Willem de Sitter

“ 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. ”

“ 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 . ”

“ If in the system () two groups of stars have any systematic motion relatively to each other, or all stars have a systematic motion relatively to the axes of reference, the same will be the case in the system () , apart from small changes (of the second order) in the constants defining the direction of motion relatively to the ecliptic, which are, however, of no importance, as they are constant corrections to quantities whose values must be derived from observation. If no such systematic motion exists in () , neither does it exist in () . ”

“ 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. ”

“ 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. ”