fraction of material inertia to the inertia of the ether itself4 ,the density of ether outside being #a1 and that of the loaded ether inside being 1 the effect of the load is expressible as -#a1 while the free ether is the same inside as out4 ,suppose now that the matter is moved along4 ,the extra loading1 being part of the matter1 of course travels with it1 and thereby affects the speed of light to the extent of the load1--that is to say1 by an amount proportional to -#a as contrasted with 4 ,this is ,fresnel's predicted ratio 7-#a73 1 or #a-a_/2 and in ,fizeau's experiment with running water--especially as repeated later1 with modern accuracy1 by ,michelson--this represents exactly the amount of observed effect upon the light4 ,but if1 instead of running water1 stagnant water is used--that is stationary with respect to the earth1 though still moving violently through the ether--then the 7-#a7 effect of the load will be fixed to the matter1 and can produce no extra or motile effect4 ,the only part that could produce an effect of that kind would be the free ether1 of density #a4 ,but then this--on the above view--is absolutely stationary1 not being carried along by the earth at all2 hence this can give no effect either4 ,consequently the whole effect of an ether-drift past the earth is zero1 on optical experiments1 according to the theory of ,fresnel2 and that is exactly what all the experiments just described have confirmed4 ,since then ,prof4 ,mascart1 with great pertinacity1 has attacked the phenomena of thick plates1 ,newton's rings1 double refraction1 and the rotatory phenomenon of quartz2 but he has found absolutely nothing attributable to a stream of ether past the earth4 ,the only positive result ever supposed to be attained was in a very difficult polarisation observation by ,fizeau in #ahei4 ,unless this has been repeated1 it is safest to ignore it2 but ,i believe that ,lord ,rayleigh has repeated it1 and obtained a negative result4 ,fizeau also suggested1 but did not attempt1 what seems an easier experiment1 with fore and aft thermopiles and a source between them1 to observe the drift of a medium by its convection of energy2 but arguments based on the law of exchanges#e tend to show1 and do show as ,i think1 that a probable alteration of radiating power due to motion through a medium would just compensate the effect otherwise to be expected4 ,we may summarise most of these statements as follows3-- ,summary4 ,a real and apparent change of wave-length4 ,source alone ,a real but not apparent error in direction4 moving produces ,no lag of phase or change of intensity1 except that appropriate to altered wave-length4 ,no change of frequency4 ,medium alone ,no error in direction4 moving1 or ,a real lag of phase1 but undetectable source and receiver without control over the moving medium4 together1 produces ,a change of intensity corresponding to different distance1 but compensated by change of radiating power4 ,an apparent change of wave-length4 ,an apparent error in direction4 ,receiver alone ,no change of phase or of intensity1 moving produces except that appropriate to different virtual velocity of light4 ,i may say1 then1 that not a single optical phenomenon is able to show the existence of an ether stream near the earth4 ,all optics go on precisely as if the ether were stagnant with respect to the earth4 99 99 99 99 99 ,well1 then1 perhaps it is stagnant4 ,the experiments ,i have quoted do not prove that it is so4 ,they are equally consistent with its perfect freedom and with its absolute stagnation2 though they are not consistent with any intermediate position4 ,certainly1 if the ether were stagnant nothing could be simpler than their explanation4 ,the only phenomena then difficult to explain would be those depending on light coming from distant regions through all the layers of more or less dragged ether4 ,the theory of astronomical aberration would be seriously complicated2 in its present form it would be upset 7p4 #de74 ,but it is never wise to control facts by a theory2 it is better to invent some experiment that will give a different result in stagnant and in free ether4 ,none of those experiments so far described are really discriminative4 ,they are1 as ,i say1 consistent with either hypothesis1 though not very obviously so4 ,illustration3 ,,fig4 #aj4 ,the course of the light and of the two half-beams in ,michelson's most famous experiment4 ,the light is split at ,a1 one half sent towards ,b and back1 the other half to ,c and back4 ,compare with ,fig4 #g4 ,michelson ,experiment4 ,mr4 ,michelson1 however1 of the ,united ,states1 invented a plan that looked as if it really would discriminate2 and1 after overcoming many difficulties1 he carried it out4 ,it is described in the ,philosophical ,magazine for #ahhg4 ,michelson's famous experiment consists in looking for interference between two half-beams of light1 of which one has been sent to and fro across the line of ether drift1 and the other has been sent to and fro along the line of ether drift4 ,a semi-transparent mirror set at #de is employed to split the beam1 and a pair of normal and ordinary mirrors1 set perpendicular to the two half-beams1 are employed to return them back whence they came1 so that they can enter the eye through an observing telescope4 ,it differs essentially from the interference kaleidoscope1 ,fig4 #g1 inasmuch as there is now no luminous path ,b ,c1 and no contour enclosed by the light4 ,each half-beam goes to and fro on its own path1 and these paths1 instead of being coincident1 are widely separate1--one ,north and ,south1 for instance1 and the other ,east and ,west4 ,under these conditions the bands are much more tremulous than they were in the arrangement of ,fig4 #g1 and are subject to every kind of disturbance4 ,the apparatus has to be excessively steady1 and no fluctuation even of temperature must be permitted in the path of either beam4 ,to secure this1 the source1 the mirrors1 and the observing telescope1 were all mounted upon a massive stone slab2 and this was floated in a bath of mercury4 ,the slab could then be slowly turned round1 so that sometimes the path ,a ,b and sometimes the path ,a ,c lay approximately along or athwart the direction of the earth's motion in space4 ,and inasmuch as the motion along would take a little longer than the motion across1 though everything else was accurately the same1 some shift of the interference bands might be expected as the slab rotated4 ,but whereas in all the experiments previously described the effect looked for was a first-order effect1 of magnitude one in ten or twenty thousand1--depending1 that is to say1 on the first power of the ratio of speed of earth to speed of light1--the effect now to be expected depends on the square of that same ratio1 and therefore cannot be greater1 even in the most favourable circumstances1 than #a part in a hundred million4 ,it is easy to realise therefore that it is an exceptionally difficult experiment1 and that it required both skill and pertinacity to perform it successfully4 ,that it is an exceptionally difficult experiment will be realised when ,i say that it would fail in conclusiveness unless one part in #djj millions could be clearly detected4 ,mr4 ,michelson reckons that by his latest arrangement he could see #a in #djjj millions if it existed 7which is equivalent to detecting an error of #a_/ajjj of an inch in a length of #fj miles72 but he saw nothing4 ,everything behaved precisely as if the ether was stagnant2 as if the earth carried with it all the ether in its immediate neighbourhood4 ,and that was his conclusion4 ,theory of ,michelson ,experiment4 ,the theory of the ,michelson experiment can be expressed thus3 its optical diagram being the same as is expressed geometrically in ,fig4 #f4 ,if a relatively fixed source and receiver move through the ether with velocity u1 such that u_/v the aberration constant2 then the time of any to and fro journey ,s ,m1 inclined at angle to the direction of the drift1 is increased1 above what it would be if there were no drift1 in the ratio 7#a-sin7 _/ 7#a-7 ,this follows from merely geometrical considerations4 ,hence if a ray is split1 and half sent so that #j while the other half is sent so that #ij 7as in ,fig4 #aj71 the one will lag behind the other by a distance times the distance travelled2 which1 though very small1 may be a perceptible fraction of a wave-length1 and therefore may cause a perceptible shift of the bands4 ,but when the experiment is properly performed1 no such shift is observed4 ,the experiment thus seems to prove that there is no motion through the ether at all1 that there is no etherial drift past the earth1 that the ether immediately in contact with the earth is stagnant--or that the earth to that extent carries all neighbouring ether with it4 ,if we wish to evade this conclusion1 there is no easy way of doing so4 ,for it depends on no doubtful properties of transparent substances1 but on the straightforward fundamental principle underlying all such simple facts as that--,it takes longer to row a certain distance and back1 up and down stream1 than it does to row the same distance in still water2 or that it takes longer to run up and down a hill1 than to run the same distance laid out flat2 or that it costs more to buy a certain number of oranges at three a penny and an equal number at two a penny than it does to buy the whole lot at five for twopence4 ,hence1 although there may be some way of getting round ,mr4 ,michelson's experiment1 there is no obvious way2 and if the true conclusion be not that the ether near the earth is stagnant1 it must lead to some other important and unknown fact4 ,that fact has now come clearly to light4 ,it was first suggested by the late ,professor ,g4,f4 ,fitz,gerald1 of ,trinity ,college ,dublin1 while sitting in my study at ,liverpool and discussing the matter with me4 ,the suggestion bore the impress of truth from the first4 ,it independently occurred also to ,professor ,h4,a4 ,lorentz1 of ,leiden1 into whose theory it completely fits1 and who has brilliantly worked it into his system4 ,it may be explained briefly thus3-- ,electric charges in motion constitute an electric current4 ,similar charges repel each other1 but currents in the same direction attract4 ,consequently two similar charges moving in parallel lines will repel each other less than if stationary1--less also than if moving one after the other in the same line4 ,likewise two opposite charges1 a fixed distance apart1 attract each other less when moving side by side1 than when chasing each other4 ,the modification of the static force1 thus caused1 depends on the squared ratio of their joint speed to the velocity of light4 ,atoms of matter are charged2 and cohesion is a residual electric attraction 7see end of ,appendix #a74 ,so when a block of matter is moving through the ether of space its cohesive forces across the line of motion are diminished1 and consequently in that direction it expands1 by an amount proportioned to the square of aberration magnitude4 ,a light journey1 to and fro1 across the path of a relatively moving medium is slightly quicker than the same journey1 to and fro1 along 7see p4 #fd74 ,but if the journeys are planned or set out on a block of matter1 they do not remain quite the same when it is conveyed through space3 the journey across the direction of motion becomes longer than the other journey1 as we have just seen4 ,and the extra distance compensates or neutralises the extra speed2 so that light takes the same time for both4 ,,footnotes3 #d ,the word stationary is ambiguous4 ,i propose to use stagnant1 as meaning stationary with respect to the earth1 i4e4 as opposed to stationary in space4 #e ,lord ,rayleigh1 ,nature1 ,march #be1 #ahib4 ,,chapter ,v ,,special ,,experiment ,,on ,,etherial ,,viscosity ,the balance of evidence at this stage seems to incline in the sense that there is no ether drift1 that the ether near the earth is stagnant1 that the earth carries all or the greater part of the neighbouring ether with it1--a view which1 if true1 must singularly complicate the theory of ordinary astronomical aberration3 as is explained at the beginning of the last chapter4 ,but now put the question another way4 ,can matter carry neighbouring ether with it when it moves8 ,abandon the earth altogether2 its motion is very quick1 but too uncontrollable1 and it always gives negative results4 ,take a lump of matter that you can deal with1 and see if it pulls any ether along4 ,that is the experiment which ,i set myself to perform1 and which in the course of the years #ahia-ig ,i performed4 ,it may be thus described in essence3-- ,take a steel disk1 or rather a couple of large steel disks a yard in diameter clamped together with a space between4 ,mount the system on a vertical axis1 and spin it like a teetotum as fast as it will stand without flying to pieces4 ,then take a parallel beam of light1 split it into two by a semi-transparent mirror1 ,m1 a piece of glass silvered so thinly that it lets half the light through and reflects the other half1 somewhat as in ,fig4 #g2 and send the two halves of this split beam round and round in opposite directions in the space between the disks4 ,they may thus travel a distance of #bj or #cj or #dj feet4 ,ultimately they are allowed to meet and enter a telescope4 ,if they have gone quite identical distances they need not interfere1 but usually the distances will differ by a hundred-thousandth of an inch or so1 which is quite enough to bring about interference4 ,the mirrors which reflect the light round and round between the disks are shown in ,fig4 #aa4 ,if they form an accurate square the last two images will coincide1 but if the mirrors are the least inclined to one another at any unaliquot part of #cfj the last image splits into two1 as in the kaleidoscope is well known1 and the interference bands may be regarded as resulting from those two sources4 ,the central white band bisects normally the distance between them1 and their amount of separation determines the width of the bands4 ,there are many interesting optical details here1 but ,i shall not go into them4 ,illustration3 ,,fig4 #aa4 ,diagrammatic ,plan of ,optical ,frame for ,ether ,machine2 with ,steel ,disks1 one yard in diameter1 inside the frame4 ,the actual apparatus is shown in ,figs4 #ac and #ad and ,fig4 #ab4 ,m is a semi-transparent mirror1 reflecting half an incident beam and transmitting the other half4 ,the two half-beams each go three times round the square contour1 in opposite directions1 and then reunite4 ,it is an extension of the idea of ,fig4 #g4 ,the thing to observe is whether the motion of the disks is able to replace a bright band by a dark one1 or vice versa4 ,if it does1 it means that one of the half-beams1 viz4 that which is travelling in the same direction as the disks1 is helped on a trifle1 equivalent to a shortening of journey by some quarter millionth of an inch or so in the whole length of #cj feet2 while the other half-beam1 viz4 that travelling against the motion of the disks1 is retarded1 or its path virtually lengthened1 by the same amount4 ,if this acceleration and retardation actually occurs1 waves which did not interfere on meeting before the disks moved1 will interfere now2 for one will arrive at the common goal half a length behind the other4 ,now a gradual change of bright space to dark1 and vice versa1 shows itself1 to an observer looking at the bands1 as a gradual change of position of the bright stripes1 or a shift of the bands4 ,a shift of the bands1 and especially of the middle white band1 which is much more stable than the others1 is what we look for4 ,the middle band is1 or should be1 free from the concertina-like motion which is liable to infect the others4 ,at first ,i saw plenty of shift4 ,in the first experiment the bands sailed across the field as the disks got up speed until the crosswire had traversed a band and a half4 ,the conditions were such that had the ether whirled at the full speed of the disks ,i should have seen a shift of three bands4 ,it looked very much as if the light was helped along at half the speed of the moving matter1 just as it is inside water4 ,on stopping the disks the bands returned to their old position4 ,on starting them again in the opposite direction1 the bands ought to have shifted the other way too1 if the effect was genuine2 but they did not2 they went the same way as before4 ,the shift was therefore wholly spurious2 it was caused by the