Gaussage would be about 50 in small transformers, up to 40,000 in large dynamos. The latter could be conveniently reckoned in kilogausses. To make the gauss 1 ampère-turn appears to have great advantages in practice, and connects it directly with its usual source. = The idea of permeance is very useful, and the identification of its dimensions with those of inductance is neat. But I think it is liable to cause confusion, for the permeance of the core of a coil will be a different number of henrys from the inductance of its wire. Moreover, the argument as to identical dimensions might equally be applied to the case of ampères and gausses. I would therefore have a new unit strictly connected with the henry, so that inductance=n2 × permeance in a coil of n turns. As to the units of permeance: with the above meanings of gauss and weber the permeance of a circuit would be 4μA/107, as you point out, instead of μA/1. But I wish to suggest a change in the method of reckoning, namely, still to retain the value of the permeance as webers per sq. cm. webers gausses and permeability as therein giving up the convention of unit permeability of space, and giving it the value 1.2566 x 10-8 unit of permeance for a unit cube. In this way both the troublesome 10-8 and 4/10 are dealt with in an easily intelligible way. To avoid the high power of 10 it may be measured in micro-units of permeance, so that permeability of space and air 012566 micro-unit of permeance for a unit cube, and permeability of soft iron-up to 25 micro-units for a unit cube. Thus we have permeance Au/l, where u is to be obtained from tables of its value, which can easily be altered to this method. Inductance then becomes weber-turns webers gausses ampères or n2 =n2 μ permeance. [Of course your phrase 'weber-turns per ampère' means the same as the above webers ampères, and does not necessarily mean the weber-turns caused by one ampère.] It may be objected that the c.g.s. units of strength of field, unit magnetic pole and intensity of magnetisation do not bear any simple relation to these practical units. This is chiefly important in the use of the magneto-metric measurement of iron, and in the measurement of the mechanical form of attraction between two magnetic surfaces in contact. But the expressions are not in reality much complicated; e.g., present c.g.s. unit of intensity of magnetisation is given by 4I=(-) H, where =permeability of space=1, and H=c.g.s. unit of magnetic force. This becomes 4πI=(μ' —μ' ̧) H' 108, where H' is the gauss-gradient in the magnetic substance, and μ'='012566 micro-unit of permeance for a cubic centimetre. As the single magnetic pole is unchanged, the force on it will be strength of pole gauss gradient x 1.2566; butas this is not a calculation of frequent occurrence, except in magnetic surveys, the complication will not be serious. Other magnetic relationships are almost entirely of academic interest only, and would be carried out in c.g.s. units. Also the transition would present no difficulties to people with a little scientific knowledge. I am of opinion also that as the legal volt has no direct connection with induction and velocity of motion, it is not necessary to define the practical units as they are defined absolutely. That is, ohm and ampère are the starting points, volt is obtained from them, weber from volt, gauss from ampère, permeance unit from weber and gauss, henry from weber and ampère or from permeance, and so on. This is much more easily explained to practical and unscientific men than the absolute derivations are, and it is the order in which they learn them. Yours very truly, FRANCIS G. BAILY. REMARKS ON THE ABOVE (especially on pages 203 and 204). According to the proposal of the Chicago Chamber of Delegates, the quantity which we call 'inductance,' and which is to be expressed in henrys,' is defined by the equation both being comprehended in one definition, the inductance L or M being calculated by dividing E in volts by This dC in ampères per second. that the former be called 'the total inductance,' and the latter the differential inductance.' The distinction would be somewhat analogous to the distinction between the 'mean specific heat from 0° to t°' and the 'true specific heat at t°.' Both total and differential inductance should be expressed in henrys,' for they are quantities of the same kind, and when there is no iron, &c., in the field they are equal. I think that the above mode of definition, involving as it does no magnitude except current and time, is more readily comprehended than Dr. Lodge's proposed definition, in which the magnitudes involved are