perhaps a sense of the fitness of things indicates, that for any given year the claim and debt will cancel each other, and leave every year's possession to pay the whole year's tax on the estate possessed.

Difference between incomes from terminable tenures and those from terminable things.-That a terminable income by paying at the same annual rate as a perpetual income is equally paying according to its capital-value, is a proposition insisted on by Mr. Warburton and by Mr. Mill in the two Commissions on the Income-tax; and as far as the above class of terminable income is concerned, the proposition is true. But these gentlemen unfortunately carried it into a region where it had no status, and in virtue of it denied the applicability of capital-value, if not of arithmetical proportion generally, as a reforming measure of the income-tax. As there are incomes and incomes, so there are terminable incomes and terminable incomes. If the terminable income be the terminable tenure of a pure interest-value, such, practically speaking, as a life-interest in land or in consols, to tax it at the same rate as a permanent income is to tax each according to its capital-value. If, however, the terminable income be an income that is made up partly of interest-value and partly of capital that terminates, not simply as a legal right, but by gradually exhausting its source, then to charge such income at the same annual rate as a permanent one of similar amount is not to tax it according to its capital-value-a truth repeatedly demonstrated by the actuaries before Mr. Hume's committee, and evident from the reflection that the capital-value of the source is, by the very nature of the income, continually passing away, whilst the tax remains the same.. Under the conditions stated, the tax on the one terminable income would be a tax on pure interest-value, the tax on the other would be a tax on a mixture of interestvalue plus capital. By combining the propositions of the actuaries and of Mr. Warburton, each true in its own sphere, but each erroneous when applied to the other, we may conclude that the results obtained from the capitalization of tenures are identical with those obtained from the absolute valuation of sources; and both may be quoted in confirmation of those obtained from the principle of interest-value.

Capital-value in relation to personal riches and property. Common measure of value as needful for equal exemption as for equal taxation.—Another application of capital-value as a measure, however, cannot be so quoted. The taxation of a particular property according to capital-value may be interpreted as taxation, not according to the worth of that particular property, but according to the absolute worth or financial position of the person who owns it; and such a method of levy has been erroneously defended as taxation according to ability. In this view a rich man ought (considerations of practicability apart) to pay a heavier duty upon his dog, his bottle of wine or whiskey, than a poor man; and, the estates being equal, the owner of a permanent tenure would pay more for each year's possession than would the owner of a limited one. Such a theory of capital-value may not be general, but it has a certain degree of popularity, and seems to be constantly getting itself mixed up not only with discussions but even with legislation on the incidence of the income-tax. It may be questioned whether the operation of this theory is not visible, for example, in the exemption from imperial direct taxation (recently so largely extended) of large masses of property in the country including many thousands of acres of land, in consequence of the accident of their ownership. Property thus exempted becomes property taxable by mere change of possession, irrespective of the intrinsic nature or value of the property itself. To exempt in an income-tax the necessary

outgoings of the source of income, be it labour or land, is merely to confine the tax to its own stated objects, viz. to income proper; but to exempt or lower the rate on this income proper, merely in consideration of the personal status of its owner, is to travel into quite a different region-it may be into the region of national charity, or into that of some other principle, but assuredly far away from that of equality in taxation. It may be added that such exemptions, even when admitted, need a common measure of value for their rational application. There are small incomes and small incomes-. incomes that are pure interest-values, incomes that are pure drafts on capital, and incomes that are mixtures of interest-value and draft on capital; and the equal exemption of these kinds, as in the present income-tax, is as unequal as would be their equal taxation. As before said, the interest-value measure itself would exempt all small labour-incomes to the extent of their necessities without further special rule.

BEARINGS OF COMMON MEASURE Of Value on GenERAL TAXATION AND

NATIONAL INCOME.