centrifugal force of the blast of air thrown off from the moving disks4 ,the mirrors and frame had to be protected from this4 ,many other small changes had to be made1 and gradually the spurious shifts have been reduced and reduced1 largely by the skill and patience of my assistant1 ,mr4 ,benjamin ,davies1 until presently there was barely a trace of them4 ,but the experiment is not an easy one4 ,not only does the blast exert pressure1 but at high speeds the churning of the air makes it quite hot4 ,moreover1 the tremor of the whirling machine1 in which from four to nine horse-power is sometimes being expended1 is but too liable to communicate itself to the optical part of the apparatus4 ,of course elaborate precautions are taken against this4 ,although the two parts1 the mechanical and the optical1 are so close together1 their supports are entirely independent4 ,but they have to rest on the same earth1 and hence communicated tremors are not absent4 ,they are the cause of most of the slight residual trouble4 ,the whole experiment is described in fairly full detail in the ,philosophical ,transactions of the ,royal ,society for #ahic and #ahig4 ,and there also are described some further modifications whereby the whirling disks are electrified--likewise without optical effect1 and are also magnetised2 or rather a great iron mass1 strongly magnetised by a current1 is used to replace the steel disks4 ,the effect was always zero1 however1 when spurious results were eliminated2 and it is clear that at no practicable speed does either electrification or magnetisation confer upon matter any appreciable viscous grip upon the ether4 ,atoms must be able to throw it into vibration1 if they are oscillating or revolving at sufficient speed2 otherwise they would not emit light or any kind of radiation2 but in no case do they appear to drag it along1 or to meet with resistance in any uniform motion through it4 ,only their acceleration is effectual4 ,in the light of ,larmor's electron theory1 we know now that acceleration of atoms1 or rather of a charge upon an atom1 necessarily generates radiation1 proportional in amount to the square of the acceleration--whether that be tangential or normal4 ,there is no theoretical reason for assuming any influence on uniform velocity4 ,and even the influence on acceleration is exceedingly small under ordinary circumstances4 ,only during the violence of collision are ether waves freely excited4 ,the present experiment1 however1 has nothing to do with acceleration3 it is a test of viscosity4 ,an acceleration term exists in motion through even a perfect fluid4 ,illustration3 ,,fig4 #ab4 ,general view of whirling part of ,ether machine1 with pair of steel disks1 and motor4 ,to face page #gb4 ,illustration3 ,,fig4 #ac4 ,general view of optical framework--sustaining mirrors1 telescope1 and collimator--to surround the disks of the ,ether machine4 ,compare fig4 #aa4 ,to face page #gc4 ,the conclusion at which ,i arrived in #ahib and #ahic is thus expressed 7p4 #ggg of vol4 #ahd ,philosophical ,transactions of the ,royal ,society73 ,i feel confident either that the ether between the disks is quite unaffected by their motion1 or1 if affected at all1 by something less than the thousandth part4 ,at the same time1 so far as rigorous proof is concerned1 ,i should prefer to assert that the velocity of light between two steel plates moving together in their own plane an inch apart is not increased or diminished by so much as the #a_/bjjth part of their velocity4 ,that was the conclusion in #ahic2 but since then observations have been continued1 and it is now quite safe to change the #a_/bjjth into #a_/ajjjth4 ,the spin was sometimes continued for three hours to see if an effect developed with time2 and many other precautions were taken1 as briefly narrated in the ,philosophical ,transactions for #ahig4 ,the following illustrations give an idea of the apparatus employed4 ,fig4 #ab shows a photograph of the whirling machine before being bolted down to its stone pier2 with the pair of disks at top ready to be whirled by an armature on the shaft1 which is supplied with a current sometimes of nine horse-power4 ,the armature winding was of low resistance1 and was specially braced1 so as to give high speed without flying out1 and without generating too much back-,e ,m ,f4 ,the ampere-meter and volt-meter and the carbon rheostat 7in armature circuit71 for regulating the speed1 are plainly seen4 ,the smooth pulley on the shaft is for applying a brake4 ,the small disk above it is perforated to act as a siren for estimation of speed2 but other arrangements for this purpose were subsequently added4 ,the two large disks at top were of the best circular-saw steel2 they are somewhat thicker at middle than at edge1 and are strongly bolted up between iron cheeks1 which are attached to the shaft4 ,the lower end of the shaft is a step-bearing of hardened steel in a vessel of oil4 ,the upper collar is elastic1 so as to allow for a steadying teetotum action at high speeds4 ,fig4 #ac is a photograph of the optical square1 which was ultimately to be placed in position surrounding the disks4 ,the slit and collimator are shown2 the micrometer end of the observing telescope is out of the picture4 ,the mirrors on the sides of the square are accurately plane2 they are adjustable on geometric principles1 and are pressed against their bearings by strong spiral springs4 ,they were made by ,hilger4 ,a drawing of the arrangement is given in ,fig4 #ad1 and here the double micrometer eye-piece is visible4 ,in ,fig4 #ae the whole apparatus is shown mounted4 ,the whirling machine strongly bolted down to a stone pier independent of the floor2 the optical frame independently supported by a gallows frame from other piers4 ,the centrifugal mercury speed-indicator is visible in front1 and ,mr4 ,davies is regulating the speed4 ,at the back is seen a boiler-plate screen for the observer with his eye at the telescope4 7,see ,frontispiece47 ,illustration3 ,lodge ,phil4 ,trans4 #ahic4 ,a4 ,plate #ca4 ,the mirror frame is pivoted on a vertical axis here ,horizontal axis of frame ,mode of mounting the semi-transparent mirror ,m so as to give altitude and azimuth movement to the reflected beam ,details of brass plate supporting fourth mirror front1 side and back views ,back view shows the three slots in which the ends of the supporting screws rest giving a fine adjustment1 the plate being supported by three rigid pushes and three elastic pulls4 ,,fig4 #ad ,plan of optical frame with steel disk in position1 and glazed drum to isolate them from the frame4 ,g represents one of the panes of optical glass4 ,supports of telescope and collimator also shewn1 and part of the fixing of the four mirrors #a4b4c4d41 three of them let into recesses in the wooden frame1 each mirror held by a brass plate supported by three finely cut screws against which it is pressed by the spring-bolts shewn ,m is the semi-transparent mirror ,west1 ,newman lith ,,fig4 #ad4 ,to face page #gd4 ,the expense of the apparatus was borne by my friend the late ,george ,holt1 shipowner1 of ,liverpool4 ,fig4 #af exhibits something like the appearance seen in the eye-piece1 with the interference bands on each side of the middle band1 and with the micrometer wires set in position--each moved by an independent micrometer head4 ,the straight vertical wire was usually set in the centre of the middle white band1 and the ,x wire on the yellow of the first coloured band on one side or the other4 ,the method of observation now consists in setting a wire of the micrometer accurately in the centre of the middle band1 while another wire is usually set on the first band to the left4 ,then the micrometer heads are read1 and the setting repeated once or twice to see how closely and dependably they can be set in the same position4 ,then we begin to spin the disks1 and when they are going at some high speed1 measured by a siren note and in other ways1 the micrometer wires are reset and read--reset several times and read each time4 ,then the disks are stopped and more readings are taken4 ,then their motion is reversed1 the wires set and read again2 and finally the motion is once more stopped and another set of readings taken4 ,by this means the absolute shift of middle band1 and its relative interpretation in terms of wave-length1 are simultaneously obtained2 for the distance from the one wire to the other1 which is often two revolutions of a micrometer head1 represents a whole wave-length shift4 ,in the best experiments ,i do still often see something like a fiftieth of a band shift2 but it is caused by residual spurious causes1 for it repeats itself with sufficient accuracy in the same direction when the disks are spun the other way round4 ,of real reversible shift1 due to motion of the ether1 ,i see nothing4 ,i do not believe the ether moves4 ,it does not move at a five-hundredth part of the speed of the steel disks4 ,further experience confirms and strengthens this estimate1 and my conclusion is that such things as circular saws1 flywheels1 railway trains1 and all ordinary masses of matter do not appreciably carry the ether with them4 ,their motion does not seem to disturb it in the least4 ,the presumption is that the same is true for the earth2 but the earth is a big body1--it is conceivable that so great a mass may be able to act when a small mass would fail4 ,i would not like to be too sure about the earth--at least not on a strictly experimental basis4 ,what ,i do feel sure of is that if moving matter disturbs ether in its neighbourhood at all1 it does so by some minute action1 comparable in amount perhaps to gravitation1 and possibly by means of the same property as that to which gravitation is due--not by anything that can fairly be likened to etherial viscosity4 ,so far as experiment has gone1 our conclusion is that the viscosity or fluid friction of the ether is zero4 ,and that is an entirely reasonable conclusion4 ,illustration3 ,,fig4 #af4 ,approximate appearance of the interference bands and micrometer wires as seen in the eye-piece of the telescope of the ,ether machine4 ,illustration3 ,,fig4 #ah4 ,appearance of the interference bands in the channel of the iron spheroid4 ,they were reflected in the upper iron as shown4 ,to face page #gf4 ,oblate spheroid for ,whirling ,machine4 ,illustration3 ,,fig4 #ag4 ,section of oblate spheroid of soft iron for whirling machine1 showing arrangement for winding central core with wire so as to be able to magnetise it strongly while spinning inside the optical frame4 ,to face page #gg4 ,,magnetisation4 ,for testing the effect of magnetism1 an oblate spheroid was made of specially selected soft iron1 #c feet in diameter1 weighing nearly a ton4 ,its section is shown in ,fig4 #ag4 ,it had an annular channel or groove1 half an inch wide and #a foot deep1 round the bottom of which was wound a kilometre of insulated wire to a depth of #d inches2 the terminals of which were brought out to sliding contacts on the shaft1 so that the whole could be very highly magnetised while it was spinning4 ,everything was arranged so as to be symmetrical about the central axis4 ,to the coil of wire1 whose resistance was #cj ohms1 #aaj volts was ordinarily1 and #bbj volts exceptionally1 applied4 ,the magnetic field with #aaj volts was about #ahjj c4g4s41 on the average1 all over the main region through which the beam of light circulated4 ,this light-bearing space1 or gap in the magnetic circuit1 was only half an inch wide2 and accordingly in the eye-piece the iron surfaces could be seen1 above and below1 as well as the interference bands in the luminous gap4 ,the whole appearance is depicted in ,fig4 #ah4 ,,electrification4 ,for the electrification experiment1 a third and insulated disk was clamped between the two steel disks and kept electrified to sparking tension4 ,the arrangement is shown diagrammatically on a smaller scale in ,fig4 #ai4 ,illustration3 ,,fig4 #ai4 ,arrangement for electrifying a third or middle steel disk to sparking potential while spinning4 ,the electrification test was exceptionally easy to apply1 by connecting the insulated charging pin to a ,voss machine in action3 because when the disks were spinning and the bands in good condition1 the electrification could be instantaneously applied1 taken off1 reversed1 or whatever was desired2 and the effect of the sudden lowering of potential by sparks passing between the revolving plates could be exactly looked for4 ,the conclusion of my second ,philosophical ,transactions paper--that of #ahig--;is that neither an electric nor a magnetic transverse field confers viscosity upon the ether1 nor enables moving matter to grip and move it rotationally4 ,,question ,,of ,a ,,possible ,,longitudinal ,,magnetic ,,drift4 ,later ,i tried a longitudinal magnetic field also2 arranging a series of four large electric bobbins or long coils along the sides of a square inscribed at #de in the optical square1 ,figs4 #aa and #ac2 so that the light went along their axes4 ,the details of this experiment have been only partially recorded1 but the salient points are to be found stated in the ,philosophical ,magazine for ,april1 #aijg1 pages #die-ejj4 ,the result was again negative2 that is to say1 a magnetic field causes no perceptible acceleration in a beam of light sent along the lines of force4 ,the extra velocity that could have been observed would have been #a_/ith of a millimetre per second1 or #af miles per hour1 for each ,c4,g4,s4 unit of field intensity4 ,another mode of expressing the result is that the difference of magnetic potential applied1 namely1 a drop of two million ,c4,g4,s4 units of magnetic potential1 does not hurry light along it by so much as #a_/ejth part of a wave-length4 ,there may be reasons for supposing that some much slower drift or conveyance than this is really caused in the ether by a magnetic field2 but if so1 the ether must be regarded as so excessively dense that the amount of such a drift for any practicable magnetic field seems almost hopelessly beyond experimental means of detection4 ,,chapter ,,vi ,,etherial ,,density ,this leads us to enter upon the question of whether it is possible to determine with any approach to accuracy the actual density or massiveness of the ether of space1 compared with those forms of matter to which our senses have made us accustomed4 ,the arguments on which an estimate may be made of the density or massiveness of the ether as compared with that of matter depend on the following considerations1 the validity of which again is dependent upon an electrical theory of matter4 ,in this theory1 or working hypothesis1 an assumption has to be made3 but it is one for which there is a large amount of justification1 and the reasons for it are given in many books1--among others in my book on ,electrons1 and likewise at the end of the new edition of ,modern ,views of ,electricity1 also in my ,romanes ,lecture1 published by the ,clarendon ,press in #aijc4 ,put briefly1 the assumption is that matter is composed1 in some way or other1 of electrons2 which again must be considered to be essentially peculiarities1 or singularities1 or definite structures1 in the ether itself4 ,indeed1 a consideration of electrons alone is sufficient for the argument1 provided it be admitted that they have the mass which experiment shows them to possess1 and the size which electrical theory deduces for them3 the basis of the idea--which1 indeed1 is now experimentally proved--being that their inertia is due to their self-induction1--i4e4 to the magnetic field with which they must be surrounded as long as they are in motion4 ,the mass1 or inertia1 of an electron is comparable to the thousandth part of that of the atom of hydrogen4 ,its linear dimension1 let us say its diameter1 is comparable to the one-hundred-thousandth part of what is commonly known as molecular or atomic dimension2 which itself is the ten-millionth part of a millimetre4 ,hence1 the mass and the bulk of an electron being known1 its density is determined1 provided we can assume that its mass is all dependent on what is contained within its periphery4 ,but that last assumption is one that quite definitely cannot be made3 its mass is for the most part outside itself1 and has to be calculated by magnetic considerations4 7,see ,appendix #b47 ,these details are gone into in my paper in the ,philosophical ,magazine for ,april1 #aijg1 and in ,chapter ,,xvii of ,modern ,views of ,electricity4 ,but without repeating arguments