# 1911 Encyclopædia Britannica/Units, Physical

**UNITS, PHYSICAL.** In order that our acquaintance with any part of nature may become exact we must have not merely
a qualitative but a quantitative knowledge of facts. Hence
the moment that any branch of science begins to develop to
any extent, attempts are made to measure and evaluate the
quantities and effects found to exist. To do this we have
to select for each measurable magnitude a *unit* or standard of
reference (Latin, *unitas*, unity), by comparison with which
amounts of other like quantities may be numerically defined.
There is nothing to prevent us from selecting these fundamental
quantities, in terms of which other like quantities are to be
expressed, in a perfectly arbitrary and independent manner,
and as a matter of fact this is what is generally done in the early
stages of every science. We may, for instance, .choose a certain
length, a certain volume, a certain mass, a certain force or
power as our units of length, volume, mass, force or power,
which have no simple or direct relation to each other. Similarly
we may select for more special measurements any arbitrary
electric current, electromotive force, or resistance, and call
them our units. The progress of knowledge, however, is greatly
assisted if all the measurable quantities are brought into relation
with each other by so selecting the units that they are related
in the most simple manner, each to the other and to one common
set of measurable magnitudes called the *fundamental quantities.*

The progress of this co-ordination of units has been greatly
aided by the discovery that forms of physical energy can be
converted into one another, and that the conversion is by
definite rule and amount (see Energy). Thus the mechanical
energy associated with moving masses can be converted into
heat, hence heat can be measured in mechanical energy units.
The amount of heat required to raise one gramme of water
through 1° C. in the neighbourhood of 10° C. is equal to forty-two
million *ergs*, the *erg* being the kinetic energy or energy of
motion associated with a mass of 2 grammes when moving
uniformly, without rotation, with a velocity of 1 cm. per second.
This number is commonly called the “mechanical equivalent
of heat,” but would be more exactly described as the “mechanical
equivalent of the specific heat of water at 10° C.” Again,
the fact that the maintenance of an electric current requires
energy, and that when produced its energy can be wholly
utilized in heating a mass of water, enables us to make a similar
statement about the energy required to maintain a current of
one ampere through a resistance of one ohm for one second, and
to define it by its equivalent in the energy of a moving mass.
Physical units have therefore been selected with the object of
establishing simple relations between each of them and the
fundamental mechanical units. Measurements based on such
relations are called absolute measurements. The science of
dynamics, as far as that part of it is concerned which deals
with the motion and energy of material substances, starts
from certain primary definitions concerning the measurable
quantities involved. In constructing a system of physical
units, the first thing to consider is the manner in which we
shall connect the various items. What, for instance, shall be
the unit of force, and how shall it be determined by simple
reference to the units of mass, length and time?

The modern absolute system of physical measurement is founded upon dynamical notions, and originated with C. F. Gauss. We are for the most part concerned in studying motions in nature; and even when we find bodies at rest in equilibrium it is because the causes of motion are balanced rather than absent. Moreover, the postulate which lies at the base of all present-day study of physics is that in the ultimate issue we must seek for a mechanical explanation of the facts of nature if we are to reach any explanation intelligible to the human mind. Accordingly the root of all science is the knowledge of the laws of motion, and the enunciation of these laws by Newton laid the foundation of a more exact knowledge of nature than had been possible before. Our fundamental scientific notions are those of length, time, and mass. No metaphysical discussion has been able to resolve these ideas into anything simpler or to derive them from each other. Hence in selecting units for physical measurements we have first to choose units for the above three quantities.

