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 .ETHER

107 straight lines. Again, we may split a narrow beam of constant throughout the region; at a distant place in free light by partial reflection from a transparent plate, and aether where there is no motion, they must thus be equal recombine the constituent beams after they have traversed to - ?/, -v,-w, as they refer to axes moving with the different circuits of nearly equivalent lengths, so as to matter. Hence the paths and times of passage of all rays obtain interference fringes. The position of these fringes relative to the material system will not be altered by a will depend on the total retardation of the one beam with uniform motion of the system, provided the velocity of respect to the other; and thus it might be expected to radiation relative to the system, in material of index p, is vary with the direction of the Earth’s motion relative to diminished by p“2 times the velocity of the system in the the apparatus. But it is found not to vary at all, even direction of the radiation, that is, provided the absolute up to the second order of the ratio of the Earth’s velocity velocity of radiation is increased by 1 — p~2 times the said to that of light. It has in fact been found, with the velocity; this involves that the free aether for which p is very great precision of which optical experiment is cap- unity shall remain at rest. This statement constitutes the able, that all terrestrial optical phenomena — reflection, famous hypothesis of Fresnel, which thus ensures that all refraction, polarization linear and circular, diffraction— phenomena of ray-path and refraction, and all those are entirely unaffected by the direction of the Earth’s depending on phase, shall be unaffected by uniform conmotion; and this is our main experimental clue. vection of the material medium, in accordance with the We pass on now to the theory. We shall make the results of experiment. natural supposition that motion of the aether, say with Is the uEther Stationary or Mobile ?—This theory secures velocity (u,v,w) at the point is simply super- that the times of passage of the rays shall be independposed on the velocity V of the optical undulations through ent of the motion of the system, only up to the first order that medium, the latter not being intrinsically altered, of the ratio of its velocity to that of radiation. But a l^ow the direction and phase of the light are those of the classical experiment of Michelson, in which the ray-path ray which reaches the eye; and by Fermat’s principle, was wholly in air, showed that the independence extends established by Huygens for undulatory motion, the path to higher orders. This result is inconsistent with the of a ray is that track along which the disturbance travels aether remaining at rest, unless we assume that the dimenin least time, in the restricted sense that any alteration of sions of the moving system depend, though to an extent any short reach of the path will increase the time. Thus so small as to be not otherwise detectable, on its orientathe path of the ray when the aether is at rest is the curve tion with regard to the aether that is streaming through which makesy^s/Y least; but when it is in motion it is it. It is however in complete accordance with a view the curve which makes fds/(V + lu + mv + nw) least, where that would make the aether near the Earth fully par(l, m, n) is the direction vector of 5s. The latter integral take in its orbital motion—a view which the null effect of becomes, on expanding in a series, convection on all terrestrial optical and electrical phenoJdsJV -/(udx + vdy + wdz)/V2 + judx + vdy + wdz)2/V3ds + ..., mena also strongly suggests. But the aether at a great since lds = dx. If the path is to be unaltered by the distance must in any case be at rest; while the facts of motion of the aether, as the law of astronomical aberration astronomical aberration require that the motion of that suggests, this must differ from yds/Y by terms not depend- medium must be irrotational. These conditions cannot be ing on the path—that is, by terms involving only the consistent with sensible convectiori of the aether near the beginning and end of it. In the case of the free aether V Earth without involving discontinuity in its motion at some is constant; thus, if we neglect squares like (u/Y)2, the intermediate distance : so that we are thrown back on the condition is that udx + vdy + wdz be the exact differential previous theory. Another powerful reason for taking the aether to be of some function <£. If this relation is true along all stationary is afforded by the character of the equations of paths, the velocity of the aether must be of irrotational type, like that of frictionless fluid. Moreover, this is electrodynamics; they are all of linear type, and superprecisely, the condition for the absence of interference position of effects is possible. How the kinetics of a between the component of a split beam; because, the time medium in which the parts can have finite relative motions will lead to equations which are not linear—as, for example, ■of passage being to the first order those of hydrodynamics—and the phenomena will be far yds/Y -Audx + vdi/ + wdz)/V2, more complexly involved. It is true that the theory of the second term will then be independent of the path vortex rings in hydrodynamics is of a simpler type; but (4> being a single valued function) and therefore the same electric currents cannot be likened to permanent vortex for the paths of both the interfering beams. If therefore rings, because their circuits can be broken and the element the aether can be put into motion, we conclude that such of steadiness on which the simplicity depends thereby anotion, in free space, must be of strictly irrotational type. destroyed. But our experimental data are not confined to free Dynamical Theories of the jEther.—The analytical equaspace. If c is the velocity of radiation in free space and tions which represent the propagation of light in free I1 the refractive index of a transparent body, V = c/p; cEther, and also in aether modified by the presence of thus it is the expression G-‘l/ij:udx + v'dy + tv'dz) that matter, were originally developed on the analogy of the is to be integrable exactly, where now (id,v',w') is what equations of propagation of elastic effects in solid media is added to Y owing to the velocity (u,v,w') of the medium. (See Wave Theory, Ency. Brit. vol. xxiv.). Various As however our terrestrial optical apparatus is now all types of elastic solid medium have thus been invented to in motion along with the matter, we must deal with the represent the tether, without complete success in any case. rays relative to the moving system, and to them also In MacCullagh’s hands the correct equations were derived Fermat’s principle clearly applies; thus Y + (yu + mv' + nw') from a single energy formula by the principle of least is here the velocity of radiation in the direction of the action ; and while the validity of this dynamical method Jay, but relative to the moving material system. How was maintained, it was frankly admitted that no mechanical the expression above given cannot be integrable exactly, analogy was forthcoming. When Clerk Maxwell pointed under all circumstances and whatever be the axes of co- out the way to the common origin of optical and electrical ordinates, unless (p2%',p'V,pW) is the gradient of a con- phenomena, these equations naturally came to repose on tinuous function. In the simplest case, that of uniform an electric basis, the connexion having been first definitely translation, these components of the gradient will each be exhibited by FitzGerald in 1878 ; and according as the