here1 it will suffice to say that although the estimates may be made in various ways1 differing entirely from each other1 yet the resulting differences are only slight2 the calculated densities come out all of the same order of magnitude1 namely1 something comparable to #aj ,c4,g4,s4 units1--that is to say1 a million million grammes per cubic centimetre1 or1 in other words1 a thousand tons to the cubic millimetre4 ,but1 throughout1 we have seen reason to assert that the ether is incompressible2 arguments for this are given in ,modern ,views of ,electricity1 ,chapter ,i4 ,and1 indeed1 the fundamental medium filling all space1 if there be such1 must1 in my judgment1 be ultimately incompressible2 otherwise it would be composed of parts1 and we should have to seek for something still more fundamental to fill the interstices4 ,the ether being incompressible1 and an electron being supposed composed simply and solely of ether1 it follows that it cannot be either a condensation or a rarefaction of that material1 but must be some singularity of structure1 or some portion otherwise differentiated4 ,it might1 for instance1 be something analogous to a vortex ring1 differentiated kinetically1 i4e4 by reason of its rotational motion1 from the remainder of the ether2 or it might be differentiated statically1 and be something which would have to be called a strain-centre or a region of twist1 or something which cannot be very clearly at present imagined with any security2 though various suggestions have been made in that direction4 ,the simplest plan for us is to think of it somewhat as we think of a knot on a piece of string4 ,the knot differs in no respect from the rest of the string1 except in its tied-up structure2 it is of the same density with the rest1 and yet it is differentiated from the rest2 and1 in order to cease to be a knot1 would have to be untied--a process which as yet we have not learned how to apply to an electron4 ,if ever such a procedure becomes possible1 then electrons will thereby be resolved into the general body of the undifferentiated ether of space1--that part which is independent of what we call matter4 ,the important notion for present purposes is merely this3 that the density of the undifferentiated or simple ether1 and the density of the tied-up or be-knotted or otherwise modified ether constituting an electron1 are one and the same4 ,hence the argument above given1 at least when properly worked out1 tends to establish the etherial density as of the order #aj times that of water4 ,there ought to be nothing surprising 7though ,i admit that there is something very surprising7 in such an estimate2 inasmuch as many converging lines of argument tend to show that ordinary matter is a very porous or gossamer-like substance1 with interspaces great as compared with the spaces actually occupied by the nuclei which constitute it4 ,our conception of matter1 if it is to be composed of electrons1 is necessarily rather like the conception of a solar system1 or rather of a milky way2 where there are innumerable dots here and there1 with great interspaces between4 ,so that the average density of the whole of the dots or material particles taken together1--that is to say1 their aggregate mass compared with the space they occupy1--is excessively small4 ,in the vast extent of the ,cosmos1 as a whole1 the small bulk of actual matter1 compared with the volume of empty space1 is striking--as we shall show directly2 and now on the small scale1 among the atoms of matter1 we find the conditions to be similar4 ,even what we call the densest material is of extraordinarily insignificant massiveness as compared with the unmodified ether which occupies by far the greater proportion of its bulk4 ,when we speak of the density of matter1 we are really though not consciously expressing the group-density of the modified ether which constitutes matter1--not estimated per unit1 but per aggregate2 just as we might estimate the group or average density of a cloud or mist4 ,reckoned per unit1 a cloud has the density of water2 reckoned per aggregate1 it is an impalpable filmy structure of hardly any density at all4 ,so it is with a cobweb1 so perhaps it is with a comet's tail1 so also with the ,milky ,way1 with the cosmos1--and1 as it now turns out1 with ordinary matter itself4 ,for consider the average density of the material cosmos4 ,it comes out almost incredibly small4 ,in other words1 the amount of matter in space1 compared with the volume of space it occupies1 is almost infinitesimal4 ,lord ,kelvin argues that ultimately it must be really infinitesimal 7,philosophical ,magazine1 ,aug41 #aija1 and ,jan41 #aijb71 that is to say that the volume of space is infinitely greater than the total bulk of matter which it contains4 ,otherwise the combined force of gravity--or at least the aggregate gravitational potential--on which the velocity generated in material bodies ultimately depends1 would be far greater than observation shows it to be4 ,the whole visible universe1 within a parallax of #a_/ajjj second of arc1 is estimated by ,lord ,kelvin as the equivalent of a thousand million of our suns2 and this amount of matter1 distributed as it is1 would have an average density of #af #aj grammes per c4c4 ,it is noteworthy how exceedingly small is this average or aggregate density of matter in the visible region of space4 ,the estimated density of #aj c4g4s4 means that the visible cosmos is as much rarer than a vacuum of a hundred millionths of an atmosphere1 as that vacuum is itself rarer than lead4 ,it is because we have reason to assert that any ordinary mass of matter consists1 like the cosmos1 of separated particles1 with great intervening distances in proportion to their size1 that we are able to maintain that the aggregate density of ordinary stuff1 such as water or lead1 is very small compared with the continuous medium in which they exist1 and of which all particles are supposed to be really composed4 ,so that lead is to the ether1 as regards density1 very much as the vacuum above spoken of is to lead4 ,the fundamental medium itself must be of uniform density everywhere1 whether materialised or free4 ,,chapter ,,vii ,,further ,,explanations ,,concerning ,,the ,,density ,,and ,,energy ,,of ,,the ,,ether ,a reader may suppose that in speaking of the immense density or massiveness of ether1 and the absurdly small density or specific gravity of gross matter by comparison1 ,i intend to signify that matter is a rarefaction of the ether4 ,that1 however1 is not my intention4 ,the view ,i advocate is that the ether is a perfect continuum1 an absolute plenum1 and that therefore no rarefaction is possible4 ,the ether inside matter is just as dense as the ether outside1 and no denser4 ,a material unit--say an electron--is only a peculiarity or singularity of some kind in the ether itself1 which is of perfectly uniform density everywhere4 ,what we sense as matter is an aggregate or grouping of an enormous number of such units4 ,how then can we say that matter is millions of times rarer or less substantial than the ether of which it is essentially composed8 ,those who feel any difficulty here1 should bethink themselves of what they mean by the average or aggregate density of any discontinuous system1 such as a powder1 or a gas1 or a precipitate1 or a snowstorm1 or a cloud1 or a milky way4 ,if it be urged that it is unfair to compare an obviously discrete assemblage like the stars1 with an apparently continuous substance like air or lead1--the answer is that it is entirely and accurately fair2 since air1 and every other known form of matter1 is essentially an aggregate of particles1 and since it is always their average density that we mean4 ,we do not even know for certain their individual atomic density4 ,the phrase specific gravity or density of a powder is ambiguous4 ,it may mean the specific gravity of the dry powder as it lies1 like snow2 or it may mean the specific gravity of the particles of which it is composed1 like ice4 ,so also with regard to the density of matter1 we might mean the density of the fundamental material of which its units are made--which would be ether2 or we might1 and in practice do1 mean the density of the aggregate lump which we can see and handle2 that is to say1 of water or iron or lead1 as the case may be4 ,in saying that the density of matter is small1--,i mean1 of course1 in the last1 the usual1 sense4 ,in saying that the density of ether is great1--,i mean that the actual stuff of which these highly porous aggregates are composed is of immense1 of wellnigh incredible1 density4 ,it is only another way of saying that the ultimate units of matter are few and far between--i4e4 that they are excessively small as compared with the distances between them2 just as the planets of the solar system1 or worlds in the sky1 are few and far between1--the intervening distances being enormous as compared with the portions of space actually occupied by lumps of matter4 ,it may be noted that it is not unreasonable to argue that the density of a continuum is necessarily greater than the density of any disconnected aggregate3 certainly of any assemblage whose particles are actually composed of the material of the continuum4 ,because the former is all there1 everywhere1 without break or intermittence of any kind2 while the latter has gaps in it1--it is here1 and there1 but not everywhere4 ,indeed1 this very argument was used long ago by that notable genius ,robert ,hooke1 and ,i quote a passage which ,professor ,poynting has discovered in his collected posthumous works and kindly copied out for me3-- ,as for matter1 that ,i conceive in its essence to be immutable1 and its essence being expatiation determinate1 it cannot be altered in its quantity1 either by condensation or rarefaction2 that is1 there cannot be more or less of that power or reality1 whatever it be1 within the same expatiation or content2 but every equal expatiation contains1 is filled1 or is an equal quantity of materia2 and the densest or heaviest1 or most powerful body in the world contains no more materia than that which we conceive to be the rarest1 thinnest1 lightest1 or least powerful body of all2 as gold for instance1 and ther1 or the substance that fills the cavity of an exhausted vessel1 or cavity of the glass of a barometer above the quicksilver4 ,nay1 as ,i shall afterwards prove1 this cavity is more full1 or a more dense body of ther1 in the common sense or acceptation of the word1 than gold is of gold1 bulk for bulk2 and that because the one1 viz4 the mass of ther1 is all ther3 but the mass of gold1 which we conceive1 is not all gold2 but there is an intermixture1 and that vastly more than is commonly supposed1 of ther with it2 so that vacuity1 as it is commonly thought1 or erroneously supposed1 is a more dense body than the gold as gold4 ,but if we consider the whole content of the one with that of the other1 within the same or equal quantity of expatiation1 then are they both equally containing the materia or body4--,from the ,posthumous ,works of ,robert ,hooke1 ,m4,d41 ,f4,r4,s41 #agje1 pp4 #aga-b 7as copied in ,memoir of ,dalton1 by ,angus ,smith74 ,newton's contemporaries did not excel in power of clear expression1 as he himself did2 but ,professor ,poynting interprets this singular attempt at utterance thus3--,all space is filled with equally dense materia4 ,gold fills only a small fraction of the space assigned to it1 and yet has a big mass4 ,how much greater must be the total mass filling that space4 ,the tacit assumption here made is that the particles of the aggregate are all composed of one and the same continuous substance1 --practically that matter is made of ether2 and that assumption1 in ,hooke's day1 must have been only a speculation4 ,but it is the kind of speculation which time is justifying1 it is the kind of truth which we all feel to be in process of establishment now4#f ,we do not depend on that sort of argument1 however2 what we depend on is experimental measure of the mass1 and mathematical estimate of the volume1 of the electron4 ,for calculation shows that however the mass be accounted for--whether electrostatically or magnetically1 or hydrodynamically--the estimate of ratio of mass to effective volume can differ only in a numerical coefficient1 and cannot differ as regards order of magnitude4 ,the only way out of this conclusion would be the discovery that the negative electron is not the real or the main matter-unit1 but is only a subsidiary ingredient2 whereas the main mass is the more bulky positive charge4 ,that last hypothesis however is at present too vague to be useful4 ,moreover1 the mass of such a charge would in that case be unexplained1 and would need a further step2 which would probably land us in much the same sort of etherial density as is involved in the estimate which ,i have based on the more familiar and tractable negative electron4 7,see ,appendix #b47 ,it may be said why assume any finite density for the ether at all8 ,why not assume that1 as it is infinitely continuous1 so it is infinitely dense--whatever that may mean--and that all its properties are infinite8 ,this might be possible were it not for the velocity of light4 ,by transmitting waves at a finite and measurable speed1 the ether has given itself away1 and has let in all the possibilities of calculation and numerical statement4 ,its properties are thereby exhibited as essentially finite--however infinite the whole extent of it may turn out to be4 ,parenthetically we may remark that gravitation has not yet exhibited any similar kind of finite property2 and that is why we know so little about it4 ,,etherial ,,energy4 ,instead then of saying that the density of the ether is great1 the clearest mode of expression is to say that the density of matter is small4 ,just as we can say that the density of the visible cosmos is small1 although in individual lumps its density is comparable to that of iron or rock4 ,at the risk of repetition1 ,i have explained this over again1 because it is a matter on which confusion may easily arise4 ,the really important thing about ether is not so much its density1 considered in itself1 as the energy which that density necessarily involves1 on any kinetic theory of its elasticity4 ,for it is not impossible--however hopeless it may seem now--that a modicum of that energy may some day be partially utilised4 ,lord ,kelvin's incipient kinetic theory of elasticity is a complicated matter1 and ,i will only briefly enter upon it4 ,but before doing so1 ,i want to remove an objection which is sometimes felt1 as to the fluid and easily permeable character of a medium of this great density1--that is to say1 as to the absence of friction or viscosity--the absence of resistance to bodies moving through it4 ,as a matter of fact there is no necessary connexion whatever between density and viscosity4 ',density' and ',viscosity' are entirely different things2 and1 if there is no fluid friction1 a fluid may have any density you please without interposing any obstacle to constant velocity4 ,to acceleration it does indeed oppose an obstacle1 but that appears as essentially a part of the inertia or massiveness of the moving body4 ,it contributes to its momentum2 and1 if the fluid is everywhere present1 it is impossible to discriminate between1 or to treat separately1 that part of the inertia which belongs to the fluid displaced1 and that part which belongs to the body moving through it1--except by theory4 ,as for the elasticity of the ether1 that is ascertainable at once from the speed at which it transmits waves4 ,that speed--the velocity of light--is accurately known1 #c #aj centimetres per second4 ,and the ratio of the elasticity or rigidity to the density is equal to the square of this speed2--that is to say1 the elasticity must be #i #aj times the density2 or1 in other words1 #aj ,c4,g4,s4 units4 ,that is an immediate consequence of the estimate of density and the fact of the velocity of light2 and if the density is admitted1 the other cannot be contested4 ,but we must go on to ask1 ,to what is this rigidity due8 ,if the ether does not consist of parts1 and if it is fluid1 how can it possess the rigidity appropriate to a solid1 so as to transmit transverse waves8 ,to answer this we must fall back upon ,lord ,kelvin's kinetic theory of elasticity3--that it must be due to rotational motion--intimate fine-grained motion throughout the whole etherial region--motion not of the nature of locomotion1 but