11. Common measure of value necessary to the adjustment of general taxation: fallacies from its absence." Your Committee also feel that it would be unjust to make any alteration in the present incidence of the income-tax, without at the same time taking into consideration the pressure of other taxation upon the various interests of the country, some of it imposed by recent legislation, and in one case especially, that of the succession duty, to some extent by way of compensation." This, written in 1861, is the last sentence of the Report of the Select Committee appointed in that year on the equalization of the Income-tax; and perhaps no paragraph could be quoted as a stronger argument for the necessity of determining a common measure of value. It may, indeed, be thought by some that for the purpose of internally equalizing a tax over its own area, be that area sugar, coffee, or incomes, a preliminary inquiry into the pressure of taxation in general is somewhat of a work of supererogation; and it may not be mathematically obvious to others what possible sort of compensation can exist between the inequalities of a tax, or a set of taxes, that are almost stationary, and those of one that changes with every national emergency-that in twenty years has actually compassed the extremes of sixteenpence and twopence in the pound, with every variety of intermediate oscillation. But assuming it to be advisable for the purpose in question, as it must doubtless be always generally useful, to know the comparative pressure of taxation as a whole upon the interests of the country, it is clear that such a knowledge implies their valuation through a common measure, and is, indeed, as impossible without it as would be the knowledge of the weights of different things without weighing them by a true balance. Eminent statists have, indeed, attacked this problem, using income itself as the means of the comparison, though oftentimes without a sufficient preliminary examination of the accuracy of their instrument. Comparing the statistics of different classes of income, as collected from the government returns and from inquiries specially made, with the statistics of the corresponding classes of taxation, they have sometimes concluded that general taxation is, as a whole, tolerably equal. The truth of this conclusion evidently depends upon the uniformity of the standard employed. As, however, this uniformity has no existence (the government returns alone presenting at least five or six different modes of estimate), the argument can prove nothing as regards general equality, except its absence; but does prove that taxation

in general, regarded as a larger income-tax, is equally in want of a common measure with the income-tax proper. So far from the measurement of the income-tax proper being dependent on the measurement of general taxation, the measure that underlies them both is one and the same; and, indeed, the true view of an income-tax is that it should be a perfectly just and equal tax in itself, rather than an imperfect tax compensating the imperfections of other taxes.

Common measure of value necessary for finding national income and wealth: fallacies from its absence. The evil consequences of a want of a common measure of value, seen in the comparison of incomes for purposes of taxation, is also seen when they are added together for the exhibition of the amount of national income and wealth. To find this national income, the government returns of the income-tax have been taken, and to this miscellaneous aggregate the exempted incomes of the country, including manual-labour wages, have been added, as if all were of one equal and uniform denomination. Much of such income, however, as has been repeatedly pointed out, is only the consumption of capital. Within the period of a generation, say thirty years, all the value of human labour, plus the cost of maintaining it, passes into the category of labour-income. Within longer but varying periods the value of all houses, plus the cost of repairing them, passes into the category of house-income. Within still more varying periods all the mining wealth of the country must pass into the category of mining-income and disappear; and all capital of terminable annuities passes into terminable income. By some writers this medley of so-called income (but no more income than the payments for exports are income, or drafts on bankers are income) has ever been capitalized at one (and that an extreme) rate, to get the national wealth, the result of the whole process being an exaggerated and practically mischievous estimate of national income, of national wealth, and of the nation's capacity to bear taxation. Probably no better example than this could be given of the necessity of a common measure of value. Common measures (common units) are the souls of statistics, as, indeed, they are of knowledge generally. Without them statistics are a mere incoherent mass of facts, usurping the semblance and function of exact science. A common measure of income, discovering the amount of the element common to rent, wages, profits, and interest, determines the true increment of wealth considered in its widest sense, and expresses both the extent and the ratio of economic progress. This common measure may be briefly described as interest-value : it is an essential, if not the fundamental, basis of taxation.

Report of the Committee, consisting of Professor CLERK MAXWELL, Professor J. D. EVERETT, and Dr. A. SCHUSTER, for testing experimentally Ohm's Law.

THE statement of Ohm's law is that, for a conductor in a given state, the electromotive force is proportional to the current produced.

The quotient of the numerical value of the electromotive force divided by the numerical value of the current is defined as the resistance of the conductor; and Ohm's law asserts that the resistance, as thus defined, does not vary with the strength of the current.

The difficulty of testing this law arises from the fact that the current generates heat and alters the temperature of the conductor, so that it is extremely difficult to ensure that the conductor is at the same temperature when currents of different strengths are passed through it.

Since the resistance of a conductor is the same in whichever direction the current passes through it, the resistance, if it is not constant, must depend upon even powers of the intensity of the current through each element of the conductor. Hence if we can cause a current to pass in succession through two conductors of different sections, the deviations from Ohm's law will be greater in the conductor of smaller section; and if the resistances of the conductors are equal for small currents, they will be no longer equal for large currents.

The first method which occurred to the Committee was to prepare a set of five resistance-coils of such a kind that their resistance could be very accurately measured. Mr. Hockin, who has had great experience in measuring resistance, suggested 30 ohms as a convenient magnitude of the resistance to be measured. The five coils and two others to complete the bridge were therefore constructed, each of 30 ohms, by Messrs. Warden, Muirhead, and Clark, and it was found that a difference of one in four millions in the ratio of the resistance of two such coils could be detected.

