=

(d) The Work of Dynamo Machines.

From Joule's law the work consumed by the machine per second is A c I2 R = cIE, where c = 0.00181 according to Kohlrausch, if the work is expressed in horse-power, the E.M.F. in Daniell's, the resistance in Siemens' Dan. units, and the current in S.U. Foucault's currents induced in the iron core, the formula becomes

units. If account is taken of the so-called

A = cIE + p E2,

and the experiments show that p

=

0-0009, and that for c should be substituted a constant c1 0-00163. The following table contains the results of the experiments. The horse-power required to rotate the machine empty is

deducted:

=

11. THE ELECTRICAL TRANSMISSION OF POWER.

If it is assumed that the brushes in the two machines, the generator and the motor, are in the same positions, since the same current exists in both, the effective magnetism must be equally strong in both. With this proviso the following formulæ are obtained (E, c and R have their usual meaning, M is the effective magnetism, v the number of revolutions per minute, n the convolutions on the armature, A the work, S the heat produced by the current, N the useful effect, 1 refers to the generator, 2 to the motor) :

The formulæ do not always agree with the experiments. This is especially the case with the useful effect. From the formulæ this should have a value as high as 90 per cent., for N depends only on the ratio of the two velocities, and the velocity of the motor can increase until it reaches the difference between the velocity of the generator and the velocity for which a current is first produced. In practice, the useful effect reaches 40 to 60 per cent. Further, the work A, comes out smaller, and the E2 greater than according to theory, and the more so the smaller the work Ag is. The explanation of this decrease is to be found in the socalled Foucault's currents, which are induced in the iron core of the armature. The chief cause of these currents lies in the action of the electro-magnets on the rotating core of the armature. In the generator these induced currents are in the same direction as the currents in the wires of the armature; they weaken the effective magnetism and the E.M.F., and increase the work expended A1. In the motor the converse is the case. If c1, c2 represent the Foucault currents, u the resistance in their circuit, M1, M2 the effective magnetism, as a first approximation we obtain

M is here the effective magnetism which would obtain, if the Foucault currents did not exist, and e is a constant. Putting

E2

S = c I (E1 — E2 ), F1 = p E, F2 = p E A1 = A2 + S+F1 + F2

(12)

By introducing the values for I W1 1 1⁄2 these formulæ become

From the formulæ (12) the work can be calculated from E1, E2, and I1, whatever may be the position of the brushes; but in using formulæ (13) to deduce the work from the current, resistance and number of revolutions, the brushes must be in the same position on both machines. A full series of experiments was made, the work being measured by a dynamometer, the current by a Siemens' electro-dynamometer, and the difference of potential between the two poles of the machines by a torsion galvanometer: all the measurements were taken simultaneously by six persons, and it was found that the theoretical and the experimental values coincide very nearly. A few examples are appended.

C. R. ALDER WRIGHT-ON THE DETERMINATION OF CHEMICAL AFFINITY IN TERMS OF ELECTRO-MOTIVE FORCE.

(Parts III. and IV. Phil. Mag., Vol. II., No. 67, March, pp. 169-196; No. 68, April, pp. 261-283, and No. 69, May, pp. 348-369.)

The author first discusses the most recent valuations of the B.A. unit of resistance, and of the mechanical equivalent of heat, and finally concludes that at present the chances of the B.A. standard ohm being below the true theoretical value, 109 C.G.S. units, are about equal to the chances that it is above that value; so that it is assumed by him that the B.A. standard ohm really possesses its nominal value, and consequently that the E.M.F. of Clark's cell is 1.457 volts, as determined by Clark. The same kind of reasoning, however, indicates that Joule's water friction values of the mechanical equivalent of heat

are somewhat too low; the value 42 × 106 represents pretty nearly the most probable value of J, so that the factor for reducing gramme degrees to E.M.F. units (when affinity is calculated from the one form of measurement to the other) is 4,410-0—e.g., the energy measured as heat by 10,000 gramme degrees, is measured by 0-441 × 108 E.M.F. units 0-441 volts. Clark's cells are found to remain permanent for some few months, especially when put up in hermetically sealed glass vessels rendered vacuous by a Sprengel pump instead of the ordinary paraffin wax-sealed vessels.

