ABSOLUTE MEASUREMENTS

IN

ELECTRICITY AND MAGNETISM.

CHAPTER I.

INTRODUCTORY.

TWENTY-FIVE years ago the experimental sciences of electricity and magnetism were in great measure mere collections of qualitative results, and, in a less degree, of results quantitatively estimated by means of units which were altogether arbitrary. These units, depending as they did on constants of instruments and conditions of experimenting which could never be made fully known to the scientific public, were a source of much perplexity and labour to every investigator, and to a great extent prevented the results which they expressed from bearing fruit to the furtherance of scientific progress. Now happily all this has been changed. The absolute system of units introduced by Gauss and Weber, and rendered a practical reality in this country by the labours of the British Association Committee on Electrical Standards, has changed experimental electricity and magnetism into sciences of which the very

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essence is the most delicate and exact measurement, and enables their results to be expressed in units which are altogether independent of the instruments, the surroundings, and the locality of the investigator.

The record of the determinations of units made by members of the Committee, for the most part by methods and instruments which they themselves invented, forms one of the most interesting and instructive books* in the literature of electricity, and when the history of electrical discovery is written the story of their work will form one of its most important chapters. But besides placing on a sure foundation the system of absolute units they conferred a hardly less important benefit on electricians by giving them a convenient nomenclature for electrical quantities. The great utility of the practical units and nomenclature, which the Committee recommended, soon became manifest to every one who had to perform electrical measurements, and has led within the last few years to their adoption, with only slight alterations, by nearly all civilized nations. Although it is only five years since the recommendations † of the Paris Congress of Electricians were issued, they have been almost universally adopted and appreciated by those engaged in electrical work, and have thus begun to yield excellent fruit by rendering immediately available ́for comparison and as a basis for further research the results of experimenters in all parts of the world.

But in order that the full benefit of the conclusions of the Paris Congress may be obtained it is essential in the first place that convenient instruments should be

*

Reports of the British Association Committee on Electrical Standards, edited by Prof. Jenkin, F.R.S. + See Appendix below.

used, adapted to give directly, or by an easy reduction from their indications, the number of amperes of current flowing in a particular circuit, and the number of volts of difference of potential between any two points in that circuit. To be generally useful in practice these instruments should be easily portable, and should have a very large range of sensibility; so that, for example, the instrument, which suffices to measure the full potential produced by a large dynamo-electric machine, may be also available for testing, if need be, the resistances of the various parts of the armature and magnets by the readiest and most satisfactory method; namely, by comparing by means of a galvanometer of high resistance the difference of potential between the two ends of the unknown resistance with that between the ends of a known resistance joined up in the same electrical circuit. In like manner the ampere measurer should be one that could be introduced without sensible disturbance into a circuit of low resistance to measure either a small fraction of an ampere, or the whole current flowing through a circuit containing a large number of electric lamps. These conditions are more or less fulfilled by a large variety of practical instruments recently patented by different inventors. Among these is a very complete set of potential and current measurers, due to Sir William Thomson, and adapted for all kinds of work. My main purpose in the present work is to give an account, both theoretical and practical, of the measurement of currents and potentials in absolute measure; and to apply this to the graduation of instruments for use in practical electrical work. Of such instruments I shall take some of Sir William Thomson's as examples, and after describing them, show how they may be graduated, or their graduation tested,

by the experimenter himself. It will be convenient to introduce definitions of absolute units of measurement of magnetic and electric quantities when they are required; and in so doing I shall endeavour to give a clear account of the foundation of the absolute system of electrical measurement, and to show how from the fundamental units are derived the practical units of current, quantity, potential, and resistance. I shall then give and explain a few rules for the calculation of currents and resistances in derived circuits: and describe among others some methods of determining resistances which are useful in many important practical cases, but which so far as I know are not treated of in the ordinary text-books of electricity. The remainder of the work will contain a brief account of the measurement of energy spent in the circuits of generators transmitting power to electric lamps or motors, or in the charging circuit of a secondary battery; a chapter on the practical determination in absolute units of the intensities of powerful magnetic fields, such as those of the field magnets of dynamo machines, and another on the dimensions of units; and, lastly, a few tables of useful electrical data.

CHAPTER II.

DETERMINATION OF THE HORIZONTAL COMPONENT OF THE EARTH'S MAGNETIC FIELD.

ALL the methods by which galvanometers may be graduated so as to measure currents and potentials in absolute units, involve, directly or indirectly, a comparison of the indications of the instrument to be graduated with those of a standard instrument, of which the constants are fully known for the place at which the comparison is made. There are various forms of such standard instruments, as, for example, the tangent galvanometer which Joule made, consisting of a single coil of large radius and a small needle hung at its centre, or the Helmholtz modification of the same instrument with two large equal coils placed side by side at a distance apart equal to the radius of either; or some form of "dynamometer," or instrument which instead of the needle of the galvanometer has a movable coil, in which the whole or a known fraction of the current in the fixed coil flows. The measurement consists essentially in determining the couple which must be exerted by the earth's magnetic force on the needle or suspended coil, in order to equilibrate that exerted by the current. But the former depends on the value, usually denoted by H, of the horizontal component of the earth's magnetic force, and it is necessary therefore, except when some such method as that of Kohlrausch,