be sure that even the most solid metallic bars do not slightly contract by age, or undergo variations in their structure by change of temperature. M. Fizeau was induced to try whether a quartz crystal, subjected to several hundred alternations of temperature, would be modified in its physical properties, and he was unable to detect any change in the coefficients of expansion". It does not follow however, that, because no apparent change was discovered in a quartz crystal, newly-constructed bars of metal would undergo no change. The only principle, as it seems to me, upon which the perpetuation of a standard of length can be ultimately rested, is that, if a variation of length occurs, it will in all probability be of different amount in different substances. If then a great number of standard metres were constructed of all kinds of different metals, alloys; hard rocks, such as granite, serpentine, slate, quartz, limestone ; artificial substances, such as porcelain, glass, &c., &c., careful comparison would show from time to time the comparative variations of length of these different substances. The most variable substances would be the most divergent, and the true standard would be furnished by the mean length of those which agreed most closely with each other, just as uniform motion is that of those bodies which agree most closely in indicating the efflux of time. The Terrestrial Standard. The second method assumes that the globe itself is a body of invariable dimensions. The founders of the metrical system selected the ten-millionth part of the distance from the equator to the pole as the definition of the metre, and the late Sir John Herschel proposed that 'Philosophical Magazine,' (1868), 4th Series, vol. xxxvi. p. 32. the English inch, which is now almost exactly the 500,500,000th part of the polar axis of the earth, should be made exactly equal to the 500,000,000th part, and be adopted as our standard. The first imperfection in such a method is that the earth is certainly not invariable in size; for we know that it is superior in temperature to surrounding space, and must be slowly cooling and contracting. There is much reason to believe that all earthquakes, volcanoes, mountain elevations, and changes of sea level, are evidences of this contraction as asserted by Mr. Mallet?. But such is the vast bulk of the earth and the duration of its past existence, that this contraction is perhaps less rapid in proportion than that of any bar or other material standard which we can construct. The second and chief difficulty of this method arises from the vast size of the earth, which prevents us from making any comparison with the ultimate standard, except by a trigonometrical survey of a most elaborate and costly kind. The French physicists, who first proposed the method, attempted to obviate this inconvenience by carrying out the survey once for all, and then constructing a standard metre, which should be exactly the one ten millionth part of the distance from the pole to the equator. But since all measuring operations are merely approximate, as so often stated in previous pages, it was impossible that this operation could be perfectly achieved. Accordingly it was shown by Colonel Puissant in 1838, that the supposed French metre was erroneous to the considerable extent of one part in 5527, the quadrant of the earth's circumference measuring 10,001,789 instead of 10,000,000 of such metres. It then became necessary either to alter the length of the assumed metre, or otherwise to abandon its supposed relation to the earth's dimensions. p 'Proceedings of the Royal Society,' 20th June, 1872, vol. xx. p. 438. The French Government and the present International Metrical Commission have for obvious reasons decided in favour of the latter course, and have thus reverted to the first method of defining the metre by a given bar. As from time to time the ratio between this assumed standard metre and the dimensions of the earth becomes more and more accurately known, we have the better means of restoring that metre by actual reference to the globe if required. But until lost, destroyed, or for some clear reason discredited, the bar metre and not the globe is the standard. Any of the more accurate measurements of the English trigonometrical survey might in like manner be employed to restore our standard yard, in terms of which the results are recorded. The Pendulum Standard. The third method of defining a standard length, by reference to the seconds' pendulum, was first proposed by Huyghens, and was at one time adopted by the English Government. From the principle of the pendulum (p. 353) it clearly appears that if the time of oscillation and the force actuating the pendulum be the same, the length must be the same. We do not get rid of theoretical difficulties, for we must practically assume the attraction of gravity at some point of the earth's surface, say London, to be unchanged from time to time, and the sidereal day to be invariable, neither assumption being absolutely correct so far as we can judge. The pendulum, in short, is only an indirect means of making one physical quantity of space depend upon two other physical quantities of time and force. The practical difficulties are, however, of a far more a Thomson and Tait's Elements of Natural Philosophy,' Part 1. p. 119. в b serious character than the theoretical ones. The length of a pendulum is not the ordinary length of the instrument, which might be greatly varied, without affecting the duration of a vibration, but the distance from the centre of suspension to the centre of oscillation. There is no direct means of determining this centre, which depends upon the average momentum of all the particles of the pendulum as regards the centre of suspension. Huyghens discovered that the centres of suspension and oscillation are interchangeable, and Captain Kater pointed out that if a pendulum vibrates with exactly the same rapidity when suspended from two different points, the distance between these points is the true length of the equivalent simple pendulum'. But the practical difficulties in employing Kater's reversible pendulum are considerable, and questions regarding the disturbance of the air, the force of gravity or even the interference of electrical attractions have to be entertained. It has been shown that all the experiments made under the authority of government for establishing the ratio between the standard yard and the seconds' pendulum, were vitiated by an error in the corrections for the resisting, adherent or buoyant power of the air in which the pendulum swung. Even if such corrections were rendered unnecessary by operating in a vacuum, other difficult questions remains. Gauss' mode of comparing the vibrations of a wire pendulum when suspended at two different lengths is open to equal or greater practical difficulties. Thus it is found that the pendulum standard cannot compete in accuracy and certainty with the simple bar standard, and the method would only be useful as an accessory mode of restoring the bar standards if at any time again destroyed. r Kater's Treatise on Mechanics,' Cabinet Cyclopædia, p. 154. Unit of Density. Before we can measure and define the phenomena of nature, we require a third independent unit, which shall enable us to define the quantity of matter which occupies any given space. All the motions and changes of nature, as we shall see, are probably so many manifestations of energy; but energy requires some substratum or material machinery of molecules, in and by which it may be exerted. Very little observation shows that, as regards force, there may be two modes of variation of matter. The force required to set a body in motion, varies in simple proportion to the bulk or cubic dimensions of the matter, but also according to its quality. Two cubic inches of iron of uniform quality, will require twice as much force to produce a certain velocity in a given time as one cubic inch; but one cubic inch of gold will require more force than one cubic inch of iron. There is then some new measurable quality in matter apart from its bulk, which we may call density, and which is, strictly speaking, indicated by its capacity to resist and absorb the action of force. For the unit of density we may assume that of any substance which is uniform in quality, and can readily be referred to from time to time. Pure water at any definite temperature, for instance that of snow melting under an inappreciable pressure, furnishes a natural and invariable standard of density, and by testing equal bulks of various substances compared with a like bulk of ice-cold water, as regards the velocity produced in a unit of time by the same force, we should ascertain the densities of those substances as expressed in that of water. Practically the force of gravity is used to measure density; for a simple and beautiful experiment with the |