Willem de Sitter

“ The transformation from to or inversely, is a Lorentz-transformation.
The chief consequence of the principle of relativity is that it is impossible to observe any but relative motions. The "general" system only differs from any other possible system in that no convention is made as to its origin or the direction of its axes. It is thus not possible, from the point of view of the principle of relativity, to speak of "absolute" velocity or position otherwise than as velocity or position relative to any, not specified, "general" system of reference. ”

“ Thus if we knew only this one star, we should have to adopt as upper limit for this value 0.12. There are however a considerable number of stars with large values of u0, whose observed excentricity is very small or zero. Several of these certainly have very small parallaxes. It would evidently be absurd to assume that all of these possessed exactly that true excentricity and position of the periastron which would cancel the apparent excentricity for an observer on our earth. ”

“ In the theory of Ritz light emitted by a source moving with velocity u is propagated through space in the direction of the motion of the source with the velocity c+u, c being the velocity of light emitted by a motionless source. In other theories (Lorentz, Einstein ) the velocity of light is always c, independent of the motion of the source. ”

“ The principle of relativity, first developed in connection with the electromagnetic theory of light, has in recent years been more and more considered as of universal application, and the claim has been made that the whole of our physical sciences should be framed in conformity with it. ”

“ The smallest values, of course, are found from the stars having the smallest parallaxes. Unfortunately the parallax of most spectroscopic doubles is still unknown, and it is thus impossible to give numerical values. We can however assume as certain that for the majority of these stars a value would be found which is still smaller than that given above.
Postscript. During the discussions at the meeting the remark was made (by Prof. Korteweg) that the star β Aurigae might have a true excentricity of such amount as exactly to cancel the spurious excentricity produced by the motion. ”

“ Also the physical laws, which are differential equations defining as functions of and certain constants, are in general altered by a change of the system of reference. Physical science has, however, been so built up that there are certain transformations which leave the form of the equations unaltered. In the classical, or Newtonian, mechanics these are all orthogonal transformations of the three coordinates combined with an arbitrary uniform velocity of these axes and an arbitrary change of the units of length and time. ”

“ The principle of relativity can be enunciated as the postulate that the transformations, with respect to which the laws of nature shall be invariant, are "Lorentz-transformations." [1] A Lorentz-transformation is defined by a modulus and an axis. Taking the latter as the axis of , the transformation-formulæ are—
where is a universal constant, which, according to the electromagnetic theory, is equal to the velocity of light in free space. In Newtonian mechanics the value of this constant is . ”

“ P. Guthnick [1] and E. Freundlich [2] have brought forward the hypothesis that the velocity of light might depend on the velocity of the source in a manner differing from the simple addition postulated by the theory of Ritz. ”

“ Astronomical time is defined by the rotation of the Earth, and is measured by the hour-angle of the axis of . Such deviations from uniformity as are derived from the action of known causes—which are, however, negligible, and remain negligible under the new law—are allowed for, and the thus corrected rotation is supposed to be uniform. ”

“ The motion in one century is—
The effect of the secular terms in is, of course, only to make the observed mean motion disagree with the value derived from Kepler's third law. As we have no sufficiently accurate means of independently determining the mean distances, this can never be detected.
The formulæ (35) are valid for all excentricities, and can thus also be used for comets. The perturbations in remain of the same order as for planets. Those in and become zero for a parabola. Only the perturbation in would appear to become very large at perihelion. ”

“ Now it is easily seen that the hypothesis of Ritz leads to results which are absolutely inadmissible.
Consider one of the components of a double star, and an observer situated at a great distance Δ. Let at the time t, the projection of the star's velocity in the direction towards the observer be u. ”

“ Determinations of time are made at intervals, and are used to regulate the clock. Equal intervals on the clock are then supposed to be equal intervals of "time." The construction of the clock depends on the laws of the simple pendulum, which swings under the action of gravitation. ”

“ In the equations of motion there appear the invariants—
To express these in simultaneous relative coordinates we have—
6. The equations of motion can be given in three forms:—
and similarly for the other coordinates.
is the force according to the ordinary definition, or "Newtonian" force; is called the "Minkowskian" force. [6] The mass is a constant. ”

“ Seeliger's rotation is practically determined from the motions of the node of Mercury and the perihelion of Mars, the excesses of which over their theoretical values, as determined by Newcomb, are 1.2 and 2.1 times their respective probable errors. If the density of the second ellipsoid were so determined as to represent the node of Venus exactly, the residual in the perihelion of Mars would be reduced to 1.6 times its p.e. ”