« EelmineJätka »
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 cqual 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 clectromotive 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, docs 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 temperaturo 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 tho 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 Mossrs. 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 doublo 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 beforo its resistanco 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 wiro 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-needlo 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 tho 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 gal. vanometer-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 tho 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 ou part.
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 conducior measured in appropriate units by means of an electrometer be E, and the quantity of electricity that passes through any section of the conductor in unit time, measured either by a galvanometer or by a voltameter, be C, then, according to Ohm's law *, is directly proportional to the length of the conductor, and inversely proportional to the area of its section.
The coefficient of proportionality for a definite † substance depends merely on the temperature of the substance ; for unit length and unit section of a given substance the value of the ratio for a given temperature is called tho specific resistance of the substance for that temperature, and is one of the most important of its physical constants.
This law has been directly verified by its discoverer, and by Becquerel, Davy, Fechner, Kohlrausch, and others; and indirectly it has been verified for a great variety of substances with a degree of accuracy approached in few physical measurements.
Lately, in discussing some experiments of his own, Dr. Schuster has raised the question whether after all Ohm's law is only an approximation, the limit of whoso accuracy lies within the region of experiment. We might suppose that the ratio of was some function of C?, say
where R is a constant very nearly equal to what has hitherto been called the specific resistance, and S is a small constant which, according to Dr. Schuster's suggestion, would be positive. It is clear that can only be an even function of C, unless we admit unilateral conductivity, for which there is no experimental evidence in a purely metallic circuit.
A Committee of the British Association, appointed to consider the subject, were of opinion that it was of importance to attempt a further experimental verification of Ohm's law.
At the suggestion of Professor Maxwell, the experimental details of two methods of verification proposed by him were undertaken by the writer of this Report. Of the two experiments representing these methods the second is by far the most conclusive. It not only avoids the difficulty of eliminating temperature effects, which to a certain extent interfere with the first experiment, but it pushes the verification of Ohm's law very near the natural limit of all such verifications, viz, the limit of the solid continuity of the conductor. It has thus been rendered probable that experiment cannot detect any deviation from Ohm's law, either in the direction indicated by Dr. Schuster, or in the opposite direction as suggested by Weber, even in wires that have been brought by the electric current to a temperature beyond red heat.
A third experiment was also tried by the writer of this Report ; its result agreed with the others, but, owing to certain peculiarities, it is less conclusive than they are. It led, however, to interesting results of another kind, which
* The current is supposed to be steady.
+ By definite is meant in a given physical condition, except as regards E.M.F. and flow of E, and temperature. The last is excepted because we are brought face to face with possible temperature variations in the first experiment.
We suppose the conductor to be of unit length and unit section. It is of course the specific resistance which is in question; and this, if variable, will depend on the current per unit of section.
scem to show, among other things, that conclusions respecting the accuracy of Ohm's law cannot safely be drawn from experiments of the nature of those made by Dr. Schuster.
FIRST EXPERIMENT. Suppose that we had five resistance-coils, which, when compared with each other by means of the samo current, were equal, say each =R. That is to say, if any two of the resistance-coils were inserted in the branches A B and BD of a Wheatstone's bridge, the other two arms, A C and CD, being two other equal resistances, then the galvanometer G inserted between B and C would indicate no current. Fig. 1.
Supposo now that we replace the coil R in BD by four of the equal coils arranged in multiple arc, as in fig. 2. Thon, if Ohm's law be true (i. e. if resistance be independent of current), if p be the resistance between B and D,
1 1 1 2R T 2R = R'
i.e. p=R, and there will still be no deflection in the galvanometer. But if Ohm's law be not true, and the resistance be a function of the current, then, sinco the current through A B is nearly the same as in the first experiment, while that through BED and BFD is half, the resistances in BE, E D, BF, FD will bo no longer equal to R, but either greater or less, and the galvanometer will be deflected.
Under the direction of Professor Maxwell, part of the funds at the disposal of the Committee were devoted to providing two sets of coils specially adapted for the above experiment. One set consisted of five coils of silkcovered German silver wire (diameter •6 millim.), each of resistance as nearly as possible equal to 30 B.A. units. These were all wound together in tho usual way round one bobbin ; the terminals consisted of ten pieces of stout copper wire, insulated from each other by a ring-shaped piece of ebonito, through which all of them passed. These stout wires were bent over, and