Calibration.—The calibration of the subdivisions of a divided scale is done in a similar way, except that in this case the carriage of the comparator moves in the direction of the length of the bar. The microscopes are fixed successively at a series of suitable inter vals apart, for example, i dm., 2 dm., 3 dm., etc., and each princi pal interval of i dm., 2 dm., etc., is compared with every other in terval of the same magnitude throughout the metre. By computa tion from the results so obtained the value of each decimetre is determined in relation to the whole length of the scale. In a similar manner each centimetre of one decimetre is compared with every centimetre of another decimetre, and as a result the value of each centimetre is found in relation to the whole of the other decimetre, and so in turn, in relation to the whole length of the metre. Milli metres are derived from centimetres in the same way, and so on. The complete calibration of a divided scale will be seen to be a very laborious process involving an enormous number of observa tions. The process is, however, simplified by the fact that the whole of the measurements are made on the one bar, so that, provided reasonable precautions are taken to ensure constancy of temperature, exact temperature measurements are not important.
The apparatus used to determine coefficients of expansion is similar to the transverse comparator, but has two independent water baths mounted on the carriage. One of these, containing a bar preferably of invar, is kept at a constant temperature, while the other, containing the bar under examination, is brought suc cessively to a series of suitable temperatures. The two bars are compared at each temperature of the second, and so the variations of its length with temperature are determined.
A number of machines of different types, and varying sensitivity, are available for comparing end standards by contact measure ment, or, if the end faces are of sufficiently perfect finish, they may be directly compared by the method of optical interference. In the latter case the two bars are brought in turn between two semi-silvered optically flat glass surfaces, and the number of wave . lengths in the small spaces at either end between the measuring surface of the bar, and the semi-silvered surfaces of the optical flats are determined by direct measurement of the angular diam eters of the interference rings formed by monochromatic light. This enables the fraction of a wave length to be determined with exactness, and if several different wave lengths are used in turn, whose mutual ratios are known, the whole number of waves is easily determined by deduction, as only a particular set of cor responding whole numbers will give fractions agreeing in every case with the series actually observed.
In the mechanical contact type of measuring machine the bar is measured between two opposed anvils, one of which may either be fixed, or may be movable by means of a micrometer screw, while the other is capable of a small movement operating some form of sensitive indicator. The two bars to be compared are inserted in turn between the anvils, and if the whole difference between them is sufficiently small the movement of the indicator over a cali brated scale may suffice to determine it. If the difference is greater, the indicator must be brought to a fixed mark by an adjustment of the moving anvil, the difference in length being then ascertained by the difference in reading of the micrometer wheel.
Mode of Calibration of End Standards.—The calibration of a set of subdivisional end standards is effected by taking them to gether in pairs of nominally equal added lengths, and comparing their sums, in the manner just described. In the last 20 years there have been developed, first by the firm of C. E. Johansson, Sweden, and later at the National Physical Laboratory, England, and by Hoke in America, methods of producing short flat-ended gauges of such perfection that any two of them if put together will adhere firmly to each other by "wringing." The process of wringing appears to depend essentially on the presence of a very minute trace of liquid (grease or moisture) between the sur faces of the gauges. This wringing film is extremely thin, and the bond between the two surfaces appears to be formed by short chains of liquid molecules, only two or three molecules long, attached at either end to the molecules of the solid surfaces.