*Fundamental Units.*—Two systems of fundamental units are
in common use: the British system, having the yard and
pound as the standard units of length and mass, frequently
termed the “foot-pound-second” (F.P.S.) system; and the
“centimetre-gramme-second” system (C.G.S.), having the
centimetre and gramme as standard units of length and mass,
termed the “metric” system. The fundamental unit of time
is the same in both systems, namely, the “mean solar second,”
86,400 of which make 1 solar day (see Time). Since these
systems and the corresponding standards, together with their
factors of conversion, are treated in detail in the article
Weights and Measures, we need only deal here with such
units as receive special scientific use, *i.e.* other than in ordinary
commercial practice. The choice of a unit in which to express
any quantity is determined by the magnitude and proportional
error of the measurement. In astronomy, where immense
distances have to be very frequently expressed, a common unit
is the mean radius of the earth's orbit, the “astronomical unit”
of length, i.e. 92,900,000 miles. But while this unit serves well
for the region of our solar system, its use involves unwieldy
numerical coefficients when stellar distances are to be expressed.
Astronomers have therefore adopted a unit of length termed the
“light year,” which is the distance traversed by light in a year;
this unit is 63,000 times the mean radius of the earth's orbit.
The relative merits of these units as terms in which astronomical
distances may be expressed is exhibited by the values of the
distance of the star α. Centauri from our earth, namely,
25,000,000,000,000 miles = 275,000 astronomical units = 4.35
light years.

As another example of a physical unit chosen as a matter of
convenience, we may refer to the magnitudes of the wave-lengths
of light. These quantities are extremely small, and admit of
correct determination to about one part in ten-thousand, and
range, in the visible spectrum, from about 6 to 4 ten-millionths
of a metre. Since their values are determined to four significant
figures, it is desirable to choose a unit which represents the value
as an integer number; the unit is therefore a ten-thousand millionth
of a metre, termed a “tenth metre,” since it is 10^{−10}
metres. Sometimes the, thousand-millionth of a metre, the
“micro millimetre,” denoted by μμ, serves as a unit for wave
lengths. Another relatively minute unit is the “micron,”
denoted by μ, and equal to one-millionth of a metre; it is especially
used by bacteriologists.

*Units in Mechanics.*—The quantities to be measured in
mechanics (*q.v.*) are velocity and acceleration, dependent on the
units of length and time only, momentum, force, energy or work
and power, dependent on the three fundamental' units. The
unit of velocity in the British system is 1 foot, 1 yard, or 1 mile
per second; or the time to which the distance is referred may be
expressed in hours, days, &c., the choice depending upon the
actual magnitude of the velocity or on custom. Thus the muzzle
velocity of a rifle or cannon shot is expressed in feet per second,
whereas the speed of a train is usually expressed in miles per
hour. Similarly, the unit on the metric system isr metre, or any
decimal multiple thereof, per second, per hour, &c. Since
acceleration is the rate of increase of velocity per unit time, it
is obvious that the unit of acceleration depends solely upon the
units chosen to express unit velocity; thus if the unit of velocity
be one foot per second, the unit of acceleration is one foot per
second per second, if one metre per second the unit is one metre
per second per second, and similarly for other units of velocity.
Momentum is defined as the product of mass into velocity;
unit momentum is therefore the momentum of unit mass into
unit velocity; in the British system the unit of mass may be the
pound, ton, &c., and the unit of velocity any of those mentioned
above; and in the metric system, the gramme, kilogramme, &c.,
may be the unit of mass, while the metre per second, or any other
metric unit of velocity, is the remaining term of the product.

Force, being measured .by the change of momentum in unit time, is expressed in terms of the same units in which unit momentum is defined. The common British unit is the “poundal,” the force which in one second retards or accelerates the velocity of a mass of one pound by one foot per second. The metric (and scientific) unit, named the “dyne,” is derived from the centimetre, gramme, and second. The poundal and dyne are related as follows:—1 poundal= 13,825.5 dynes.

A common unit of force, especially among engineers, is the “weight of one pound,” by which is meant the force equivalent to the gravitational attraction of the earth on a mass of one pound. This unit obviously depends on gravity; and since this varies with the latitude and height of the place of observation (see Earth, Figure of), the “force of one pound” of the engineer is not constant. Roughly, it equals 32.17 poundals or 980 dynes. The most frequent uses of this engineer's unit are to be found in the expressions for pressure, especially in the boilers and cylinders of steam engines, and in structures, such as bridges, foundations of buildings, &c. The expression takes the form: pounds per square foot or inch, meaning a force equivalent to so many pounds' weight distributed over a square foot or inch, as the case may be. Other units of pressure (and therefore special units of force) are the “atmosphere” (abbreviated “atmo”), the force exerted on unit area by the column of air vertically above it; the “millimetre or centimetre of mercury,” the usual scientific units, the force exerted on unit area by a column of mercury one millimetre or centimetre high; and the “foot of water,” the column being one foot of Water. All these units admit of ready conversion:—1 atmo= 760 mm. mercury= 32 feet of water= 1,013,600 dynes.

