CHAPTER II.

PRACTICAL UNITS-OHM'S LAW-FUNDAMENTAL UNITS

In dealing, in the previous chapter, with the general attributes of electricity, the only degree of comparison arrived at was to say that one electrification, resistance, or current was greater or less than another. And to a somewhat considerable extent this was, until within the last few years, deemed sufficient. It is, however, now essential that more precision in comparing or measuring forces and their properties and effects should be obtained. Measurement is, in fact, the most important branch of electrical science, as, indeed, it is of every other physical science.

Instead of simply saying that one lump of iron is heavier or weightier than another, it is usual to say by how much they differ. Thus one lump may have a mass of ten pounds, and another a mass of twenty pounds. The latter is therefore ten pounds heavier than the former. We have here introduced a unit of measurement, viz. the pound, or unit of mass. Similarly, the inch or foot may be used as a unit of length, the second as a unit of time, the pint as a unit of capacity, the sovereign as a unit of coinage, and so on. These units are all such as everybody can readily appreciate. They are so frequently employed that no mental effort is required to understand what is meant when any one of them is mentioned.

In dealing with electricity the first thing we wish to measure is naturally the amount of the electrical difference between two bodies which causes an electrical stress and which may result in a current of electricity. But we are confronted with two difficulties. The first is that by none of the everyday units -by no unit employed for any other purpose-are we able to indicate exactly the electric potential of a body. Moreover, electricity being only a form of energy which induces or causes a certain condition of

matter, and not matter itself, it is impossible to measure it directly. We can only measure it by its effect upon material substances. In the next place, inasmuch as it is impossible to obtain or even to conceive of a body altogether devoid of electrification (although it is not always perceptible), it is impossible to fix on an absolute zero potential, and measure potentials from that point. In just the same way it is impracticable to have a zero level, some arbitrary point such as the sea-level at high tide having to be employed if we wish to measure the relative height of two or more points. It is, consequently, necessary to look elsewhere for a starting-point, and to fix on a convenient arbitrary potential zero. We take as a zero the potential of the earth's surface, and consider that bodies which are said to be positively electrified are at a higher potential than the earth, while negatively electrified bodies are at a lower potential. Positive and negative potentials may therefore be said to correspond to height and depth in their relation to the sea-level. Inasmuch, however, as we are unable to detect any potential at all unless we take two points or bodies whose potentials are different, the measurement of potential itself again presents difficulties. On the other hand, when we are called upon to measure the potentials of two bodies, what we really desire to know is the difference between those potentials; or, if we call the potential of one body P, and that of the other P1, we want to know the value of P-P1; for, after all, it is this difference of potential that determines the flow of electricity. This difference of potential, which, when the conditions are favourable, is competent to develop and maintain a current of electricity, is known as electro-motive force, a term which is frequently contracted into the initials E.M.F., or, shorter still, into E. only. It is this electro-motive force, then, that we desire to measure, and the practical unit by which it is measured is known as the volt. We will, for the present, rest satisfied with the simple statement that the volt is approximately equal to, although actually a fraction less than, the electro-motive force of a single Daniell cell. (See Chapter III.)

Reference was made in the previous chapter to 'resistance,' and it was described as the converse of conductivity, which again we described as the ability of a body to transmit a current of electricity. It is easy to show that resistance may be expressed as a ratio

-the ratio of electro-motive force to current--and many authorities insist that it should always be regarded thus. It may also be expressed as a velocity,' or the ratio of length to time, but we prefer to deal with it as it appeals to practical electricians-viz. as an attribute of matter, varying with different substances, and in virtue of which such matter opposes or resists the passage of electricity, whence the current has to do 'work' or expend 'energy' in effecting the passage. The law of the conservation of energy teaches us that energy is indestructible, and it follows, therefore, that if energy has to be expended in impelling a flow of electricity against a greater or less amount of resistance, the equivalent of that energy must be developed in some other form. This other form is usually heat; or, in other words, when a body opposes a certain amount of resistance to the passage of electricity, heat is produced, the actual amount of heat being an exact counterpart of the energy expended in overcoming the resistance, and varying therefore directly as that resistance. Consequently, if we have two conductors, the resistance of one of which is twice that of the other, and if we send currents of equal strength through both wires, twice as much heat will be developed in the conductor of the higher resistance as will be developed in that offering the lower resistance. We shall have occasion to deal with this subject more fully in a future chapter, but we may add here, that if we wish to perform work at any point by means of an electric current conducted by a wire to that point, we must keep the resistance of that wire down to the lowest practical limit, because every fraction of the energy frittered away in heating the conductor means so much less energy available for the particular work which we wish the current to perform at the far end of the conductor. It is apparent, then, that we require a unit by which we shall be able to compare the resistances of various substances, and the unit selected is called the ohm. It was decided by an International Congress of Electricians which assembled in Paris in 1884 as being equal to the resistance which is offered to the flow of electricity by a column of mercury one square millimetre (the millimetre is equal to 003937 of an inch, or a small fraction less than of an inch) in section, and 106 centimetres long (the centimetre is equal to 03937 of an inch), the temperature being at the freezing point

