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Part 2. Some Proposed Systems of Units

Part 2. Some Proposed Systems of Units

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of electrostatic units of electric charge in one electromagnetic unit of the same.

There is sometimes a question as to whether electric current is to be expressed

in electrostatic or electromagnetic units, since it has both electric and magnetic

attributes. I t is usually expressed in electrostatic units in the Gaussian system.

It may be observed from the dimensions of K given in Table 2, part 3, that

[ I / K p ]= [ L 2 / T 2 ]which has the dimensions of a square of a velocity. This

velocity was found experimentally to be equal to that of light, when K and p

were expressed in the same system of units. Maxwell proved theoretically that

l/V/Kp is the velocity of any electromagnetic wave. This was subsequently

proved experimentally. When a Gaussian system is used, this equation becomes

c / V K i = z * . For the ether K = 1 in electrostatic units and p= 1 in electromagnetic units. Hence c=v for the ether, or the velocity of an electromagnetic

wave in the ether is equal to the ratio of the cgs electromagnetic to the cgs

electrostatic unit of electric charge. This constant c is of primary importance

in electrical theory. Its most probable value is 2.99776 x 1O’O centimeters per


Part 3.-Electrical

and magnetic units

Absolute (“practical”) electromagnetic system (1948).-This

electromagnetic system is based upon the units of lo9 cm,

g, the sec and p of

the ether. The principal quantities are the resistance unit, the ohm= lo8 emu

units; the current unit, the ampere= lo-’ emu units; and the electromotive

force unit, the volt = lo8 emu units. (See Table 6.)

The International electric units.-The

units used before January 1,

1948, in practical electrical measurements, however, were the “International

Units.” They were derived from the “practical” system just described, or as

the latter is sometimes called, the “absolute” system. These international units

were based upon certain concrete standards that were defined and described.

With such standards electrical comparisons can be more accurately and readily

made than could absolute measurements in terms of the fundamental units.

Two electric units, the international ohm and the international ampere, were

chosen and made as nearly equal as possible to the ohm and ampere of the

“practical” or “absolute” systeni.1°


The unit of quantity of electricity is the coulomb. The faraday is the

quantity of electricity necessary to liberate 1 gram equivalent in electrolysis.

It is equivalent to 96,488 absolute coulombs (Birge).

Standards.-There are no standards of electric quantity. The silver voltameter may be used for its measurement since under ideal conditions the mass

of metal deposited is proportional to the aiiiount of electricity which has flowed.


The unit used for capacity is the microfarad or the one-millionth of the farad,

which is the capacity of a condenser that is charged to a potential of 1 volt by

1 coulomb of electricity. Capacities are commonly measured by comparison

with standard capacities. The values of the standards are determined by

1OThere was, however, some slight error in these values that had to be taken into

account for accurate work. (See Table 5.)



measurement in terms of resistance and tiiiie. T h e standard is some form of

condenser consisting of two sets of metal plates separated by a dielectric.

T h e condenser should be surrounded by a metal shield connected to one set

of plates rendering the capacity independent of the surroundings. A n ideal

condenser would have a constant capacity under all circumstances, with zero

resistance in its leads and plates, and no absorption in the dielectric. Actual

condensers vary with tlie temperature, atmospheric pressure, and the voltage,

frequency, and time of charge and discharge. A well-constructed air condenser with heavy metal plates and suitable insulating supports is practically

free from these effects and is used as a standard of capacity.

Practically, air-condenser plates must be separated by 1 mrn or more and so

cannot be of great capacity. T h e more the capacity is increased by approaching

the plates, the less the mechanical stability and the less constant the capacity.

Condensers of great capacity use solid dielectrics, preferably mica sheets with

conducting plates of tinfoil. A t constant temperature the best mica condensers

are excellent standards. The dielecti ic absorption is sinall but not quite zero,

SO that tlie capacity of these stantlards found varies with different methods of

measurement, so for accurate results care must be taken.


T h e henry, the unit of self-inductance and also the unit of mutual inductance,

is the inductance in a circuit when the electromotive force induced i n this

circuit is 1 volt, while the inducing current varies at the rate of 1 ampere per


Inductance standards.-Inductance

standards are measured in international units in terms of resistance and time or resistance and capacity by alternate-current bridge methods. Inductances calculated froni dimensions are in

absolute electroniagnetic units. T h e ratio of the international to the absolute

henry is the same as the ratio of tlie corresponding ohms.

Since inductance is measured i n terms of capacity and resistance by the

Iiridge method ahout as siinply and as conveniently as by comparison with

standard inductances, it is not necessary to maintain standard inductances.

They are however of value i n magnetic, ~lternating-current, antl absolute

electrical measurenients. A standard inductance is a circuit so wound that

when used i n a circuit it adds a definite ainount of inductance. I t must have

either such a form o r so great an inductance that the mutual inductance of tlie

rest of the circuit upon it may he negligible. I t usually is a wire coil wound all

in tlie saiiie direction to make sel f-induction a iiiaxiniuiii. X standard. tlie inductance of which may be calculated from its dimensions, should be a single

layer coil of very simple geometrical form. Stantlards of very siiiall inductance,

calculable from their tliiiiensions, are of soiiie simple device, such as a pair of

parallel wires or a single turn of wire. With such standards great care must

be used that tlie mutual inductance upon them of tlie leads and other parts of

tlie circuit is negligil)le. Any intluctance standard should be separated by long

leads from the measuring bridge or other apparatus. It must be wound so that

the distributed capacity between its turns is neg1igil)le ; otherwise the apparent

inductance will vary with tlie frequency.


