the instrument is such that when a current traverses the two coils, the suspended coil rotates in a counter-clockwise direction, the distance through which it can move being limited by the stops. The torsion head is now rotated in a clockwise direction, until the pointer attached to the coil is brought back to zero. Since the same current flows through both coils, the resultant magnetic effect between them must be proportional to the product of the currents in each-that is, to the square of the current. Also, since in the torsion control the controlling force is proportional to the angle of torsion 4, we have C2 ∞ & and C = K√ where K is a constant depending on the torsion control and winding of the instrument, and must be determined experimentally for the dynamometer. 175. Determination of the Constant of the Dynamometer.—To determine the constant K, we must send a known current through the instrument, and find the angle of torsion 4, required to bring the suspended coil back to zero. The current may be measured by means of a current balance, standard galvanometer, or voltameter. The dynamometer, after having been levelled as described, is connected in series with a variable resistance, secondary battery, voltameter, and break-circuit key. The current is first adjusted until the deflection of the torsion head required to produce equilibrium is pretty large, the instrument being much more sensitive at high than at low readings, since the squares of the readings increase less rapidly at high than at low values. The voltameter plates are then removed, and after being prepared as described previously, (par. 165), are weighed, and replaced in the voltameter; the electrolysis should be allowed to go on for about one hour, the current being kept constant by means of the variable resistance. The current C is calculated from the gain in weight of the cathode, and then the constant calculated, since— being the angle of torsion as read off on the dial. Two or three such determinations may be made at various parts of the scale, and the mean of the values thus obtained taken as the constant of the instrument. 176. Calibration of a Direct Current Reading Instrument.— The Siemens' electro-dynamometer affords a very simple means of absolutely calibrating a direct-reading ammeter, the ammeter being connected in series with the dynamometer, and with a variable resistance, battery, and break-circuit or reversing key. Simultaneous readings are taken on both instruments with various currents, the currents being calculated from the reading on the Siemens' electro-dynamometer, by multiplying the square root of the reading of the torsion angle by the dynamometer constant. Thus a calibration curve may be plotted for the direct-reading instrument, or a table of corrections made out. In using the electro-dynamometer in connection with other apparatus, care must be taken that the magnetic effect of the current in the other apparatus does not affect it. 177. In order to determine the constant of a Siemens’ electro-dynamometer, it was connected in series with a copper voltameter, carbon resistance, break-circuit key, and six secondary cells. The copper cathode was carefully weighed before the deposit. The time of deposit was one hour, and the temperature of the bath was 11° C. The dynamometer reading was kept constant III. ELECTRO-MOTIVE FORCE. 179. THE absolute determination of an electro-motive force in electro-magnetic measure is made from the relations which subsist between electro-motive force, current, and resistance, the produce of current and resistance being equal to electro-motive force. This being so, if current and resistance are expressed in absolute units, the electro-motive force will be in absolute units; if current is in ampères and resistance in ohms, electromotive force will be in volts, the volt being the practical unit of electro-motive force, and being that necessary to send a current of one ampère through a resistance of one ohm. STANDARDS OF E.M.F. 180. A standard of E.M.F. might be arranged by sending a known current through a known resistance, and using the E.M.F. at the ends of the resistance as the standard. This is done in some cases, but it is found much more convenient to employ some form of voltaic cell whose E.M.F. is a known multiple of the unit. If such secondary standards are to be employed, they must fulfil certain conditions. (a) They must be easily made and reproduced. (b) They must remain absolutely constant under constant physical conditions. (c) Their alteration with the alteration of conditions must be accurately known. (d) They must always return to their original value when the original conditions are reproduced. |