But it is obvious that this attitude into which our understanding of mathematical space has forced us presupposes that all the frames of reference we might select were on exactly the same footing, that is, were indistinguishable from one another. Galileo and Newton noticed that such was not the case. In certain frames we were pulled hither [Pg 107] and thither by strange forces unsymmetrically distributed, and objects placed on the floor did not remain where they had been put. Space around us appeared to be in a chaotic condition, as, for example, on a rotating disk or in a train rounding a curve. In other frames no such forces were apparent (excluding the force of gravitation), and space appeared stagnant and quiet, the same everywhere. These latter frames are called Galilean or Inertial. Now, a Galilean frame did not manifest itself as unique. So far as the most delicate mechanical experiments could detect, there appeared to exist an indefinite number of such frames, all moving in respect to one another with various constant speeds along straight lines, without suffering any relative rotation during their motion. Mechanical experiments conducted in any one of these Galilean frames showed that free bodies followed straight lines with constant speeds (Newton’s law of inertia), and when referred to these frames, mechanical phenomena, including the planetary motions, were susceptible of being formulated by very simple laws. As viewed from Galilean frames, the other frames, the non-Galilean ones (those filled with strange forces), were found to be moving with accelerated or rotationary motions. Mechanical experiments conducted in the non-Galilean frames proved that the disposition of the strange unsymmetrical so-called inertial forces bore a close relationship with the apparent motions of these frames as viewed from the Galilean ones. It was possible, therefore, for an experimenter situated in one of these strange frames to anticipate, without looking outside, exactly how his frame would appear to be moving when viewed by a Galilean observer (i.e., an observer in a Galilean frame), at least so far as acceleration and rotation were concerned. Thus, in a non-Galilean frame moving with respect to a Galilean frame along a straight line with some definite acceleration, the forces of inertia would be disposed in a parallel way, pulling in the direction opposite to that of the relative acceleration. In a non-Galilean frame rotating with respect to a Galilean observer, the disposition of the inertial forces would be much more complicated. There would be the centrifugal force pulling outwards and the so-called Coriolis forces pulling sideways.