1

=

voltages corresponding to the mean square values V, V1 and V2 respectively at any instant (t), then v=v1+v2; also if (a) instantaneous current in amps. flowing through PR at this same instant t, we have the instantaneous value of the power in Watts (w) given to PR at that instant as w = va ;

Efficiency of Transformers. (Blakesley's Three Dynamometer Method.)

Solution of Inferences.-Referring to p. 263, on which will be found a formula derived by Mr. Blakesley for expressing the power given to the primary of a transformer in his method of measuring the efficiency of such an appliance, Professor Ayrton and Mr. Taylor have deduced the following general proof of this relation, which makes no assumption whatever as to the nature of the current, whether sinusoidal or otherwise, but only that there is no magnetic leakage between primary and secondary windings. This is approximately true for "closed circuit" though not for " 'open circuit" transformers, so that the method cannot be considered a very good one.

Let a1 a instantaneous values of the currents and V1 V2 those of the E.M.F.'s in the primary and secondary windings having N1N, turns respectively, and B = the mean density of lines in the core, then if R1R2 = ohmic resistances of the primary and secondary

2

we have

2

But

Ra, since we assume no leakage,

N1

Na

Integrating this last equation between the limits of the period

N2 2

N1 R1

Hence if A is the split dynamometer reading we finally have

APPARATUS

Preparation of the Clark Standard Cell.

Definition of the Cell. The cell consists of zinc and mercury in a saturated solution of zinc sulphate and mercurous sulphate in water, prepared with mercurous sulphate in excess, and is conveniently contained in a cylindrical glass vessel.

Preparation of Materials.-The Mercury.-To secure purity it should be first treated with acid in the usual way, and subsequently distilled in vacuum.

The Zinc.-Take a portion of a rod of pure zinc, and solder to one end a piece of copper wire. Clean the whole with glass paper, carefully removing any loose pieces of zinc. Just before making up the cell, dip the zinc into dilute sulphuric acid, wash with distilled water, and dry with a clean cloth or filter paper.

The Zinc Sulphate Solution.-Prepare a saturated solution of pure (re-crystallized) zinc sulphate by mixing in a flask distilled water with nearly twice its weight of crystals of pure zinc sulphate, and adding a little zinc carbonate, in the proportion of about 2 per cent. by weight of zinc sulphate crystals, to neutralize any free acid. The whole of the crystals should be dissolved with the aid of gentle heat, i. e. not greater than 30° C., and the solution filtered while still warm into a stock bottle. Crystals should form as it cools.

The Mercurous Sulphate.-Take mercurous sulphate sold as pure, which is white, and wash it thoroughly with cold distilled water by agitation in a flask; drain off the water, and repeat the process at least twice, but after the last washing, drain off as much

water as possible. Mix the washed sulphate, in the proportion of about 12 per cent. by weight of ZnSO4, crystals, with the zinc sulphate solution, adding sufficient crystals of zinc sulphate from the stock bottle to ensure saturation, and a small quantity of pure mercury. Shake them well up together to form a paste of the consistency of cream. Heat the paste sufficiently to dissolve the crystals, but not above 30° C. Keep the paste for one hour at this temperature, agitating it from time to time, and then allow it to cool.

Crystals of zinc sulphate should then be distinctly visible throughout the mass. If this is not the case, add more crystals from the stock bottle, and repeat the process. This method

ensures the formation of a saturated solution of zinc and mercu

rous sulphates in water. The presence of the free mercury throughout the paste preserves the basicity of the salt, and is of the utmost importance. Contact is made with the mercury by means of a platinum wire about No. 22 B.W.G., which is prevented from making contact with the other materials of the cell by being sealed into a glass tube, the ends of the wire projecting beyond those of the tube. One end forms the terminal; the other end, and part of the glass tube, dip into the mercury.

To set up the Cell.-The cell may be conveniently set up in a small test tube of about 2 cms. in diameter and 6 or 7 cms. deep.

Place the mercury in the bottom of this tube, filling it to a depth of, say, 1·5 cms.

Cut a cork about 0.5 cm. thick to fit the tube. At one side of the cork bore a hole through which the zinc rod can pass tightly; at the other side bore another hole for the glass tube which covers the platinum. At the edge of the cork cut a nick through which the air can pass when the cork is pushed into the tube.

Pass the zinc rod about 1 cm. through the cork. Carefully clean the glass tube and platinum wire, then heat the exposed end of the wire red hot, and insert it in the mercury in the test tube, taking care that the whole of the exposed platinum is covered.

Shake up the paste, and introduce it without contact with the upper part of the sides of the test tube, filling the tube above the mercury to a depth of rather more than 2 cms.

Y

Now insert the cork and zinc rod, allowing the glass tube to pass through the hole in the cork made for it.

Push the cork gently down until its lower surface is nearly in contact with the liquid. The air will thus be nearly all expelled, and the cell should be left in this condition for at least twenty-four hours before sealing, which should be done in the following way

Melt some marine glue until it is fluid enough to pour by its own weight into the test tube above the cork, using enough to cover completely the zinc and soldering. The glass tube should project above the top of the marine glue.

The cell thus set up may be mounted in any desirable way; do it so that the cell is immersed in a water-bath up to the level, say, of the upper surface of the cork. Its temperature can then be determined more accurately than is possible when the cell is in air.

Instruments for Standard Measurements of the Highest Accuracy.

The potentiometer in general must rank as one of the first of this kind, not solely from the point of view of accuracy, but also because of the ease and rapidity with which the measurements possible with it can be taken. The principle underlying its use is contained in the Clark-Poggendorff method of comparing E.M.F.s, and an elementary application of this principle in Poggendorff's method of calibrating a voltmeter, a detailed description of which will be found in the author's work entitled Practical Electrical Testing for first and second year students. It may, however, here be remarked that when using the potentiometer for measuring current, resistance, and high voltages, the principle, as is well known, consists in reducing any of the three electrical quantities which are to be measured, to the form of electrical pressure, or E.M.F., so that it can be compared by means of a potentiometer with a standard pressure such as that of the Clark cell.