According to Ohm's law, the resistance of a system consisting of four equal resistance-coils joined in two series of two should be equal to that of any one of the coils. The current in the single coil is, however, of double the intensity of that in any one of the four coils. Hence if Ohm's law is not true, and if the five coils when compared in pairs with the same current are found to have equal resistances, the resistance of the four coils combined would no longer be equal to that of a single coil.

A system of mercury-cups was arranged so that when the system of five coils was placed with its electrodes in the cups, any one of the coils might be compared with the other four combined two and two. After this comparison had been made, the system of five coils was moved forward a fifth of a revolution, so as to compare the second coil with a combination of the other four, and so on.

The experiments were conducted in the Cavendish Laboratory by Mr. G. Chrystal, B.A., Fellow of Corpus Christi College, who has prepared a report on the experiments and their results.

A very small apparent deviation from Ohm's law was observed; but as this result was not confirmed by the much more searching method of experiment afterwards adopted, it must be regarded as the result of some irregularity in the conducting-power of the connexions.

The defect of this method of experiment is that it is impossible to pass a current of great intensity through a conductor without heating it so rapidly that there is no time to make an observation before its resistance has been considerably increased by the rise of temperature.

A second method was therefore adopted, in which the resistances were compared by means of strong and weak currents, which were passed alternately through the wires many times in a second. The resistances to be compared were those of a very fine and short wire enclosed in a glass tube, and a long thick wire of nearly the same resistance. When the same current was passed through both wires, its intensity was many times greater in the thin wire than in the thick wire, so that the deviation, if any, from Ohm's law would be much greater in the thin wire than in the thick one.

Hence, if these two wires are combined with two equal large resistances in

Wheatstone's bridge, the condition of equilibrium for the galvanometer will be different for weak currents and for strong ones. But since a strong current heats the fine wire much more than the thick wire, the law of Ohm could not be tested by any ordinary observation, first with a weak current and then with a strong one, for before the galvanometer could give an indication the thin wire would be heated to an unknown extent.

In the experiment, therefore, the weak and the strong current were made to alternate 30 and sometimes 60 times in a second, so that the temperature of the wire could not sensibly alter during the interval between one current and the next.

If the galvanometer was observed to be in equilibrium, then, if Ohm's law is true, this must be because no current passes through the galvanometer, derived either from the strong current or the weak one. But if Ohm's law is not true, the apparent equilibrium of the galvanometer-needle must arise from a succession of alternate currents through its coil, these being in one direction when the strong current is flowing, and in the opposite direction when the weak current is flowing.

To ascertain whether this is the case, we have only to reverse the direction of the weak current. This will cause the alternate currents through the galvanometer-coil to flow both in the same direction, and the galvanometer will be deflected if Ohm's law is not true.

Mr. Chrystal has drawn up a report of this second experiment, giving an account of the mode in which the various difficulties were surmounted. Currents were employed which were sometimes so powerful as to heat the fine wire to redness; but though the difficulty of obtaining a steady action of the apparatus was much greater with these intense currents, no evidence of a deviation from Ohm's law was obtained; for in every experiment in which the action was steady, the reversal of the weaker current gave no result.

The methods of estimating the absolute values of the currents are described in the Report.

A third form of experiment, in which an induction-coil was employed, is also described; but though this experiment led to some very interesting results, the second experiment gives the most searching test of the accuracy of Ohm's law. Mr. Chrystal has put his result in the following form.

If a conductor of iron, platinum, or German silver of one square centimetre in section has a resistance of one ohm for infinitely small currents, its resistance when acted on by an electromotive force of one volt (provided its temperature is kept the same) is not altered by so much as 12 part.

1 1012

It is seldom, if ever, that so searching a test has been applied to a law which was originally established by experiment, and which must still be considered a purely empirical law, as it has not hitherto been deduced from the fundamental principles of dynamics. But the mode in which it has borne this test not only warrants our entire reliance on its accuracy within the limit of ordinary experimental work, but encourages us to believe that the simplicity · of an empirical law may be an argument for its exactness, even when we are not able to show that the law is a consequence of elementary dynamical principles.

First Experiment. Christmas 1875. By G. CHRYSTAL, Cavendish Laboratory, Cambridge. Communicated by J. CLERK MAXWELL.

If the electromotive force between two points of a uniform linear conductor measured in appropriate units by means of an electrometer be E, and