When we inquire where the freely moving body is, no perfectly 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 angles.”[215] 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 2,500 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, 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 known that invariability of 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 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 cognisance.
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 disturbance from other planets, but it is believed that these perturbations must in the course of time run through their rhythmical courses, leaving 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 slight resistance in passing through space, like that which is so apparent in Encke’s comet. There may also be 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.[216] It is probably an untrue assumption then, that the earth’s orbit remains quite invariable. It is just possible that some other body may be found in the course of time 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 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 choose may ultimately be shown to be subject to disturbing forces.
The pendulum, although so admirable an instrument for subdivision of time, fails as a standard; for though the same pendulum affected by the same force of gravity performs equal vibrations in equal times, yet the slightest change in the form or weight of the pendulum, the least corrosion of any part, or the most minute displacement of the point of suspension, falsifies the results, and there enter many other difficult questions of temperature, friction, resistance, length of vibration, &c.
Thomson and Tait are of opinion[217] 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. But 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 spring could be observed with the requisite accuracy. More recently Professor Clerk Maxwell has made the novel suggestion, discussed in a subsequent section, that undulations of light in vacuo would form the most universal standard of reference, both as regards time and space. According to this system the unit of time would be the time occupied by one vibration of the particular kind of light whose wave length is taken as the unit of length.
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. As to the phenomena of outward nature, they tend more and more to resolve themselves into motions of molecules, and motion cannot be conceived or measured without reference both to time and space.
Turning now to space measurement, 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 submultiple of some dimension of the globe.
(3) By adopting the length of the simple seconds pendulum, as a standard of reference.