body which seems to us to move uniformly is not doing so, but is subject to fits and starts unknown to us, because we have no absolute standard of time, then all other bodies must be subject to exactly the same arbitrary fits and starts, otherwise there would be a discrepancy between them disclosing the irregularities. Just as in comparing together a number of chronometers, we should soon detect bad ones by their irregular going, as measured by the others, so in nature we detect disturbed movement by its discrepancy from that of other bodies, which we believe to be undisturbed, and which agree very nearly among themselves. But inasmuch as the measure of motion. involves time, and the measure of time involves motion, there must be ultimately an assumption. We may define equal times, as times during which a moving body under the influence of no force describes equal spaces, but all we can say in its support is, that it leads us into no known difficulties, and that to the best of our experience, one freely moving body gives exactly the same results as any other. When we inquire where the freely moving body is, no satisfactory answer can be given. Practically the rotating globe is sufficiently accurate, and Thomson and Tait say: Equal times are times during which the earth turns through equal anglesh'. No long time has passed since astronomers thought it impossible to detect any inequality in its movement. Poisson was supposed to have proved that a change in the length of the sidereal day, amounting to one ten-millionth part in 2500 years, was incompatible with an ancient eclipse recorded by the Chaldæans, and similar calculations were made by Laplace. But it is now known that these calculations were somewhat in error, 8 Rankine, Philosophical Magazine,' Feb. 1867, vol. xxxiii. p. 91. hTreatise on Natural Philosophy,' vol. i. p. 179. and that the dissipation of energy arising out of the friction of tidal waves, and the radiation of the heat into space, has slightly decreased the rapidity of the earth's rotatory motion. The sidereal day is now longer by one part in 2,700,000, than it was in 720 B.C. Even before this discovery, it was certain that the invariable rotation depended upon the perfect maintenance of the earth's internal heat, which is requisite in order that the earth's dimensions shall be unaltered. Now the earth being far superior in temperature to empty space, must cool more or less rapidly, so that it cannot furnish an absolute measure of time. Similar objections could be raised to all other rotating bodies within our cognizance. The moon's motion round the earth, and the earth's motion round the sun, form the next best measure of time. They are subject, indeed, to all kinds of disturbance from other planets, but it is believed that these must in the course of time run through their rhythmical courses, and leave the mean distances unaffected, and consequently, by the third Law of Kepler, the periodic times unchanged. But there is more reason than not to believe that the earth encounters a certain slight resistance in passing through space, like that which is so apparent in Encke's comet. There may also be a certain dissipation of energy in the electrical relations of the earth to the sun, possibly identical with that which is manifested in the retardation of comets i. It is probably an untrue assumption then, that the earth's orbit remains quite invariable, and if so our last hope of getting a really uniform measure of time disappears, and we are reduced to accepting such as are sufficient for all practical pur poses. iProceedings of the Manchester Philosophical Society, 28th Nov. 1871, vol. xi. p. 33. It is just possible that in the course of time, some other body may be found to furnish a better standard of time than the earth in its annual motion. The greatly superior mass of Jupiter and its satellites, and their greater distance from the sun, may render the electrical dissipation of energy less considerable even than in the case of the earth. But the choice of the best measure will always be an open one, and whatever moving body we assume, may ultimately be shown to be subject to disturbing forces. The pendulum, although so admirable an instrument for subdivision of time, entirely fails as a standard; for though the same pendulum affected by the same force of gravity would perform equal vibrations in equal times, yet the slightest change in the form or weight of the pendulum, the slightest corrosion of any part, or the most minute displacement of the point of suspension, would falsify the results, and there enter many other difficult questions of temperature, resistance, length of vibration, &c. Thomson and Tait are of opinion that the ultimate standard of chronometry must 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. Although their suggestion is no doubt theoretically correct, it is hard to see how we can be sure that the dimensions and elasticity of a piece of wrought metal will remain perfectly unchanged for the few millions of years contemplated by them. A nearly perfect gas, like hydrogen, is perhaps the only kind of substance in the unchanged elasticity of which we could have confidence. Moreover, it is difficult to perceive how the undulations of such a k The Elements of Natural Philosophy,' part i. p. 119. spring could be observed with the requisite accuracy. We thus appear to be devoid of any hope of establishing a sure standard of the efflux of time. The Unit of Space and the Bar Standard. Next in importance after the measurement of time is that of space. Time comes first in theory, because phenomena, our internal thoughts for instance, may change in time without regard to space magnitude. As to the phenomena of outward nature, they tend more and more to re solve themselves into the motion of molecules, and motion cannot be conceived or measured without reference both to time and space. Turning now to space measurements, we find it almost equally difficult to fix and define once and for ever, a unit magnitude. There are three different modes in which it has been proposed to attempt the perpetuation of a standard length. (1) By constructing an actual specimen of the standard yard or metre, in the form of a bar. (2) By assuming the globe itself to be the ultimate standard of magnitude, the practical unit being a sub.. multiple of some dimension of the globe. (3) By adopting the length of a simple pendulum, beating seconds as a standard of reference. At first sight it might seem that there was no great difficulty in this matter, and that any one of these methods might serve well enough; but the more minutely we inquire into the details, the more hopeless appears to be the attempt to establish an invariable standard. We must in the first place point out a principle not of an obvious character, namely, that the standard length must be defined by one single object'. To make two bars of exactly the 1 See Harris''Essay upon Money and Coins,' part ii. [1758] p. 127. same length, or even two bars bearing a perfectl length with complete accuracy, whether byn, de. on the surface, or by the terminal points from time to time have no means of proving that substances of these different rotation of the earth is uniform, except bould be furnished by with other moving bodies, believed to be reed most closely with in motion, so we cannot detect the change that of those bodies w variable dimensions. Just as we cannot t bar, except by comparing it with some posed to be invariable. But how are we aces would be the mod གས་ g the efflux of time. is the invariable bar? It is certain terrestrial Standard. and apparently invariable substances de assumes that the glob mensions. The bulb of a thermometer cemensions. The founder by age, besides undergoing rapid change the ten-millionth par when warmed or cooled through 100 tor to the pole as the de has recently confirmed the statements concerning zine, (1868), 4th Series, vol. 7 m Watts' Dictionary of Chemistry,' vol. v. pp. Sir John Herschel P thermometer-bulb. Scient fie Subjets, (1866) p |