CHAPTER V. Applications of the Laws of Dilatation. 68. Since all the bodies around us are subject to continual change of volume owing to their varying temperature, it is necessary to take account of this in very many operations and investigations whether of a scientific or strictly practical nature. Let us, in the first place, proceed to describe the influence which change of temperature exerts on our standards of length, weight, density and time. STANDARDS OF LENGTH. 69. Supposing that a yard is taken to denote a certain absolute distance, and that the length of a bar is precisely one yard at the temperature 62° Fahr., it is clear that, owing to the expansion of the material of the bar, its length will be greater than a yard for temperatures higher than 62°, but less than a yard for temperatures below 62°. If now we employ this bar as a standard by means of which to measure the absolute distance between any two points in terms of the yard as a unit of length, and if it be inconvenient or impossible to make this comparison at 62° Fahr., it will be necessary to know the precise temperature of our standard bar in order that we may know its real length. The formation of a standard of length is an object of national importance, and we shall now shortly describe the respective standards authorised by the Governments of England and France. 70. English standard. The English standard of length was formerly the parliamentary standard yard executed by F Bird in the year 1760. A yard was defined to be the straight line or distance between the centres of the two points in the gold studs in the brass rod formerly in the House of Commons, whereon the words "Standard yard 1760” were engraved, the temperature of the standard being 62° Fahr. On October 16, 1834, a fire occurred in the Houses of Parliament, in which the standards were destroyed. The bar of 1760 was recovered, but one of its gold pins having a point was melted out, and the bar was otherwise injured. A committee was therefore formed to reproduce this standard yard in the best manner possible, and this was admirably accomplished chiefly through the labours of the late Mr. Sheepshanks. A new standard and four authorised copies were made and lodged at the office of the Exchequer, the Royal Mint, the Royal Society of London, the Royal Observatory, Greenwich, and the new palace at Westminster; and it was enacted (July 30, 1855), "that the straight line or distance between the centres of the two gold plugs in the bronze bar deposited in the office of the Exchequer shall be the genuine standard yard at 62° Fahr., and if lost it shall be replaced by means of its copies." Many other copies of this standard have since been made, the errors of which have been very accurately ascertained. When the length of a substance has to be measured with precision it is necessary to compare it either with the standard or one of its copies of which the error is known. It is here that a knowledge of the laws of dilatation becomes of importance, for to make the comparison accurately we must know 1. The precise temperature at which the comparison is made. 2. The coefficient of expansion of the standard used. Suppose, for instance, that our standard is of brass, that we are comparing a platinum scale with it at the temperature of 72° Fahr., and that we find the length of our scale to be 35.998 inches as read by the standard at this temperature ; then in order to find the true length of our platinum scale at this temperature we must know the coefficient of expansion of the brass standard. Suppose this to be .00001 for 1° Fahr., then if the standard is right at 62°, its length, or the true value of 36 apparent inches, will be = 36 inches x 1.0001 at 72°, 36.0036 inches; and hence the true length of our platinum scale (which is .002 inch less than 36 apparent inches) will be as nearly as possible 36.0016 inches at the temperature 72° Fahr. If we now wish to ascertain its length at 62° we find the coefficient of dilatation for platinum for 10° Fahr. to be .000048. Hence its length at 62° will be as nearly as possible 36.0016 1.000048 = €35.9999 inches. Thus we see that the two scales agree almost exactly at 62°, but they differ sensibly at 72°: this is owing to the one scale being made of brass and the other of platinum. 71. French standard. The French standard of length is the mètre which represents with considerable accuracy the 10,000,000th part of a quadrantal arc of a meridian on the earth's surface. The French standard platinum mètre made by Borda represents a mètre at o°C, and all the copies of this standard are made so as to denote mètres and parts of a mètre at this temperature. One mètre is equal to 39.37079 English inches; that is to say, the length of the French standard platinum mètre at 32° Fahr. bears to the length of the English standard bronze yard at 62° Fahr. the proportion of 39.37079: 36; but this will not be the proportion between these standards if compared together at any common temperature. The French standard is sub-divided and multiplied according to the decimal scale, and the relation between our measures and those of France will be seen from the following tables. = = 10.764299 English square feet; 1076.429934 Centiare, or square mètre Also Millilitre, or cubic centimètre Centilitre, or 10 cubic centimètres Hectolitre, or decistère Kilolitre, or Stère, or cubic mètre STANDARDS OF WEIGHT. 72. These are at the same time standards of mass, since the weight of a body at the same point of the earth's surface is proportional to its mass. If all weighings could be made in vacuo, temperature would exercise no influence upon our measures of weight. But since weighings must be made in air, and since a substance weighed in air is apparently lighter than in vacuo by the weight of air which it displaces, and since the weight of a certain bulk of air of given pressure depends upon its temperature, it is necessary to know this temperature in very accurate determinations: the effect is however very small. We shall now shortly describe the standards of weight or mass authorised by the Governments of England and France. 73. English standard. Formerly in this country the standard of weight was the double pound Troy made by Mr. Bird, and it was resolved that the pound Troy should contain 5760 grains, and that 7000 such grains should make one pound avoirdupois. This standard was destroyed at the burning of the Houses of Parliament, but was restored in a very accurate manner by Professor W. H. Miller of Cambridge, with this difference, that whereas the old standard denoted one pound Troy, the new one represents one pound avoirdupois. Accordingly a standard and four authorised copies, all made of platinum, were constructed by this gentleman and deposited in the same places with the standard yard and its. copies; and it was enacted, "that the platinum weight deposited in the Exchequer shall be denominated the imperial standard pound avoirdupois, and that the 7th of it shall be a grain, while 5760 such grains shall denote one pound Troy." 74. French standard. In France the weight of a décimètre cubed of distilled water at the temperature of its greatest density (supposed equal to 4°C) is adopted as the standard of weight, and is called the Kilogramme, while the gramme is a centimètre cubed of distilled water at the same temperature*. The following table exhibits the relation between French and English measures of weight: *It will thus be noticed that considerations of temperature enter into the fundamental conception of the French standard of weight, and in so far it is different from the English pound, which is merely an arbitrary standard. We shall afterwards take occasion to make some remarks on the comparative merits of the French and English systems. |