the relative strengths of the currents be C and F, we

No. 4 (d) or, if r' be nought and s be so chosen that F equals C,

Method No. 5.-In making the first test let the galvanometer be shunted with a shunt of s ohms, and let a resistance of r ohms be in the main circuit, while, in making the second test, let the shunt be changed to one of s' ohms and the added resistance to r' ohms.

Then, if G and G" be the relative strengths of the currents, we have

or c=

Gs' {(g+8) r+gs} - G" s {(g + 8') r' + gs'}.

G" 8 (g+8')-G 8' (g+8)

This last case includes all those previously given in this section, for they may be obtained from this last case by simply giving different values to r, r', s and s', as seen from the following table :—

151. Remarks on the Preceding Methods of Measuring the Resistance of Cells. All the preceding methods of measuring the resistance of a cell are based on the assumption that its E.M.F. remains exactly the same during the carrying out of the pair of tests that have to be made, whichever method of measurement be employed. In consequence of the time, however, during which each of the two currents has to be allowed to flow while the galvanometer deflection is becoming steady, and also in consequence of its being necessary for the carrying out of the measurement that these two currents passing through the cell should differ considerably in strength, the assumption that the E.M.F. of the cell remained wholly unchanged would be quite wrong in the case of cells like the Leclanché, which polarise rapidly. On this account the "condenser method of measuring the resistance of cells," to be subsequently described in Volume II., is preferable for use with such cells.

In employing any of the preceding methods, care must be taken not to use resistances that are very large compared with the resistance of the cell to be measured; for not only would the introduction of such large resistances render the test very unsensitive, but, in addition, any small percentage error which might exist in this large resistance would itself be comparable with the resistance to be measured, and so would introduce a large error into the answer.

For example, to weigh a few grains of some powder in a weighing-machine used for weighing luggage at a railway station would certainly lead to hopeless inaccuracy; but beginners are apt to forget that, although a coil of 10,000 ohms and another of th of an ohm may be put into boxes of about the same size, there is the same sort of difference between these resistances as there is between the weight of 30 tons and of 1 ounce, and therefore that giving r and r' in the preceding tests values of thousands of ohms must invariably lead to

error when the resistance of the cell to be tested is 2 or 3 ohms, or less.

If, then, the galvanometer used for measuring the resistance of a cell be very sensitive and of high resistance, methods Nos. 1, 2, and 4 would be quite unsuitable to be employed, since, to reduce the galvanometer deflection to readable limits, it would be necessary to give. ra large value. Methods Nos. 3 or 5, on the other hand, could be successfully used, since the galvanometer being shunted in both the tests, the deflection could be made to have the desired value in each case without making r very large. And if the cell were one that was not seriously polarised when the external resistance was small, method No. 3 (d) would be a very convenient one to employ.

If, on the other hand, the galvanometer, although having a high resistance, be not very sensitive, so that when the cell to be tested is applied direct to its terminals the deflection is not unreadably large, then method No. 2 (b) may be employed with advantage; for it is to be observed that the formula in this case which gives the resistance of the cell does not involve the high resistance of the galvanometer, but only that of the shunt, and this may be made comparable with that of the cell.

Sincer has the value nought in this method No. 2 (b), and the high resistance galvanometer is therefore applied directly between the terminals of the cell, this method may be regarded as measuring, first, a current which is proportional to the E. M.F. of the cell; second, a current proportional to the P.D. between its terminals when the galvanometer and the cell are shunted with a resistance of s ohms-that is, when the cell is allowed to send a current through an external resistance of s ohms. But this is practically the method described in § 119, page 366; and the s in method No. 2 (b) is, therefore, simply the value of x in Fig. 169, page 366.

Hence, all the equations given on pages 364, 365,

and 366 apply also in this case, only if E is the E.M.F. in volts of the cell, and if V is the P.D. in volts between its terminals when it is sending a current of A amperes through the shunt or external resistance of s ohms, it must be remembered, first, that in method No. 2 (b) we do not actually measure the current with an ammeter; second, that the currents C and D do not indicate the values of E and of V in volts, but only are proportional to E and V-that is to say,

From this, however, it follows that the equation

which is given under the method No. 2 (b), is simply

the equation

a form in which the last equation but two on page 364 can be at once written. Consequently, the equation used in method No. 2 (b) is simply a statement of the fact that the P.D. employed in sending the current through the cell bears to the P.D. employed in sending it through the external circuit the ratio that the resistance of the cell does to the external resistance.

In § 149, page 492, it was explained that the method given in § 119 for measuring the resistance of a cell was specially suitable when the cell's resistance was very small; and the reason that in method No. 2 (b) we have been again led to the equations given in § 119 is that by assuming in method No. 2 (b) that r was nought, that g was large relatively to s, and that s was comparable in value with c, we have in reality made the assumption that c was small.