circulation in closed curves1 returning upon itself1--vortex motion of a kind far more finely grained than any waves of light or any atomic or even electronic structure4 ,now if the elasticity of any medium is to be thus explained kinetically1 it follows1 as a necessary consequence1 that the speed of this internal motion must be comparable to the speed of wave propagation2--that is to say that the internal squirming circulation1 to which every part of the ether is subject1 must be carried on with a velocity of the same order of magnitude as the velocity of light4 ,this is the theory then1--this theory of elasticity as dependent on motion1--which1 in combination with the estimate of density1 makes the internal energy of the ether so gigantic4 ,for in every cubic millimetre of space we have1 according to this view1 a mass equivalent to what1 if it were matter1 we should call a thousand tons1 circulating internally1 every part of it1 with a velocity comparable to the velocity of light1 and therefore containing--stored away in that small region of space--an amount of energy of the order #aj ergs1 or1 what is the same thing1 #c #aj kilowatt centuries2 which is otherwise expressible as equal to the energy of a million horse-power station working continuously for forty million years4 ,,summarised ,,brief ,,statements ,,concerning ,,the ,,ether 7,as communicated by the author to the ,british ,association at ,leicester1 #aijg74 #a4 ,the theory that an electric charge must possess the equivalent of inertia was clearly established by ,j4,j4 ,thomson in the ,philosophical ,magazine for ,april1 #ahha4 #b4 ,the discovery of masses smaller than atoms was made experimentally by ,j4,j4 ,thomson1 and communicated to ,section ,a at ,dover in #ahii4 #c4 ,the thesis that the corpuscles so discovered consisted wholly of electric charges was sustained by many people1 and was clinched by the experiments of ,kaufmann in #aijb4 #d4 ,the concentration of the ionic charge1 required to give the observed corpuscular inertia1 can be easily calculated2 and consequently the size of the electric nucleus1 or electron1 is known4 #e4 ,the old perception that a magnetic field is kinetic has been developed by ,kelvin1 ,heaviside1 ,fitz,gerald1 ,hicks1 and ,larmor1 most of whom have treated it as a flow along magnetic lines2 though it may also1 perhaps equally well1 be regarded as a flow perpendicular to them and along the ,poynting vector4 ,the former doctrine is sustained by ,larmor1 as in accordance with the principle of ,least ,action1 and with the absolutely stationary character of the ether as a whole2 the latter view appears to be more consistent with the theories of ,j4,j4 ,thomson4 #f4 ,a charge in motion is well known to be surrounded by a magnetic field2 and the energy of the motion can be expressed in terms of the energy of this concomitant field1--which again must be accounted as the kinetic energy of ethereous flow4 #g4 ,putting these things together1 and considering the ether as essentially incompressible--on the strength of the ,cavendish electric experiment1 the facts of gravitation1 and the general idea of a connecting continuous medium--the author reckons that to deal with the ether dynamically it must be treated as having a density of the order #aj grammes per cubic centimetre4 7,see ,appendix #b47 #h4 ,the existence of transverse waves in the interior of a fluid can only be explained on gyrostatic principles1 i4e4 by the kinetic or rotational elasticity of ,lord ,kelvin4 ,and the internal circulatory speed of the intrinsic motion of such a fluid must be comparable with the velocity with which such waves are transmitted4 #i4 ,putting these things together1 it follows that the intrinsic or constitutional vortex energy of the ether must be of the order #aj ergs per cubic centimetre4 ,conclusion4--,thus every cubic millimetre of the universal ether of space must possess the equivalent of a thousand tons1 and every part of it must be squirming internally with the velocity of light4 ,,footnote3 #f ,it does not seem to have been noticed that in ,query #bb1 quoted in the ,introduction to the present book1 ,newton seems to throw out a curious hint in this same direction1--though he immediately abandons it again4 ,he does not appear to have carefully edited his queries2 probably they were published posthumously4 ,,chapter ,,viii ,,ether ,,and ,,matter ,,the ,,mechanical ,,necessity ,,for ,a ,,continuous ,,medium ,,filling ,,space ,in this chapter ,i propose to summarise in simple and consecutive form most of the arguments already used4 ,thirty years ago ,clerk ,maxwell gave to the ,royal ,institution of ,great ,britain a remarkable address on ,action at a ,distance4 ,it is reported in the ,journal ,r4,i41 ,vol4 ,,vii1 and to it ,i would direct attention4 ,most natural philosophers hold1 and have held1 that action at a distance across empty space is impossible2 in other words1 that matter cannot act where it is not1 but only where it is4 ,the question ,where is it8 is a further question that may demand attention and require more than a superficial answer4 ,for it can be argued on the hydrodynamic or vortex theory of matter1 as well as on the electrical theory1 that every atom of matter has a universal though nearly infinitesimal prevalence1 and extends everywhere2 since there is no definite sharp boundary or limiting periphery to the region disturbed by its existence4 ,the lines of force of an isolated electric charge extend throughout illimitable space4 ,and though a charge of opposite sign will curve and concentrate them1 yet it is possible to deal with both charges1 by the method of superposition1 as if they each existed separately without the other4 ,in that case1 therefore1 however far they reach1 such nuclei clearly exert no action at a distance in the technical sense4 ,some philosophers have reason to suppose that mind can act directly on mind without intervening mechanism1--and sometimes that has been spoken of as genuine action at a distance2 but no proper conception or physical model can be made of such a process1 nor is it clear that space and distance have any particular meaning in the region of psychology4 ,the links between mind and mind may be something quite other than physical proximity2 and in denying action at a distance across empty space ,i am not denying telepathy or other activities of a non-physical kind4 ,for although brain disturbance is certainly physical1 and is an essential concomitant of mental action whether of the sending or receiving variety1 yet we know from the case of heat that a material movement can be excited in one place at the expense of corresponding movement in another1 without any similar kind of transmission or material connexion between the two places3 the thing that travels across vacuum is not heat4 ,in all cases where physical motion is involved1 however1 ,i would have a medium sought for4 ,it may not be matter1 but it must be something2 there must be a connecting link of some kind1 or the transference cannot occur4 ,there can be no attraction across really empty space4 ,and even when a material link exists1 so that the connexion is obvious1 the explanation is not complete2 for when the mechanism of attraction is understood1 it will be found that a body really only moves because it is pushed by something from behind4 ,the essential force in nature is the vis a tergo4 ,so when we have found the traces1 or discovered the connecting thread1 we still run up against the word cohesion2 and we ought to be exercised in our minds as to its ultimate meaning4 ,why the whole of a rod should follow1 when one end is pulled1 is a matter requiring explanation2 and the only explanation that can be given involves1 in some form or other1 a continuous medium connecting the discrete and separated particles or atoms of matter4 ,when a steel spring is bent or distorted1 what is it that is really strained8 ,not the atoms--the atoms are only displaced2 it is the connecting links that are strained--the connecting medium--the ether4 ,distortion of a spring is really distortion of the ether4 ,all stress exists in the ether4 ,matter can only be moved4 ,contact does not exist between the atoms of matter as we know them2 it is doubtful if a piece of matter ever touches another piece1 any more than a comet touches the sun when it appears to rebound from it2 but the atoms are connected1 as the comet and the sun are connected1 by a continuous plenum without break or discontinuity of any kind4 ,matter acts on matter only through the ether4 ,but whether matter is a thing utterly distinct and separate from the ether1 or whether it is a specifically modified portion of it--modified in such a way as to be susceptible of locomotion and yet continuous with all the rest of the ether1 which can be said to extend everywhere far beyond the bounds of the modified and tangible portion--are questions demanding1 and ,i may say in process of receiving1 answers4 ,every such answer involves some view of the universal and possibly infinite uniform omnipresent connecting medium1 the ,ether of space4 ,it has been said1 somewhat sarcastically1 that the ether was made in ,england4 ,the statement is only an exaggeration of the truth4 ,i might even urge that it has been largely constructed in the ,royal ,institution2 for1 ,i will summarise now the chief lines of evidence on which its existence is believed in1 and our knowledge of it is based4 ,first of all1 ,newton recognised the need of a medium for explaining gravitation4 ,in his ,optical ,queries he shows that if the pressure of this medium is less in the neighbourhood of dense bodies than at great distances from them1 dense bodies will be driven towards each other2 and that if the diminution of pressure is inversely as the distance from the dense body1 the law of force will be the inverse square law of gravitation4 ,all that is required1 therefore1 to explain gravity1 is a diminution of pressure1 or increase of tension1 caused by the formation of a matter unit--that is to say of an electron or corpuscle4 ,and although we do not yet know what an electron is--whether it be a strain centre1 or what kind of singularity in the ether it may be--there is no difficulty in supposing that a slight1 almost infinitesimal1 strain or attempted rarefaction should be produced in the ether whenever an electron comes into being--to be relaxed again only on its resolution and destruction4 ,strictly speaking it is not a real strain1 but only a stress2 since there can be no actual yield1 but only a pull or tension1 extending in all directions towards infinity4 ,the tension required per unit of matter is almost ludicrously small1 and yet in the aggregate1 near such a body as a planet1 it becomes enormous4 ,the force with which the moon is held in its orbit would be great enough to tear asunder a steel rod four hundred miles thick1 with a tenacity of #cj tons per square inch2 so that if the moon and earth were connected by steel instead of by gravity1 a forest of pillars would be necessary to whirl the system once a month round their common centre of gravity4 ,such a force necessarily implies enormous tension or pressure in the medium4 ,maxwell calculates that the gravitational stress near the earth1 which we must suppose to exist in the invisible medium1 is #cjjj times greater than what the strongest steel could stand2 and near the sun it should be #bejj times as great as that4 ,the question has arisen in my mind1 whether1 if the whole sensible universe--estimated by ,lord ,kelvin as equivalent to about a thousand million suns--were all concentrated in one body of specifiable density1#g the stress would not be so great as to produce a tendency towards etherial disruption2 which would result in a disintegrating explosion1 and a scattering of the particles once more as an enormous nebula and other fragments into the depths of space4 ,for the tension would be a maximum in the interior of such a mass2 and1 if it rose to the value #aj dynes per square centimetre1 something would have to happen4 ,i do not suppose that this can be the reason1 but one would think there must be some reason1 for the scattered condition of gravitative matter4 ,too little is known1 however1 about the mechanism of gravitation to enable us to adduce it as the strongest argument in support of the existence of an ether4 ,the oldest valid and conclusive requisition of an ethereous medium depends on the wave theory of light1 one of the founders of which was the ,royal ,institution ,professor of ,natural ,philosophy at the beginning of last century1 ,dr4 ,thomas ,young4 ,no ordinary matter is capable of transmitting the undulations or tremors that we call light4 ,the speed at which they go1 the kind of undulation1 and the facility with which they go through vacuum1 forbid this4 ,so clearly and universally has it been perceived that waves must be waves of something--something distinct from ordinary matter--that ,lord ,salisbury1 in his presidential address to the ,british ,association at ,oxford1 criticised the ether as little more than a nominative case to the verb to undulate4 ,it is truly that1 though it is also truly more than that2 but to illustrate that luminiferous aspect of it1 ,i will quote a paragraph from the lecture of ,clerk ,maxwell's to which ,i have already referred3-- ,the vast interplanetary and interstellar regions will no longer be regarded as waste places in the universe1 which the ,creator has not seen fit to fill with the symbols of the manifold order of ,his kingdom4 ,we shall find them to be already full of this wonderful medium2 so full1 that no human power can remove it from the smallest portion of space1 or produce the slightest flaw in its infinite continuity4 ,it extends unbroken from star to star2 and when a molecule of hydrogen vibrates in the dog-star1 the medium receives the impulses of these vibrations1 and after carrying them in its immense bosom for several years1 delivers them1 in due course1 regular order1 and full tale1 into the spectroscope of ,mr4 ,huggins1 at ,tulse ,hill4 ,this will suffice to emphasise the fact that the eye is truly an etherial sense-organ--the only one which we possess1 the only mode by which the ether is enabled to appeal to us2 and that the detection of tremors in this medium--the perception of the direction in which they go1 and some inference as to the quality of the object which has emitted them--cover all that we mean by sight and seeing4 ,i pass then to another function1 the electric and magnetic phenomena displayed by the ether2 and on this ,i will only permit myself a very short quotation from the writings of ,faraday1 whose whole life may be said to have been directed towards a better understanding of these ethereous phenomena4 ,indeed the statue in the entrance hall of the ,royal ,institution1 ,albemarle ,street1 may be considered as the statue of the discoverer of the electric and magnetic properties of the ,ether of space4 ,faraday conjectured that the same medium which is concerned in the propagation of light might also be the agent in electromagnetic phenomena4 ,for my own part1 he says1 considering the relation of a vacuum to the magnetic force1 and the general character of magnetic phenomena external to the magnet1 ,i am much more inclined to the notion that in the transmission of the force there is such an action1 external to the magnet1 than that the effects are merely attraction and repulsion at a distance4 ,such an action may be a function of the ther2 for it is not unlikely that1 if there be an ther1 it should have other uses than simply the conveyance of radiation4 ,this conjecture has been amply strengthened by subsequent investigations4 ,one more function is now being discovered2 the ether is being found to constitute matter--an immensely interesting topic1 on which there are many active workers at the present time4 ,i will make a brief quotation from ,professor ,sir ,j4,j4 ,thomson1 where he summarises the conclusion which we all see looming before us1 though it has not yet been completely attained1 and would not by all be similarly expressed3-- ,the whole mass of any body is just the mass of ether surrounding the body which is carried along by the ,faraday tubes associated with the atoms of the body4 ,in fact1 all mass is mass of the ether2 all momentum1 momentum of the ether2 and all kinetic energy1 kinetic energy of the ether4 ,this view1 it should be said1 requires the density of the ether to be immensely greater than that of any