It also showed that the comparative affinity of nitric acid has hitherto been placed somewhat too high. Taking hydrochloric acid as 100, nitric acid scarcely exceeds 75.

The weaker acids, being for the most part without action on the test solution, give satisfactory results. Oxalic and tartaric acids must, however, be excepted, the acid set free tends to form acid salts of sparing solubility, these are precipitated: thus the conditions are changed.

The results obtained are here tabulated :

The first column of this table shows the absolute number of molecules of the sodium salt which must be added without regard to the basicity of its acid, in order that one molecule of sulphuric acid may be so completely saturated with base as no longer to give a reaction for free sulphuric acid.

In the second column these numbers are modified in such manner as to cause them to justly represent the comparative affinity of the acid. With monobasic acids the number of molecules is divided by 2, with quadribasic acids it is multiplied by 2. For a tribasic acid it is multiplied by 3. Bibasic acids only remain unchanged. Next, unity is subtracted because it is always the excess of the salt which must be present in order to keep the sulphuric acid saturated with base that gives the measure of the affinity of the acid. Were this correction not applied, the entire result would be vitiated.

The third column gives the numbers as they appear when hydrochloric acid is taken as 100.

Instead of adding salts of different acids to sulphuric acid, we may add various acids to a salt formed by the union of sulphuric acid to a strong base, for example, to sodium sulphate.

Sulphuric acid is now recognized as being a weaker acid than hydrochloric, and yet we have seen that it is able to detach a certain quantity of base from a chloride. Further,

that if the chloride is present in sufficient excess, the sulphuric acid may take up enough base to completely saturate itself. The general fact that a certain quantity of acid may be expelled from a salt by another acid, even much weaker than the first, has been shown by the researches of Thomsen and of Ostwald. So that if, for example, we add acetic acid to a solution of sodium sulphate, a distinctly recognizable quantity of sulphate is decomposed and converted into acetate. A condition of equilibrium is produced in which the liquid contains both acids in a free state and both salts. In some way that we do not yet understand the presence of the free acid maintains the combined acid in its combination. The sodium acetate exists only by virtue of the free acetic acid present.

The existence of this state of equilibrium was first proved by Thomsen, who deduced it from the thermochemical changes which took place on mixing the solutions. Ostwald reached similar conclusions by making accurate determinations of the changes of volume and, consequently, of specific gravity which resulted from the mixing of the solutions, and in other ways.

In both these cases the conclusions are reached by logical deductions from the phenomena observed. But with the aid of the herapathite test, the expulsion of sulphuric acid by a very much weaker acid can be rendered immediately evident to the eye. Thus if to the solution of sodium sulphate we add acetic acid, and place two or three drops of the mixture in a warm porcelain basin and add some of the test liquid to it, in a few minutes we have a great number of small black rosettes of herapathite which crystallize out. Solution of sodium sulphate not containing acetic acid gives no such reaction with the herapathite test. It dries up to a pale yellow residue.

Acids vary very much in their ability to detach sulphuric acid from soda. The following acids, when added to sodium sulphate and tested by the herapathite test, give the results here noted.

Malic acid, gives an abundant crystallization.
Succinic acid, acts similarly.

Lactic acid, a moderate reaction.

Mucic acid, about the same as lactic.

Vanadic acid, traces.

Arsenic acid, abundant crystallization.

Hippuric acid, distinct traces.

Salicylic acid, distinct crystallization.

Of course the stronger organic acids, tartaric, oxalic, and citric, separate sulphuric acid with abundant crystallizations of herapathite when they are made to act on sodium sulphate

and the test is applied. It was observed that an acid oxalate acts like a free acid. Thus, when a solution of potassium binoxalate or quadroxalate is added to one of sodium sulphate, sulphuric acid is detached precisely as if free oxalic acid had been used.

It is clear that extremely weak acids, such as hippuric and salicylic, are able to take a certain quantity of base even from so strong an acid as sulphuric, setting free a recognizable quantity of this latter acid. Carbonic acid is still weaker than these. Ostwald, in determining the relative affinities of acids by the rate of the decomposition of acetamide and by the inversion of cane-sugar, found no appreciable effect from carbonic acid. It therefore became of interest to ascertain if any sensible decomposition of sodium sulphate would result from the action of this acid.

Perfectly pure carbonic anhydride was passed for a long time through a solution of sodium sulphate without setting free a recognizable trace of sulphuric acid. This was expected, the experiment was only preliminary to its repetition under

pressure.

