Hendrik Lorentz

“ Since a molecule of a circular-polarizing substance must have a so-called "helical" structure, then the particles from which it consists may be mutually connected, so that the displacement of one of them produces a circular motion of one or many others. Let, for example, a positive ion A be in motion along the line G, and by that the moment shall be produced, so that the velocity is proportional to , and this motion may be accompanied by the rotation (in a circle with G as its axis) of some other ions B that are also positive. Between the velocities of A and B there is a constant relation. ”

“ To come to the basic equations for the phenomena of electricity in moving bodies, I joined an opinion that has been represented in recent years by several physicists; I have indeed assumed that small electrically charged molecules exist in all bodies, and that all electric processes are based on the location and motion of these "ions". ”

“ In favor of Fresnel's theory several well-known reasons can be cited. Especially the impossibility of locking the aether between solid or liquid walls. As far as we know, a space devoid of air behaves (in the mechanical sense) like a real vacuum, when ponderable bodies are in motion. When we see how the mercury of a barometer rises to the top when the tube is inclined, or how easily a closed metal shell can be compressed, one can not avoid the idea, that solid and liquid bodies let the aether pass through without hindrance. ”

“ In a polarized light beam, the light vector is parallel at all points to a certain line; it can be decomposed into three mutually perpendicular components, the first having the direction of the beam, while the second lies in the plane of incidence and the third is perpendicular to it. Now, since the properties of a polarized beam, except the intensity and period of oscillation, only depends on one magnitude — such as the azimuths of the polarizer —, then the ratios between the mentioned components must have specific values, as soon as the ratio between the second and third is given ”

“ The conservation of energy. § 13. To justify our hypotheses, it is necessary to show its agreement with the energy law. We consider an arbitrary system of ponderable bodies that contain ions, around which only the aether exists up to an infinite distance, and around it we put an arbitrarily closed surface . During an element of time , the work that affects ponderable matter and which stems from , is
where it is to be noted, that no work is done by the forces (which are derived from ) , because they are always perpendicular to the direction of motion. ”

“ What we have already stated without proof, namely that the period T exists throughout in the medium, is nothing else than what Petzval, in his attacks against Doppler's theory, called the law of the immutability of the oscillation period (Wiener Sitz.-Ber., vol 8, p. 134, 1852) . He only forgot to notice, that this law only would apply, if we consider the phenomena as a function of t and the relative coordinates.
The proof of the theorem is, by the way, easy to give, when the oscillations are infinitely small, and when we have to do with homogeneous linear differential equations. ”

“ We can however be satisfied with forward and backward motion at molecular distances, if we only assume that one ion often transfers its charge to another, or that two oppositely charged ions, if they meet, or after they were "connected" with one another, exchange their charges against each other. ”

“ We want to say, that a rotation in a plane corresponds to a certain direction of the perpendicular, and namely it shall be the direction into that side, at which an observer must be located, so that for him the rotation is counter-clockwise. ”

“ If a certain motion exists in a system, then, as it was shown in § 18, also the inverse motion is possible, as soon as forces of non-electric origin are the same for a certain location of the ions as well, as in the original case. From this it directly follows, that all motions in a body, that besides ions also contain uncharged mass particles, can be reversed, in case all molecular forces are determined by the configurations and not, for example, depending on the velocities. ”

“ It is noteworthy, the we are led exactly to the above presupposed changes of dimensions, when we first (without consideration of the molecular motion) assume, that in a rigid body which remains at its own, the forces, attractions or repulsions which act on an arbitrary molecule, are mutually in equilibrium, and second — for which, however, there is no reason — when we apply to these molecular forces the law which we have derived in § 23 for the electrostatic actions. ”

“ If we decompose the velocity of translation in two component that are perpendicular to the plate, or parallel, then, if we neglect magnitudes of second order, the effects of those components remain side by side. The problem can thus be reduced to two simpler cases. It is now possible, without making special assumptions about the nature of light oscillations, that a translation perpendicular to the plate, can not have the expected influence of Fizeau; we will derive some general considerations. As for the other direction of translation, we can not speak so determined ”

“ Here, we don't discuss the subtle, related question concerning the localization of the energy. We can restrict ourselves with the fact, that the entire energy located in an arbitrary space — the "electric" portion calculated by formula (12) — always varies, as if the energy would travel according to the way determined by (13) .
Tensions in the aether. § 15. The forces determined by our formula (V) , not only require the motion of ions in ponderable bodies, but also in some circumstances can unify themselves to an action, that tends to set the body into motion. ”

