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have been vaguely present in many minds, propounded the hypothesis that the apparent conspiracy might be in effect a law of nature. He suggested, tentatively, that there might be a true law to the effect that " it is of necessity impossible to determine absolute motion by any experiment whatever." This hypothetical law may again be put in the equivalent form : " The phenomena of nature will be the same to two observers who move with any uniform velocity whatever relative to one another." This may be called the hypothesis of relativity.

The hypothesis in itself was not of a sensational character. Indeed, from the quotations which have already been given from Newton's works, it appears probable that Newton himself would have accepted the hypothesis without hesitation: he might even have regarded it as superfluous. The true significance of the hypothesis can only be understood by a reference to the scientific history of the two centuries which had elapsed since Newton. The Newtonian view that absolute rest was to be found only " in the remote regions of the fixed stars, or perhaps far beyond them," had given place to a belief that absolute rest was to be found all around us in an aether which permeated all bodies. What was striking about the hypothesis was its implication either that we could not measure the velocity relative to ourselves of a medium which surrounded us on all sides, or else that no such medium existed.

The hypothesis demanded detailed and exhaustive examina- tion. It was for the mathematician to test whether the hypothe- sis was in opposition to known and established laws of physics, and to this task Einstein, Lorentz and others set themselves. If a single firmly established law proved to be in opposition to the hypothesis, then of course the hypothesis would require to be abandoned. It was unlikely that such an event would occur among the well-established laws, for if it did, the phenomena governed by that law would enable direct measurement to be made of the earth's velocity through the aether, a measurement which had so far eluded all attempts of experimenters. It was among the more obscure and less well-established laws, if any- where, that discrepancies were to be looked for.

It is impossible here to give a complete account of the many tests to which the relativity hypothesis has been subjected. The result of all can be summed up in one concise and quite general statement: Wherever the hypothesis of relativity has appeared to be in conflict with known or suspected natural laws, further experiment, where possible, has, without a single exception, shown the laws to be erroneous, and has moreover shown the alternative laws suggested by the hypothesis of relativity to be accurate. It is only in somewhat exceptional cases that the hypothesis of relativity of itself suffices to determine fully the form of a natural law; these cases constitute the most striking triumphs of the theory. As instances may be mentioned the determination of the law connecting the mass of an electron with its velocity; of the law expressing the velocity of light through a transparent medium rn motion (Fizeau's water-tube experi- ment); and of the formulae for the magnetic forces on moving dielectric media (experiments of Eichenwald and H. A. Wilson). 1

Befo e passing on from the general statement which has been made, particular mention must be made of one special case. A natural law which was at an early stage seen to be in conflict with the hypothesis of relativity was Newton's famous law of gravitation namely, that every particle of matter attracts every other particle with a force proportional to the product of the two masses, and to the inverse square of their distance apart. Either, then, Newton's great law had to be abandoned, or els; the hypothesis of relativity had to be discarded, in which case it would immediately become possible, in theory at least, to determine the earth's velocity through space by gravitational mans. It is the choice between these two alternatives that has led to the most surprising developments of the theory of relativity; and to these we shall return later.

1 For references to the original papers dealing with these and other tests of the hypothesis of relativity see Cunningham, The Principle of Relativity, or J. H. Jeans, Mathematical Theory of Electricity and Magnetism (4th ed.).

Space and Time. The hypothesis of relativity, as has already been explained, postulates that the phenomena of nature will be the same to any two observers who move relative to one another with any uniform velocity whatever. The hypothesis has been so amply tested as regards all optical and electromag- netic phenomena that no doubt is felt, or can rationally be felt, as to its truth with respect to these phenomena. The hypothesis can be examined and developed in two opposite directions. We may, on the one hand, proceed from the general hypothesis to the detailed laws implied in it; this has already been done, with completely satisfactory results as regards confirmation of the hypothesis. Or we may regard the hypothesis of relativity as being itself a detailed law and attempt to generalize upward to something still wider. It is this possibility which must for the moment claim our attention.

In 1905 Einstein examined in full the consequences of the hypothesis that one simple optical phenomenon namely, the transmission of a ray of light in free space was, in accordance with the hypothesis of relativity, independent of the velocity of the observer. If an aether existed, and provided a fixed framework of reference, then light set free at any instant would obviously travel with a velocity which would appear to an observer at rest in this aether to be the same in all directions, and the wave front at any instant would be a sphere having the observer as centre. On the hypothesis of relativity the phenom- enon of light transmission must remain unaffected by the motion of the observer, so that the light must appear to a moving observer also, to travel with a uniform velocity in all directions, and-thus to the moving observer also the wave front must appear to be a sphere of which he will be the centre. It is, however, quite obvious that the same spherical wave front cannot appear to each of two observers who have moved some distance apart to be centred round himself, unless the use either of the common conceptions of science or of the ordinary words of language is greatly changed. In fig. 2 it is not possible in ordinary language that both O and P should at the same instant be at the centre of the sphere ABC. The change to which Einstein was forced is one which has an intimate bearing upon our fundamental conceptions of the nature of space and time; this change it will be necessary to explain in some detail.

Suppose that two observatories, say Greenwich and Paris, wish to synchronize their clocks, with a view to, let us say, an exact determination of their longitude difference. Paris will send out a wireless signal at exact midnight as shown by the Paris clock, and Greenwich will note the time shown by the Greenwich clock at the instant of receipt of the signal. Green- wich will not, however, adjust their clock so as to show exact midnight when the signal is received; a correction of about -ooi second must be made to allow for the time occupied by the signal in traversing the distance from Paris to Greenwich. To turn to mathematical symbols, if t is the time at which a signal is sent out from one station, the time of receipt at a second

X

station is taken to be t -\, where x is their distance apart, and c

c is the velocity of light. This represents the ordinary practice of astronomers, but it is clear that if the earth is travelling through a fixed aether with a velocity in the direction of the line joining the two observatories, the velocity of transmission of the signal relative to the two observatories will not be c but c+u, and the

time of receipt at the second station will be t a -\

c+u

Thus it

appears that it is impossible to synchronize two clocks unless we know the value of, and that the ordinary practice of astronomers will not, as they expect, synchronize their clocks, but set them at an interval apart equal to

which may, to an approximation, be put equal to

C

According to the hypothesis of relativity, it is impossible ever to determine the value of u, and so is impossible ever truly