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of each inch of the wire should be carefully tested by some method such as that given in the next section, and recorded for future reference.

B is a battery of cells that will send through the resistance r1 and the wire JK a fairly constant current, and produce between the points J and K a P.D. as large as the voltmeter v is intended to be calibrated for. In circuit with the standard cell, s, preferably of the Clark

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Fig. 216.-Potentiometer Method for Testing a Voltmeter. type, and the delicate galvanometer G, there is inserted a resistance r2 sufficiently large to keep the current passing through the cell small even when the point of contact of the key with the wire J K is at some distance away from the position that gives no current through the cell and galvanometer. If s is a Clark's cell r

should be not less than about 2,000 ohms.

To make a measurement the plug P is inserted, and the resistance r1 is adjusted until the P.D. between the ends of the wire J K produces the required deflection of the voltmeter. The handle H of the key is then depressed for an instant when, if there be any deflection of the galvanometer, the handle H is liberated and the key

slid in the proper direction along the wire J K, and contact again made, and so on, until a point м is found such that no current passes through the galvanometer on depressing H. Then, if E be the E.M.F. of the standard cell in volts at the temperature at which the test is made, the true value of the P.D. which is producing the voltmeter deflection is given by the expression

resistance of the whole wire J K

resistance of the portion J M

× E volts.

The resistance r1 is now altered so as to produce another deflection of the voltmeter, and the position of the key again adjusted until no current flows through the galvanometer on depressing H, &c.

In order to enable the contact-maker c to touch any one of the five wires composing JK, C can be slid along the slot in the lever L of the key at right angles to the wires; and, to prevent the platinised knife-edge, attached to the lower part of c, being pressed too hard against the stretched wire, and damaging it, the flat spring 8 is made rather weak. Hence, on depressing H, first the knife-edge attached to c comes into contact with the wire, and, on still further depressing H, the lever turns about the knifeedge until it comes against the stop placed underneath it.

As the accuracy of the preceding method is quite independent of the current passing through the voltmeter, the method can be employed either with a voltmeter of high resistance or with one of low resistance, and therefore passing an appreciable current. Further, the method may be made very sensitive, since the whole of the wire JK is employed in determining the value in volts of each point of the voltmeter scale. But it possesses the disadvantage that a fresh adjustment of the resistance 1, as well as a fresh adjustment of the position of the key C H L, have to be made for each point on the voltmeter scale whose absolute value we desire to ascertain. While, therefore, the method may very suitably be employed when the relative calibration of a

voltmeter is already known, and the absolute value of one point only has to be determined, it is somewhat tedious to use when many points of the scale have to be calibrated absolutely.

155. Foster's Method of Subdividing a Wire into Lengths having Equal Resistances. The stretched wire of a potentiometer, or of a Wheatstone's bridge, can be easily calibrated by using the following method, due to Prof. G. C. Foster. Let what are called the "unknown" and "known" resistances in Fig. 127, page 248, have values of a and b ohms respectively, these values not differing much from one another; and let coils, having resistances of x and y ohms respectively which also do not differ much from one another, be inserted in place of the short-circuiting pieces, $, and sa, in Fig. 127. Move the sliding key, K, until balance is obtained, at some point, P say, and let the resistances of the two portions of the whole wire, w w, on the two sides of the point P be land m ohms respectively, then

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Next interchange the coils having resistances x and y ohms, but not the other pair, and move the sliding key, K, to a new point, p' say, at which balance is obtained, and let the resistances of the two portions into which the wire is divided be now l' and m' ohms, then

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since each expression is the resistance of the whole wire, therefore also

l— l' = m' m.

But each of the latter expressions is the resistance of the wire between the points P and P', at which the sliding key was placed in the two tests to obtain balance; consequently,

2 x resistance of wire PP' =

2 (x

or, resistance of wire PP' = x y.

y),

Next, vary slightly the value of a, or of b, by shunting, for example, the coil marked "unknown," or the coil marked "known," in Fig. 127, and repeat the preceding. Then two new points q and q' in the wire will be found such that

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resistance of wire Q Q' resistance of wire P P'.

In this way, then, the wire may be subdivided into any desired number of portions, all having exactly the same resistance-viz. that equal to the difference between the resistances of the coils which are interchanged in the test.

The resistances of the metal strips connecting the parts of the bridge together, as well as the resistances of the contacts at the ends of the coils, and at the ends of the wire, w w, are included in the resistances, a, b, x, y, l, m, l', m'. But the actual values of these contact resistances do not affect the answer, since this only involves the resistance of a piece of the wire w w and the difference between the resistances of two coils. It is very important, however, that no change occurs in any one of the contact resistances while the tests are being made; for if such a variation occurred comparable in magnitude with the values of the resistances of the coils, &c., some one or more of the equations given above would be incorrect, and, therefore, we could not conclude that the resistance of the piece of the wire between the points Q and Q' was equal to that of the piece between the points P and P'.

It would not, therefore, be a good plan to attach the ends of the interchangeable coils to the rest of the bridge, by means of the screws and nuts that are used to hold the short-circuiting pieces, S1, S2, in Fig. 127; for such a mode of attachment might introduce an alteration in the contact resistances when the coils were interchanged in position. A better plan would be to employ four metal mercury cups, each being fitted with a lug suitable for being held by one of the screws and nuts, and to construct the terminals of the movable coils in the form of thick rods, like the terminal rods, w, w, of the standard coil (Fig. 134, page 276). Then, if the mercury cups, as well as the ends, E, E, of the rods, were well amalgamated, and if the ends not merely dipped into the mercury in the cups, but also pressed on the metallic bottoms of the cups, the contact resistances would be so small that any small percentage change in them would be quite negligible.

In the preceding the wire to be calibrated is supposed to form part of a Wheatstone's bridge; but if that is not the case-if, for example, the stretched wire belongs to a potentiometer, as in Fig. 216, page 511-then it must be joined up to a Wheatstone's bridge so as to take the place of the bridge wire. But this can be done with two pieces of connecting wire attached to the binding screws at the points J and K of the potentiometer, and to binding screws at the ends of the bridge, since the resistance of such connecting wires, if constant, will not affect the calibration of the potentiometer wire with Foster's method.

With such a combination, then, there is no necessity to spread out the metal strips in line as shown at the back of Fig. 127, page 248, and the arrangement can be made much more compact by fixing five metal bars ab, cde, fjk, lmn, and pq side by side. Binding screws are soldered to the strips at the points a, d, j, m, and q, the binding screws at a and q being for the purpose of connecting the bridge arrangement with the potentiometer, at d and m for the battery, and at j for the

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