Energy of work is measured by force acting over a distance. The scientific unit is the “erg,” which is the energy expended when a force of one dyne acts over one centimetre. This unit is too small for measuring the quantity of energy associated, for instance, with engines; for such purposes a unit ten-million times as great, termed the “joule,” is used. The British absolute unit is the “poundal-foot.” As we noticed in the case of units of force, common-life experience has led to the introduction of units dependent on gravitation, and therefore not invariable: the common British practical unit of this class is the “foot pound”; in the metric system its congener is the “kilogramme metre.”

Power is the rate at which force does work; it is therefore expressed by “units of energy per second.” The metric unit in use is the “watt,” being the rate equal to one joule per second. Larger units in practical use are: “kilowatt, equal to 1000 watts; the corresponding energy unit being the

kilowatt-second, and 3600 kilowatt-seconds or 1 kilowatt-hour
called a “Board of Trade unit” or a “kelvin.” This last
is a unit of energy, not power. In British engineering
practice the common unit of power is the “horse-power”
(**HP**), which equals 550 foot-pounds performed per second,
or 33,000 foot-pounds per minute; its equivalent in the
metric system is about 746 watts, the ratio varying, however,
with gravity.

*Units of Heat.*—In studying the phenomena of heat, two
measurable quantities immediately present themselves:—(1)
temperature or thermal potential, and (2) quantity of heat.
Three arbitrary scales are in use for measuring temperature
(see Thermometry), and each of these scales affords units
suitable for the expression of temperature. On the Centigrade
scale the unit, termed a “Centigrade degree,” is one-hundredth
of the interval between the temperature of water boiling
under normal barometric pressure (760 mm. of mercury) and
that of melting ice; the “Fahrenheit degree” is one-hundred and-eightieth,
and the “Réaumur degree” is one-eightieth
of the same difference. In addition to these scales there is the
“thermo-dynamic scale,” which, being based on dynamical
reasoning, admits of correlation with the fundamental units.
This subject is discussed in the articles Thermodynamics and
Thermometry.

Empirical units of “quantity of heat” readily suggest themselves
as the amount of heat necessary to heat a unit mass of
any substance through unit temperature. In the metric system
the unit, termed a “calorie,” is the quantity of heat required
to raise a gramme of water through one degree Centigrade.
This quantity, however, is not constant, since the specific heat of
water varies with temperature (see Calorimetry). In defining
the calorie, therefore, the particular temperatures must be
specified; consequently there are several calories particularized
by special designations:—(1) conventional or common gramme calorie,
the heat required to raise 1 gramme of water between
150° C. and 17° C. through 1° C.; (2) “mean or average gramme
calorie,” one-hundredth of the total heat required to raise the
temperature of 1 gramme of water from 0° C. to 100° C.; (3)
“zero gramme calorie,” the heat required to raise 1 gramme of
water from 0° C. to 1° C. These units are thus related:—1
common calorie= 1.987 mean calories=0.992 zero calories.
A unit in common use in thermo-chemistry is the *major calorie*,
which refers to one kilogramme of water and 1° C. In the
British system the common unit, termed the “British Thermal
Unit” (B.Th.U.), is the amount of heat required to raise one
pound of water through one degree Fahrenheit.

A correlation of these units of quantity of heat with the
fundamental units of mass, length and time attended the
recognition of the fact that heat was a form of energy; and
their quantitative relationships followed from the experimental
determinations of the so-called “mechanical equivalent
of heat,” *i.e.* the amount of mechanical energy, expressed in
ergs, joules, or foot-pounds, equivalent to a. certain quantity of
heat (cf. Calorimetry). These results show that a gram-calorie
is equivalent to about 4.2 joules, and a British thermal unit to
780 foot-pounds.

