depending simply on incompressibility, which is not sensibly implicated in the electric and optical activities. With reference to all such further refinements of theory, it is to be borne in mind that the perfect fluid of hydrodynamic analysis is not a merely passive inert plenum; it is also a continuum with the property that no finite internal slip or discontinuity of motion can ever arise in it through any kind of disturbance; and this property must be postulated, as it cannot be explained.
Motion of Material Atoms through the Aether.—An important question arises whether, when a material body is moved through the aether, the nucleus of each atom carries some of the surrounding aether along with it; or whether it practically only carries on its strain-form or physical atmosphere, which is transferred from one portion of aether to another after the manner of a shadow, or rather like a loose knot which can slip along a rope without the rope being required to go with it. We can obtain a pertinent illustration from the motion of a vortex ring in a fluid; if the circular core of the ring is thin compared with its diameter, and the vorticity is not very great, it is the vortical state of motion that travels across the fluid without transporting the latter bodily with it except to a slight extent very close to the core. We might thus examine a structure formed of an aggregation of very thin vortex rings, which would move across the fluid without sensibly disturbing it; on the other hand, if formed of stronger vortices, it may transport the portion of the fluid that is within, or adjacent to, its own structure along with it as if it were a solid mass, and therefore also push aside the surrounding fluid as it passes. The motion of the well-known steady spherical vortex is an example of the latter case.
Convection of Optical Waves.—The nature of the motion, if any, that is produced in the surrounding regions of the aether by the translation of matter through it can be investigated by optical experiment. The obvious body to take in the first instance is the earth itself, which on account of its annual orbital motion is travelling through space at the rate of about 18 miles per second. If the surrounding aether is thereby disturbed, the waves of light arriving from the stars will partake of its movement; the ascertained phenomena of the astronomical aberration of light show that the rays travel to the observer, across this disturbed aether near the earth, in straight lines. Again, we may split a narrow beam of light by partial reflexion from a transparent plate, and recombine the constituent beams after they have traversed different circuits of nearly equivalent lengths, so as to obtain interference fringes. The position of these fringes will depend on the total retardation in time of the one beam with respect to the other; and thus it might be expected to vary with the direction of the earth’s motion relative to the apparatus. But it is found not to vary at all, even up to the second order of the ratio of the earth’s velocity to that of light. It has in fact been found, with the very great precision of which optical experiment is capable, that all terrestrial optical phenomena—reflexion, refraction, polarization linear and circular, diffraction—are entirely unaffected by the direction of the earth’s motion, while the same result has recently been extended to electrostatic forces; and this is our main experimental clue.
We pass on now to the theory. We shall make the natural supposition that motion of the aether, say with velocity (u,v,w) at the point (x,y,z), is simply superposed on the velocity V of the optical undulations through that medium, the latter not being intrinsically altered. Now the direction and phase of the light are those of the ray which reaches the eye; and by Fermat’s principle, established by Huygens for undulatory motion, the path of a ray is that track along which the disturbance travels in least time, in the restricted sense that any alteration of any short reach of the path will increase the time. Thus the path of the ray when the aether is at rest is the curve which makes ∫ds/V least; but when it is in motion it is the curve which makes ∫ds/(V+lu+mv+nw) least, where (l,m,n) is the direction vector of δs. The latter integral becomes, on expanding in a series,
∫ds/V − ∫(udx + vdy + wdz)/V2 + ∫(udx + vdy + wdz)2/V3ds + ...,
since lds＝dx. If the path is to be unaltered by the motion of the aether, as the law of astronomical aberration suggests, this must differ from ∫ds/V by terms not depending on the path—that is, by terms involving only the beginning and end of it. In the case of the free aether V is constant; thus, if we neglect squares like (u/V)2, the condition is that udx + vdy + wdz be the exact differential of some function φ. If this relation is true along all paths, the velocity of the aether must be of irrotational type, like that of frictionless fluid. Moreover, this is precisely the condition for the absence of interference between the component of a split beam; because, the time of passage being to the first order
∫ds/V − ∫(udx + vdy + wdz)/V2,
the second term will then be independent of the path (φ being a single valued function) and therefore the same for the paths of both the interfering beams. If therefore the aether can be put into motion, we conclude (with Stokes) that such motion, in free space, must be of strictly irrotational type.
But our experimental data are not confined to free space. if c is the velocity of radiation in free space and µ the refractive index of a transparent body, V＝c/µ; thus it is the expression c−2 ∫µ2(u′dx + v ′dy + w ′dz) that is to be integrable explicitly, where now (u′,v ′,w ′) is what is added to V owing to the velocity (u,v,w) of the medium. As, however, our terrestrial optical apparatus is now all in motion along with the matter, we must deal with the rays relative to the moving system, and to these also Fermat’s principle clearly applies; thus V + (lu′ + mv ′ + nw ′) is here the velocity of radiation in the direction of the ray, but relative to the moving material system. Now the expression above given cannot be integrable exactly, under all circumstances and whatever be the axes of co-ordinates, unless (µ2u′,µ2v ′,µ2w ′) is the gradient of a continuous function. In the simplest case, that of uniform translation, these components of the gradient will each be constant throughout the region; at a distant place in free aether where there is no motion, they must thus be equal to −u,−v,−w, as they refer to axes moving with the matter. Hence the paths and times of passage of all rays relative to the material system will not be altered by a uniform motion of the system, provided the velocity of radiation relative to the system, in material of index µ, is diminished by µ−2 times the velocity of the system in the direction of the radiation, that is, provided the absolute velocity of radiation is increased by 1−µ−2 times the velocity of the material system; this involves that the free aether for which µ is unity shall remain at rest. This statement constitutes the famous hypothesis of Fresnel, which thus ensures that all phenomena of ray-path and refraction, and all those depending on phase, shall be unaffected by uniform convection of the material medium, in accordance with the results of experiment.
Is the Aether Stationary or Mobile?—This theory secures that the times of passage of the rays shall be independent of the motion of the system, only up to the first order of the ratio of its velocity to that of radiation. But a classical experiment of A. A. Michelson, in which the ray-path was wholly in air, showed that the independence extends to higher orders. This result is inconsistent with the aether remaining at rest, unless we assume that the dimensions of the moving system depend, though to an extent so small as to be not otherwise detectable, on its orientation with regard to the aether that is streaming through it. It is, however, in complete accordance with a view that would make the aether near the earth fully partake in its orbital motion—a view which the null effect of convection on all terrestrial optical and electrical phenomena also strongly suggests. But the aether at a great distance must in any case be at rest; while the facts of astronomical aberration require that the motion of that medium must be irrotational. These conditions cannot be consistent with sensible convection of the aether near the earth without involving discontinuity in its motion at some intermediate distance, so that we are thrown back on the previous theory.
Another powerful reason for taking the aether to be stationary is afforded by the character of the equations of electrodynamics; they are all of linear type, and superposition of effects is possible. Now the kinetics of a medium in which the parts can have finite
