Page:The American Cyclopædia (1879) Volume XVI.djvu/561

 WEIGHTS AND MEASURES 541 with the bronze standard No. 11, the yard on the Troughton scale was found to be nearly Tinnr f an mcn too long, and hence all the copies furnished to the states are subject to that minute correction, since the British yard is unquestionably the only authentic represen- tative of the old standard from which our measures are derived. The use of the metric standards has been legalized, but not made ob- ligatory, in Great Britain since 1864, and in the United States since 1866. Metric Stan- dards. In France, as before mentioned, a radi- cal change was made in the existing standards by the adoption in 1795 of a system according to which the -nr.Tnnr.Tnnr P art of a meridional quadrant of the earth should be the unit of. length measure, called the metre; the unit of surface measure being the square of ten metres, called the are; the unit of capacity measure, the cube of a tenth part of the metre, called the litre ; that of the measure of solidity, having the capacity of a cubic metre, called the st&re; and the unit of weight being the weight of that quantity of distilled water at its maximum density which fills the cube of the T^ part of a metre, called the gramme. Each unit has its decimal multiples and subdi- visions, which are indicated by prefixes placed before the names of the several fundamental units. The prefixes denoting multiples, de- rived from the Greek, are deca, ten; hecto, hundred ; kilo, thousand ; and myria, ten thou- sand. Those denoting subdivisions are taken from the Latin, and are deci, tenth ; centi, hundredth; and milli, thousandth. We thus have kilometre, metre, millimetre; kilogramme, gramme, milligramme. A complete list of the metric measures and their equivalents in Amer- ican units will be found below in the general table of weights and measures of all countries, under the head of France. An arc of the me- ridian extending from Dunkirk to Barcelona, and comprising about 10 of latitude, was measured trigonometrically, in order to deduce from it, with the aid of other arcs previously measured in Peru and in Sweden, the length of the meridional quadrant passing through Paris. Thia length was found in terms of the toise or old fathom (six-foot) measure of France, which was used in the measurement of the base lines ; and its ten-millionth part, or the length of the metre, was determined to be 443-296 lines, the line being the T J T of a foot. It ap- pearing thus that four metres would exceed two toises by the 19th part of a toise, very nearly, the following process of constructing the metre was adopted : Nineteen pieces were made, as nearly as possible equal to each other, so that their aggregate would be a toise ; upon careful comparison it was found that one had almost exactly the required length. This piece, together with the two toises that had served in the base measurements, was placed in the comparator and compared with four single metre bars abutted together, which were simi- larly compared with each other, and adjusted by grinding and polishing their ends until they had the desired length. These bars were, like the toises, of iron ; one of them was chosen for the French standard, from which the platinum metre of the archives, which is the legal stan- dard of France, was copied. Another of these original metres was brought to the United States, and has served as the standard for the geodesy of the coast survey, and for the con- struction of a metric standard for this country. The kilogramme was constructed by means of a cylinder of one fourth of a metre diameter and equal height, very carefully admeasured ; it was hollow, and just heavy enough to sink freely in water. The volume of water dis- placed by it being weighed by means of an approximate kilogramme and fractions, the cor- rection required to reduce the experimental weight to the prescribed value of the weight of a cubic decimetre of water at its maximum density was deduced, making due allowances for the buoyancy of the air and all other requi- site corrections. Finally a kilogramme of plati- num was deposited in the archives of France as the prototype unit of weight. It has been found to be equal to 15,432-348 grains, or 2-2046212 pounds avoirdupois, by the most careful comparisons. The metre was found to be 39-37079 English inches, but the most recent and elaborate comparisons, made at the ord- nance survey office in Southampton, indicate that it is only 39-37043 inches. The difficulty in making an exact comparison between the metre and the inch or the yard, arises from the fact that the metre is an end measure, of plati- num, having its standard length at 32 F., while the yard is a line measure, of bronze, standard at 62 F. They cannot therefore be directly compared, and the dilatation by temperature comes into effect, and requires to be ascer- tained with the utmost accuracy. The means of comparison for standards of length are dif- ferent, according to their being line or end measures. In the former case, when, as in the British yard, the standard length is contained between lines drawn upon the bar, the com- parator is necessarily optical, which enables us to measure by means of micrometer micro- scopes the minute differences between differ- ent measures traced from the same standard by mechanical means. But when the stan- dards are end measures, or contained between the terminal planes of the bar, the compari- son is necessarily made by actual contact, the rotation of a mirror or tilting of a deli- cate level being used as the means of indi- cating the minute differences. In standard measures of the latter kind, it is now custo- mary to make the terminal surfaces very small and ground off parallel to each other by means of cylindrical bearings near each end of the bar. It is only by such means that parallelism approaching to geometrical accuracy can be obtained. In both kinds of comparison, a pre- cision of the Trofore P art of an inch ma y k reached. The greatest difficulty in obtaining