*Electrical Units.*—The next most important units are the electrical
units. We are principally concerned in electrical work with
three quantities called respectively, electric current, electromotive
force, and resistance. These are related to one another
by Ohm’s law, which states that the electric current in a circuit
is directly as the electromotive force and inversely as the resistance,
when the current is unvarying and the temperature of
the circuit constant. Hence if we choose units for two of these
quantities, the above law defines the unit for the third. Much
discussion has taken place over this question. The choice
rs decided by the nature of the quantities themselves. Since
resistance is a permanent quality of a substance, it is possible
to select a certain piece of wire or tube full of mercury, and
declare that its resistance shall be the unit of resistance, and
lf the substance is permanent we shall possess an unalterable
standard or unit of resistance. For these reasons the practical
unit of resistance, now called the international ohm, has been
selected as one of the above three electrical units.

It has now been decided that the second unit shall be the unit of electric current. As an electric current is not a thing, but a process, the unit current can only be reproduced when desired. There are two available methods for creating a standard or unit electric current. If an unvarying current is passed through a neutral solution of silver nitrate it decomposes or electrolysis it and deposits silver upon the negative pole or cathode of the electrolytic cell. According to Faraday’s law and all subsequent experience, the same current deposits in the same time the same mass of silver. Hence we may define the unit current by the mass of silver it can liberate per second. Again, an electric current in one circuit exerts mechanical force upon a magnetic pole or a current in another circuit suitably placed, and we may measure the force and define by it a unit electric current. Both these methods have been used. Thirdly, the unit of electromotive force may be defined as equal to the difference of potential between the ends of the unit of resistance when the unit of current flows in it.

Apart, however, from the relation of these electrical units to each other, it has been found to be of great importance to establish a simple relation between the latter and the absolute mechanical units. Thus an electric current which is Absolute electrical units. passed through a conductor dissipates its energy as heat, and hence creates a certain quantity of heat per unit of time. Having chosen our units of energy and related unit of quantity of heat, we must so choose the unit of current that when passed through the unit of resistance it shall dissipate 1 unit of energy in 1 unit of time.

A further consideration has weight in selecting the size of
the units, namely, that they must be of convenient magnitude
for the ordinary measurements. The founders of the
modern system of practical electrical units were a British Association units
committee appointed by the British Association in
1861, at the suggestion of Lord Kelvin, which made its
first report in 1862 at Cambridge (see *B. A. Report*). The five
subsequent reports containing the results of the committee’s
work, together with a large amount of most valuable matter
on the subject of electric units, were collected in a Volume
edited by Prof. Fleeming Jenkin in 1873, entitled *Reports of the*
*Committee on Electrical Standards.* This committee has continued
to sit and report annually to the British Association
since that date. In their second report in 1863 (see *B.A.*
*Report*, Newcastle-on-Tyne) the committee recommended the
adoption of the absolute system of electric and magnetic units
on the basis originally proposed by Gauss and Weber, namely,
that these units should be derived from the fundamental dynamical
units, but assuming the units of length, mass and time
to be the metre, gramme and second instead of the millimetre
milligramme and second as proposed by Weber. Considerable
differences of opinion existed as to the choice of the fundamental
units, but ultimately a suggestion of Lord Kelvin’s was
adopted to select the centimetre, gramme, and second, and to
construct a system of electrical units (called the C.G.S. system)
derived from the above fundamental units. On this system
the unit of force is the *dyne* and the unit of work the *erg*. The
dyne is the uniform force which when acting on a mass of
1 gramme for 1 second gives it a velocity of 1 centimetre per
second. The erg is the work done by 1 dyne when acting
through a distance of 1 centimetre in its own direction. The
electric and magnetic units were then derived, as previously
suggested by Weber, in the following manner: If we consider
two very small spheres placed with centres 1 centimetre apart
in air and charged with equal quantities of electricity, then if
the force between these bodies is 1 dyne each sphere is said
to be charged with 1 unit of electric quantity on the electrostatic
system. Again, if we consider two isolated magnetic
poles of equal strength and consider them placed 1 centimetre
apart in air, then if the force between them is 1 dyne these
poles are said to have a strength of 1 unit on the electromagnetic
system. Unfortunately the Committee did not take into
account the fact that in the first case the force between the
electric charges depends upon and varies inversely as the dielectric
constant of the medium in which the experiment is
made, and in the second case it depends upon the magnetic
permeability of the medium in which the magnetic poles exist.
To put it in other words, they assume that the dielectric constant
of the cir cum ambient medium was unity in the first case, and
that the permeability was also unity in the second case.

