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Part 3. Electrical and Magnetic Units
Capacitance of an insulated conductor is proportional to the ratio of the
quantity of electricity in a charge to the potential of the charge. The dimensional formula is the ratio of the two formulae for electric quantity and
potential or [M'L:T-lK'/M'L'T-'K-'] or [ L K ] .
Conductance of any part of an electric circuit, not containing a source of
electromotive force, is the ratio of the current flowing through it to the difference of potential between its ends. The dimensional formula is the ratio of the
formulae for current and potential or [M'L;T-2K'/M'L'T'K-i] or [ L T - l K ] .
Electrical conductivity, like the corresponding term for heat, is quantity
per unit area per unit potential gradient per unit of time. The dimensional
formula is [ M ' L g T ' K 4 / L 2 ( M 4 L
/ L ) T ] or [ T ' K ] .
Electric current (statampere-unit quantity) is quantity of electricity flowinn through a cross section per unit of time. The dimensional formula is the
raTio of tKe formulae for electric quantity and for time or [ M * L > P K ' / T or
Electric field intensity strength at a point is the ratio of the force on a
quantity of electricity at a point to the quantity of electricity. The dimensional
formula is therefore the ratio of the formulae for force and electric quantity or
[ M L T-2/M L 2 T-lK' ] or [ h14L-3 T-lK-' I .
Electric potential difference and electromotive force (emf) (statvoltwork = 1 erg) .-Change of potential is proportional to the work done per unit
of electricity in producing the change. The dimensional formula is the ratio of
the formulae for work and electrical quantity or [ML2Z'2/M'L;T1K4]or
Electric surface density of an electrical distribution at any point on a surface is the quantity of electricity per unit area. The dimensional formula is the
ratio of the formulae for quantity of electricity and for area or [ M'L-' T ' K ' ] .
Quantity of electricity has the dimensional formula [ M' LZT' K ' ] , as
Resistance is the reciprocal of conductance. The dimensional formula is
Resistivity is the reciprocal of conductivity. The dimensional formula is
[ TK-'1 .
Specific inductive capacity is the ratio of the inductive capacity of the
substance to that of a standard substtnce and therefore is a number.
Exs.-Find the factor for converting quantity of electricity expressed in ft-grain-sec
units to the same expressed in cgs units. The formula is Im*lgt-'k'], in which m=0.0648,
1 = 30.48, t = 1, k = 1 ; the factor is 0.06483 X 30.481, or 42.8.
Find the factor reauired to convert electric ootential from mm-mp-sec units to CPS
units. The formula is [ m ' l * t - l / d ] ,in which m =b.OOl, 1 = 0.1, t = 1, k-= 1 ; the factor is
0.001, x 0.14, or 0.01.
Find the factor required to convert electrostatic capacity from ft-grain-sec and specificinductive capacity 6 units to cgs units. The formula is [Ikl in which I = 30.48, k = 6;
the factor is 30.48 X 6 , or 182.88.
SMITHSONIAN PHYSICAL TABLES
Many of the magnetic quantities are analogues of certain electric quantities.
The dimensions of such quantities in the electromagnetic system differ from
those of the corresponding electrostatic quantities in the electrostatic system
only in the substitution of permeability p for K.
Conductance is the reciprocal of resistance, and the dimensional formula is
Conductivity is the quantity of electricity transmitted per unit area per unit
potential gradient per unit of time. The dimensional formula is [M'L'p-'/
TI or [L-*Tp-'].
Current, I (abampere-unit magnetic field, Y = 1 cm), flowing in circle,
radius r, creates magnetic field at its center, 2 ~ l / r .Dimensional formula is
product of formulae for magnetic field intensity and length or [M'L'Fp-'I.
Electric field intensity is the ratio of electric potential or electroinotive
force and length. The dimensional formula is [M'L*T L p ' ] .
E le ctric potential, or electromotive force (emf) (abvolt-work- 1 erg),
as in the electrostatic system, is the ratio of work to quantity of electricity.
