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
second.
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°
Q U A N T I T Y O F ELECTRICITY
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.
CAPACITY
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.)
SMITHSONIAN PHYSICAL TABLES
17
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.
INDUCTANCE
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
second.
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 A N D ENERGY
Power and energy, although mechanical antl not primarily electrical quantities, are nieasural)le with greater precision I)y electrical methods than in any
SMITHSONIAN PHYSICAL TABLES
18
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.
MAGNETIC U N I T S
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.”
11
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
Ordinary
magnetic
units
Quantity
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
SMITHSONIAN PHYSICAL TABLES
{
gilbert
gilbert per
cm
maxwell
maxwell per
cm2 gauss
oersted
Ampere-turn
units
ampere-turn
ampere-turn per
cm
maxwell
maxwell per cm2
{gauss
{
ampere-turn per
maxwell
maxwell per cm‘
maxwell
Ordinary
units in 1
ampereturn unit
4s/10
4s/10
1
1
1
4s/10
1/4s
1/4s
1 /4s
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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.
SMITHSONIAN PHYSICAL TABLES