The result of this choice was that two systems of measurement
were created, one depending upon the unit of electric quantity
so chosen, called the *electrostatic system*, and the other depending
upon the unit magnetic pole defined as above, called the
*electromagnetic system* of C.G.S. units. Moreover, it was found
that in neither of these systems were the units of very convenient
magnitude. Hence, finally, the committee adopted a
third system of units called the practical system, in which convenient
decimal multiples or fractions of the electromagnetic
units were selected and named for use. This system, moreover,
is not only consistent with itself, but may be considered to be
derived from a system of dynamical units in which the unit of
length is the earth quadrant or 10 million metres, the unit of
mass is 10^{−11} of a gramme and the unit of time is 1 second. The
units on this system have received names derived from those
of eminent discoverers. Moreover, there is a certain relation
between the size of the units for the same quantity on the
electrostatic (E.S.) system and that on the electromagnetic
(E.M.) system, which depends upon the velocity of light in the
medium in which the measurements are supposed to be made.
Thus on the E.S. system the unit of electric quantity is a point
charge which at a distance of 1 cm. acts on another equal charge
with a force of 1 dyne. The E.S. unit of electric current is a
current such that 1 E.S. unit of quantity flows per second across
each section of the circuit. On the E.M. system we start with
the definition that the unit magnetic pole is one which acts
on another equal pole at a distance of 1 cm. with a force of
1 dyne. The unit of current on the E.M. system is a current
such that if flowing in circular circuit of r cm. radius each unit
of length of it will act on a unit magnetic pole at the centre
with a force of 1 dyne. This E.M. unit of current is much larger
than the E.S. unit defined as above. It is *v* times greater,
where *v*=3×10^{10} is the velocity of light in air expressed in
cms. per second. The reason for this can only be understood
by considering the *dimensions* of the quantities with which
we are concerned. If L, M, T denote length, mass, time,
and we adopt certain sized units of each, then we may measure
any derived quantity, such as velocity, acceleration, or force
in terms of the derived dynamical units as already explained.
Suppose, however, we alter the size of our selected units of
L, M or T, we have to consider how this alters the corresponding
units of velocity, acceleration, force, &c. To do this we
have to consider their dimensions. If the unit of velocity is
the unit of length passed over per unit of time, then it is
obvious that it varies directly as the unit of length, and
inversely as the unit of time. Hence we may say that
the dimensions of velocity are L/T or LT^{−1}; similarly the
dimensions of acceleration are L/T^{2} or LT^{−2}, and the dimensions
of a force are MLT^{−2}.

For a fuller explanation see above (Units, Dimensions of), or
Everett’s *Illustrations of the C.G.S. System of Units.*

Accordingly on the electrostatic system the unit of electric
quantity is such that *f*=*q*^{2}/K*d*^{2}, where *q* is the quantity of
the two equal charges, *d* their distance, *f* the mechanical
force or stress between them, and K the dielectric
Electrostatic and electro-magnetic units. constant of the dielectric in which they are immersed.
Hence since *f* is of the dimensions MLT^{−2}, *q*^{2}
must be of the dimensions of KML^{3}T^{−2}, and *q* of the
dimensions M^{1/2}L^{3/2}T^{−1}K^{1/2}. The dimensions of K, the dielectric
constant, are unknown. Hence, in accordance with the suggestion
of Sir A. Rücker (*Phil. Mag.*, February 1889), we must
treat it as a fundamental quantity. The dimensions of an
electric current on the electrostatic system are therefore those
of an electric quantity divided by a time, since by current we
mean the quantity of electricity conveyed per second. Accordingly
current on the E.S. system has the dimensions M^{1/2}L^{3/2}T^{−1}K^{1/2}.

