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which are more or less suitable according to the instruments and apparatus available, and to the local conditions governing the test. We will deal with these various methods in turn, and, in all cases, the E.M.F. to be determined will be represented by a battery designated by the letter E. It may be mentioned that nearly all the tests for electromotive force consist in a more or less direct comparison of the E.M.F. to be measured witä the known E.M.F. of a standard cell, Clark's standard, previously described, being the one generally adopted for the purpose.

The Equal Deflection method consists in connecting the standard cell Es Fig. 49, through an adjustable re

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sistance R, and a key, K, with the galvanometer G. The resistance in circuit in this case, and, in fact, in all cases where Clark's standard cell is employed, should be sufficiently high to ensure that no appreciable current is taken from the standard cell, as otherwise polarisation is set up, and its E.M.F. falls from the constant value of 1.435 true volt at 15.5° C., thereby impairing the accuracy of the test. For this reason, the galvanometer G should be of the high resistance type (a Thomson reflecting instrument answers very well), and the resistance R should also have a fairly high value. The connections being made as illustrated in the figure, the key K is closed, and the deflection of the galvanometer needle observed and noted. K is then opened, and Es replaced by the battery E, the E.M.F. of which it is required to measure. K is then again closed, and R adjusted to R1 such that the original deflection is again obtained on the galvano

comes

RI meter, then = Es volts. This result will be suffi.

R ciently approximate for all practical purposes if the rcsistance of the batteries E and Es be so low as to be negligible compared with the resistances R and Ri, and the resistance of the galvanometer G.

If a shunt S be employed with the battery E, or shunts S and Si for both measurements, then the formula be

G + S
Ꭱl

Ꭱl

G + S

and
E = Es

S
E = Es
R

G + SI
R

SI respectively, S and si being the shunts employed with E and Es respectively. It is essential in employing the last two formulæ that the resistances of the galvanometer, shunts, and batteries are so small compared with R and Rl as to be negligible. In such case it is needful to employ a more stable standard Es, such as a Daniell cell yielding 1.079 volt, than Clark's type, in conjunction with a galvanometer of comparatively low resistance.

The equal resistance method is somewhat similar to the foregoing, but necessitates a knowledge of the internal resistances of the standard cell Es and the cell E under test respectively, unless these resistances be so low in value as to be negligible compared with R and Ri.

The connections for the test are the same as in Fig. 49, The standard cell is first placed in circuit, and its deflection d noted on depressing K. Es is then replaced by the cell E under test, and the resistance R is adjusted until the total resistance in circuit is the same as in the preceding case, and the second deflection dl is also observed, then the electromotive force of the cell under test

dl E = Es

d đ The total resistance of the circuit mentioned above includes, of course, the resistance of the respective cells, the galvanometer, and the resistance R, but if the internal resistances of the two cells be very low compared with the other resistances in the circuit, they may be neglected with sufficiently approximate accuracy to the subsequent results.

Wheatstone's method may also be noted by the same Fig. 49; the standard cell Es is connected with the galvanometer G through a resistance R, and the consequent deflection d noted. The resistance R is then increased to R + r, R and r being as nearly equal as it is possible to make them, and a second deflection dl is obtained. The E.M.F. under test E is then connected in circuit in place of the standard cell Es, and, by varying the resistance R to R1, the same deflection d as was obtained in the first instance is reproduced. R1 is then increased to RI + rl such that the second deflection dl is reproduced

rl on the galvanometer; then the E.M.F. of E = Es volts.

Poggendorff's method for the determination of electromotive force differs somewhat from the foregoing tests, and is represented in Fig. 50, where E is the E.M.F. to be determined, R the main variable resistance, q a subsidiary resistance, only required when the resist

K

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ance of E is unknown, Es a standard cell, G the galvanometer, and K, K1 ordinary circuit keys. If Es be a Clark's cell, an additional resistance of some 10, 000w is required in series with it and the galvanometer, to prevent an excessive passage of current from it into the circuit, but, if the cell be of a more stable type, such as the Daniell, for instance, no such auxiliary resistance is required, nor is its presence indicated in the figure.

The mode of procedure is as follows. Let us suppose in the first instance that we know the resistance of the battery E, then r is omitted, and K and Kl being closed, R is adjusted until a balance or zero reading is obtained on the galvanometer G. Then the required E.M.F. E=Es R + Re

volts, where Re is the resistance of the

R source of E.M.F. (E.). If, on the other hand, Re be an unknown quantity, include the subsidiary resistance r in the circuit, and proceed as before to adjust R with K and K1 closed, until no deflection results upon the galvanometer. Next vary r to rl, and R to Ri, until a balance is again obtained with K and Kl closed; then the E.M.F. to be determined, E = Es

(r-,l) + (R-RI)

Ꭱ - Ꭱl volts.

The variable resistances R and r, in this test are conveniently provided by the proportional and adjustable arms of a Wheatstone bridge, the connections in such case being as indicated by Fig. 51, R being unplugged in the adjustable arm, and r, if needed, in the proportional arms.

As will readily be conceived from the attendant dia

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grams of connections, this method consists in opposing one E.M.F. (under test) to the other (standard), and so adjusting the resistances in circuit that these electromotive forces exactly balance one another, and no current, in consequence, flows through the galvanometer.

Kempe's method of determining electromotive forces is somewhat ingenious and simple in its application. Its two phases are represented by diagrams A and B, Fig. 52, respectively. In the first instance, the standard E.M.F., Es, and the E.M.F. under test, E, are opposed to one another, and connected with the terminals of a Thomson reflecting galvanometer; the resulting deflection d, due to the preponderance of one E.M.F. over the other, is duly noted. The electromotive forces are then, as indicated in diagram B, connected up in series to assist one another, and the resultant deflection being rather large, a shunt s is introduced across the terminals of the galvanometer G. The introduction of this shunt, according to the law of divided circuits, materially lowers the total resistance of this particular circuit which we are now

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dealing with, and, to cope with this decrease, what is known as a

as a "compensating resistance," R, is introduced into the circuit, R being of such a value as to render the total resistance of the circuit the same as it was before the introduction of the shunt s.

The second deflection di is also duly noted, together

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