same identical unit repeatedly, as in length measurement, we must find a number of exactly equivalent units, as in weight measurement. In other words we must discover a number of events all of which possess exactly the same time-quality of duration. As every one knows, the device we employ for this purpose, at any rate where short durations are concerned, is that of the successive beats or swings of a pendulum. And to save the trouble of counting these we employ a machine called a clock, which registers and indicates the number for us. But what is our guarantee that these distinct units are really of the same duration? Is this of the same validity as where distinct foot-rules or distinct weights are concerned? This question demands closer enquiry.

The fact is that there is one general assumption underlying every employment of a unit or standard. It may be described, in a general way, as being a reliance upon the Uniformity of Nature; not in the causative or sequence sense of that manysided expression, but in that of continuity or permanence. Something was said about the nature of this distinction in a former chapter, but it deserves some further consideration in the present application.

Start with a purely practical example. It is obvious that the utility of a carpenter's foot-rule depends upon the fact that the wood of which it is made does not continue permanently to shrink, and does not vary in magnitude from time to time. It does shrink a little when the wood is quite fresh, and it varies a little with the temperature ever afterwards, but it does not vary in any degree which matters for the carpenter or for those who employ him. But when we come to finer work this consideration is of importance. For instance, it is a serious difficulty in the way of accurately graduating our thermometers, that the glass tube, (and consequently the scale marked upon it,) continues slightly and slowly to shrink for a number of years after the instrument is made. So, again, the difficulty of retaining a fixed length in our measuring rods when we want to survey very accurately in a hot climate. Mr Piazzi Smyth, in his quaint work on the great pyramid, considered that one of the qualifications entitling the central sarcophagus to play the part of an eternal measure of volume rested on the fact that the porphyry of which it was made, unlike the glass of our

thermometer tubes, had probably had many thousands of years to finish its process of contraction'.

These practical difficulties can be met by practical expedients, the amount of time and trouble demanded for this purpose being dependent upon the degree of accuracy required for the operation in hand. But turn now to what I have called, in contradistinction, the speculative-practical difficulties: i.e. those which we can readily conceive as presenting themselves though we feel sure that they never will actually trouble us. We live in a world in which we find ourselves surrounded by plenty of rigid matter which does not seem to vary perceptibly either in size or in shape. But we can conceive it otherwise; and, were it otherwise, it is not easy to see how we should ever acquire any such thing as a unit of length or any other unit which involves this. Suppose our experience were such as would be presented to a colony of jelly-fish which lived on the surface of the water in the midst of an ocean. So far as they and the water and most of the sea-weeds were concerned, they would hardly find a material at hand which would furnish them with the notion of any such thing as a standard of size or shape. Mass they might understand from the experience of their own bodies, but in the entire absence of anything rigid they could scarcely realize what was meant by a linear standard or anything which depended on this. Anything to call Science would be out of their reach, for they would have nothing to provide practice in measurement, or even to furnish the notion of measurement quantitatively.

It is here, then, that we are reminded of the necessity of Uniformity of Nature, not in the sense of Causation, but in that of Persistency, -and persistency in details of physical structure,—if we are to be able to measure or infer with quantitative accuracy. The mere indestructibility of mass or matter, remember, is not enough. On the common molecular theory, and still more on the Boscovichian theory of mere mathematical

1 It is proverbially difficult to get at the first version of any suggestion or theory; but I confess I was surprised at the following passage-"C'est ainsi que Mr Greave, mathématicien anglois, a voulu se servir des Pyramides d'Egypte, qui ont duré assez et dureront apparemment encore quelque temps pour conserver nos mesures, en marquant à la postérité les propositions [? proportions] qu'elles ont à certaines longueurs dessinées dans une de ces Pyramides" (Leibnitz, Ed. Erdmann, p. 239).

points as centres of force, there is no absolute contradiction involved in the supposition that all substances should be in a constant state of flux or vibration, not only in respect of their shape but in respect of their size also.

not so.

This assumption underlies every selection of our units. It might seem as if a unit of weight, at any rate, or rather, to keep to the strict truth, a unit of mass, would be secured so long as we regard matter as indestructible. But this is really What we have to employ are sensible portions of matter, and everything turns upon the assurance that these do not vary in amount. The particles of matter must not only not vanish, but they must adhere continuously together: that is, the standard must not in any degree dissolve or corrode. We feel pretty sure that this condition is secured in respect of gold and platinum, and perhaps of some precious stones, &c.; but it is by no means sure that we could continue to trust to the invariability even of these for millions of years if we decided to look so far ahead1.