We may obtain the dimensions of an electric current on the
magnetic system by observing that if two circuits traversed by the
same or equal currents are placed at a distance from each other,
the mechanical force or stress between two elements of the circuit,
in accordance with Ampere’s law (see Electro-kinetics), varies
as the square of the current C, the product of the elements of length
*ds*, *ds*′ of the circuits, inversely as the square of their distance d, and
directly as the permeability, μ, of the medium in which they are
immersed. Hence C^{2}*ds* *ds*′μ/*d*^{2} must be of the dimensions of a force
or of the dimensions MLT^{−2}. Now, *ds* and *ds*′ are lengths, and *d*
is a length, hence the dimensions of electric current on the E.M.
system must be M^{1/2}L^{1/2}T^{−1}μ^{−1/2}. Accordingly the dimensions of
current on the E.S. system are M^{1/2}L^{3/2}T^{−2}K^{1/2}, and on the E.M. system
the are M^{1/2}L^{1/2}T^{−1}μ^{−1/2}, where μ and K, the permeability and dielectric
constant of the medium, are of unknown dimensions, and
therefore treated as fundamental quantities.

The ratio of the dimensions of an electric current on the two
systems (E.S. and E.M.) is therefore LT^{−1}K^{1/2}μ^{1/2}. This ratio must be
a mere numeric of no dimensions, and therefore the dimensions of
√Kμ must be those of the reciprocal of a velocity. We do not know
what the dimensions of, μ and K are separately, but we do know,
therefore, that their product has the dimensions of the reciprocal
of the square of a velocity.

Again, we may arrive at two dimensional expressions for electromotive
force or difference of potential. Electrostatic difference of
potential between two places is measured by the mechanical work
required to move a small conductor charged with a unit electric
charge from one place to the other against the electric force. Hence
if V stands for the difference of potential between the two places,
and Q for the charge on the small conductor, the product QV must
be of the dimensions of the *work* or *energy*, or of the force×length,
or of ML^{2}T^{−2}. But Q on the electrostatic system of measurement
is of the dimensions M^{1/2}L^{3/2}T^{−1}K^{1/2}; the potential difference V must
be, therefore, of the dimensions M^{1/2}L^{1/2}T^{−1}K^{−1/2}. Again, since by
Ohms law and Joule’s law electromotive force multiplied by a
current is equal to the power expended on a circuit, the dimensions
of electromotive force, or, what is the same thing, of
potential difference, in the electromagnetic system of measurement
must be those of power divided by a current. Since mechanical
power means *rate of doing work*, the dimensions of power must
be ML^{2}T^{−3}. We have already seen that on the electromagnetic
system the dimensions of a current are M^{1/2}L^{1/2}T^{−1}μ^{−1/2}; therefore the
dimensions of electromotive force or potential on the electromagnetic
system must be M^{1/2}L^{3/2}T^{−2}μ^{1/2}. Here again we find that the ratio
of the dimensions on the electrostatic system to the dimensions on
the electromagnetic system is L^{−1}TK^{−1/2}μ^{−1/2}.

In the same manner we may recover from fundamental facts and
relations the dimensions of every electric and magnetic quantity on
the two systems, starting in one case from electrostatic phenomena
and in the other case from electromagnetic or magnetic. The
electrostatic dimensional expression will always involve K, and
the electromagnetic dimensional expression will always Involve
μ, and in every case the dimensions in terms of K are to those in
terms of μ for the same quantity in the ratio of a power of LT^{−1}K^{1/2}μ^{1/2}.
This therefore confirms the view that whatever may be the true
dimensions in terms of fundamental units of μ and K, their product
is the inverse square of a velocity.

Table I. gives the dimensions of all the principal electric and magnetic quantities on the electrostatic and electromagnetic systems.

It will be seen that in every case the ratio of the dimensions on
the two systems is a power of LT^{−1}K^{1/2}μ^{1/2}, or of a velocity multiplied
by the square root of) the product K and μ; In other words, it is the
product of a velocity multiplied by the geometric mean of K and μ.
This quantity 1/√Kμ must therefore be of the dimensions of a
velocity, and the questions arise, What is the absolute value of this
velocity? and, How is it to be determined? The answer is, that
the value of the velocity in concrete numbers maybe obtained by
measuring the magnitude of any electric quantity in two ways,
one making use only of electrostatic phenomena, and the other
only of electromagnetic. To take one instance:—It is easy to show
that the electrostatic capacity of a sphere suspended in air or in
vacuo at a great distance from other conductors is given by a number
equal to its radius in centimetres. Suppose such a sphere to be
charged and discharged rapidly with electricity from any source,
such as a battery. It would take electricity from the source at a
certain rate, and would in fact act like a resistance in permitting
the passage through it or by it of a certain quantity of electricity
per unit of time. If K is the capacity and *n* is the number of discharges
per second, then *n*K is a quantity of the dimensions of an
electric conductivity, or of the reciprocal of a resistance. If a
conductor, of which the electrostatic capacity can be calculated,
and which has associated with it a commutator that charges and
discharges it *n* times per second, is arranged in one branch of a
Wheatstone's Bridge, it can be treated and measured as if it were
a resistance, and its equivalent resistance calculated in terms of
the resistance of all the other branches of the bridge (see *Phil. Mag.*,
1885, 20, 258).

