absolute motion, and absolute motion implies absolute time and absolute space. We will quote his description of the celebrated experiment with a pail of water :

The effects which distinguish absolute from relative motion are, the forces receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion they are greater or less, according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; after, by the sudden action of another force, it is whirled about the contrary way, and while the cord is untwisting itself, the vessel continues for some time in this motion; the surface of the water will at first be plane, as before the vessel began to move; but the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little from the middle, and ascend to the sides of the vessel, forming itself into a concave figure (as I have experienced), and the swifter the motion becomes, the higher will the water rise, till at last, performing its revolutions in the same times with the vessel, it becomes relatively at rest in it. This ascent of the water shows its endeavour to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, discovers itself, and may be measured by this endeavour. At first, when the relative motion of the water in the

vessel was greatest, it produced no endeavour to recede from the axis: the water showed no tendency to the circumference, nor any ascent towards the sides of the vessel, but remained a plane surface, and therefore its true circular motion had not yet begun. But afterwards, when the relative motion of the water had decreased, the ascent thereof towards the sides of the vessel proved its endeavour to recede from the axis; and this endeavour showed the real circular motion of the water perpetually increasing, till it had acquired its greatest quantity when the water rested relatively in its vessel. .

This experiment, it is certain, cannot be interpreted as a case of relative motion between the pail and the water. For at first, when the pail begins to spin, and before the water has taken up the motion, there is relative motion between the pail and the water, and the surface of the water is flat. In the last stage, after the water has taken up the motion of the pail and become depressed in the middle, the pail is suddenly stopped. The water continues to rotate, so again there is relative motion between the pail and the water. But this time the surface of the water is not flat, but depressed in the middle. Between these two cases, therefore, we have an observable physical difference. Yet, if the motion between pail and water is to be regarded as purely relative there is no difference between the two cases. Newton therefore concluded, logically enough, that the motion was absolute. It might be objected to his conclusion that, after all, the pail of water is rotating with respect to the fixed stars. This objection has some validity

if it be meant to assert that rotation, like translation, is motion with respect to some point of reference. But it can hardly be interpreted to mean that the rotation of the pail of water is relative to the fixed stars in the sense that we could equally well assume the pail of water to be at rest and the whole stellar universe rotating round it. We may say that, as a matter of fact, we have never observed a case of rotation "in empty space." Newton imagined that if his experiment were performed in a universe containing nothing but the pail of water the same result would be obtained. We cannot make such an assumption. The experiment is performed in a universe containing, amongst other things, the fixed stars. We cannot say what would happen in a universe not containing those bodies. Newton, although he based his dynamical laws on observation, assumed that they held good in all circumstances. Thus that property of a body called its inertia, in virtue of which it persists in its state of rest or of uniform motion in a straight line, unless acted on by some force, is assumed by Newton to be an absolute property of the body, in the sense that it would be just the same in empty space at an infinite distance from all other bodies. Such assumptions are very natural, but one important aspect of Einstein's work is that he insists that none but observable factors shall be invoked in explaining phenomena, and that we shall not dogmatise about what would happen in conditions we can never experience. Thus Einstein does not regard Newton's absolute space as a legitimate entity to import into scientific descriptions,

since it cannot be observed, and he refuses to base arguments on the assertion that a body's inertia would remain unaltered in certain conditions, when those conditions are forever inaccessible to observation.

In working out his system of dynamics and in applying it to astronomy Newton makes no use of his notion of absolute space, apart from this question of rotation. His laws do not require the notion of absolute position. And his notion of absolute time is only used as a sort of inaccessible ideal towards which time-keeping instruments approximate. Consider, for instance, his first law of motion. It states that a body acted on by no forces remains at rest or in a state of uniform motion in a straight line. The word " rest "here does not mean rest in absolute space. The system of reference in which the body is at rest may itself be in motion. The notion of uniform "motion is the notion that equal distances are traversed in equal times. This notion of equal" times doubtless makes reference to Newton's absolute time, whose intervals measured only approximately even by the most accurate of clocks. Newton doubtless thought his law to be rigorously true in the sense that it would be verified by yard measures and clocks made by God Himself. And it would be verified more and more accurately as man made or discovered more and more accurate measuring instruments. But a more important aspect of this law, from the modern point of view, is that it makes reference to an unobservable condition of affairs. It speaks of a body " acted on

are

by no forces." No such body can be observed. Every body of which we have experience exists in the neighbourhood of gravitating masses. Newton, of course, explained the fact that we do not observe bodies moving in straight lines with uniform velocities by saying that they were acted on by forces. What Newton has really done, in enunciating his first law of motion, is again to make appeal to empty space. He states that in certain unobservable conditions, namely, at an infinite distance from all gravitating masses, a body, thrown into space, would move in a straight line with uniform velocity. Having assumed this he then explains the fact that observed bodies, such as planets, and stones thrown into the air, do not move in this way, by inventing a force of gravitation that pulls them out of their straight line course. Thus we may say that Newton's force of gravitation is made inevitable by assuming his first law of motion and then trying to make this law relevant to the observed behaviour of bodies.

Theoretically speaking, an entirely different approach to the whole question could have been made, as Einstein has shown. But it is highly improbable that Einstein or anybody else, in Newton's place and time, could have done other than adopt his conceptions. Einstein's outlook, in the absence of the necessary mathematical technique, could have been no more than a vague and disturbing intuition, impossible to formulate intellectually.

Newton continued on the path opened up by Galileo. He succeeded in isolating those of our perceptions between which quantitative relations exist,