UNDO.ATORY THKORY OF LIGHT. 



I'XDl'LATORY THKORT OK LIGHT. 



XavrUm. the aiuiplu -ity with which the cxwtenco of rays fell in with 

 the output-til \i c-iuiiiarrd with the uuduUtory theory, the want of 

 uffioient familiarity with tin- conception of undulations, and the 

 mtUieuiatical ditlicultis* inherent in their investigation, conspired to 

 retard the program of the undulatory theory. *nd mined the oor- 

 pux-nUr theory to be that chiefly iu vogue up to the commencement 

 of the pr.~-ut century. About that time the uudulotory theory wu 

 revived by Dr. Young, who, guidod by the analogy of sound, WM led 

 to the discovery of the important principle of interference (ItfTKK- 

 rEMKClt], wad applied it successfully to the explanation of the colour* 

 of thin plaU*, and of the fringe* teen in the middle of the shadow of a 

 aleoder opaque body, which latter were proved to be uu-on tota/Vy due to 

 interference, since they disappeared when the light which (*ssod, or was 

 about to pan by one aide of the opaque body wai intercepted by a 

 screen, though the light which passed by the other side remained the 

 tame at before. The came principle,!!! the hand* of Dr. Young, 11 t 

 an explanation far more complete than any that had hitherto been niv. n 

 of various oth-rs of the curious phenomena of diffraction [DIFFRACTION 

 or LIMIT], and at his suggestion Dr. \Volla*ton undertook an experi- 

 mental investigation of tl'.e l-iw of extraordinary refraction in Iceland 

 par, which ended in a complete verification of the construction which 

 llu\fhen hail given iiiuler the n"idan.-- of the theory of undulations, 

 a construction which wu further verified by Mains in France, by 

 observation* made in a totally different manner. 



Later mill. Freanel, iu his celebrated memoir on diffraction, reduced 

 the explanation of the phenomena of ditlractiou to two principles, 

 Huyghen*'* principle, and the principle of interference, which ore neces- 

 sary consequences of the most fundamental assumptions of the undu- 

 latory theory, and proved by exact measures the accordance of theory 

 and olwervaiion ; and Kraunhofer, by observations on pure diffraction 

 spectra, admitting of almost o&tronomie.il pi. i -ion. verified the formula! 

 \\ hi li result for that case from the principle of interference. Mean- 

 while a new and splendid class of phenomena, those relating to 

 polarisation and the colours of crystalline plate*, &c., engaged the 

 attention of the most celebrated experimentalists ; and though these 

 for a time seemed difficult of explanation on any theory, they fell 

 naturally into their place* whuu the hypothesis of transverse vibrations 

 [Poi.AKisATlox or LIUIIT], which occurred indc|>cndently to Young 

 and Fresnel. wan introduced into the undulatory theory. Guided by 

 this hypothesis, and by dynamical eon.-ider.itions, Fresnel constructed 

 hi* celebrated theory of double refraction, which, without bein_-. or 

 professing to be, a pel fectly rigorous nii.-chanic.-il theory, is one of the 

 most wonderful scientific generalisations which the human mind has 

 achieved ; and while it explained the previously known laws of double 

 refraction and the polarisation of each of the refracted rays, corrected 

 in some respects the laws previously assumed by ex|>eriincutalista, and 

 led to the discovery of new and unexpected phenomena. Thus while 

 in the progress of optical science the corpuscular theory remained 

 almost entirely barren of result*, beyond the explanation of the 1 .iws 

 of reflection and refraction and of the aberration of light, and even 

 appeared to be contradicted by certain phenomena, the theory of 

 undulations has continually been acquiring fresh strength, by bringing 

 complicated phenomena into i.ainiony with one .mother, and with the 

 fundamental h} p ' '' theory. And within the last few years 



M. l-'oiie-ndi, by provm HI' at, that light travels faster 



in air than in water, has given the coup de yrdre to the corpuscular 

 theory. 



The fundamental assumptions of the undulatory theory are these : 

 1 . That all s|iace to the remotest visible star is filled with a rare and 

 elastic medium, or tlln r, which also penetrates the substance of air, water, 

 glass, and bodies in general. 2. That light consists in a succession of 

 tremors or undulations pro|>agated in this ether. 3. That self-luminous 

 bodies, or ratlu-r their ultimate molecules, arc in a state of vibratory 

 agitation, which they are capable of communicating to the ether, in which 

 they are propagated onwards by virtue of itn elasticity, just as sonorous 

 i arc in a state of vibration, and communicate their vibrations to 

 the surrounding air. by which they ate propagated onwards in waves 

 of sound. 4. That these ethereal vibration* are capable of atle, tin.' 

 the nerves of the retina so as to produce the sensation of light, in a 

 manner bearing a more or Kw clow analogy to that in \\hi h HP- vibr.i- 

 tions of the air affect the auditory nerves so as to produce the sensation 

 of sound. ;">. Tliat, as in sound, j./i.Vi depends upon the frequency of 

 the at-iinl vibrations, while for a note of given pitch I'.udnru depends 

 on the amplitude of the excursions to and fro of the particles of air, 

 so in light r-J..ai- du|'iids on the frequency of the ethereal vibrations, 

 while for light of a given kind brightnea depend* on the amplitude of 

 the excursion* of the particles of ether. 6. That the ethereal vibra- 

 tions within refracting media are affected by the presence of the 

 material (nrticlt* in such a way as to be propagated with lets velocity 

 than in vocu, whether it be from an increase of density of the ether, 

 or a diminution of its elasticity, or from the ether having to thread iti 

 way among the material particles, or from some similar cause. 