The dimensional formula is [ML2T-'/M'L'p-'] or [M'LI T ' p ' ] .
Electrostatic capacity is the ratio of quantity of electricity to difference of
potential. The dimensional formula is [ L-'T2p-'].
I n t e n s i t y of magnetization ( I ) of any portion of a magnetized body is
the ratio of the magnetic moinent of that portion and its volume. The dimensional formula is [MfLgT-1pL1/L3]
Magnetic field str e n g t h , magnetic i n t e n s i t y or magnetizing f o r c e ( I )
is the ratio of the force on a magnetic pole placed at the point and the magnetic
pole strength. The dimensional formula is therefore the ratio of the formulae
for a force and magnetic quantity, or [MLT2/M'LzT-'p']or [M*L-'T-'p-*].
Magnetic flux (a) characterizes the magnetized state of a magnetic circuit.
Through a surface enclosing a magnetic pole it is proportional to the magnetic
pole strength. The dimensional formula is that for magnetic pole strength.
Magnetic induction ( B ) is the magnetic flux per unit of area taken perpendicular to the direction of the magnetic flux. The dimensional formula is
[ M'Lz T-'p4/L2]or [M'L -*T-'p'].
Magnetic moment ( M ) is the product of the pole strength by the length of
the magnet. The dimensional formula is [M'LzT'lp.l].
Magnetic pole s t r e n g t h or q u a n t i t y of magnetism
been shown to have the dimensional formula [M'L;T-'p'].
Magnetic potential or magnetomotive force at a point is measured by
the work which is required to bring unit quantity of positive magnetism from
zero potential to the point. The dimensional formula is the ratio of the formulae
for work and magnetic quantity [ M L 2 T 2 / X i L ~ T - ' por
Magnetic reluctance is the ratio of magnetic potential difference to magnetic flux. The dimensional formula is [ L ? p - l ] .
SMITHSONIAN PHYSICAL TABLES
Magnetic susceptibility ( K ) is the ratio of intensity of magnetization
produced and the intensity of the magnetic field producing it. The dimensional
formula is [M'L-'T-'p'/M'L-'T-' P 1 or [PI.
Mutual inductance of two circuits is the electromotive force produced in
one per unit rate of variation of the current in the other. The dimensional
formula is the same as for self-inductance.
Peltier effect, coefficient of, is measured by the ratio of the quantit,ppf
heat and quantity of electricity. The diinensional formula is [ML2T2/M1L p '1
the same as for electromotive force.
Q u a n t i t y of electricity is the product of the current and time. The diniensional formula is [M'L1p-+].
Resistance of a conductor is the ratio of the difference of potential between its ends and the constant current flowing. The dimensional formula is
[ll,f1L T-?p1/M4L1T-1p -& ] or [ L T - l p ] .
Resistivity is the reciprocal of conductivity as just defined. The dimensional formula is [ L 2 T 1 p ] .
Self-inductance is for any circuit the electromotive force produced in it by
unit rate of variation of the current through it. The dimensional formula is
the product of the formulae for electromotive force and time divided by that
for current or [ M 1 L 8 T 2 p 1 ~ T ~ M ' L ' T - 1 p - or
1] [ L p ] .
Thermoelectric power is measured by the ratio of electromotive force and
temperature. The dimensional formula is [ M'L2T-'pW1].
Exs.-Find the factor required to convert intensity of magnetic field from ft-grain-min
units to cgs units. The formula is [ m ~ / - ~ f - l p;&~n
l = 0.0645, 1 = 30.48, t = 60, and p = 1 ;
the factor is 0.0648: X 30.45-:, or 0.046108.
How many cgs units of magnetic moment make one ft-grain-sec unit of the same quantity? The formula is [ m i l t-'p!I ; 1% = 0.0648. 1 = 30.48, f = 1, and p = 1 ; the number
is 0.06481 x 30.48a, or 1305.6,
If the intensity of magnetization of a steel bar is 700 in cgs units, what will it be in
mm-mg-sec units? The formula is [ ? t z + l ~ f - * p; *m
] = 1000, 1 = 10, t = 1, p = 1 ; the intensity is 700 x 1000' X ,lo', or 70000.
