225*.] An arrangement similar to Wheatstone’s Bridge has been employed with advantage by Sir W. Thomson in determining the resistance of the galvanometer when in actual use. It was suggested to Sir W. Thomson by Mance’s Method. (See Art. 226.)

Let the battery be placed, as before, between B and C in the figure of Article 221, but let the galvanometer be placed in CA instead of in OA. If bβ − cγ is zero, then the conductor OA is conjugate to BC, and, as there is no current produced in OA by the battery in BC, the strength of the current in any other conductor is independent of the resistance in OA. Hence, if the galvanometer is placed in CA its deflexion will remain the same whether the resistance of OA is small or great.

We therefore observe whether the deflexion of the galvanometer remains the same when O and A are joined by a conductor of small resistance, as when this connexion is broken, and if, by properly adjusting the resistances of the conductors, we obtain this result, we know that the resistance of the galvanometer is

b= ∗ Proc. R. S., Jan. 19, 1871. cγ , β

where c, γ, and β are resistance coils of known resistance.

It will be observed that though this is not a null method, in the sense of there being no current in the galvanometer, it is so in the sense of the fact observed being the negative one, that the deflexion of the galvanometer is not changed when a certain contact is made. An observation of this kind is of greater value than an observation of the equality of two different de- flexions of the same galvanome- ter, for in the latter case there is time for alteration in the strength of the battery or the sensitiveness of the galvanometer, whereas when the deflexion remains constant, in spite of certain changes which we can repeat at pleasure, we are sure that the current is quite independent of these changes.

Fig. 50.

The determination of the resistance of the coil of a galvanometer can eas- ily be effected in the ordinary way of using Wheatstone’s Bridge by placing another galvanometer in OA. By the method now described the galvanometer itself is employed to measure its own resistance. Mance’s∗ Method of determining the Resistance of the Battery. 226*.] The measurement of the resistance of a battery when in action is of a much higher order of difficulty, since the resistance of the battery is found to change considerably for some time after the strength of the current through it is changed.

In many of the methods commonly used to measure the Proc. R. S., Jan. 19, 1871

resistance of a battery such alterations of the strength of the current through it occur in the course of the operations, and therefore the results are rendered doubtful.

In Mance’s method, which is free from this objection, the battery is placed in BC and the galvanometer in CA. The connexion between O and B is then alternately made and broken.

If the deflexion of the galvanometer remains unaltered, we know that OB is conjugate to CA, whence cγ = aα, and a, the resistance of the battery, is obtained in terms of known resistances c, γ, α.

Fig. 51.

When the condition cγ = aα is fulfilled, then the current through the gal- vanometer is Eα y= , bα + c(b + α + γ) and this is independent of the resistance β between O and B. To test the sen- sibility of the method let us suppose that the condition cγ = aα is nearly, but not accurately, fulfilled, and that y0 is the current through the galvanometer when O and B are connected by a conductor of no sensible resistance, and y1 the current when O and B are completely disconnected.

To find these values we must make β equal to 0 and to ∞ in the general formula for y, and compare the results.

In this way we find y0 − y1 α cγ − aα

, y γ (c + α)(α + γ) where y0 and y1 are supposed to be so nearly equal that we may, when their difference is not in question, put either of them equal to y, the value of the current when the adjustment is perfect. The resistance, c, of the conductor AB should be equal to a, that of the battery, α and γ, should be equal and as small as possible, and b should be equal to α + γ.

Since a galvanometer is most sensitive when its deflexion is small, we should bring the needle nearly to zero by means of fixed magnets before mak- ing contact between O and B.

In this method of measuring the resistance of the battery, the current in the battery is not in any way interfered with during the operation, so that we may ascertain its resistance for any given strength of current, so as to determine how the strength of current affects the resistance.

If y is the current in the galvanometer, the actual current through the bat- tery is x0 with the key down and x1 with the key up, where b x1 = y 1 + , ( α + γ) b αc x0 = y 1 + + , ( γ γ(α + c) ) the resistance of the battery is a= cγ , α and the electromotive force of the battery is c E = y (b + c + (b + γ)) .∗ α ∗

[This method, as has been pointed out by Professor Oliver Lodge, is not free from error on account of the variation of the E.M.F. of the battery, as the current through it is diminished or increased by raising or depressing the key.]

COMPARISON OF ELECTROMOTIVE FORCES

The method of Art. 225 for finding the resistance of the galvanometer dif- fers from this only in making and breaking contact between O and A instead of between O and B, and by exchanging α and β we obtain for this case y0 − y1 β cγ − bβ

. y γ (c + β)(β + γ) On the Comparison of Electromotive Forces. 227*.] The following method of comparing the electromotive forces of voltaic and thermoelectric arrangements, when no current passes through them, requires only a set of resistance coils and a constant battery. Fig. 52.

POGGENDORFF’S COMPENSATION METHOD

Let the electromotive force E of the battery be greater than that of either of the electromotors to be compared, then, if a sufficient resistance, R1 , be interposed between the points A1 , B1 of the primary circuit EB1 A1 E, the electromotive force from B1 to A1 may be made equal to that of the elec- tromotor E1 . If the electrodes of this electromotor are now connected with the points A1 , B1 no current will flow through the electromotor. By placing a galvanometer G1 in the circuit of the electromotor E1 , and adjusting the resistance between A1 and B1 , till the galvanometer G1 indicates no current, we obtain the equation E1 = R1 C, where R1 is the resistance between A1 and B1 , and C is the strength of the current in the primary circuit.

In the same way, by taking a second electromotor E2 and placing its elec- trodes at A2 and B2 , so that no current is indicated by the galvanometer G2 , E2 = R2 C, where R2 is the resistance between A2 and B2 . If the observations of the galvanometers G1 and G2 are simultaneous, the value of C, the current in the primary circuit, is the same in both equations, and we find E1 ∶ E2 ∶∶ R1 ∶ R2 .

In this way the electromotive force of two electromotors may be com- pared∗ . The absolute electromotive force of an electromotor may be measured either electrostatically by means of the electrometer, or electromagnetically by means of an absolute galvanometer. This method, in which, at the time of the comparison, there is no cur- rent through either of the electromotors, is a modification of Poggendorff’s method, and is due to Mr. Latimer Clark, who has deduced the following values of electromotive forces: ∗

[Any number of batteries may be compared by the help of only one galvanometer if one pole of each battery is connected with the same electrode of the galvanometer, the other poles being connected through separate keys to points A1 , A2 , &c. upon the wire and the keys being depressed one at a time but in rapid succession.]221 POGGENDORFF’S COMPENSATION METHOD. Concentrated solution of Daniell I. Amalgamated Zinc H2 SO4 + 4 aq. II. „ H2 SO4 + 12 aq. III. „ H2 SO4 + 12 aq. Bunsen I. „ „ „ II. „ „ „ Grove „ H2 SO4 + 4 aq. CuSO4 CuSO4 Cu2 (NO3 ) HNO3 sp. g. l. 38 HNO3 Volts. Copper = 1.079 Copper = 0.978 Copper = 1.00 Carbon = 1.964 Carbon = 1.888 Platinum = 1.956 A Volt is an electromotive force equal to 100,000,000 units of the centimetre-gramme-second system.