“ Yet great difficulties arise, when we also want to form the equations of motion for the oscillating ions themselves. To express in these equations the relations, which are the basis for dispersion, birefringence, and circular polarization, it would be required an understanding of molecular processes that wasn't achieved by us by far. We want to restrict ourselves, to derive from a very simple presupposition the most probable shape of the sought relations, and then help on ourselves as good as possible. ”

“ The treatment of the problems that are now coming into play is most simple, when instead of the co-ordinate system used above, we introduce another one which is rigidly connected with ponderable matter and therefore shares its displacement.
While the coordinates of a point with respect to the fixed system were called x, y, z, let those, which refer to the moving system and which I call the relative coordinates, denoted by (x) , (y) , (z) for the time being. ”

“ If a state of motion exists in a system of bodies, in which the components of the light vector are certain functions of relative coordinates and time t, thus also the functions that arise when we replace t by -t, represents the values of the components that correspond to a possible motion. ”

“ Which direction Earth's motion may have, whether from the polarizer to the analyzer, or vice versa, light will always be erased at the presupposed position of the analyzer, as long as nothing is changed as regards the relative period of oscillation and the direction of the rays in relation to the apparatus. ”

“ Ponderable matter, which is not charged, has only to be considered by us, when it exerts molecular forces on the ions. Concerning the electric phenomena, it has no influence at all and everything happens, as if the space where it is located would only contain the aether. ”

“ If a conductor C is confronted with a charged body K, then there exists, according to a known theorem, always a certain amount of charge on the surface of C, which together with K exerts no action on the ions in the interior of the conductor. ”

“ If we would like to observe magnitudes so small, then we probably can hope to succeed only by an interference method. Thus we would have to work with two mutually perpendicular rods, and of two mutually interfering light beams, let one travel back and forth with respect to the first rod, and the other with respect to the second rod. By that we come again, however, to Michelson's experiment, and we wouldn't observe any displacement of the fringes during the rotation. ”

“ We also arrive at a possible motion, when we take the mirror image of an arbitrary, given motion in relation to a stationary plane, namely in such a way that both the translational velocity, as well as all light-vectors are replaced by the mirror images.
If we are dealing with the pure aether, then we satisfy these conditions if we choose the dielectric displacement as the light vector. ”

“ By we understand the component of the vector into the direction l; by therefore the components into the axis-directions.
For a vector with components we sometimes also write .
e. If is a scalar magnitude, then we understand by the derivative with respect to time t. The letter denotes a vector with components: , or etc.
f. The expression
we call the "integral of vector over the surface ", and the magnitude
the "line integral of line s".
g. If a vector in any point of space is given, then
has everywhere a certain value, independent of the choice of coordinate system. ”

“ If the ponderable matter is moving, then — since it carries the charge along with it — at a certain point of space there always exists another , and soon it is (when we are dealing with mutually separated ions) different from zero here and there. Yet the condition of the aether has constantly to obey equation (I) .
§ 6. The change of , that happens with time at a certain point of space, constitutes an electric current (Maxwell's displacement current) that can be represented by . We assume that it exists also in the interior of charged matter. ”

“ Furthermore, we can conclude, that the vector which is present in Poynting's theorem, falls into the wave normal. We can easily convince ourselves, that it has the direction, in which the waves are propagating, and we find for its magnitude
.
The energy flux through a plane which is parallel to the waves, thus amounts for the unit of area and time
§ 76. From a light bundle as the one considered above, others of the same kind can arise by refraction and mirroring at plane limiting surfaces. ”

“ Thus, if the adoption of this transition or exchange of the ionic charges - one of course still very dark process - is the essential complement to any theory that requires an entrainment of electricity by ions, then a persistent electric current never consists of a convection alone, at least not when the centers of two touching or interconnected particles are in some distance from each other. ”

“ The trajectory of Earth deviates as little from a circle, that, when we are dealing with sun rays, we can neglect the velocity component , on which the variation of the oscillation period depends (§ 37) . ”

“ It is now to be noticed, that the molecules of a light source, e.g. a flame, must be considered as totally independent from one another, so that, as it is ordinarily expressed, the rays emanated by two of these particles cannot mutually interfere. From that if follows, that arbitrary variations in the phases of the single molecules cannot have any influence on the observable phenomena. ”

“ If we add the increase of the energy in the interior of , and the work of the forces, by which the aether is acting on the ponderable body, then we must, if the energy theorem shall be satisfied, obviously obtain zero.
The increase energy in a full period T would be zero, if the surface together with the body K would be displaced over the distance , and at this place would have taken the location ; it factually consists of the energy amount, which, at time , is more contained in than in . ”