Page:1902 Encyclopædia Britannica - Volume 26 - AUS-CHI.pdf/551

CALIBRATION 501 exceeds that of the Gay-Lussac method in consequence of the line. Or the curve may be replotted with the new much larger number of independent observations. It may he ordinates thus obtained. In drawing the curve from the noticed, for instance, that the correction at point 5 is 27'l thousandths by the complete calibration, which is 2 thousandths corrections obtained at the points of calibration, the exact less than the value 29 obtained by the Gay-Lussac method, but form of the curve is to some extent a matter of taste, but agrees well with the value 27 thousandths obtained by taking the curve should generally be drawn as smoothly as only the first and last observations with the thread of 5°. The disadvantage of the method lies in the great number of observa- possible on the assumption that the changes are gradual tions required, and in the labour of adjusting so many different and continuous. The ruling of the straight line across the curve to threads to suitable lengths. It is probable that sufficiently good results may be obtained with much less trouble by using fewer express the corrections in terms of the fundamental threads, especially if more cai’e is taken in the micrometric deter- interval, corresponds to the first part of the process of mination of their errors. The method adopted for dividing up the fundamental interval of any thermometer into sections and steps for calibration may be widely varied, and is necessarily modified in cases where auxiliary bulbs or “ampoules” are employed. The Paris mercurystandards, which read continuously from 0° to 100° C., without intermediate ampoules, were calibrated by Chappuis in five sections of 20° each, to determine the corrections at the points 20°, 40°, 60°, 80°, which may be called the “principal points” of the calibration, in terms of the fundamental interval. Each section of 20° was subsequently calibrated in steps of 2°, the corrections being at first referred, as in the example already given, to the mean degree of the section itself, and being afterwards expressed, by a simple transformation, in terms of the fundamental interval, by means of the corrections already found for the ends of the section. Supposing, for instance, that the corrections at the points 0° and 10° of Table III. are not zero, but C0 and C' respectively, the correction On at any intermediate point n will evidently be given by the formula, Cn = C°-{-cn +(C — C°)n/ . . . (3) calibration mentioned above under the term “ Standardizawhere cn is the correction already given in the table. If the corrections are required to the thousandth of a degree, it tion.” It effects the reduction of the readings to a is necessary to tabulate the results of the calibration at much common standard, and may be neglected if relative values more frequent intervals than 2°, since the correction, even of a only are required. A precisely analogous correction occurs good thermometer, may change by as much as 20 or 30 thousandths in the case of electrical instruments. A potentiometer, in 2°. To save the labour and difficulty of calibrating with shorter for instance, if correctly graduated or calibrated in parts threads, the corrections at intermediate points are usually calculated by a formula of interpolation. This leaves much to be of equal resistance, will give correct relative values of any desired, as the section of a tube often changes very suddenly and differences of potential within its range if connected to a capriciously. It is probable that the graphic method gives equally constant cell to supply the steady current through the good results with less labour. Slide- Wire.—-The calibration of an electrical slide-wire into slide-wire. But to determine at any time the actual value parts of equal resistance is precisely analogous to that of a of its readings in volts, it is necessary to standardize it, capillary tube into parts of equal volume. The Carey Foster or determine its scale-value or reduction-factor, by commethod, employing short steps of equal resistance, effected by parison with a standard cell. transferring a suitable small resistance from one side of the slideA very neat use of the calibration curve has been made by wire to the other, is exactly analogous to the Gay-Lussac method, and suffers from the same defect of the accumulation of small Prof. Rogers in the automatic correction of screws of dividing errors unless steps of several different lengths are used. The machines or lathes. It is possible, by the process of grinding as calibration of a slide-wire, however, is much less troublesome than applied by Rowland (see Ency. Brit. vol. xxi. pp. 552-3), to make that of a thermometer tube for several reasons. It is easy to a screw which is practically perfect in point of uniformity, but obtain a wire uniform to one part in 500 or even less, and the even in this case errors may he introduced by the method of section is not liable to capricious variations. In all work of pre- mounting. In the production of divided scales, and more cision the slide-wire is supplemented by auxiliary resistances by particularly in the case of optical gratings, it is most important which the scale may be indefinitely extended. In accurate that the errors should be as small as possible, and should be electrical thermometry, for example, the slide-wire itself would automatically corrected during the process of ruling. With this correspond to only 1°, or less, of the whole scale, which is less object a scale is ruled on the machine, and the errors of the than a single step in the calibration of a mercury thermometer, uncorrected screw are determined by calibrating the scale. A so that an accuracy of a thousandth of a degree can generally be metal template may then be cut out in the form of the calibrationobtained without any calibration of the slide-wire. In the rare correction curve on a suitable scale. A lever projecting from the cases in which it is necessary to employ a long slide-wire, such as nut which feeds the carriage or the slide-rest is made to follow the cylinder potentiometer of Latimer Clark, the calibration is best the contour of the template, and to apply the appropriate correceffected by comparison with a standard, such as a Thomson-Varley tion at each point of the travel, by turning the nut through a small angle on the screw. A small periodic error of the slide-box. screw, recurring regularly at each revolution, may be similarly Graphic Representation of Results.—The results of a corrected by means of a suitable cam or eccentric revolving with calibration are often best represented by means of a cor- the screw and actuating the template. This kind of error is rection curve, such as that illustrated in the diagram, which important in optical gratings, but is difficult to determine and is plotted to represent the corrections found in Table III. correct. The abscissa of such a curve is the reading of the instruCalibration by Comparison with a Standard. — The ment to be corrected. The ordinate is the correction to commonest and most generally useful process of calibration be added to the observed reading to reduce to a uniform is the direct comparison of the instrument with a standard scale. The corrections are plotted in the figure in terms over the whole range of its scale. It is necessary that the of the whole section, taking the correction to be zero at standard itself should have been already calibrated, or else the beginning and end. As a matter of fact the corrections that the law of its indications should be known. A conat these points in terms of the fundamental interval were tinuous current ammeter, for instance, can be calibrated, found to be — 29 and - 9 thousandths respectively. The so far as the relative values of its readings are concerned, correction curve is transformed to give corrections in terms by comparison with a tangent galvanometer, since it is of the fundamental interval by ruling a straight line known that the current in this instrument is proportional joining the points +29 and + 9 respectively, and reckon- to the tangent of the angle of deflexion. Similarly an ing the ordinates from this line instead of from the base- alternating current ammeter can be calibrated by com-