The existing state of knowledge is partly discussed as regards the values of the counter E.M.F. set up during electrolysis, of the "subsequent polarisation ' (E.M.F. between the electrodes after rupture of the current), and of the E.M.F. of gas batteries; and it is shown that the fluctuations in these values introduced by varying the conditions, and various other facts, as also the results of a number of new determinations described at length, are all in accordance with the following general theory. Let it be granted that the first effect of electrolysis is to break up the electrolyte, not into the products finally formed, but into primary "nascent" products, the conversion of which into the ultimate products would be accompanied by heat evolution; then the E.M.F. requisite to break up the electrolyte wholly into nascent products would be a fixed constant amount exceeding that requisite to break it up into the ultimate products. The attractive action of the electrodes, and their chemical action upon the products of electrolysis, however, cause more or less of the "nascent" products to be transformed ab initio into other bodies, the amount of such transformation varying with the rate of current flow and other conditions; so that finally the counter E.M.F. set up, i.e., the amount of work actually done in breaking up the electrolyte at the moment, is variable, being less than the limiting maximum by an amount dependent upon the conditions of the experiment. This theory is expressed by the following formula:

e = E + [(1 − n) H — ≈ (n h) — ≥ (H)] x J,

where e is the counter E.M.F. set up, E the E.M.F. representing the work done in breaking up a gramme equivalent of electrolyte into final products, n the fraction of a gramme equivalent of products evolved otherwise than as nascent products (at either pole, severally), H the heat of transformation of nascent into final product, and h the heat evolved by the condensation of the product upon the electrode surface, Σ (H) being the algebraic sum of the heat evolutions due to chemical actions between the electrodes and the products, diffusion, &c.

From this formula and the results of a large number of experimental determinations, it results that the E.M.F. of any given electro-motor in which a gas is evolved (like Smee's cell), or a metal deposited (as in Daniell's battery), is a function of the current generated, being less the greater the current. A number of experiments in proof of this are detailed, as are also many others leading to the following general results. The passage of a given quantity of electricity through an electrolyte causes the decomposition of one and the same amount of substance irrespective of the time taken in its passage; in other

words, conduction without electrolysis does not take place, and Faraday's law is true for excessively minute currents as well as for those of considerable magnitude. With very feeble currents, however, and with certain electrolytes, e.g., water, the quantity of products of decomposition actually collected after a given time does not absolutely correspond with the quantity of electricity that has passed, even after obvious sources of suppression have been eliminated, especially occlusion in or condensation on the electrodes, solution in the fluid, or suppression by the chemical action of dissolved gases. The cause of this is the "diffusion discharge" produced (in the case of water) by the diffusion towards electrode of water containing dissolved oxygen, and towards the + electrode of fluid containing dissolved hydrogen (and similarly in other cases), thus causing an unavoidable suppression by chemical action. When the amount of suppression due to this cause is determined, and added to the observed amount of decomposition, the total corresponds exactly with the quantity of electricity that has passed.

the

In the electrolysis of acidulated water, until the sources of loss of hydrogen other than "diffusion discharge" are eliminated (viz., solution in the fluid, condensation on and absorption by the electrode, and action of dissolved oxygen originally present in the fluid), the counter E.M.F. set up when a given steady current traverses a given voltameter is short of its maximum value for that current. Simultaneously a deficiency in the amount of hydrogen collected, as compared with that due to the quantity of electricity passing, is noticed (even after correction for diffusion discharge), whilst on breaking circuit the rate of fall of the "subsequent polarisation" of the electrodes is more rapid than its minimum value for that current. On the other hand, as soon as the counter E.M.F. reaches its maximum, the deficiency in hydrogen disappears (after correction for diffusion discharge), and the rate of fall of the polarisation after breaking circuit reaches its minimum. The more nearly completely the sources of loss are eliminated, the more nearly does the counter E.M.F. set up approach its maximum, the less is the deficiency in the hydrogen collected, and the more nearly does the rate in fall of the subsequent polarisation approach its minimum.

In the case of all the electrolytes examined, the value of the counter E.M.F. set up, e, is found to increase as the current increases, but at a less rapid rate, so that the curves traced out by plotting currents as abscissæ and counter E.M.F. values as ordinates are concave downwards.

So long as the rate of flow per unit area of electrode surface remains the same, the value of e is constant-i.e., if the electrode surface and the current vary in the same way, so that the "density of the current" with reference to the electrode surface is constant, then e remains the same. With a given current, increasing the electrode surface diminishes the value of e.

The values of e depend on the material of which the electrodes are made. Other things being equal, carbon gives higher values than platinum, and platinum than gold.

In the case of acidulated water, rendering the solution more dilute increases the value of e; whilst from former observers' work it results that increasing the temperature decreases e.