To a reader acquainted with the theory of sound the conception ol 

 an undulation it already familiar ; but for the take of other* it may be 

 well to use one or two illustrations. Conceive then a long rope to be 

 stretched horizontally between a Axed support at one end, and the ham- 

 of a |- r.n holding it at the other. If the person now rapidly move 

 hi* hand I.. ' .irk again, the rope near the operator will 1 1 



hrown into the form of a curve, and this curve will be seen to trarrl 

 .-.I end. Vet it is evident that what to 



travels is not matter, but an affection of matter. The different portion* 

 of the rope merely move laterally to and fro : what progresses is a 

 certain Halt of t/iimjt, a state of displacement and motion which the 

 different portions of the rope attune IN ivecttti'm. Again, if a stone be 

 dropped into still water, a series of circular waves travel outwards from 

 the (wiiit f disturbance, but the particles ol water do not to progress, 

 at may be teen by watching the motion of a floating cork, but merely 

 move a little backward* and forwards, and up and down, oscillating 

 about a mean position. Lastly, take the case of a gun fired in air. 

 Here the air oompreswd by the explosion nnmnt upon the quieaeeut 

 air surrounding it, oompresaing it and at the same time moving it a 

 ittle forwards ; this shell of air act* in a similar manner upon the 

 -hell immediately outside it, and to on. Thus a wave of condensation 

 immediately followed, in point of fact, by a wave of rarcfuct. 

 >ropagated outwards from the place of discharge, while the particles of 

 air themselves merely move a little to and fro iu the direction of pro- 

 pagation. In the tint example undulations are propagated along 

 u the second along a iitrjart, in the third in r/ntri, or in three dimen- 

 sions ; and in this respect the third example best illustrates the undii- 

 atioua which we contemplate in the theory of light. 



In all case* of undulation we must carefully distinguish between the 

 velocity i if prufiayalioii , or the rate at which a certain firm or M 

 ti,iii<ji is propagated, and the retocity of the particle* of the medium in 

 which the undulations take place. The former depends only on tln> 

 density and elasticity of the medium. Density we must conceive to 

 be measured by the inertia of the portion of the medium contained in 

 a given volume, and therefore we must attribute inertia to our sup- 

 posed ether ; but whether it possesses uxight, whether it is subject to 

 -he influence of gravitation, is a question which we need not speculate 

 about. By elasticity is merely meant the force whereby the medium 

 tends to regain its primitive state, whether by resisting change of 

 volume, as in the cose of air, or change of figure, as in the cats of india- 

 rubber. We know that the velocity of propagation of sound in air is" 

 about 1100 feet per second, that of light in vacuo about 1U2^>00 miles 

 !>er second. The velocity of the particles may, however, be as small as 

 we please ; and in the theories of sound and light (with the exce ptioii, 

 at least, of the explanation of certain phenomena relating to very vio- 

 lent sounds), it is sufficient to treat the motions of the particles at 

 indefinitely small, so that w c may apply the general dynamical prin- 

 ciple of the superposition of small motions. In other words, ii the 

 medium (air or ether) would be disturbed in one way by one cause 

 acting alone, and in another way by another, the actual disturbance at 

 any point when the two causes act together will be got by compound- 

 ing the disturbances (expressed by displacements or velocities, as the 

 case may be) due to the two causes taken separately. Tin- 

 direction of motion of the particles of the medium may 1 

 fectly open question so far as relates to the conception of an undula- 

 tion and the explanation of phenomena thereby, and by the appl 

 of the principle of the co-existence of small motions. Thus, in the 

 example of the rope, the motion is rectilinear, and perpendicular to the 

 direction of propagation ; and if the operator, instead of moving hi* 

 hand backwards and forwards moved it round and round, the path of 

 any particle would be a curve lying in a plane perpendii-ular to the 

 n of propagation. In the example of waves on water, each (ar- 

 ticle moves in a curve lying in a vertical plane passing through tin- 

 direction of propagation ; while in the third example the motion i - 

 simply to and fro in the direction of propagation. 



A single pulsation of air is audible as a noite, though it does not 

 convey the idea of pitch ; but even in the most transitory light, such 

 as that of the electric spark, the phenomena of dispersion and inter- 

 ference indicate that we have to deal with a succession of a great num- 

 ber of similar undulations. Upturning, for simplicity of conception, to 

 the illustration of the rope, let us therefore suppose that the o; 

 moves his hand backwards and forwards in a regular periodic manner. 

 The rope will be thrown into the form of a sinuous curve, which travels 

 along it. The distance from any (article to the next before or behind 

 which is in the same state of motion, is called the latytk of a war, . It 

 is evident that a single wave-length comprises two bow-shaped portions 

 of the curve, the displacements in which are on opposite sides of the 

 mean position, and which may be distinguished as positive and negative ; 

 and also that any two points distant by half a wave's length are in 



exactly opposite states of displacement and motion, at least if we sup- 

 pose the positive and negative portions of the curve exactly alii* 

 we reflect on the motion of any particular particle, we shall readily see 

 that it goes through its changes once while the wave-form progresses 



by one "wave's length. Hence, if r be the velocity of propagation, \ 

 the length of a wave, and r the periodic time of vibration of a single 

 particle, we have the fundamental relation A = rr, which applies to 

 undulations in general, since what was said in the case of the rope holds 

 good generally. In the case of light, the absence of prismatic colour* 

 when a star 1 by aberration from its mean position, tin- 



absence of changes of colour when one of Jupiter's satellite* enters or 

 emerges from his shadow, and the existence of periodic stars, such a- 

 Algol, which rapidly change in brightness without changing in colour, 



tin- velocity of propagation of light in vacuo is the 

 for all colours. The phenomena of interference furnish us with 