Table I.—Dimensions of Electric Quantities

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Quantity Symbol Dimensions Dimensions Ration

Accordingly, we have two methods of measuring the capacity of
a conductor. One, the electrostatic method, depends only on
the measurement of a length, which in the case of a sphere in free
space is its radius; the other, the electromagnetic method, determines
the capacity in terms of the quotient of a time by a resistance.
The ratio of the electrostatic to the electromagnetic value of the
same capacity is therefore of the dimensions of a velocity multiplied
by a resistance in electromagnetic value, or of the dimensions of a
velocity squared. This particular experimental measurement has
been carried out carefully by many observers, and the result has
been always to show that the velocity *v* which expresses the ratio
is very nearly equal to 30 thousand million centimetres per second;
*v*=nearly 3× 10^{10}. The value of this important constant can be
determined by experiments made to measure electric quantity,
potential, resistance or capacity, both in electrostatic and in electromagnetic
measure. For details of the various methods employed,
the reader must be referred to standard treatises on Electricity
and Magnetism, where full particulars will be found (see Maxwell,
*Treatise on Electricity and Magnetism*, vol. ii. ch. xix. 2nd ed.;
also Mascart and Joubert, *Treatise on Electricity and Magnetism*,
vol. ii. ch. viii., Eng. trans. by Atkinson).

Table II. gives a list of some of these determinations of *v*, with
references to the original papers.

It will be seen that all the most recent values, especially those
in which a comparison of capacity has been made, approximate to
3 × 10^{10} centimetres per second, a value which is closely in accord
with the latest and best determinations of the velocity of light.

We have in the next place to consider the question of practical electric units and the determination and construction of concrete standards. The committee of the British Association charged with the duty of arrangingPractical units a system of absolute and magnetic units settled also on a system of practical units of convenient magnitude, and gave names to them as follows:–

10^{9} absolute electromagnetic |
units of resistance | = 1 ohm |

10^{8} 〃 〃 |
units of electromotive force | = 1 volt |

110th of an 〃 〃 | unit of current | = 1 ampere |

110th of an 〃 〃 | unit of quantity | = 1 coulomb |

10^{−9} 〃 〃 |
units of capacity | = 1 farad |

10^{−15} 〃 〃 |
units of capacity | = 1 microfarad |

Since the date when the preceding terms were adopted, other multiples of absolute C.G.S. units have received practical names, thus:—

10^{7} ergs or absolute C. G. S. units of energy = 1 joule

10^{7} ergs per second or C.G.S. units of power = 1 watt

10^{9} absolute units of inductance = 1 henry

10^{8} absolute units o magnetic flux = 1 weber^{[1]}

1 absolute unit of magneto motive force = 1 gauss^{[1]}

An Electrical Congress was held in Chicago, U.S.A. in August 1893, to consider the subject of international practical electrical units, and the result of a conference between scientific representatives of Great Britain, the United States, France, Germany, Italy, Mexico, Austria, Switzerland, Sweden and British North America, after deliberation for six days, was a unanimous agreement to recommend the following resolutions as the definition of practical international units. These resolutions and definitions were confirmed at other conferences, and at the last one held in London in October 1908 were finally adopted. It was agreed

to take:—

“As a unit of resistance, the *International Ohm*, which is
based upon the ohm equal to 10^{9} units of resistance of the
C.G.S. system of electromagnetic -units, and is represented
by the resistance offered to an unvarying electric current
by a column of mercury at the temperature of melting ice
14.4521 grammes in mass, of a constant cross-sectional area
and of the length of 106.3 cm.