known substance4 ,yes1 far denser--so dense that matter by comparison is like gossamer1 or a filmy imperceptible mist1 or a milky way4 ,not unreal or unimportant1--a cobweb is not unreal1 nor to certain creatures is it unimportant1 but it cannot be said to be massive or dense2 and matter1 even platinum1 is not dense when compared with the ether4 ,not till last year1 however1 did ,i realise what the density of the ether must really be1#h compared with that modification of it which appeals to our senses as matter1 and which for that reason engrosses our attention4 ,is there any other function possessed by the ether1 which1 though not yet discovered1 may lie within the bounds of possibility for future discovery8 ,i believe there is1 but it is too speculative to refer to1 beyond saying that it has been urged as probable by the authors of ,the ,unseen ,universe1 and has been thus tentatively referred to by ,clerk ,maxwell3-- ,whether this vast homogeneous expanse of isotropic matter is fitted not only to be a medium of physical interaction between distant bodies1 and to fulfil other physical functions of which1 perhaps1 we have as yet no conception1 but also 444 to constitute the material organism of beings exercising functions of life and mind as high or higher than ours are at present--is a question far transcending the limits of physical speculation4 ,and there for the present ,i leave that aspect of the subject4 ,ether and ,matter4 ,i shall now attempt to illustrate some relations between ether and matter4 ,the question is often asked1 is ether material8 ,this is largely a question of words and convenience4 ,undoubtedly1 the ether belongs to the material or physical universe1 but it is not ordinary matter4 ,i should prefer to say it is not matter at all4 ,it may be the substance or substratum or material of which matter is composed1 but it would be confusing and inconvenient not to be able to discriminate between matter on the one hand1 and ether on the other4 ,if you tie a knot on a bit of string1 the knot is composed of string1 but the string is not composed of knots4 ,if you have a smoke or vortex-ring in the air1 the vortex-ring is made of air1 but the atmosphere is not a vortex-ring2 and it would be only confusing to say that it was4 ,the essential distinction between matter and ether is that matter moves1 in the sense that it has the property of locomotion and can effect impact and bombardment2 while ether is strained1 and has the property of exerting stress and recoil4 ,all potential energy exists in the ether4 ,it may vibrate1 and it may rotate1 but as regards locomotion it is stationary--the most stationary body we know3 absolutely stationary1 so to speak2 our standard of rest4 ,all that we ourselves can effect1 in the material universe1 is to alter the motion and configuration of masses of matter2 we can move matter1 by our muscles1 and that is all we can do directly3 everything else is indirect4 ,but now comes the question1 how is it possible for matter to be composed of ether8 ,how is it possible for a solid to be made out of fluid8 ,a solid possesses the properties of rigidity1 impenetrability1 elasticity1 and such-like2 how can these be imitated by a perfect fluid such as the ether must be8 ,the answer is1 they can be imitated by a fluid in motion2 a statement which we make with confidence as the result of a great part of ,lord ,kelvin's work4 ,it may be illustrated by a few experiments4 ,a wheel of spokes1 transparent or permeable when stationary1 becomes opaque when revolving1 so that a ball thrown against it does not go through1 but rebounds4 ,the motion only affects permeability to matter2 transparency to light is unaffected4 ,a silk cord hanging from a pulley becomes rigid and viscous when put into rapid motion2 and pulses or waves which may be generated on the cord travel along it with a speed equal to its own velocity1 whatever that velocity may be1 so that they appear to stand still4 ,this is a genuine case of kinetic rigidity2 and the fact that the wave-transmission velocity is equal to the rotatory speed of the material1 is typical and important1--for in all cases of kinetic elasticity these two velocities are of the same order of magnitude4 ,a flexible chain1 set spinning1 can stand up on end while the motion continues4 ,a jet of water at sufficient speed can be struck with a hammer1 and resists being cut with a sword4 ,a spinning disk of paper becomes elastic like flexible metal1 and can act like a circular saw4 ,sir ,william ,white tells me that in naval construction steel plates are cut by a rapidly revolving disk of soft iron4 ,a vortex-ring1 ejected from an elliptical orifice1 oscillates about the stable circular form1 as an india-rubber ring would do2 thus furnishing a beautiful example of kinetic elasticity1 and showing us clearly a fluid displaying some of the properties of a solid4 ,a still further example is ,lord ,kelvin's model of a spring balance1 made of nothing but rigid bodies in spinning motion4#i ,this arrangement utilises the processional movement of balanced gyrostats--concealed in a case and supporting a book--to imitate the behaviour of a spiral spring1 if it were used to support the same book4 ,if the ether can be set spinning1 therefore1 we may have some hope of making it imitate the properties of matter1 or even of constructing matter by its aid4 ,but how are we to spin the ether8 ,matter alone seems to have no grip of it4 ,as already described1 ,i have spun steel disks1 a yard in diameter1 #djjj times a minute1 have sent light round and round between them1 and tested carefully for the slightest effect on the ether4 ,not the slightest effect was perceptible4 ,we cannot spin ether mechanically4 ,but we can vibrate it electrically2 and every source of radiation does that4 ,an electrical charge1 in sufficiently rapid vibration1 is the only source of ether-waves that we know2 and if an electric charge is suddenly stopped1 it generates the pulses known as ,x-rays1 as the result of the collision4 ,not speed1 but sudden change of speed1 is the necessary condition for generating waves in the ether by electricity4 ,we can also infer some kind of rotary motion in the ether2 though we have no such obvious means of detecting the spin as is furnished by vision for detecting some kinds of vibration4 ,rotation is supposed to exist whenever we put a charge into the neighbourhood of a magnetic pole4 ,round the line joining the two1 the ether is spinning like a top4 ,i do not say it is spinning fast3 that is a question of its density2 it is in fact spinning with excessive slowness1 but it is spinning with a definite moment of momentum4 ,j4,j4 ,thomson's theory makes its moment of momentum exactly equal to e m1 the product of charge and pole2 the charge being measured electrostatically and the pole magnetically4 ,how can this be shown experimentally8 ,suppose we had a spinning top enclosed in a case1 so that the spin was unrecognisable by ordinary means--it could be detected by its gyrostatic behaviour to force4 ,if allowed to precess it will respond by moving perpendicularly to a deflecting force4 ,so it is with the charge and the magnetic pole4 ,try to move the charge suddenly1 and it immediately sets off at right angles4 ,a moving charge is a current1 and the pole and the current try to revolve round one another2--a fact which may be regarded as exhibiting a true gyrostatic action due to the otherwise unrecognisable etherial spin4 ,the fact of such magnetic rotation was discovered by ,faraday4 ,i know that it is usually worked out in another way1 in terms of lines of force and the rest of the circuit2 but ,i am thinking of a current as a stream of projected charges2 and no one way of regarding such a matter is likely to exhaust the truth1 or to exclude other modes which are equally valid4 ,anyhow1 in whatever way it is regarded1 it is an example of the three rectangular vectors4 ,the three vectors at right angles to each other1 which may be labelled ,current1 ,magnetism1 and ,motion respectively1 or more generally ,e1 ,h1 and ,v1 represent the quite fundamental relation between ether and matter1 and constitute the link between ,electricity1 ,magnetism1 and ,mechanics4 ,where any two of these are present1 the third is a necessary consequence4 ,this principle is the basis of all dynamos1 of electric motors1 of light1 of telegraphy1 and of most other things4 ,indeed1 it is a question whether it does not underlie everything that we know in the whole of the physical sciences2 and whether it is not the basis of our conception of the three dimensions of space4 ,lastly1 we have the fundamental property of matter called inertia1 which can1 to a certain extent1 be explained electromagnetically1 provided the ethereous density is granted as of the order #aj grammes per cubic centimetre4 ,the elasticity of the ether would then have to be of the order #aj c4g4s42 and if this is due to intrinsic turbulence1 the speed of the whirling or rotational elasticity must be of the same order as the velocity of light4 ,this follows hydrodynamically2 in the same sort of way as the speed at which a pulse travels on a flexible running endless cord1 whose tension is entirely due to the centrifugal force of the motion1 is precisely equal to the velocity of the cord itself4 ,and so1 on our present view1 the intrinsic energy of constitution of the ether is incredibly and portentously great2 every cubic millimetre of space possessing what1 if it were matter1 would be a mass of a thousand tons1 and an energy equivalent to the output of a million-horse-power station for #dj million years4 ,the universe we are living in is an extraordinary one2 and our investigation of it has only just begun4 ,we know that matter has a psychical significance1 since it can constitute brain1 which links together the physical and the psychical worlds4 ,if any one thinks that the ether1 with all its massiveness and energy1 has probably no psychical significance1 ,i find myself unable to agree with him4 ,,footnotes3 #g ,on doing the arithmetic1 however1 ,i find the necessary concentration absurdly great1 showing that such a mass is quite insufficient4 7,see ,appendix #a47 #h ,see ,lodge1 ,philosophical ,magazine1 ,april1 #aijg4 ,also ,appendix #b below4 #i ,address to ,section ,a of ,british ,association at ,montreal1 #ahhd4 ,,chapter ,,ix ,,strength ,,of ,,the ,,ether ,to show that the ether cannot be the slight and rarefied substance which at one time1 and indeed until quite lately1 it was thought to be1 it is useful to remember that not only has it to be the vehicle of light and the medium of all electric and magnetic influence1 but also that it has to transmit the tremendous forces of gravitation4 ,among small bodies gravitational forces are slight1 and are altogether exceeded by magnetic and electric or chemical forces4 ,indeed gravitational attraction between bodies of a certain smallness can be more than counterbalanced even by the pressure which their mutual radiation exerts--almost infinitesimal though that is2--so that as a matter of fact1 small enough bodies of any warmth will repel each other unless they are in an enclosure of constant temperature1 i4e4 unless the radiation pressure upon them is uniform all round4 ,the size at which radiation repulsion over-balances gravitational attraction1 for equal spheres1 depends on the temperature of the spheres and on their density2 but at the ordinary temperature to which we are accustomed1 say #fj ,fahrenheit or thereabouts1 equality between the two forces will obtain for two wooden spheres in space if each is about a foot in diameter2 according to ,professor ,poynting's data 7,philosophical ,transactions1 ,vol4 #bjb1 p4 #eda74 ,for smaller or hotter bodies1 radiation repulsion overpowers mutual gravitation2 and it increases with the fourth power of their absolute temperature4 ,the gravitational attractive force between particles is exceedingly small2 and that between two atoms or two electrons is negligibly small1 even though they be within molecular distance of each other4 ,for instance1 two atoms of1 say1 gold1 at molecular distance1 attract each other gravitationally with a force of the order 7#aj x #aj7 _/ 7#aj7 #aj _/ #aj x #aj #aj dyne2 which would cause no perceptible acceleration at all4 ,the gravitational attraction of two electrons at the same distance is the forty-thousand-millionth part of this1 and so one would think must be entirely negligible4 ,and yet it is to the aggregate attraction of myriads of such bodies that the resultant force of attraction is due2--a force which is felt over millions of miles4 ,the force is not only felt indeed1 but must be reckoned as one of prodigious magnitude4 ,when dealing with bodies of astronomical size1 the force of gravitation overpowers all other forces2 and all electric and magnetic attractions sink by comparison into insignificance4 ,these immense forces must be transmitted by the ether1 and it is instructive to consider their amount4 ,,some ,,astronomical ,,forces ,,which ,,the ,,ether ,,has ,,to ,,transmit4 ,arithmetical ,calculation of the ,pull of the ,earth on the ,moon4 ,the mass of the earth is #fjjj trillion 7#f #aj7 tons4 ,the mass of the moon is #a_/hjth that of the earth4 ,terrestrial gravity at the moon's distance 7which is #fj earth radii7 must be reduced in the ratio #a3fj2 that is1 it must be #a_/cfjjth of what it is here4 ,consequently the pull of the earth on the moon is #f #aj _/ #hj #cfjj tons weight4 ,a pillar of steel which could transmit this force1 provided it could sustain a tension of #dj tons to the square inch1 would have a diameter of about #djj miles2 as stated in the text1 page #ajb4 ,if this force were to be transmitted by a forest of weightless pillars each a square foot in cross-section1 with a tension of #cj tons to the square inch throughout1 there would have to be #e million million of them4 ,arithmetical ,calculation of the ,pull of the ,sun on the ,earth4 ,the mass of the earth is #f #aj tons4 ,the intensity of solar gravity at the sun's surface is #be times ordinary terrestrial gravity4 ,at the earth's distance1 which is nearly #bjj solar radii1 solar gravity will be reduced in the ratio of #a3bjj squared4 ,hence the force exerted by the sun on the earth is 7#be #f #aj7_/7bjj7 tons weight4 ,that is to say1 it is approximately equal to the weight of #cg #aj ordinary tons upon the earth's surface4 ,now steel may readily be found which can stand a load of #cg tons to every square inch of cross-section4 ,the cross-section of a bar of such steel1 competent to transmit the sun's pull to the earth1 would therefore have to be #aj square inches1 or say #gjj #aj square feet4 ,and this is equivalent to a million million round rods or pillars each #cj feet in diameter4 ,hence the statement in the text 7page #bf7 is well within the mark4 ,the ,pull of the ,earth on the ,sun4 ,the pull of the earth on the sun is1 of course1 equal and opposite to the pull of the sun on the earth1 which has just been calculated2 but it furnishes another mode of arriving at the result1 and may be regarded as involving simpler data--i4e4 data more generally known4 ,all we need say is the following3-- ,the mass of the ,sun is #caf1jjj times that of the ,earth4 ,the mean distance of the sun is1 say1 #bc1jjj earth radii4 ,hence the weight or pull of the sun by the earth is #cafjjj_/7bcjjj7 #f #aj tons weight4 ,in other words1 it is approximately equal to the ordinary commercial weight of #cf #aj tons1 as already calculated4 ,the ,centripetal ,force acting on the ,earth4 ,yet another method of calculating the sun's pull is to express it in terms of the centrifugal force of the earth2 namely1 its mass1 multiplied by the square of its angular velocity1 multiplied by the radius of its orbit2--that is to say1 ,f ,m 7#b_/,t7 r where ,t is the length of a year4 ,the process of evaluating this is instructive1 owing to the manipulation of units which it involves3-- ,f #f x #aj tons x 7#d x #ib x #aj miles7_/7#cfe days7 which of course is a mass multiplied by an acceleration4 ,the acceleration is-- 7#dj x #ib x #aj7_/acccjj x 7#bd7 miles per hour per hour 7#cfhj x #aj x #ebhj7_/acccjj x #egf x 7#cfjj7 feet per sec4 per sec4 7#aae x #ebhj7_/acccjj x #egf x #abif feet per sec4 per sec4 g_/#afdj ,hence the ,force of attraction is that which1 applied to the earth's mass1 produces in it an acceleration equal to the #a_/afdjth part of what ordinary terrestrial gravity can produce in falling bodies2 or ,f #f #aj tons g_/#afdj #f_/afdj x #aj tons weight2 which is the ordinary weight of #cg #aj tons1 as before4 ,the slight numerical discrepancy between the above results is of course due to the approximate character of the data selected1 which are taken in round numbers as quite sufficient for purposes of illustration4 ,if we imagine the force applied to the earth by a forest of round rods1 one for every square foot of the earth's surface--i4e4 of the projected earth's hemisphere or area of equatorial plane1--the force transmitted by each would have to be #bgjj tons2 and therefore1 if of #cj-ton steel1 they would each have to be eleven inches in diameter1 or nearly in contact1 all over the earth4 ,pull of a ,planet on the ,earth4 ,while we are on the subject1 it seems interesting to record the fact that the pull of any planet on the earth1 even ,neptune1 distant though it is1 is still a gigantic force4 ,the pull of ,neptune is #a_/bj1jjjth of the sun's pull3 i4e4 it is #ah billion tons weight4 ,pull of a ,star on the ,earth4 ,on the other hand1 the pull of a fixed star1 like ,sirius--say a star1 for example1 which is #bj times the mass of the sun and #bd light years distant--is comparatively very small4 ,it is easily found by dividing #bj times the sun's pull by the squared ratio of #bd years to #h minutes2 and it comes out as #cj million tons weight4 ,such a force is able to produce no perceptible effect4 ,the acceleration it causes in the earth and the whole solar system1 at its present speed through space1 is only able to curve the path with a radius of curvature of length thirty thousand times the distance of the star4 ,force required to hold together the ,components of some ,double ,stars4 ,but it is not to be supposed that the transmission of any of these forces gives the ether the slightest trouble1 or strains it to anywhere near the limits of its capacity4 ,such forces must be transmitted with perfect ease1 for there are plenty of cases where the force of gravitation is vastly greater than that4 ,in the case of double stars1 for instance1 two suns are whirling round each other2 and some of them are whirling remarkably fast4 ,in such cases the force holding the components together must be enormous4 ,perhaps the most striking case1 for which we have substantially accurate data1 is the star ,aurig2 which1 during the general spectroscopic survey of the heavens undertaken by ,professor ,pickering of ,harvard1 in connexion with the ,draper ,memorial1 was discovered to show a spectrum with the lines some days double and alternate days single4 ,clearly it must consist of a pair of luminous objects revolving in a plane approximately containing the line of vision2 the revolution being completed every four days4 ,for the lines will then be optically displaced by the motion1 during part of the orbit--those of the advancing body to the right1 those of the receding body to the left1--while in that part of the orbit which lies athwart the direction of vision1 the spectrum lines will return to their proper places1--opening out again to a maximum1 in the opposite direction1 at the next quadrant4 ,the amount of displacement can be roughly estimated1 enabling us to calculate the speed with which the sources of light were moving4 ,professor ,pickering1 in a brief statement in ,nature1 ,vol4 ,,xli1 page #djc1 #ahhi1 says that the velocity amounts to about #aej miles per second1 and that it is roughly the same for both components4 ,taking these data3-- ,equality and uniformity of speeds1 #aej miles per second each1 ,period #d days1 we have all the data necessary to determine the masses2 and likewise the gravitative pull between them4 ,for the star must consist of two equal bodies1 revolving about a common centre of gravity midway between them1 in nearly circular orbits4 ,the speed and period together easily give the radius of the circular orbit as about #h million miles4 ,equating centrifugal and centripetal forces mv _/ r m _/ 7#br7 and comparing the value of #dr _/ ,t so obtained with the r _/ ,t of the earth1 we find the mass of each body must be about #cj1jjj times that of the earth1 or about #a_/ajth that of the sun4 99 99 99 99 99 7,this is treating them as spheres1 though they must really be pulled into decidedly prolate shapes4 ,indeed it may seem surprising that the further portions can keep up with the nearer portions as they revolve4 ,if they are of something like solar density their diameter will be comparable to half a million miles1 and the natural periods of their near and far portions will differ in the ratio 7#ag_/af7c_/b #aa approximately4 ,tenacity could not hold the parts together1 but gravitational coherence would47 99 99 99 99 99 ,this1 however1 is a digression4 ,let us continue the calculation of the gravitative pull4 ,we have masses of #c #aj #f #aj tons1 revolving with angular velocity #b #d days1 in a circle of radius #h #aj miles4 ,consequently the centripetal acceleration is #d #h #aj _/ #af miles per day per day2 which comes out #cb _/ #bb ft4 per sec4 per sec41 or nearly half ordinary terrestrial gravity4 ,consequently the pull between the two components of the double star ,aurig is g _/ #b4b #ah #aj tons1 or equal to the weight of #hj #aj tons on the earth1 which is more than twenty million times as great as is the pull between the earth and our sun4 99 99 99 99 99 ,simple calculations such as these could have been made at any time2 there is nothing novel about them1 as there is about the estimate of the ether's density and vast intrinsic energy1 in ,chapters ,,vi and ,,vii4 ,but then there is nothing hypothetical or uncertain about them either2 they are certain and definite3 whereas it may be thought there is something doubtful about the newer contentions which involve consideration of the mass and size of electrons and of the uniform and incompressible character of etherial constitution4 ,even the idea of massiveness as applied to the ether involves an element of uncertainty1 or of figurativeness2 because until we know more about ether's peculiar nature 7if it is peculiar71 we have to deal with it in accordance with material analogies1 and must specify its massiveness as that which would have to be possessed by it if it fulfilled its functions and yet were anything like ordinary matter4 ,it cannot really be ordinary matter1 because ordinary matter is definitely differentiated from it1 and is presumably composed of it2 but the inertia of ordinary matter1 however it be electrically or magnetically explained1 must in the last resort depend on something parentally akin to inertia in the fundamental substance which fills space4 ,and this it is which we have attempted in ,chapters ,,vi and ,,vii to evaluate and to express in the soberest terms possible4 ,,chapter ,x ,,general ,,theory ,,of ,,aberration ,in ,chapter ,,iii the subject of ,aberration was treated in a simple and geometrical manner1 but it is now time to deal with it more generally4 ,and to do this compactly ,i must be content in the greater part of this chapter to appeal chiefly to physicists4 ,the following general statements concerning aberration can be made3-- #a4 ,a ray of light in clear space is straight1 whatever the motion of the medium1 unless eddies exist2 in other words1 no irrotational disturbance of ether can deflect a ray4 #b4 ,but if the observer is in motion1 the apparent ray will not be the true ray1 and his line of vision will not truly indicate the direction of an object4 #c4 ,in a stationary ether the ray coincides with wave-normal4 ,in a moving ether the ray and wave-normal enclose an aberration angle 1 such that sin v_/,v1 the ratio of the ether speed to the light speed4 #d4 ,in all cases the line of vision depends on motion of the observer1 and on that alone4 ,if the observer is stationary1 his line of vision is a ray4 ,if he moves at the same rate as the ether1 his line of vision is a wave-normal4 #e4 ,line of vision depends not at all on the motion of the ether1 so long as it has a velocity-potential4 ,hence if this condition is satisfied the theory of aberration is quite simple4 ,general ,statement as to ,negative ,results in the ,subject4 ,it is noteworthy that almost all the observations which have been made with negative results as to the effect of the ,earth's orbital motion on the ether are equally consistent with complete connexion and complete independence between ether and matter4 ,if there is complete connexion1 the ether near the earth is relatively stagnant1 and negative terrestrial results are natural4 ,if there is complete independence1 the ether is either absolutely stationary or has a velocity-potential1 and the negative results are1 as has been shown1 thereby explained4 ,direct experiment on the subject of etherial viscosity proves that that is either really or approximately zero1 and substantiates the independence explanation4 ,definition of a ,ray4 ,a ray signifies the path of a definite or identical portion of radiation energy--the direction of energy-flux4 ,in other words1 it may be considered as the path of a labelled disturbance2 for it is some special feature which enables an eye to fix direction3 it is that which determines the line of collimation of a telescope4 ,now in order that a disturbance from ,a may reach ,b1 it is necessary that adjacent elements of a wave front at ,a shall arrive at ,b in the same phase2 hence the path by which a disturbance travels must satisfy this condition from point to point4 ,this condition will be satisfied if the time of journey down a ray and down all infinitesimally differing paths is the same4 ,the equation to a ray is therefore contained in the statement that the time taken by light to traverse it is a minimum2 or ,a1,b ds_/,v minimum ,if the medium1 instead of being stationary1 is drifting with the velocity v1 at angle to the ray1 we must substitute for ,v the modified velocity ,v cos v cos 2 and so the function that has to be a minimum1 in order to give the path of a ray in a moving medium1 is ,time of journey ,a1,b ds _/ ,v7cos cos 7 ,a1,b 7,v cos - v cos 7 _/ 7,v7#a-77 ds minimum where is the ratio v_/,v4 ,path of ,ray1 and ,time of ,journey1 through an ,irrotationally ,moving ,medium4 ,writing a velocity-potential in the above equation to a ray1 that is putting v cos d_/ds1 and ignoring possible variations in the minute correction factor #a- between the points ,a and ,b1 it becomes ,time of journey ,a1,b cos _/ 7#a - 7 ds_/,v - 7 - 7 _/ ,v7 #a-7 minimum4 ,now the second term depends only on end points1 and therefore has no effect on path4 ,the first term contains only the second power of aberration magnitude2 and hence it has much the same value as if everything were stationary4 ,a ray that was straight1 will remain straight in spite of motion4 ,whatever shape it had1 that it will retain4 ,only cos 1 and variations in 1 can produce any effect on path2 and effects so produced must be very small1 since the value of cos is 7#a - sin74 ,a second-order effect on direction may therefore be produced by irrotational motion1 but not a first-order effect4 ,a similar statement applies to the time of journey round any closed periphery4 ,michelson's ,experiment4 ,we conclude1 therefore1 that general etherial drift does not affect either the path of a ray1 or the time of its journey to and fro1 or round a complete contour1 to any important extent4 ,but that taking second-order quantities into account1 the time of going to and fro in any direction inclined at angle to a constant drift is1 from the above expression1 ,t ,t #b,t cos _/ 7#a-7 7#a - sin7 _/ 7#a - 7 #b,t1 where #b ,t is the ordinary time of the double journey without any drift4 ,hence some slight modification of interference effects by reason of drift would seem to be possible2 since the time of a to-and-fro light-journey depends subordinately on the inclination of ray to drift4 ,the above expression applies to ,michelson's remarkable experiment#aj of sending a split beam to and fro1 half along and half across the line of the earth's motion2 and is1 in fact1 a theory of it4 ,there ought to be an effect due to the difference between #j and #ij4 ,but none can be detected4 ,hence1 either something else happens1 or the ether near the earth is dragged with it so as not to stream through our instruments4 ,alternative ,explanation4 ,but if the ether is dragged along near moving matter1 it behaves like a viscous fluid1 and all idea of a velocity-potential must be abandoned4 ,this would complicate the theory of aberration 7pp4 #de and #fa71 and moreover is dead against the experimental evidence described in ,chapter ,v4 ,the negative result of ,mr4 ,michelson's is1 however1 explicable in another way1--namely1 by the ,fitz,gerald-,lorentz theory that the linear dimensions of bodies are a function of their motion through the ether4 ,and such an effect it is reasonable to expect2 since1 if cohesion forces are electrical1 they must be affected by motion1 to a known and calculable amount1 depending on the square of the ratio of the speed to the velocity of light4 7,see end of ,chap4 ,,iv47 ,the theory of ,professor ,h4,a4 ,lorentz1 accordingly1 shows that the shape of ,michelson's stone supporting block will be distorted by the motion2 its dimensions across and along the line of ether drift being affected differently4 ,and the amount of the change will be such as precisely to compensate and neutralise the optical effect of motion which might otherwise be perceived4 ,this theory is now generally accepted4 ,it is this neutralising or compensatory effect1--which acts equally on to-and-fro motion of light1 to-and-fro motion of electric currents1 and on the shape of material bodies1--that renders any positive result in experiments on ether-drift so difficult or impossible to obtain2 so that1 in spite of the speed with which we are rushing through space1 no perceptible influence is felt on either electrical or optical phenomena1 except those which are due to relative motion of source and observer4 ,some ,details in the ,theory of the ,doppler ,effect1 or ,effect of ,motion on ,dispersion by ,prism or ,grating4 ,when light is analysed by a prism or grating into a spectrum1 the course of each ray is deflected--refracted or diffracted--by an amount corresponding to its frequency of vibration or wave-length4 ,motion of the medium1 so long as it is steady1 affects neither frequency nor wave-length1 and accordingly is without influence on the result4 ,it produces no ,doppler effect except when waxing or waning4 ,motion of the source alone crowds the waves together on the advancing side and spreads them out on the receding side4 ,an observer therefore whom the source is approaching receives shorter waves1 and one from whom the source is receding receives longer waves1 than normal4 ,at any fixed point waves will arrive1 therefore1 with modified frequency4 ,so long as a source is stationary the wave-lengths emitted are quite normal1 but motion of an observer may change the frequency with which they are received1 in an obvious way2 they are swept up faster if the receiver is approaching1 they have a stern chase if it is receding4 ,all this is familiar1 and was geometrically illustrated in ,chapter ,,iii1 but there are some minor and rather curious details which are worthy of brief consideration4 ,grating ,theory4 ,for suppose a 'grating' is used to analyse the light4 ,its effect can depend on nothing kinetic2 it must be regulated by the merely geometric width of the ruled spaces on it4 ,consequently it can only directly apprehend wave-lengths1 not frequencies4 ,in the case of a moving source1 therefore1 when the wave-length is really changed1 a grating will appreciate the fact1 and will show a true ,doppler effect4 ,but in the case of a moving observer1 when all the waves received are of normal length1 though swept up with abnormal frequency1 the grating must still indicate wave-length alone1 and accordingly will show no true ,doppler effect4 ,but inasmuch as the telescope or line of vision is inclined at the angle of dispersion to the direction of the incident ray1 ordinary aberration must come in1 as it always does when an observer moves athwart his line of vision2 and so there will be a spurious or apparent ,doppler effect due to common aberration4 ,that is to say a spectrum line will not be seen in its true place1 but will appear to be shifted by an amount almost exactly imitative of a real ,doppler effect--the imitation being correct up to the second order of aberration magnitude4 ,the