76. Resistance of Electrolytes (Kohlrausch Alternating-current Method).

Introduction.-In the following method, due to Professor Kohlrausch, the detrimental effects due to polarization, which tend to introduce errors in the measurement of electrolytic resistance, are almost eliminated. Such effects will be diminished still further by platinizing the electrodes (if these are not of platinum already), and by increasing their size. Although the method is superior to any at present in use in which direct currents are used, except the Stroud-Henderson one, there are difficulties arising from selfinduction and capacity which are manifest when alternating currents are used, and for this reason-it is of the utmost importance that the bridge arms have no self-induction. To realize this condition more fully, a special form of bridge is usually used, of which Fig. 210, p. 345, shows one type. The electrolytic cell may be either of the form shown in Fig. 212, p. 346, or that used in the last method. In the present method we shall employ this form of balancing cell which has been found by Drs. Stroud and Henderson to be a distinct improvement for resistances not greater than 1000 ohms or thereabouts, enabling dead silence to be obtained on the telephone, while, without the balancing cell, there is usually always a feeble buzz.

Apparatus.-Telephone, G,, for use as a galvanometer; two non-inductive resistances, 71, 72, of about 1000 or 2000 ohms each; one higher adjustable resistance, R; small induction coil, B, giving, say, in. spark for producing the alternating current, and a small battery, b, to excite it; electrolytic cell, Ce, of such a size as to give not more than about 1000 ohms resistance with the solution used; key, K; delicate thermometer graduated in 1; delicate hydrometer or chemical balance.

N.B.-If an ordinary metre bridge is used, 71, 72 will form the stretched wire, but it is not suitable to use with the balancing cell. In such cases one similar to Fig. 169 should be used. If possible, the source of alternating current B should be removed to a distance from the operator, so that the noise of the “contact breaker" may not interfere with the hearing at the telephone. It will, for

this reason and that of obtaining greater sensitiveness, be an additional help if two telephones are used in parallel, one to each ear. Vide precautions (p. 130) to be adopted.

Observations.-(1) Connect up as in Fig. 61, or, if the special bridge (p. 345) is used, then connect as there described. If the present arrangement is used,

make 1 = 1⁄2, and adjust R so that

no sound or minimum sound is heard
in G1, and note the values of R and H
temperature and of r1, " for reference
only.

B

K

FIG. 61.

N.B.-The test will be most sensitive when r, and 1⁄2 are only a little greater than the value of R required to balance, for then the arms of the bridge will be more nearly equal in resistance. Balance should then be disturbed by altering R, and re-obtained thus two or three times, and the mean value of R noted, which will thus be more accurately equal to the difference in the resistance of C and c.

(2) Repeat (1) for four or five different temperatures of the bath or solution.

(3) Repeat (1) for four or five different densities of the same solution at as nearly as possible the same temperature, and tabulate your results in exactly the same manner as in the last test.

(4) Plot two curves, one having temperatures of the electrolyte as ordinates and corresponding resistances (at constant density) as abscissæ, the other with densities as ordinates and resistances (at constant temperature) as abscissæ.

Inferences.-State clearly all the inferences deducible from your experimental results.

77. Resistance of Electrolytes
(Secohmmeter Method).

Introduction. This method may conveniently be used when an Ayrton and Perry secohmmeter is available, but not an induction coil. It differs slightly from either of the preceding

K

methods, owing to the employment of an alternating current in the arms of the bridge, produced by the secohmmeter interchanging the battery terminals while an ordinary aperiodic sensitive galvanometer is at the same time used, thus combining the advantages of the direct and alternating current methods. The precise action of the secohmmeter will be at once seen by reference to pp. 259 to 262. In the present case the commutators may be set in the midway positions, so that the galvanometer connections are reversed midway between two consecutive battery reversals. The higher the speed, the greater the sensitiveness.