For this purpose sodium sulphate with the test solution was placed in one leg of a bent tube, in the other leg was placed sodium bicarbonate; and the tube was sealed. Heat was gradually applied to the bicarbonate. In the second trial the pressure was raised so high that the stout glass tube was ultimately shattered with violence. The leg containing the test liquid and sulphate had been secured in a clamp and remained uninjured. The liquid therefore had been subjected to the action of carbonic anhydride at a high pressure-it, however, gave no indications of a separation of traces of sulphuric acid under its action. It is to be remarked that this test is more decisive than if a solution of sodium sulphate had been used and had been tested afterwards. For in this last case, on release of the pressure, the reaction might readily be reversed with recombination of sulphuric acid, had any been liberated. But with the test liquid present during the pressure this reversal could not take place.

Carbonic anhydride, therefore, does not even under pressure set free any portion of sulphuric acid from sodic sulphate.

The reactions described in this paper indicate :

1. That when to free sulphuric acid a salt is added in sufficient quantity to cause the whole of the sulphuric acid to saturate itself with the salt-base, it is possible by means of the herapathite test to determine the exact point of such

saturation. At this point there will necessarily be as much of the acid at first combined with the base, now free in the solution, as corresponds to one molecule of a bibasic acid, that is two of a monobasic acid, half a molecule of a quadribasic acid, &c. From this we can deduce the exact nature of the resulting equilibrium.

2. That a series of equilibria thus obtained with different salts enables us to determine the comparative strength of the affinities of the acids of those salts.

3. That the fact, already proved in other ways, that even small quantities of weak acids, added to sulphates, will set free a certain quantity of sulphuric acid can, by means here given, be for the first time rendered visible to the eye by a well-marked chemical reaction.

LVI. On the Design and Winding of Alternate-Current Electromagnets. By SILVANUS P. THOMPSON, D.Sc.,

1.

F.R.S., and MILES WALKER*.

IN

N designing electromagnets for use with alternate currents various considerations enter which do not enter into the design of electromagnets for use with continuous currents. Chief of these considerations are the self-inductive action of the windings, and the frequency of the alternation of the current.

As with continuous-current electromagnets, so with alternate-current magnets, the degree to which magnetization is carried in the magnetic circuit of given configuration depends upon the number of ampere-turns of the excitation. The methods of predetermining the number needed to produce any desired degree of magnetization are too well known to need any reference. Our present aim is to show how to determine the winding which will, under given circumstances as to frequency, voltage, &c., produce any desired number of ampere-turns.

2. As a preliminary, however, it is needful to touch upon the point whether an electromagnet (properly laminated, it is understood) will give an equal pull, when excited with an equal number of ampere-turns of alternating current.

Since the pull of an electromagnet upon its armature depends upon the normal tension along the magnetic field integrated over the area of the pole-face, and this tension

* Communicated by the Physical Society: read April 27, 1894.

is proportional to the square of the intensity of the magnetic flux, then, if this flux were proportional to the number of ampere-turns of excitation (as would be the case if the permeability were constant), the pull would be proportional to the square of the number of ampere-turns. Now the amperemeters for alternate currents operate upon principles that cause them to indicate the square root of the mean square values of the current. Hence it follows that, if permeability were constant, the pull should be proportional to the square of the current, whether the current be continuous or alternating. But since, with an alternating current of the same nominal value as a continuous current, the magnetism is carried at each period to a point considerably higher than with the continuous current, and since also at the higher degrees of magnetization the permeability is lower, it follows that the pull of the electromagnet when excited by alternate currents ought to be slightly less if the excitation is so great as to carry the magnetization into the regions commonly spoken of as approaching saturation. The pull ought to be independent of the frequency of the alternation provided this exceeds a certain minimum.

Experiments made show that these views are justified in practice.

An electromagnet of the form shown in fig. 1 was made up of iron stampings about 0.5 millim. thick.

The principal dimensions were as follows :—

Mean length of limbs and yoke. 38
Breadth of limb

Gross thickness of limb

Fig. 1.

cms.

3.1 cms.

2.54 cms.

The stampings of the armature were of the same thickness, number, and breadth as those of the electromagnet. In the succeeding experiments the electromagnet was wound with 163 turns of copper wire 2.03 millim. in diameter, and the armature was separated from the pole-faces by a distancepiece of wood 0·952 centim. thick.