Power and energy, although mechanical antl not primarily electrical quantities, are nieasural)le with greater precision I)y electrical methods than in any



other way. The watt and the electric units were so chosen in terms of the cgs

units that the product of the current in amperes by the electromotive force in

volts gives the power in watts (for continuous or instantaneous values). The

watt is defined as the energy expended per second by an unvarying electric

current of 1 ampere under an electric pressure of 1 volt.

Standards and measurements.-No standard is maintained for power or

energy. Measurements are always made in electrical practice in terms of some

of the purely electrical quantities represented by standards.


Cgs units are generally used for magnetic quantities. American practice is

fairly uniform in names for these units : the cgs unit of magnetomotive force

is called the gilbert; magnetic intensity, the oersted; magnetic induction, the

gauss; magnetic flux, the waxwell, following the definitions of the American

Institute of Electrical Engineers ( 1894).

Oersted, the cgs emu of magnetic intensity exists at a point where a force

of 1 dyne acts upon a unit magnetic pole at that point, i.e., the intensity 1 cm

from a unit magnetic pole.

Maxwell, the cgs emu magnetic flux is the flux through a cm2 normal to a

field a t 1 cm from a unit magnetic pole.

Gauss, the cgs emu of magnetic induction has such a value that if a conductor 1 cm long moves through the field at a velocity of 1 cm/sec, length and

induction mutually perpendicular, the induced emf is 1 abvolt.

Gilbert, the cgs emu of magnetomotive force is a field such that it requires

1 erg of work to bring a unit magnetic pole to the point.

A unit frequently used is the ampere-turn. It is a convenient unit since it

eliminates 4~ in certain calculations. It is derived from the “ampere turn per

cm.” The following table shows the relations between a system built on the

ampere-turn and the ordinary magnetic units.”


Dellinger, International system of electric and magnetic units, Nat. Bur. Standards

Bull., vol. 13, p. 599, 1916.

P a r t 4.-The

ordinary and the ampere-turn magnetic units





Magnetomotive force ....... 3

Magnetizing force .......... H


Magnetic flux ..............

Magnetic induction ......... B

Permeability ............... p

Reluctance ................. R

Magnetization intensity ..... J

Magnetic susceptibility ...... K

Magnetic pole strength. . . . . . m




gilbert per



maxwell per

cm2 gauss





ampere-turn per



maxwell per cm2



ampere-turn per


maxwell per cm‘



units in 1

ampereturn unit









1 /4s


T A B L E 4.-THE

NEW (1948) S Y S T E M O F E L E C T R I C A L U N I T S 1 2

In pursuance of a decision of the International Committee on Weights and

Measures, the National Bureau of Standards introduced, as of January 1,

1948, revised values of the units of electricity. This consummated a movement,

initiated in 1927 by the American Institute of Electrical Engineers, asking that

the National Bureau of Standards undertake the additional research necessary

in order that the absolute ohm and absolute ampere based on the cgs electromagnetic systein and the absolute volt, watt, and other units derived from

them could be legalized in place of the international ohm and ampere and their

derived units. This work was done, and the magnitude of the old international

units in terms of the adopted absolute units is given in Table 5. This means

that the electrical units now in use represent, as nearly as it is possible to make

them, exact multiples of the cgs emu system, with the numerical relations

shown in Table 6. Units of the new systeni will actually be maintained, as

were the old international units, by groups of standard resistors and of standard

cells, and consequently the change to be made is most simply represented by

stating the relative magnitudes of the ohms and of the volts of the two systems.

During the period of transition to the new units, in order to avoid any doubt

as to the units used in giving precise data, the International Committee on

Weights and Measures recomnlended that the abbreviations int. and abs. be

used with the names of the electrical units. In a few years this will be unnecessary, except when referring to old data.

The international units were intended to be exact multiples of the units of

the centimeter-gram-second electromagnetic system, but to facilitate their reproduction, the ampere, the ohm, and the volt were defined by reference to

three physical standards, namely (1) the silver voltameter, ( 2 ) a specified

column of mercury, and (3) the Clark standard cell. This procedure was

recommended by the International Electrical Congress of 1893 in Chicago and

was incorporated in an Act of Congress of July 12, 1894. However, modifications of the international systeni were found to be necessary or expedient for

several reasons. The original proposals were not sufficiently specific to give

the precision of values that soon came to be required, and the independent definitions of three units brought the system into confiict with the customary

simple form of Ohm’s Law, Z=E/R. Furthermore, with the establishment

of national standardizing laboratories in several of the larger countries, other

laboratories no longer needed to set up their own primary standards, and

facility of reproduction of those standards became less important than the

reliability of the units.

I n preparation for the expected change in units, laboratories in several

countries made absolute measurements of resistance and of current. The results of these measurements and the magnitudes of the international units as

maintained in the national laboratories of France, Great Britain, Germany,

Japan, the U.S.S.R., and the United States were correlated by periodic comparisons of standard resistors and of standard cells sent to the International

Bureau of Weights and Measures. Nearly all the absolute measurements at

the National Bureau of Standards were carried out under the direct supervision

of Harvey L. Curtis, and the results of such measurements at the Bureau

accepted by the International Committee on Weights and Measures at its

meeting in Paris in October 1946 are as follows :

1 mean international ohm = 1.00049 absolute ohms

1 mean international volt = 1.00034 absolute volts

12Nat. Bur. Standards Circ. C-459, 1947.


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