Apparatus. Secohmmeter complete, with means for driving it (Fig. 119, p. 261); battery, B, capable of giving 30-40 volts P.D.; sensitive aperiodic reflecting galvanometer, G; electrolytic cell (preferably the form shown on p. 343); known resistances, R, r1, 2; delicate thermometer and hydrometer or chemical weighing balance, for making up the test solution.

Observations.-(1) Referring to Fig. 61 for Kohlrausch's method, dispensing with B, K, and Gr, connect points A and D to the terminals marked "bridge" on the same side of the secohmmeter as those marked "galvanometer," and the points H and F to the remaining pair marked "bridge;" also join B and G to terminals marked "battery" and "galvanometer" respectively. Adjust the galvanometer to zero (about).

(2) Repeat precisely the observations in their order, as set forth in the Kohlrausch method, and answer the inferences there mentioned.

GENERAL PRECAUTIONS TO BE USED IN THE PRECEDING METHODS.

If a metre bridge be used, the arms of the bridge should be made more equal by adding extra resistances at the ends of the stretched wire.

In all cases the utmost care should be taken in thoroughly cleaning the electrolytic cells, finally using distilled water, as mere traces of foreign substances sometimes serve to completely alter the resistance of the liquid tested.

The solutions for test must be made up with great care if the experimental results are to be compared with standard ones (vide p. 365).

78. The Ballistic Galvanometer.

In experiments on induction currents and capacity, "transient " or very short duration currents have to be measured. The ballistic galvanometer is a form of instrument specially adapted for the measurement of such, and its action depends upon the principle that, when the duration of the current is very short compared with the time of oscillation of its moving system (whether coil or magnetic needle), the total quantity Q of electricity transmitted by that current may be deduced from the first swing or "throw" of the needle, due to the magnetic impulse of the momentary current. The term "ballistic" is applied to such an instrument from its analogy to a ballistic pendulum, in that its moving system possesses a large moment of inertia. In fact, on this depends the whole principle of the galvanometer, namely, that the moment of inertia is so large that the whole quantity of electricity in the transient current has passed through the coils of the galvanometer before the needle begins to move. If a current A flows for a short interval of time dt, the latter quantity Q of electricity which passes is Q = fAdt taken between the correct limits, where A is variable as in an induced current.

This time-integral of the current has therefore to be measured by a ballistic galvanometer. Two or three forms of this type of instrument are described on pp. 283, 285, from which we see that its moving system

may be either a needle or coil.

X;

Hm

A

But, in

Hm

B

Let Fig. 62 represent an exaggerated plan of the galvanometer needle AB when freely suspended, and at rest in the magnetic meridian XY; let the strength of each of its poles be m, and their distance apart 27, and 0° AOA', where A'B' is the instantaneous position of rest when

FIG. 62.

=

angle

defected. Draw AC and BD perpendicular to AB. Then, if O is the centre of rotation, and H = the horizontal intensity of the earth's force, the force acting on each end of the needle tending to bring it back to the position AOВ = Hm. But Hm has acted through a distance AC one end, and BD the other,

.. the total work done against H = H»(AC + DB)
But AC = DB = OA − OC = 1 − 1 cos 6

= / 1 - cos 6)

..total work done = Hm(AC + DB) = Hm2l(1 — cos 6o) = HM(1 − cos 6)

where M = 2lm, the magnetic moment of the needle.

Again, if any body or mass is rotating round a fixed axis, the sum of all the products obtained by multiplying the mass of each particle m in the body by the square of its radius from that axis, is termed the moment of inertia I about the axis, or I = Σmr2.

=

If, now, G the galvanometer constant, which depends on the form of its coils, etc., then the moment of the force on the needle produced by the current A is = MGA; and if the current flows for a short time dt,

then moment of force = MGAdt = MGdq

where dq= the small quantity which flows in the time dt;

hence the total impulse on the needle = MGQ

=

where Q the whole quantity that passed in the discharge.

But this impulse is equal to the moment of momentum Iw of the needle, where = the angular velocity of needle;

Now, the kinetic energy of the needle at starting = this must equal the

total work done, namely, HM(1

We therefore see that, on the assumption that the discharge