slight outstanding difference between them is calculated in my ,philosophical ,transactions paper1 #ahic1 page #ghg4 ,it is too small to observe4 ,it is not an important matter1 but as it is rather troublesome to work out the diffraction observed by a grating advancing towards the source of light1 it may be as well to record the result here4 ,the following are the diffracted rays which require attention1--with the inclination of each to the grating-normal specified3-- ,the diffracted ray if all were stationary1 2 ,the real diffracted ray when grating is advancing1 2 ,the ray as perceived1 allowing for aberration1 2 ,the equivalent diffracted ray if all were stationary and the wave-length really shortened1 4 ,as an auxiliary we use the aberration angle 1 such that sin sin 1 where v_/,v4 ,among these four angles the following relations hold2 so that1 given one of them1 all are known4 - sin 7#a - 7 sin sin 7#a - vers 7 sin ,whence and are very nearly but not absolutely the same4 is the ray observed by an instrument depending primarily on frequency1 like a prism2 is the ray observed by an instrument depending primarily on wave-length1 like a grating4 ,prism ,theory4 ,now let a prism be used to analyse the light2 its dispersive power is in most theories held to depend directly upon frequency--i4e4 upon a time relation between the period of a light vibration and the period of an atomic or electronic revolution or other harmonic excursion4 ,let us say1 therefore1 that prismatic dispersion directly indicates frequency4 ,it cannot depend upon wave-length1 for the wave-length inside different substances is different1 and though refractive index corresponds to this1 dispersive power does not4 ,in the case of a prism1 therefore1 no distinction can be drawn between motion of source and motion of receiver2 for in both cases the frequency with which the waves are received will be altered1--either because they are really shorter1 though arriving at normal speed1 or because they are swept up faster1 although of normal length4 ,achromatic ,prism4 ,it must be noticed that the observation of ,doppler effect by a prism depends entirely on dispersion2 i4e4 on waves of different length being affected differently4 ,but prisms can be constructed whose dispersion is corrected and neutralised4 ,such achromatic prisms1 if perfectly achromatic1 will treat waves of all sizes alike2 and1 accordingly1 the shortening of the waves from a moving source will not produce any effect4 ,achromatic prisms will therefore behave to terrestrial and to extra-terrestrial sources1 i4e4 to relatively stationary and relatively moving sources1 in the same way4 ,this must be recollected in connexion with several of the negative results rightly obtained by some observers2 such as ,arago1 for instance1 who applied an achromatic prism to a star which the earth was approaching1 without observing any effect4 ,a ,doppler effect should have been observed by a dispersive prism1 but not by an achromatic one3 for the refractive index of a substance is not affected by any motion of the earth4 ,it is not reasonable to expect that refractive index would be affected1 since it depends in simple geometrical fashion on retarded velocity1 i4e4 on optical etherial loading or apparent extra internal density4 ,an achromatic grating1 however1 is 7rashly speaking7 an impossibility4 ,,effect ,,of ,,transparent ,,matter4 ,but when a ray is travelling through transparent matter1 will not motion of that matter affect its course8 ,if the matter is moved relatively to source and receiver1 as in ,fizeau's experiment with running water1 most certainly it will2 to the full effect of the loading or extra or travelling density1 7-#a71 compared with the total density 4 ,this fraction of the velocity of the material medium must directly influence the velocity of light1 for the waves will be conveyed in the sense of the material motion u1 with the additional speed u7-#a7_/4 7,see also ,appendix #c47 ,but if the transparent matter through which the light is going is stationary with respect to source and receiver--only sharing with them the general planetary motion1 i4e4 being subject to the opposite all-pervading ether drift1--then no influence due to the drift can be experienced2 for the free ether of space behaves just as it would if the matter were not there4 ,this can be shown more elaborately by the following calculation4 ,optical ,effect of ,ether ,drift through ,dense ,stationary ,bodies4 ,the calculation of the lag in phase caused by ,fresnel's etherial motion may proceed thus3--,a dense slab of thickness z1 which would naturally be traversed with the velocity ,v_/1 is traversed with the velocity 7,v_/7 cos 7v_/7 cos 2 where v is the relative velocity of the ether in its neighbourhood2 whence the time of journey through it is 7z7 _/ ,v7cos 7_/7 cos 71 instead of z_/,v1 ,so the equivalent air thickness1 instead of being 7 - #a7z1 is z _/ 7cos 7_/7 cos 7 - z 7 7 cos - cos 7 _/ 7#a - _/7 - #a 7z1 or1 to the first order of minuti1 7 - #a7z - z cos 2 being the angle between ray and ether drift inside the medium4 ,so the extra equivalent air layer due to the motion is approximately z cos 1 a quantity independent of 4 ,hence1 no plan for detecting this first-order effect of motion is in any way assisted by the use of dense stationary substances2 their extra ether1 being stationary1 does not affect the lag caused by motion1 except indeed in the second order of small quantities1 as shown above4 ,direct experiments made by ,hoek1#aa and by ,mascart1 on the effect of introducing tubes of water into the path of half-beams of light1 are in entire accord with this negative conclusion4 ,thus1 then1 we find that no general motion of the entire medium can be detected by changes in direction1 or in frequency1 or in phase2 for on none of them has it any appreciable 7i4e4 first-order7 effect1 even when assisted by dense matter4 99 99 99 99 99 ,another mode of stating the matter is to say that the behaviour of ether inside matter is such as to enable a potential-function1 v cos ds1 to exist throughout all transparent space1 so far as motion of ether alone is concerned4 7,see ,appendix #c47 ,the existence of this potential function readily accounts for the absence of all effect on direction due to the general drift of the medium1 whether in the presence of dense matter 7such as water-filled telescopes7 or otherwise4 ,whatever may be the path of a ray by reason of reflexion or refraction in a stationary ether1 it is precisely the same in a moving one if this condition is satisfied1 although the wave-normals and wave-fronts are definitely shifted4 ,however matter affects or loads the ether inside it1 it cannot on this theory be said either to hold it still1 or to carry it with it4 ,the general ether stream must remain unaffected1 not only near1 but inside matter1 if rays are to retain precisely the same course as if it were relatively stationary4 ,but it must be understood that the etherial motion here contemplated is the general drift of the entire medium2 or its correlative1 the uniform motion of all the matter concerned4 ,there is nothing to be said against aberration effects being producible or modifiable by motion of parts of the medium1 or by the artificial motion of transparent bodies and other partitioned-off regions4 ,artificial motion of matter may readily alter both the time of journey and the path of a ray1 for it has no potential conditions to satisfy2 it may easily describe a closed contour1 and may take part in conveying light4 ,but ,i must repeat that this conveyance of light by moving matter is an effect due to the material load only2 it represents no disturbance of the ether of space4 ,fresnel's law1 in fact1 definitely means that moving transparent matter does not appreciably disturb the ether of space4 ,direct experiment1 as recorded in ,chapter ,v1 shows that close to rapidly-moving opaque matter there is no disturbance either4 ,i regard the non-disturbance of the ether of space by moving matter as established4 ,,footnotes3 #aj ,philosophical ,magazine1 ,dec41 #ahhg4 #aa ,archives ,nerlandaises 7#ahfi71 ,vol4 ,,iv1 p4 #ddc1 or ,nature1 ,vol ,,xxvi1 p4 #ejj4 ,also ,chapter ,,iv above4 ,,summary4 ,the estimates of this book1 and of ,modern ,views of ,electricity1 are that the ether of space is a continuous1 incompressible1 stationary1 fundamental substance or perfect fluid1 with what is equivalent to an inertia-coefficient of #aj grammes per c4c42 that matter is composed of modified and electrified specks1 or minute structures of ether1 which are amenable to mechanical as well as to electrical force and add to the optical or electric density of the medium2 and that elastic-rigidity and all potential energy are due to excessively fine-grained etherial circulation1 with an intrinsic kinetic energy of the order #aj ergs per cubic centimetre4 ,,appendix #a ,,on ,,gravity ,,and ,,etherial ,,tension ,in the arithmetical examples of ,chapter ,,ix we reckon merely the force between two bodies2 but the ,newtonian tension mentioned in ,chapter ,,viii does not signify that force1 but rather a certain condition or state of the medium1 to variations in which1 from place to place1 the force is due4 ,this ,newtonian tension is a much greater quantity than the force to which it gives rise2 and1 moreover1 it exists at every point of space1 instead of being integrated all through an attracted body4 ,it rises to a maximum value near the surface of any spherical mass2 and if the radius be ,r and the gravitational intensity is g1 the tension at the surface is ,t g,r4 ,at any distance r1 further away1 the tension is ,t g,r_/r4 ,this follows at once thus3-- ,stating the law of gravitation as ,f mm_/r1 the meaning here adopted for etherial tension at the surface of the earth is ,t ,r1 ,e_/r dr ,e_/,r2 so that the ordinary intensity of gravity is g -d,t_/d,r ,e_/,r #d_/c,r4 ,accordingly1 near the surface of a planet the tension is ,t g,r1 or for different planets is proportional to ,r4 ,the velocity of free fall from infinity to such a planet is 7#b,t72 the velocity of free fall from circumference to centre1 assuming uniform distribution of density1 is 7,t72 and from infinity to centre it is 7#c,t74 ,expanding all this into words3-- ,the etherial tension near the earth's surface1 required to explain gravity by its rate of variation1 is of the order #f #aj c4g4s4 units4 ,the tension near the sun is #bejj times as great 7p4 #ajc74 ,with different spheres in general1 it is proportional to the density and to the superficial area4 ,hence1 near a bullet one inch in diameter1 it is of the order #aj2 and near an atom or an electron about #aj c4g4s4 ,if ever the tension rose to equal the constitutional elasticity or intrinsic kinetic energy of the ether1--which we have seen is #aj dynes per square centimetre 7or ergs per c4c47 or #aj tons weight per square millimetre1--it seems likely that something would give way4 ,but no known mass of matter is able to cause anything like such a tension4 ,a smaller aggregate of matter would be able to generate the velocity of light in bodies falling towards it from a great distance2 and it may be doubted whether any mass so great as to be able to do even that can exist in one lump4 ,in order to set up a tension equal to what is here suspected of being a critical1 or presumably disruptive1 stress in the ether #aj c4g4s41 a globe of the density of the earth would have to have a radius of eight light years4 ,in order to generate a velocity of free fall under gravity equal to the velocity of light1 a globe of the earth's density would have to be equal in radius to the distance of the earth from the sun1 or say #bf1jjj times the earth's radius4 ,if the density were less1 the superficial area would have to be increased in proportion1 so as to keep ,r constant4 ,the whole visible universe within a parallax of #a_/ajjj second of arc1 estimated by ,lord ,kelvin as the equivalent of #aj suns1 would be quite incompetent to raise etherial tension to the critical point #aj c4g4s4 unless it were concentrated to an absurd degree2 but it could generate the velocity of light with a density comparable to that of water1 if mass were constant4 ,if the average density of the above visible universe 7which may be taken as #a4f #aj grammes per c4c47 continued without limit1 a disruptive tension of the ether would be reached when the radius was comparable to #aj light years2 and the velocity of light would be generated by it when the radius was #aj light years4 ,but heterogeneity would enable these values to be reached more easily4 ,gravitation is thus supposed to be the result of a mechanical tension inherently1 and perhaps instantaneously1 set up throughout space whenever the etherial structure called an electric charge comes into existence2 the tension being directly proportional to the square of the charge and inversely as its linear dimensions4 ,cohesion is quite different1 and is due to a residual electrical attraction between groups of neutral molecules across molecular distances3 a variant or modification of chemical affinity4 ,,appendix #b ,,calculations ,,in ,,connexion ,,with ,,ether ,,density ,just as the rigidity of the ether is of a purely electric character1 and is not felt mechanically--since mechanically it is perfectly fluid1--so its density is likewise of an electromagnetic character1 and again is not felt mechanically1 because it cannot be moved by mechanical means4 ,it is by far the most stationary body in existence2 though it is endowed with high intrinsic energy of local movement1 analogous to turbulence1 conferring on it gyrostatic properties4 ,optically1 its rigidity and density are both felt1 since optical disturbances are essentially electromotive4 ,matter loads the ether optically1 in accordance with the recognised fraction 7-#a7 _/ 2 and this loading1 being part and parcel of the matter1 of course travels with it4 ,it is the only part amenable to mechanical force4 ,the mechanical density of matter is a very small portion of the etherial density2 whereas the optical or electrical density of matter--being really that of ether affected by the intrinsic or constitutional electricity of matter--is not so small4 ,the relative optical virtual density of the ether inside matter is measured by 2 but it may be really a defect of elasticity1 at least in non-magnetic materials4 ,electrical and optical effects depend upon e4 ,mechanical or inertia effects depend upon e4 ,electric charges can load the ether optically1 quite appreciably2 but as regards mechanical loading1 the densest matter known is trivial and gossamer-like compared with the unmodified ether in the same space4 ,massiveness of the ,ether deduced from ,electrical ,principles4 ,each electron1 moving like a sphere through a fluid1 has a certain mass associated with it2 dependent on its size1 and1 at very high speeds1 on its velocity also4 ,if we treat the electron merely as a sphere moving through a perfect liquid1 its behaviour is exactly as if its mass were increased by half that of the fluid displaced and the surrounding fluid were annihilated4 ,ether being incompressible1 the density of fluid inside and outside an electron must be the same4 ,so1 dealing with it in this simplest fashion1 the resultant inertia is half as great again as that of the volume of fluid corresponding to the electron3 that is to say the effective mass is #b1 where is the uniform density4 ,if an electron is of some other shape than a sphere1 then the numerical part is modified1 but remains of the same order of magnitude1 so long as there are no sharp edges4 99 99 99 99 99 ,if1 however1 we consider the moving electron as generating circular lines of magnetic induction1 by reason of some rotational property of the ether1 and if we attribute all the magnetic inertia to the magnetic whirl thus caused round its path1--provisionally treating this whirl as an actual circulation of fluid excited by the locomotion1--then we shall proceed thus3-- ,let a spherical electron e of radius a be flying at moderate speed u1 so that the magnetic field at any point1 r1 outside1 is ,h eu sin _/ r1 and the energy per unit volume everywhere is ,h_/#h4 ,but a magnetic field has been thought of by many mathematicians as a circulation of fluid along the lines of magnetic induction--which are always closed curves--at some unknown velocity w4 ,so consider the energy per unit volume anywhere3 it can be represented by the equivalent expressions w ,h_/#h _/#h