Find the factor required to convert current from cgs units to earth-quadrant-lO-=
gram-sec units. The formula is [ ~ n * l + t - ' p - ;~ Inz = lo", 1 = lo-@,p = 1 ; the factor is
10V x lo-!, or 10.
Find the factor required to convert resistance expressed in cgs units into the same expressed in earth-quadrant-10"' gram-sec units. The formula is [ I t P p l ; I = lo-', t = 1,
p = 1 ; the factor is lo-'.
of fundamental quantities
The choice of the nature of the fundamental quantities already made does
not sufficiently define the system for measurements. Some definite unit or
arbitrarily chosen standard must next be taken for each of the fundamental
quantities. This fundamental standard should hzve the qualities of permanence, reproducibility, and availability and be suitable for accurate measures.
Once chosen and made it is called the primary standard and is generally kept
at some central bureau-for
instance, the International Bureau of Weights
and Measures at Scvres, France. A primary standard may also be chosen and
made for derived units (e.g., the new absolute (1945) ohm standard.), when
it is simply a standard closely representing the unit and accepted for practieal
SMITHSONIAN PHYSICAL TABLES
purposes, its value having been fixed by certain measuring processes. Secondary or reference standards are accurately compared copies, not necessarily
duplicates, of the primaries for use in the work-of standardizing laboratories
and the production of working standards for everyday use.
Standard of length.-The primary standard of length which now almost
universally serves as the basis for physical measurements is the meter. I t is
defined as the distance between two lines at 0" C on a platinum-iridium bar
deposited at the International Eureau of Weights and Measures. This bar is
known as the International Prototype Meter, and its length was derived from
the ''metre des Archives," which was made by Eorda. Borda, Delambre,
Laplace, and others, acting as a committee of the French Academy, recommended that the standard unit of length should be the ten-millionth part of the
length, from the equator to the pole, of the meridian passing through Paris. In
1795 the French Republic passed a decree making this the legal standard of
length, and an arc of the meridian extending from Dunkirk to Barcelona was
measured by Delambre and Mechain for the purpose of realizing the standard.
From the results of that measurement the meter bar was made by Corda. The
meter is now defined as above and not in terms of the meridian length ; hence,
subsequent measures of the length of the meridian have not affected the length
of the meter.
S t a n d a r d of mass.-The primary standard of mass now almost universally
used as the basis for physical measurements is the kilogram. It is defined as
the mass of a certain piece of platinum-iridium deposited at the International
Bureau of Weights and Measures. This standard is known as the International
Prototype Kilogram. Its mass is equal to that of the older standard, the "kilogram des Archives," made by Borda and intended to have the same mass as a
cubic decimeter of distilled water at the temperature of 4" C.
Copies of the International Prototype Meter and Kilogram are possessed by
the various governments and are called National Prototypes.
unit of time universally used is the mean solar
S t a n d a r d of time.-The
second, or the 86400th part of the mean solar day. It is based on the average
time of one rotation of the earth on its axis relatively to the sun as a point of
reference= 1.002 737 91 sidereal second.
S t a n d a r d of temperature.-The standard scale of temperature, adopted by
the International Committee of Weights and Measures ( 1887), depends on
the constant-volume hydrogen thermometer. The hydrogen is taken at an
initial pressure at 0" C of 1 meter of mercury, 0" C, sea-level at latitude 45".
The scale is defined by designating the temperature of melting ice as 0" and of
condensing steam as 100" under standard atmospheric pressure.
Thermodynamic (Kelvin) Scale (Centigrade degrees).-Such
independent of the properties of any particular substance, and called the
thermodynamic, or absolute scale, was proposed in 1848 by Lord Kelvin. The
temperature is proportional to the average kinetic energy per molecule of a
International temperature scale.-See
Numerically different systems of units.-The
quantities which form the basis of a system for measurements have been chosen
and the fundamental standards selected and made. Custom has not however
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