current, flux of induction, and the number of convolutions of the coil through which the flux passes. In the definition proposed by the Chicago delegates the consideration of the number of convolutions does not enter. For a circuit or two circuits not having iron, &c., in the field we may define inductance (in henrys) as the E.M.F. (in volts) due to variation of current at unit rate (one ampère per second). When the field is modified by the presence of magnetic material the above will be the definition of 'differential inductance.' The 'total inductance' for any specified strength of current will be the mean value of differential inductance for equal increments of current from zero up to the specified strength. dB ZH I would suggest similar nomenclature in the case of permeability : should be called differential permeability, and: total permeability. B In some respects 'mean' or 'average' would be a more correct designation than 'total'; but these words would be liable to be misunderstood as referring to an average taken over the different parts of the body or circuit. 'Total' is to be understood as standing for 'calculated on totals.' As regards the magnitude of the unit of inductance. While I agree with Mr. Heaviside and Dr. Lodge that the unit pole ought to have been so defined that the mutual force between two poles is equal to their product divided by the surface of a sphere whose radius is their distance, a definition which would have made the line-integral of H due to a current C equal to C itself instead of to 4C, I deprecate a mixing up of the two systems. So long as we employ our present unit of intensity of magnetic field, which results from our present definition of the unit pole, we cannot consistently reckon the line integral as equal to the ampère-turns. It must be reckoned as 4 times the ampère-turns, and the flux N must be reckoned as 47μ times the ampère-turns. The practical inconvenience of retaining the factor 47 cannot be considerable, for it is as easy to tabu. late the values of 4μ as the values of με = dN S Next as regards 'permeance.' I do not think it can conveniently be reckoned in henrys. I would rather reckon it in 'webers per ampèreturn,' which would he written' web. per amptu'; and there can be no possible doubt as to the meaning intended when once we have fixed the magnitude of the 'weber.' There seems to be no difference of opinion a to what this magnitude should be. It is fixed by the relation E E being in volts, N in webers, and t in seconds. This is in accordance with Dr. Lodge's proposal; but Dr. Lodge has not explicitly recommended any name for the physical quantity which is measured in webers. Shall we call it 'weberage'? It greatly needs a name; for induction' may mean B instead of the surface integral of B, besides having many other meanings. dt When permeance varies according to the strength of current, I would dis1 dN tinguish between 'total permeance' and 'differential permeance' N nc n dC As regards 'gaussage' and 'gauss falI think the names will be convenient in the senses proposed by Dr. Lodge, but I cannot agree with his selection of a unit of measurement. The present definition of the unit pole (on which the present unit current is based) requires us to equate the line-integral in question to 4nC. To be consistent we must reckon gaussage as equal to 4 times the number of amptus. Dr. Lodge's proposal is to reckon C, not in ampères but in c.g.s. units, thus introducing, as it appears to me, an awkward breach of continuity. J. D. EVERETT. Professor Carey Foster has written objecting to the term 'gaussgradient,' instead of 'magnetic gradient'; he prefers the latter, just as he would prefer 'temperature-gradient' to 'degree-gradient.' Dr. Johnstone Stoney has also written, urging strongly that not the c.g.s. unit of magnetic potential, but one-tenth of this quantity, should receive a name, in order to make it harmonise with the ampère series; and further recommending that the names 'weber' and 'gauss,' as above suggested, should be interchanged. Comparison and Reduction of Magnetic Observations.