(32° Fahrenheit or o° Centigrade), and the pressure of the air equal to the pressure at the base of a column of mercury 30 inches, or 760 millimetres, in height. The Congress which determined the value of this unit also decided that it should be known as the 'legal' ohm, and it was understood to be but a provisional determination to remain in force until further and more exact experiment should decide the precise length of the column. At another Congress, held at Chicago in 1893, it was decided that the length of the mercury column should be 1063 centimetres, and that the name of this unit should be the 'international' ohm ; but this unit has not yet been adopted to any great extent, most people preferring to await further developments. A millionth part of an ohm is called a microhm, and one million ohms a megohm. The ohm is frequently indicated by the symbol o, and the megohm by the symbol ; thus 15 means 15 ohms, and 4 represents 4 megohms or 4 million ohms.

There have, in the past, been an almost unlimited number of units, more or less crude and unreliable; for it must be borne in mind that for a unit to be of any real value it must be permanent or durable, it must be susceptible of confirmation, and its derivation must be well known and invariable. One of the earlier units of resistance was that offered by a mile of the then best procurable iron wire of a certain gauge or diameter. The indefiniteness of such a unit may be conceived when it is called to mind that even now no two samples of wire can be obtained which will offer the same resistance; and still more so was this true a few years ago, when the quality of iron wire as a conductor was vastly inferior compared with what it now is, both as regards its actual resistance and its uniformity.

The only other unit which we need consider is that known as the B.A., or British Association, Unit. It was determined in London in 1863 by a committee appointed for the purpose by the British Association, and the method of determination then adopted was the basis upon which the Paris or legal ohm was afterwards calculated. These units are both based on what is called the C.G.S. system (p. 43), the Paris unit being really a correction of the B.A. unit. The practical standard of the former has, however, a great advantage over that of the latter, which

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consisted of the resistance of a certain length of wire carefully preserved in London. This was, of course, rarely used, and duplicates of the standard had to be employed for comparing or standardising other resistances. The legal ohm is manifestly capable of being reproduced more easily, and it is this fact which imparts to it its chief value. There is the further advantage that the risk of change during the course of time in the nature, and therefore in the resistance, of any given standard wire is avoided. The B.A. unit is a fraction smaller than the Paris ohm, the actual proportion being o'986 to 10. If it were possible at the present day to universally adopt a common unit, it would certainly be a great advantage, for then everybody would know what was meant when anybody else mentioned any particular resistance. But prior to 1884 a vast quantity of electrical apparatus and machinery was in use, and everything in England and certain other countries was measured by the B.A. unit, while the measurements employed on the Continent were for the most part referrible to the Siemens unit, which was the resistance of a column of mercury 1 metre (or 39:37 inches) long, the other details as to its size, temperature, and pressure being the same as those employed in devising the legal ohm. As it was, the various administrations and authorities were placed in a most unpleasant dilemma. If they re-standardised and re-marked all their then existing apparatus they would have had to incur enormous expense, while if they continued the use of their existing standards they would be perpetuating an inconvenience which they had called the Congress together to remove. In the majority of cases questions of finance compelled them to adopt the latter alternative, so that with us most apparatus continues to be measured by the B.A. unit, some of the apparatus employed in the newer industries, such as electric lighting, being measured by the legal ohm. It is probable that when the various authorities are assured that something approaching finality in the value of the unit has been attained much of the existing apparatus will be re-standardised.

The student will frequently come across the expression 'specific resistance,' and it is a most important term. It may be defined as the resistance of any particular substance as compared with the