Unfortunately, here again, ideal conditions can never be established, for we can never obtain perfect isolation, perfect rigidity and complete absence of friction. But a near approach to ideal conditions would appear to be given by the phenomenon of the earth’s rotation. And so the rotation of the earth, defining astronomical time, was regarded as furnishing science with the most reliable objective criterion of congruent time-intervals that it was possible to obtain. Nevertheless, it was well known that a definition of this sort was still far from perfect, since the rate of rotation of the earth could not be absolutely uniform, when “uniform” is defined by the standards of the principle of inertia. This realisation was brought home when the frictional resistance generated by the tides was taken into consideration.[23] The tidal friction would have for effect the slowing down of the earth’s rate of rotation (when measured against the accurate mathematical definition given by a perfectly rigid and isolated body rotating without friction). In addition to this first perturbating influence, our planet is suspected of varying in size, expanding and contracting periodically, a phenomenon known as breathing. According to the laws of mechanics, a change in shape of this sort would entail periodic fluctuations, successive retardations and accelerations in the rate of the earth’s rotation. It is instructive to understand how this discovery of the earth’s breathing was brought about. It was noticed that the moon’s motion exhibited variations which it seemed impossible to account for under [Pg 77] Newton’s law, even when due consideration was given to the perturbating effects of the sun and other planets. Not only did the moon’s motion appear to be gradually increasing, but in addition, superposed on this first uni-directional effect,[24] periodic accelerations and retardations had been observed. The gradual slowing down of the earth’s rate of rotation under the influence of the tides accounted for the apparent acceleration of the moon’s motion, but the other periodic changes in the velocity of our satellite could not be explained away in so simple a manner. Yet everything would be in order were we to assume that the earth’s rate of rotation was subjected to appropriate periodic changes; and the principles of mechanics then showed that a phenomenon of this kind could only be brought about by periodic variations in the earth’s size.