-Report of the Committee, consisting of Professor W. G. ADAMS (Chairman), Mr. C. CHREE (Secretary), Lord KELVIN, Professor G. H. DARWIN, Professor G. CHRYSTAL, Professor A. SCHUSTER, Captain E. W. CREAK, The ASTRONOMER ROYAL, Mr. WILLIAM ELLIS, and Professor A. W. RÜCKER. (Drawn up by the Secretary.) [PLATES V. and VI. Thirteen Curves illustrating Results in §§ 7-8 and §§ 11–12.] Analysis of the Results from the Kew Declination and Horizontal Force Magnetographs during the selected 'Quiet' Days of the Five Years 1890-94. By C. CHREE, Sc.D. CONTENTS. SECTIONS 1-3 Introductory 4-6 Non-cyclic Nature of Results obtained from 'Quiet' Days 7-8 Tables of Diurnal Inequalities for each Month of Year, for Quarters, Halves, and Whole Year PAGE 209 210 213 Day 221 223 9-10 Harmonic Analysis of Diurnal Inequalities; Times of Maxima, &c. . Introduction. § 1. THE hourly measurement of the Kew magnetic curves on five 'quiet' days a month, selected annually by the Astronomer Royal, has been in operation since the beginning of 1890. Tables of the mean hourly values for each month of the declination, inclination, horizontal and vertical forces, based exclusively on these quiet days, have been published annually in the 'Report' of the Kew Committee to the Royal Society. Tables have also been given of the mean diurnal variations of the several elements for the six winter months, the six summer months, and the whole year. With the consent of the Kew Committee I now propose to give a general résumé of the results deducible from the declination and horizontal force records on the selected quiet days of the five years 1890-94. For some reasons it would have been desirable to allow a larger number of years' records to accumulate before entering on a general discussion; to have included, for instance, the complete cycle of ten or eleven years believed to occur in magnetic phenomena would have possessed obvious advantages. On the other hand twenty-five quiet days for each month of the year seem a sufficient number for a comparison of the different months. Further, the frequent occurrence of certain phenomena, depending apparently on the limitation of the inquiry to 'quiet' days, which cause an appreciable amount of indeterminateness in the results, has led me to think an early survey of the situation desirable. § 2. The first thing to consider is the distribution of the selected 'quiet' days. The aim of the Astronomer Royal, he informs me, has been to ensure, first, that the five days selected each month are good specimens of 'quiet' days; and, secondly, that their mean comes near the middle of 1895. Р the month. That the second object has been very satisfactorily accomplished, so far as a five years' survey is concerned, will be seen from the following table. The figures it contains are the intervals, in days, from the beginning of the month to noon of its mean 'quiet' day, the 300 'quiet' days being grouped under the months to which they belong. In one of the 300 'quiet' days the Kew record was defective and has been omitted. Its omission reduces the entry in the table under August from 15.6 to 15.0. The departures from the theoretically exact figures, 15.5 for months of thirty-one days and 15 for months of thirty days, are so small, considering the uncertainties arising from other sources, that I have decided to neglect them in getting out annual variations. Equal weight has also been allowed to each month. § 3. In 1890 the diurnal variation at Kew was got out from measurements at the hours 1 to 24, counting from midnight. What has been styled in the Kew Report 'solar diurnal range' meant in that year the departure of the hourly values from the mean for the day taken as where by [n] is meant the value answering to the nth hour after the first midnight. In the subsequent four years measurements were taken at the first as well as the second midnight, and the mean for the day was taken as This second method of fixing the daily mean is of course not mathematically correct, as it attributes double weight to the midnight value; but the departure of the midnight value from the mean for the day-at all events when inequalities are got out only for summer, winter, and the whole year-is too small to cause appreciable error. The error in definition, if error it can be called, was, I think, fortunate for several reasons. For instance it left no additional measurements to be made for the present inquiry other than those at the first midnights of the sixty 'quiet' days of 1890. Non-cyclic Nature of Results obtained from Quiet Days. § 4. During the five years considered, the westerly declination at Kew has been diminishing by about 6'9 annually, the horizontal force increasing by about 195 x 10-6 C.G.S. units. Thus on an average there occurred in twenty-four hours a decrease of about 0'-019 in declination, an increase of about 53 × 10-8 C.G.S. units in H.F. (horizontal force). Now at Kew, declination is measured only to 0'1, and H.F. to 1 x 10-5 C.G.S. units. It is thus obvious that if two sets, each of 150 days, and As in the Kew Reports, Greenwich, not local, time is employed. Local time is, however, only 1 min. 15 sec. later than Greenwich time. |