These suggestions admit of being pushed further, into the region of the purely speculative. We remarked before that if the carpenter's rule were liable to change he could not properly measure the door. But suppose the door also was changed at the time, and in the same proportion, as well as everything that had to pass through it; would any harm ensue to any one, or would any of us be able to perceive that a change had taken place at all?

This question cannot be answered off hand. If we are to regard it as a merely geometrical one, that is, if we do not introduce any physical principles such as those of dynamics, -I apprehend that no change whatever could be said to

1 Professors Thomson and Tait have thrown out the suggestion (Elements of Nat. Phil. p. 119) that, owing to the demonstrable secular alteration in the velocity of rotation of the earth, "the ultimate standard of accurate chronometry must, if the human race live on the earth for a few million years, be founded on the physical properties of some body of more constant character than the earth: for instance a carefully-arranged metallic spring hermetically sealed in an exhausted glass vessel". Surely this is a rather sanguine view of the permanence of the properties of matter. I should not have supposed that anything which had had its shape produced by melting, drawing, or hammering, could ever afterwards be thus unchangeable. And how about its unaltered temperature? And are we certain that a solid does not 'evaporate'? But probably the suggestion is playful.

result. In fact we might go further, and say that since mere magnitude is purely relative, it is not easy to attach any significance whatever to a supposed simultaneous and proportional change in the magnitude of all things. This seems to me, in fact, like an analogous suggestion sometimes made in Political Economy, when it is asked what would follow from a similar change in all values. Cost of Production' is absolute, so far as Political Economy is concerned; but 'value' is purely relative, being nothing else than Comparative rate of Exchange. However plentiful or scarce things might be, yet if they continued to exchange against each other as before, no change of value whatever is introduced. So with the mere space attribute of magnitude. If all our measures were halved, simultaneously with all the persons who had to use them and all the objects to which they had to be applied, no perceptible change of dimensions whatever would have been introduced.

It is when we introduce physical conceptions that the real complication arises. Suppose that everything simply contracted to half its present size, no other alteration being attempted. Direct measurement, as we have just said, would detect no change. But, other things remaining the same, the world being half its former size would immediately begin to rotate faster. If it be asked, how we could ever find this out, since all the other moving objects would also have their velocities altered, the answer is that according to known existent laws these velocities would not all be altered in the same proportion. The pendulums would vibrate at a different rate, falling bodies would move at a different rate, so would the various heavenly bodies; but these various rates would no longer all preserve their old proportions. We should immediately begin to find that something was wrong.

Of course this would not furnish any absolute proof as to what had happened. Assuming the existence of such a dislocation of nature, those who found themselves in the midst of it would have the option of more than one interpretation. It might be that, not the magnitude of objects, but rather the laws of their behaviour had been changed; and probably this would seem the most plausible explanation under the circumstances, so far as we can attempt to balance probabilities in such a case. That is, the faint discrepancy observed would

make us begin to doubt the absolute truth of the familiar Laws of Motion.

The next point to notice is what may be called the arbitrary character of our units. We shall have something to say presently about their historic origin, when we come to consider more in detail the characteristics of three or four of the most important units. But so far as the actual existence of the fundamental ones is concerned, we shall best understand their nature by conceiving some one who was endowed with authority for the purpose of selecting certain objects at his arbitrary choice, and declaring that these shall be our standards. He might find them in himself if he pleased. He might say, for instance, that the length of his foot or of his forearm shall be our lineal unit; his weight our standard of weight; the rate at which he walks our standard of velocity; and the interval between the beats of his heart the standard of time. If he decided thus, he would, for various reasons, not have made a very good choice; but as against the mere capriciousness of his selection no complaint could be raised. Our present foot and pound have not a whit better warrant than this, so far as the nature of things is concerned.

The defect of such proposed standards would be found in the inconvenience of employing them, the difficulty of accurately determining them, and the certainty of sooner or later losing them. Accordingly we prefer material objects of as durable a character as possible, but the selection of them is still theoretically a matter of caprice, for it depends upon an act of the legislature. The pound and the yard are actual things: they can be visited at their proper receptacles: and they are described by Acts of Parliament. The 'second', our unit of time, stands on a slightly different footing; for it is an event, or rather a fraction of an event. It has not been defined by an Act of Parliament and it is not kept in any public repository. The original to which we appeal is a sidereal revolution of the earth, and therefore does not stand in need of safe custody anywhere. But the selection of this is really as arbitrary as is that of an assigned lump of metal.

We spoke, just above, of fundamental units. The contrast between these and such as are derivative is an important one. The logical or primary conception of a unit, in contrast with