These gauges are usually made in series, e.g., i in., 0.9 in., o.8 in. . . . 0.1 inch. Suppose we wish to calibrate such a series, of which the i in. is supposed to be already known as the result of some previous calibration. For convenience we will assume that we have available a duplicate set of pieces, which we denote by o•i' in., 0•2' in. . . . o.9' inch. To determine, for example, the value of the o.7 Adding up all these equations we see that the sums of the second columns on either side cancel out, and we get The size of each of the other pieces may be determined in a pre cisely similar manner.
It may be noted that in the determination of sizes in this man ner, the length of each gauge is automatically associated with the thickness of one wringing film, which, for clearness in conception, may be regarded as representing half a film thickness on either end surface, so that when two gauges are wrung together a whole film is established between them. As the gauges are normally used in this manner, this result is logically what is required. The wring ing films, moreover, are in any case exceedingly thin. When initially formed, their thickness depends to some extent on the viscosity of the liquid of which they are composed, but if a suffi cient length of time is allowed to elapse they tend to thin down to a limiting thickness, less than o•00000r in. for all liquids.
There is one more fundamental operation which, whatever may be the nature of the ultimate standard adopted, will always be required in its practical application to everyday requirements, and that is the determination of the length of an end standard in terms of the corresponding line standard, or vice versa. This is a matter of considerable difficulty, and sev eral methods have been employed for the purpose. Probably the best method is that introduced by Mr. H. L. P. Jolly, formerly of the National Physical Labora tory, and now of the Ordnance Survey Department, Southamp ton. It involves the use of an
intermediate end standard, and of two special parallel-faced end blocks, which can be wrung on to the ends of this standard.
' Each of the end blocks carries graduation marks as shown on its polished upper surface. The composite bar is compared in the ordinary way in a comparator, with the standard line bar. Each of the end blocks is turned round in turn, and re-wrung on the end of the bar, and the comparison repeated. We thus obtain the four results:— Each of the end blocks is then removed in turn and the other wrung centrally on the end of the bar, the new combinations being compared in a measuring machine with the standard end bar_ with the results in. gauge, we wring up in turn all the various nominally equal com binations indicated below, and compare them in a suitable measur ing machine, the small observed differences being indicated by which gives us the desired value of the line standard in terms of the end standard SE or vice versa.
To complete our survey of the fundamental operations involved in length measurement, reference must be made finally and very briefly to the process of verifying longer measures, such as are used in surveying. In the first place a long bar, graduated in multiples of the standard length unit, is required. This is compared, yard by yard, or metre by metre, with the standard line bar, in a large comparator. This bar in turn is compared either with suitable reference marks engraved on metal studs let into a mural base at intervals corresponding to the length of the bar, or else directly with the divisions of a graduated tape. The tapes or wires after verification, either directly, or by comparison with the mural base, are used to determine base lines in the field, by comparison with temporary bench marks set up at intervals apart roughly equal to the length of the tape.