densities of gas existing under the same pressure at 32° and at 60° will be (Art. 64) in the proportion of (1 + 28 x .00204): 1 or of 1.057 : I. Hence the required weight will be where the first factor is on account of the difference between the capacities of the two measures, the second on account of the difference of pressure, and the third on account of the difference of temperature. Example II.-It has been determined at Kew Observatory that the weight in vacuo at 62° Fahr. of a given volume of purified mercury is to that of the same volume of water in the proportion of 13590.86 to 1001.62 grains; what is the specific gravity of mercury at o°C according to the French method of computation? We find by the table of the absolute dilatation of mercury (Art. 52) that a unit of volume of this liquid at o°C will become 1.00298 at 62° Fahr., or 16°.6C. Hence the weight of the above volume of mercury would at o°C be 13590.86 x 1.00298 13631.361 grains. In like manner we find by the table of dilatation of water (Art. 54) that a volume of this fluid equal to unity at 4°C will at 16°.6C be 1.0011437. Hence the weight of the above volume of water would at 4°C be— 1001.62 X 1.0011437 = 1002.766 grains; and hence the specific gravity of mercury according to the French method will be- 13631.361 = 13.594: a determination by Regnault gives 13.596. REMARKS ON THE ENGLISH AND FRENCH SYSTEMS OF STANDARDS. 76. The English standards of length and weight are arbitrary; that is to say, a yard and a pound do not bear any recognized relation to any natural constant. On the other hand, the French chose their standard of length, or mètre, as that distance which was supposed to represent the ten millionth part of a quadrantal arc of a meridian of the earth's surface, while their standard of weight, or kilogramme, professed to be the weight of a décimètre cubed of distilled water at the temperature 4°C. On these principles Borda constructed the platinum mètre and platinum kilogramme, which have become the authorized standards of France. But whatever conception presided at the construction of these standards, it is evident that when once made and authorized they may to all intents be regarded as arbitrary standards. For if future and accurate investigations should determine that one ten millionth of the earth's quadrantal arc is not exactly Borda's mètre, and that a décimètre cubed of distilled water at 4°C is not exactly Borda's kilogramme, the French nation would yet adhere to Borda's platinum métre and kilogramme as their standards; and were these standards destroyed, it is probable they could best be replaced by means of copies. Nevertheless it is of importance to connect the authorized standards of a nation, always bearing in mind that they are in practice arbitrary, with certain natural constants supposed to be invariable: thus, for instance, to connect the standard of length with the length of a pendulum, vibrating seconds, or with an arc of a meridian, and also to connect the standard of weight with that of length, after the manner of the French. For it may be inferred from what we have said in Art. 45, that a standard of length, however carefully constructed and well annealed, may possibly in the course of time alter its length to a small but yet an appreciable extent. But we cannot perhaps so readily suppose that any such change can take place in the length of the second's pendulum or in that of an arc of the meridian, and hence any change in the length of the standard, if such occurred, might be detected by occasional comparisons with these natural con stants. In like manner a standard weight might ultimately become altered by slight abrasion of particles through frequent use, and it would therefore be of importance to connect it from time to time with the standard of length. Another safeguard might be the construction of a standard made of granite or marble, or of some substance which has probably become cooled by a very slow natural process, and which may therefore be supposed to be thoroughly annealed. We remark, in conclusion, that the French system has some obvious advantages. In the first place, their standards. of length and weight are divided and multiplied in, accordance with the decimal system, by which means calculation is greatly simplified. Secondly, the mètre becomes their standard of length at o°C, which is the most convenient temperature. Again, although the kilogramme may not exactly denote the weight of a cubic décimètre of distilled water at 4°C, yet it does so very nearly, and hence the French chemist when he knows the specific gravity of any substance knows also the weight of one cubic décimètre of that substance. For instance, if a substance have the specific gravity 2.5 at o ̊C, it means that a cubic décimètre of that substance will at the temperature o°C weigh 2.5 kilogrammes. On this, and other accounts, the French or metrical system of weights and measures is very widely adopted by scientific chemists. EFFECT OF TEMPERATURE UPON MEASURES OF TIME. 77. The rate of a clock depends upon the time in which its pendulum vibrates, and that of a watch upon the time of oscillation of its balance-wheel. Now the time of vibration of a pendulum depends upon its length; and since change of temperature alters the length of a pendulum it likewise alters its time of vibration, the general effect being that the higher the temperature the longer does the pendulum become and the more slowly does it vibrate. In like manner a change of temperature, by altering the dimensions of the balancewheel of a watch and the force of the spring, will alter its time of oscillation in such a manner that it will vibrate more slowly in hot weather than in cold. All good clock-makers endeavour to obviate these sources of error by means of certain compensations which we shall now describe. 78. Graham's mercurial pendulum. The first who Fig. 16. attempted to compensate for change of length of a pendulum was Mr. Graham, an English clockmaker. The rod of his pendulum, Fig. 16, was made of glass, to the lower extremity of which was attached a cylindrical vessel containing mercury. As the glass rod expands by heat the bottom of the vessel which contains the mercury will of course be rendered more distant from the point of suspension, but since the column of mercury resting on this base expands upwards its centre of gravity is raised, or brought nearer the point of suspension. The lowering of the centre of gravity due to the expansion of the glass may thus be counteracted by the rise of the same due to the expansion of the mercury. The correction for imperfect compensation is made by raising or lowering the cylinder of mercury by means of a screw. 79. Harrison's gridiron pendulum. Shortly after Graham Mr. Harrison invented the arrangement in Fig. 17, which from its form is called the gridiron pendulum. The dark lines represent iron, the lighter lines brass or zinc; and it is evident that the former being attached to the upper cross-pieces will expand downwards, while the latter, being attached to the lower cross-pieces, will expand upwards. Hence the change of position of the bob due to a change of temperature will be denoted by the difference between the upward and the downward expansions. Let L be the length of iron expanding downwards, and x its coefficient of expansion, also let L' denote the length. of the other metal expanding upwards, and let' be its coefficient of expansion, then if L K K- - L'K'o it is evident that the position of the bob will remain unaltered, even though the temperature change. = The correction for timing the pendulum is made by the screw d, while that for imperfect compensation is effected by shifting one of the cross traverses. Fig.17. In some respects this pendulum is better than the mercurial one, for should any cause render the bob of the latter somewhat warmer or colder than the rest of the pendulum, it is evident that this would produce its full effect upon the mercury, while the length of the pendulum rod would be little altered. The gridiron pendulum, on the other hand, is not liable to this imperfection. But here, as in other things, it is better to avoid the source of error than to trust too much to the perfection of the compensating arrangement; and some astronomers, in order to procure the greatest possible regu |