e of

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the

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the

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the

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= the

same name is applied to the unit of energy, for
energy is measured by the amount of work which
it represents. Since the weight of a gramme is
981 dynes, the work done in raising one gramme
vertically through one centimetre against the
action of gravity is 981 ergs.

Practical Units and Index Notation. In any uniform
system some of the units must be inconveniently large,
while others are so small that the quantities with which
we have to deal are represented by very large numbers.
Electricians find it convenient to use a system of "prac-
tical units," each of which bears to the corresponding
C.G.S. unit a ratio which is some multiple or sub-
multiple of 10. Thus the volt is equal to 100,000,000
C.G.S. units of potential; the farad is
the C.G.S. unit of capacity. The prefixes mega- and
micro- are used to signify one million and " one-
millionth part" respectively.
Thus a megadyne is a
force of one million dynes; a microfarad denotes a capa-
city of one-millionth of a farad.

66

I

1,000,000,000

of

When very large or very small numbers have to be expressed, it is convenient to adopt the index system of notation, in which numbers are expressed as the product of two factors, the second of which is a power of 10; and it is usual to choose the factors so that the first contains only one integral digit. Thus the velocity of light, which is 300,400 kilometres per second, is expressed as 3.004 x 1010 centimetres per second. A megadyne is 10o dynes; a farad is 109 (=) and a microfarad is 10-15 C.G.S. unit of capacity.

The

Work. Power, Activity, or Rate of doing C.G.S. unit of power is the power of doing work at the rate of one erg per second. The corre sponding practical unit, called the Watt, is the power of doing work at the rate of 107 ergs per second. A horse-power is equal to 746 watts. Pressure. The C.G.S. unit of intensity of pressure is a pressure of one dyne per square centimetre.

megadyne per square centimetre (106 C units) were adopted as the normal atmosp pressure: this standard would correspond barometric height of 75 centimetres, but, as pared with any barometric standard, would the advantage of being independent of the w of g.

Heat. The C.G. S. unit of heat is the amount of required to raise the temperature of a gran of water through one degree centigrade. dynamical equivalent of one heat-unit in erg 4.2 x 107: this quantity is called the mechan equivalent of heat or "Joule's equivalent," is usually represented by the letter J.

4. C.G.S. Electrostatic Units.

Quantity. The unit quantity of electricity is quantity which, when placed (in air) at a dista of one centimetre from an equal and sim quantity, repels it with a force of one dyne. Potential.-Unit difference of potential exists betw two points when the work done against the e trical forces in moving unit quantity of electri from the one point to the other is one erg. Capacity. A conductor is said to have unit capac when a charge of one unit of electricity raises potential from zero to unity.

Electro-magnetic Units.

Current.-The unit of current is that current which, when flowing along a wire one centimetre in length bent into the form of a circular arc of one centimetre radius, acts with a force of one dyne upon a unit pole placed at the centre of the circle.

Quantity.-The electro-magnetic unit of quantity is
the quantity of electricity which in one second
passes any section of a conductor in which unit
current is flowing.

Electromotive Force or Difference of Potential.-Unit
electromotive force exists between two points
when the work done against the electrical forces
in moving unit quantity of electricity from the
one point to the other is one erg.
Resistance.-A conductor is said to possess unit
resistance when unit difference of potential be-
tween its ends causes unit current to flow through

it.

Capacity.-A conductor has unit capacity when a charge of one unit of electricity raises its potential from zero to unity.

5. Practical Units.-The following system of units, based upon the C.G.S. electro-magnetic units, was devised by the British Association committee, and is in general use among practical electricians. It will be noticed that in this system the units of current, electromotive force, and resistance have been chosen so as to be of suitable magnitude for the electrical measurements which most frequently occur.

Current and Quantity. The practical unit of current is the ampère, and is one-tenth (1071) of the C.G.S. electro-magnetic unit of current. It follows

that the coulomb, or practical unit of quant is also one-tenth of the corresponding C.C unit. Electromotive Force. The practical unit of E. M is called the volt, and is 108 C.G.S. units. T is a little less than the electromotive force o Daniell cell, the E.M.F. of a standard Daniell the Post-Office pattern being 1.08 volt. Capacity. A conductor is said to have a capacity one farad when it is charged to a potential one volt by a coulomb of electricity. The far is 10 9 of the C.G.S. electro-magnetic unit capacity. Resistance.-A conductor is said to possess a resi

ance of an ohm when a difference of potential one volt between its ends causes a current of ampère to flow through it. The ohm is theref equal to 109 C.G.S. units of resistance. Material standards, intended to represent the ol as above defined, were issued by the B.A. co mittee, but their resistance is now found be somewhat too small: and, for the sake distinction, these standards and the copies them which have since been made are known "B.A. Units." According to the best det minations of Lord Rayleigh and others

I B. A. unit=0.987 true ohm.

The B.A. unit has the same resistance as a colu of mercury one square millimetre in cross-sect and 104.8 centimetres long; whereas the t ohm would probably be represented by a colu: 106.2 centimetres long.

At the International Conference of Electricians h at Paris in 1884, it was agreed that the resista of a column of mercury 106 centimetres l and I square millimetre in section, at the tempe

ntity, G.S.

M.F.
This

of a ell of

ty of

6. Change of Units.-We have seen (§ 1) that the numerical value n of a length / is given in terms of the unit-length L by the equation.

al of Farad t of

Here we notice, in the first place, that the numerical value of a concrete quantity varies directly as the quantity itself, and inversely as the unit employed in measuring it. From equation (1) we have

This second equation gives us a complete expression for the length 7, an expression which consists of two parts-the first being a number (n), and the second a quantity (L) of the same kind as that under consideration, and which we call the unit. Our everyday expressions for all physical magnitudes are, in fact, phrases which consist of a numerical and a denominational part; thus we speak of a length of ten yards, and we say that ten yards are equal to thirty feet. This last statement involves a change of units,-a process which is perfectly easy when we have only to deal separately with units of length, mass, or time; but which becomes more difficult when two or more of the units have to be simultaneously changed. In dynamical problems which involve at change of units, it is usual to change the units one at a time; but this process becomes very laborious when the fundamental units are involved in a complex manner in those derived from them, as is the case with most electrical units. In proceeding with the general theory of units, we shall consider first, as a simple example, the principle involved in the statement that