eusin _/ r2 wherefore w_/u 7_/#d7 e sin _/ r4 ,the velocity of the hypothetical circulation must be a maximum at the equator of the sphere1 where ra and #ij2 so1 calling this w1 w_/u 7_/#d7 e _/ a1 and w_/w a sin _/ r2 wherefore the major part of the circulation is limited to a region not far removed from the surface of the electron4 ,the energy of this motion is #j1 a1 w #b r sin rd dr1 whence1 substituting the above value of w1 the energy comes out equal to #d_/c a w4 ,comparing this with a mass moving with speed u1 m #h_/c a7w_/u74 ,this agrees with the simple hydrodynamic estimate of effective inertia if w #cu2 that is to say1 if the whirl in contact with the equator of the sphere is of the same order of magnitude as the velocity of the sphere4 ,now for the real relation between w and u we must make a hypothesis4 ,if the two are considered equal1 the effectively disturbed mass comes out as twice that of the bulk of the electron4 ,if w is smaller than u1 then the mass of the effectively disturbed fluid is less even than the bulk of an electron2 and in that case the estimate of the fluid-density must be exaggerated in order to supply the required energy4 ,it is difficult to suppose the equatorial circulation w greater than u1 since it is generated by it2 and it is most reasonable to treat them both as of the same order of magnitude4 ,so1 taking them as equal1 e a 7#d_/7 and m twice the spherical mass4 ,hence all the estimates of the effective inertia of an electron are of the same order of magnitude1 being all comparable with that of a mass of ether equal to the electron in bulk4 ,but the linear dimension of an electron is #aj centimetre diameter1 and its mass is of the order #aj gram4 ,consequently the density of its material must be of the order #aj grams per cubic centimetre4 ,this1 truly1 is enormous1 but any reduction in the estimate of the circulation-speed1 below that of an electron1 would only go to increase it4 ,and1 since electrons move sometimes at a speed not far below that of light1 we cannot be accused of under-estimating the probable velocity of magnetic spin by treating it as of the same order of magnitude1 at the bounding surface of the electron1 as its own speed3 a relation suggested1 though not enforced1 by gyrostatic analogies4 ,some ,consequences of this ,great ,density4 ,the amplitude of a wave of light1 in a place where it is most intense1 namely near the sun where its energy amounts to #b ergs per c4c41 comes out only about #aj of the wave-length4 ,the maximum tangential stress called out by such strain is of the order #aj atmospheres4 ,the hypothetical luminous circulation-velocity1 conferring momentum on a wave-front1 in accordance with ,poynting's investigation1 comes out #aj cm4 per sec4 ,these calculations are given in the concluding chapter of the new edition of ,modern ,views of ,electricity4 ,the supposed magnetic etherial drift1 along the axis of a solenoid or other magnetic field1 if it exist1 is comparable to #jjc centim4 per sec41 or #d inches an hour1 for a field of intensity #ab1jjj c4g4s4 ,but it is not to be supposed that this hypothetical velocity is slow everywhere4 ,close to an electron the speed of magnetic drift is comparable to the locomotion-velocity of the electron itself1 and may therefore rise to something near the speed of light2 say #a_/cjth of that speed3 but in spite of that1 at a distance of only #a millimetre away1 it is reduced to practical stagnation1 being less than a millimicron per century4 ,in any solenoid1 the ampere-turns per linear inch furnish a measure of the speed of the supposed magnetic circulation along the axis--no matter what the material of the core may be--in millimicrons per sec4 #a micron #aj metre2 #a millimicron is #aj metre #aj centimetre1 or a millionth of a millimetre4 ,to get up an etherial speed of #a centimetre per second--such as might be detected experimentally by refined optical appliances1 through its effect in accelerating or retarding the speed of light sent along the lines of magnetic force1--would need a solenoid of great length1 round every centimetre of which #ajjj amperes circulated #cjjj times4 ,that is to say1 a long field of four million c4g4s4 units of intensity4 ,in other words1 any streaming along magnetic lines of force1 such as could account for the energy of a magnetic field1 must be comparable1 in centimetres per second1 to one four-millionth of the number of c4g4s4 units of intensity in the magnetic field4 ,,appendix #c ,,fresnel',s ,,law ,a ,,special ,,case ,,of ,a ,,universal ,,potential ,,function ,the modern view of ,fresnel's ,law may be worded thus3-- ,inside a region occupied by matter1 in addition to the universal ether of space1 are certain modified or electrified specks1 which build up the material atoms4 ,these charged particles1 when they move1 have specific inertia1 due to the magnetic field surrounding each of them4 ,and by reason of this property1 and as a consequence of their discontinuity1 they virtually increase the optical density of the ether of space1 acting in analogy with weights distributed along a flexible cord4 ,thus they reduce the velocity of light in the ratio of the refractive index 3#a1 and therefore may be taken as increasing the virtual density of the ether in the ratio #a34 ,that is to say1 their loading makes the ether behave to optical waves as if--being a homogeneous medium without these discontinuous loads--it had a density times that which it has in space outside matter4 ,calling the density outside #a1 the extra density inside must be -#a1 so as to make up the total to 4 ,the -#a portion is that which we call matter1 and this portion is readily susceptible to locomotion1 being subject to--that is1 accelerated by--mechanical force4 ,the free portion of normal density #a is absolutely stationary as regards locomotion1 whether it be inside or outside a region occupied by ordinary matter1 for it is not amenable to either mechanical or electric forces4 ,they are transmitted by it1 but never terminate upon it2 except1 indeed1 at the peculiar structure called a wave-front1 which simulates some of the properties of matter4 7,if free or unmodified ether can ever be moved at all1 it must be by means of a magnetic field2 along the lines of which it has1 in several theories1 been supposed to circulate4 ,even this1 however1 is not real locomotion47 ,fizeau tested that straightforward consequence of this theory which is known as ,fresnel's ,law1 and ascertained by experiment that a beam of light was accelerated or retarded by a stream of water1 according as it travelled with or against the stream4 ,and he found the magnitude of the effect precisely in accordance with the ratio of the locomotive portion of the ether to the whole1--the fraction 7-#a7_/ of the speed of the water being added to or subtracted from the velocity of light1 when a beam was sent down or up the stream4 ,but even if another mode of expression be adopted1 the result to be anticipated from this experiment would be the same4 ,for instead of saying that a modified portion of the ether is moving with the full velocity of the body while the rest is stationary1 it is permissible for some purposes to treat the whole internal ether as moving with a fraction of the velocity of the body4 ,on this method of statement the ether outside a moving body is still absolutely stationary1 but1 as the body advances1 ether may be thought of as continually condensing in front1 and1 as it were1 evaporating behind2 while1 inside1 it is streaming through the body in its condensed condition at a pace such that what is equivalent to the normal quantity of ether in space may remain absolutely stationary4 ,to this end its speed backwards relative to the body must be u_/ and accordingly its speed forward in space must be u7#a-a_/74 ,for consider a slab of matter moving flatways with velocity u2 let its internal etherial density be 1 and let the external ether of density #a be stationary4 ,let the forward speed of the internal ether through space be xu1 so that a beam of light therein would be hurried forward with this velocity4 ,then consider two imaginary parallel planes moving with the slab1 one in advance of it and the other inside it1 and express the fact that the amount of ether between those two planes must continue constant4 ,the amount streaming relatively backwards through the first plane as it moves will be measured by u times the external density1 while the amount similarly streaming backwards through the second plane will be 7u-xu7 times the internal density4 ,but this latter amount must equal the former amount4 ,in other words1 u#a must equal 7u-xu7 4 ,consequently x comes out x 7-#a7_/2 which is ,fresnel's incontrovertible law for the convective effect of moving transparent matter on light inside it4 ,the whole subject1 however1 may be treated more generally1 and for every direction of the ray1 on the lines of ,chapter ,x1 thus3-- ,inside a transparent body light travels at a speed ,v_/2 and the ether1 which outside drifts at velocity v1 making an angle with the ray1 inside may be drifting with velocity v and angle 4 ,hence the equation to a ray inside such matter is ,t ds _/ 77,v_/7 cos v cos 7 min41 where sin _/sin v_/7,v_/7 4 ,this may be written ,t cos ds _/ 7,v_/ 7#a-77 - v cos ds _/ 7,v_/ 7#a-772 the second term alone involves the first power of the motion1 and assuming that v cos d_/ds1 and treating as a quantity too small for its possible variations to need attention1 the expression becomes ,t ,t cos _/ 7#a - 7 - 7,b - ,a7 _/ 7,v7#a - 771 ,t being the time of travel through the same space when empty4 ,now1 if the time of journey and course of ray1 however they be affected by the dense body1 are not to be more affected by reason of etherial drift through it than if it were so much empty space1 it is necessary that the difference of potential between two points ,a and ,b should be the same whether the space between is filled with dense matter or not 7or1 say1 whether the ray-path is taken through or outside a portion of dense medium74 ,in other words 7calling the outside and the inside potential function71 in order to secure that ,t shall not differ from ,t by anything depending on the first power of motion1 it is necessary that ,b-,a shall equal ,b-,a3 i4e4 that the potential inside and outside matter shall be the same up to a constant1 or that v cos v cos 2 which for the case of drift along a ray is precisely ,fresnel's hypothesis4 ,another way of putting the matter is to say that to the first power of drift velocity ,t ,t - 7 v cos - v cos 7 ds_/,v1 and that the second or disturbing term must vanish4 ,hence ,fresnel's hypothesis as to the behaviour of ether inside matter is equivalent to the assumption that a potential function1 v cos ds 1 exists throughout all transparent space1 so far as motion of ether alone is concerned4 ,given that condition1 no first-order interference effect due to drift can be obtained from stationary matter by sending rays round any kind of closed contour2 nor can the path of a ray be altered by etherial drift through any stationary matter4 ,hence filling a telescope tube with water cannot modify the observed amount of stellar aberration4 ,the equation to a ray in transparent matter moving with velocity u in a direction 1 and subject to an independent ether drift of speed v in direction 1 is ds _/ 7,v_/ cos v_/ cos u#a - 7#a_/7 cos 7 const4 ,,william ,,brendon ,,and ,,son1 ,,ltd4 ,,printers1 ,,plymouth ,science for the ,general ,reader ,,worlds ,,in ,,the ,,making ,the ,evolution of the ,universe4 ,,svante ,,arrhenius1 of the ,nobel ,institute1 ,stockholm4 ,illustrated4 #fs4 net ,explains the origin of nebul from suns and suns from nebul1 the universal distribution of life1 the conservation of energy1 etc41 and shows how all may be accounted for by the newly developed principle of the pressure of light ,,astronomy ,,with ,,the ,,naked ,,eye ,g4,p4 ,,serviss4 ,illustrated4 #fs4 net ,telling all that may be seen in the skies without the aid of the telescope ,,the ,,friendly ,,stars ,m4,e4 ,,martin4 ,illustrated4 #es4 net ,a handy volume1 enabling the reader to identify the principal stars and constellations ,,sidelights ,,on ,,astronomy ,prof4 ,,simon ,,newcomb4 ,illustrated4 #gs4 #f;d4 net ,discusses such topics as ,are the ,planets ,inhabited8 etc4 etc4 ,,the ,,chemistry ,,of ,,commerce ,prof4 ,r4,k4 ,,duncan1 author of ,the ,new ,knowledge4 ,illustrated4 #gs4 #f;d4 net2 post-free1 #gs4 #aa;d4 ,an account of the scientific processes involved in modern industry1 with valuable suggestions for their extension ,,new ,,conceptions ,,in ,,science ,,carl ,,snyder4 ,illustrated4 #gs4 #f;d4 net ,dealing with the new worlds revealed by the microscope1 telescope1 etc41 and the latest scientific theories based thereon ,,nineteenth ,,century ,,science ,dr4 ,,henry ,,smith ,,williams4 ,illustrated4 #is4 ,a review of the great scientific achievements of modern times1 and the problems now being investigated ,short studies on great subjects by distinguished living men4--,the ,standard4 ,,harper',s ,,library ,,of ,,living ,,thought ,foolscap #hvo1 gilt tops1 decorative covers1 richly gilt backs ,per ,volume3 ,cloth #bs4 #f;d4 net1 ,leather #cs4 #f;d4 net ,some ,contributors3 ,,algernon ,,charles ,,swinburne ,,count ,,leo ,,tolstoy ,w4,m4 ,,flinders ,,petrie ,,sir ,,oliver ,,lodge ,,theodore ,,watts-,,dunton ,,svante ,,arrhenius ,,ernest ,a4 ,,gardner ,,arnold ,,meyer ,,sir ,,william ,,crookes c4 c4 ,a permanently useful addition to literature4--,the ,daily ,telegraph4 ,presenting suggestive 'living' thoughts on subjects of vital interest4--,the ,times ,harper's ,library of ,living ,thought ,now ,ready3 ,,algernon ,,charles ,,swinburne ,,three ,,plays ,,of ,,shakespeare ,leads us to so many fine points of observation4 ,daily ,telegraph ,luminous and valuable4--,standard ,,count ,,leo ,,tolstoy ,,the ,,teaching ,,of ,,jesus ,will set students thinking4--,christian ,world ,w4,m4 ,,flinders ,,petrie ,,personal ,,religion ,,in ,,egypt ,,before ,,christianity ,shows what ,christianity meant to those who actually heard the teaching of the ,way ,,sir ,,oliver ,,lodge ,,the ,,ether ,,of ,,space ,advocating the view which makes the ,ether not only all pervading1 but substantial beyond conception--the most substantial thing--perhaps the only substantial thing in the material universe ,,prof4 ,c4,h4 ,,becker ,,christianity ,,and ,,islam ,a study of the similarities1 differences1 and the interaction of ideas between the two schools of religious thought ,a bold enterprise and one to be commended4--,the ,daily ,chronicle ,harper's ,library of ,living ,thought ,now ,ready3 ,,three ,,plays ,,of ,,shakespeare ,,algernon ,,charles ,,swinburne ,,the ,,teaching ,,of ,,jesus ,,leo ,,tolstoy ,,personal ,,religion ,,in ,,egypt ,,before ,,christianity ,w4,m4 ,,flinders ,,petrie ,,the ,,ether ,,of ,,space ,,sir ,,oliver ,,lodge ,,the ,,origin ,,of ,,the ,,new ,,testament ,,prof4 ,,william ,,wrede 7,university of ,breslau7 ,,christianity ,,and ,,islam ,,prof4 ,c4,h4 ,,becker 7,colonial ,institute1 ,hamburg7 ,forthcoming3 ,,diamonds ,,sir ,,william ,,crookes ,,religion ,,and ,,art ,,in ,,ancient ,,greece ,,prof4 ,,ernest ,a4 ,,gardner 7,university of ,london7 ,,the ,,life ,,of ,,the ,,universe #b vols4 ,,prof4 ,,svante ,,arrhenius 7,nobel ,institute1 ,stockholm7 ,,jesus ,,or ,,paul8 ,,prof4 ,,arnold ,,meyer 7,university of ,zurich7 ,,poetic ,,adequacy ,,in ,,the ,,twentieth ,,century ,,theodore ,,watts-,,dunton ,,revelation ,,and ,,inspiration ,,prof4 ,,reinhold ,,seeberg 7,university of ,berlin7 ,,harper ,,brothers ,april1 #aiji #de ,albemarle ,street ,london1 ,w4 99 99 99 99 99 ,transcriber's ,notes ,parentheses have been added to mathematical equations for clarity and correctness4 ,letters representing mathematical variables are not marked as italic when this would impair clarity in expressions and equations4 ,the lower and upper limits of definite integrals are indicated by curly brackets1 e4g4 #j1444;d represents a definite integral with values of ranging from #j to 4 ,the caret character is used in the expression 7#ag_/af7c_/b to signify raising the fraction #ag_/af to the power #c_/b4 ,other exponents are represented using superscripted numerals1 e4g4 x4 ,italic text is denoted by underscores and bold text by equal signs4 ,obvious punctuation and spelling errors and inconsistent hyphenation have been repaired4 ,in ambiguous cases1 the text has been left as it appears in the original book4