it may be said, would be a simple return from naturalism or positivism to animism. This would be true were the intention to personify or to consider as individual monads, all the perceptions of physical things, or all sensible qualities of things, or pure sensibilia, apprehended by the mind in its perceptions. But these, as we have seen, are not monads for they are not things-in-themselves. The monadic theory is that anything which is a thing-in-itself is a monad. Only in the meaning that it is a subject of activity with its own point of view can a thing be real, and only when so conceived is it a monad. So that whatever is real in the universe is referred to the monads, for they are the only reals. In order then to see how the experimental method depends for its rationality on such a concept let us consider it in its relation to the alternative theory, which we will call atomism. Take the latest theory of the atom, and let us agree to regard the atomic theory as in no sense hypothetical but as demonstrably actual. The atoms then are the forms which reality assumes in its basal and most elementary constitution. The atom itself as we deal with it is not simple, but we suppose it resolvable ultimately into what is the limit of simplicity, the unit charge of electricity. Let us accept this without raising the obvious difficulty that a unit of charge of electricity, if it be positive, can only exist so long as a negative charge is opposed to it, and that therefore in positing a unit charge of positive electricity we are positing also a negative. Now the whole rationale of experimenting lies in its test character. We use experiment as the crucial criterion which is infallible. We do not use experiment for the purpose of calculating probabilities. If all that an experiment could prove were that what repeatedly or unfailingly has been found to occur under certain circumstances will probably occur again under like circumstances, it would be absolutely otiose. On the contrary, the ground of the experimental method is the certainty that what has happened once if rightly interpreted reveals the absolute character of the real. If it enables me henceforward to foretell what will happen, it is not because it has established a probability, but because it has given me knowledge of a real nature. Apply this then to our case in point. We are to assume that the ultimate reality of nature is the unit electric charge; how in such case are we to rationalize the experimental method? Whatever result in any case flows from our experiment will not flow from the nature of this unit electric charge, for by the hypothesis it is what it is, it will flow from something adventitious to that nature. By the very concept of reality we are prevented from appealing to it for any character or nature it exhibits; all its properties and qualities must flow from something which in itself it does not contain. Do we demur, do we deny this indifference of the reality to quality, do we affirm that all the properties and character of nature flow from the unit electric charge? Then we find that instead of conceiving as we supposed something absolutely simple and really elementary, the limit of inertia, we are conceiving something active, self-centred and all comprehensive, we are conceiving not the atom but its opposite, the monad. There is no rationality in the experimental method unless the reality of the universe be monadic. CHAPTER XV THE PRINCIPLE OF RELATIVITY Entia non sunt multiplicanda praeter necessitatem.—Occam's Razor. THE recognition that the experimental method implies the concept of reality as monadic finds expression in the principle of relativity. The purpose of this concluding chapter is to make this clear. The principle of relativity is the direct result of a discovery due to experiment. The actual discovery was simple enough although it was negative and to the conductors of the experiment disconcerting. It was that whereas in the case of all ordinary velocities we are able to compound them, and the results of the composition accord completely with the mathematical calculations and physical deductions, in the case of the velocity of the propagation of light we are unable to introduce it into any composition, it remains constant under all circumstances and for all observers. Our failure to discover any variation due to our own velocity of relative translation is complete. For example, I may know precisely the movement of a system, say the earth, relatively to another system, say the sun; I may construct an instrument fixed in regard to the earth, moving in regard to the sun, accurately designed to register that velocity; I then compare the velocity of a light beam emitted from my moving system, and reflected to a mirror also fixed to my moving system, and in whatever direction I turn the mirror I find no difference, the interferometer registers one and the same constant velocity, showing that there is no composition of the two velocities. What is significant in this is not the fact but the interpretation. According to the principle of relativity it is absolutely simple, but the principle of relativity itself is revolutionary so far as the methodology of science is concerned. First, then, let us ask what is the simple explanation ? In my ordinary experience I am able to compound velocities, and I am continually doing so. What is the condition which enables me to do so? I do it without invoking any aid from my individual experience of muscular effort in moving. Thus when I run down a moving staircase I expend no more muscular energy than when I run down a fixed staircase, but I find no difficulty in conceiving and appreciating the increased velocity in the first case when compared with the second, and this velocity is just the sum of the two velocities, mine and that of the staircase, in relation to the system in regard to which one staircase is fixed the other moving. Now in this case and in all such cases-railway trains, passenger boats, aeroplanes, even guns and engines which use high explosives—the composition of velocities depends for its condition upon reference to a system at rest. And for the purpose of any composition some system must be absolutely at rest so far as the velocities compounded are concerned. Not only must there exist such a system but we must be able to utilize it, to refer our velocities to it, otherwise we are helpless. Suppose when on the moving staircase I had no fixed system to refer to, I could not compound the velocity of my own muscular exerted movement with the movement of the staircase, the condition would be absent and no experience could supply it. I may arbitrarily consider any moving system at rest, but so long as I do so I cannot compound my velocity with any velocity it may have relatively to some other system. If I would do so for anything like a moving staircase or train I must have the earth at rest for my reference. If I wish to consider the earth's movement and compound that, I can do so by speaking fancifully of a translation of 5000 miles a minute through space, but then I take the sun to be at rest. If I am still unsatisfied and wish to compound the movement of the solar system itself, I must take the stars or at least the stellar system as at rest. There seems no limit, and in nature so far as we can see there is none, but there is a practical limit. It is only theoretically, for example, that I can compound the velocity of my own muscularly induced movements with the velocity of the earth's translation, and when I do so in theory I have no possible means of using the result I obtain. It is different with regard to all the velocities which refer to the earth as at rest, for I am so constituted that this earth is my terra firma for all the purposes of practical life. I am able by making use of it to compound all the velocities in which I take part. To compound velocities, therefore, it is not sufficient to assume some system at rest, it is absolutely necessary as a condition of the compounding that there should be a system at rest, and the earth is this system for human observation. Now precisely the reason why we cannot compound the velocity of light with velocities of translation is that for light there is no system at rest, nothing absolute to which we can refer it, no background against which we can observe it. And it is not the slightest use to assume one, because we cannot make practical use of any assumption. Newton thought he could compound velocities by assuming absolute space and time. It was an illusion. Even in his own case the assumption was useless and his absolute space and time did not and could not enter as factors into his own equations of relative movement. It is quite simple, therefore, to see what is the fact in the case of the constancy of the velocity of light. We seem to think we have in space and time (or in a hypothetical ether if we hold that theory) an absolute system at rest, but it is a useless assumption for the purpose, because at most it is no more than an ideal background for thought, it stands for nothing in nature which we can make practical use of as we do of the earth. Consequently what happens is just what would happen in the case of terrestrial velocities if we had not the earth at rest for our system of reference, the velocity remains constant, and the space and time units, whose ratio is the velocity, automatically accommodate themselves. Let me give as an illustration a terrestrial velocity Ꮓ |