# Page:LorentzGravitation1916.djvu/3

point of the border of the moon and finally that of the observer's eye. A similar remark may be made when the moment of reappearance is read on a clock. Let us suppose that the light-vibration itself lights the dial-plate, reaching it when the hand is at the point $a$; then we may say that three world-lines, viz. that of the light-vibration, that of the hand and that of the point $a$ intersect.
After having constructed a field-figure $F$ we may introduce "coordinates", by which we mean that to each point $P$ we ascribe four numbers $x_{1},x_{2},x_{3},x_{4}$, in such a way that along any line in the field-figure these numbers change continuously and that never two different points get the same four numbers. Having done this we may for each point $P$ seek a point $P'$ in a four-dimensional extension $R'_{4}$, in which the numbers $x_{1},\dots x_{4}$ ascribed to $P$ are the Cartesian coordinates of the point $P'$. In this way we obtain in $R'_{4}$ a figure $F'$, which just as well as $F$ can serve as field-figure and which of course may be quite different according to the choice of the numbers $x_{1},\dots x_{4}$, that have been ascribed to the points of $F$.