“As a unit of current, the *International Ampere*, which is
one-tenth of the unit of current of the C.G.S. system of
electromagnetic units, and which is represented sufficiently
well for practical use by the unvarying current which,
when passed through a solution of nitrate of silver in water,
deposits silver at the rate of 0.00111800 of a gramme per
second.

“As a unit of electromotive force, the *International Volt*, which is
the electromotive force that, steadily applied to a conductor whose
resistance is one international ohm, will produce a current of one
international ampere. It is represented sufficiently well for
practical purposes by 1000010184 of the E.M.F. of a normal or saturated
cadmium Weston cell at 20° C., prepared in the manner described
in a certain specification.

“As a unit of quantity, the *International Coulomb*, which is the
quantity of electricity transferred by a current of one international
ampere in one second.

“As the unit of capacity, the *International Farad*, which is the
capacity of a condenser charged to a potential of one international
volt by one international coulomb of electricity.

“As a unit of work, the *Joule*, which is equal to 107 units of
work in the C.G.S. System, and which is represented sufficiently
well for practical use by the energy expended in one second by an
international ampere in an international ohm.

“As a unit of power, the *Watt*, which is equal to 10^{7} units of
power in the C.G.S. System, and which is represented sufficiently
well for practical use by the work done at the rate of
second.

“As the unit of inductance, the *Henry*, which is
in a circuit when an electromotive force induced in
one international volt, while the inducing current
rate of one ampere per second.”

A table should appear at this position in the text.See Help:Table for formatting instructions. |

TABLE II.-OBSERVED VALUES of *V* IN CENTIMETRES PER SECOND

Date. Name. Reference. Electric Quantity Measured. *v* in Centimetres per Second.

1856 W. Weber and Electrodynamische Quantity 3.107 × 10^{10}
R. Kohlrausch Masrbestirnmungen and Pogg. Ann.xcix., August 10,1856

1867; Lord Kelvin Report of British Potential
1868 and W. F. King Assoc..1369.D~ 434;
and Reports on Electrical Standards, F. Jenkin, p. 186 2.81 × 10^{10}

1868 J. Clerk Maxwell Phil. Trans. Roy. Soc., 1868, p. 643 2.84 × 10^{10}

1872 Lord Kelvin and Phil. Trans. Roy. Dugald M'Kichan- Soc.. 1873, p. 409 2.89 × 10^{10}

1878 W. E. Ayrton and Jaurn. Soc. Tel. Eng.J. Perry vol. viii. p. 126 Capacity 2.94 × 10^{10}

1880 Lord Kelvin and Shida, Phil. Mag., 1880, vol. 10, x. p. 431 Potential 2.995 × 10^{10}

1881 A. G. Stoletow Soc. Franc. de Phys., 1881 Capacity 2.99 × 10^{10}

1882 F. Exner . Wien. Ber., 1882 Potential 2.92 × 10^{10}

1883 Sir J. J. Thomson Phil. Trans. Roy. Soc., 1883, p. 707 Capacity 2.963 × 10^{10}

1884 I. Klemencic . Journ. Soc. Tel. Eng., 1887, p. 162 3.019 × 10^{10}

1888 F. Himstedt . . *Electrician*, March 23, 1888, vol. xx. p. 530 3.007 × 10^{10}

1888 Lord Kelvin, Ayrton and Perry | *British Association*, Bath; and *Electrician*, Sept. 28, 1888 | Potential 2.92 × 10^{10}

1888 H. Fison, Electrician, vol. xxi. p. 215; and Proc. Phys. Soc. Lond., June 9, 1888 Capacity 2.965 × 10^{10}

1889 Lord Kelvin *Proc. Roy. Inst.*, 1889 Potential 3.004 × 10^{10}

1889 H. A. Rowland Phil—Mag-#889 Quantity 2.981 × 10^{10}

1889 E. B. Rosa *Phil. Mag.*,1889 Capacity 3.000 × 10^{10}

1890 Sir J. J. Thomson and G. F. C. Searle *Phil. Trans.*, .1890 .., 2.995 × 10^{10}

1891 M. E. Maltby. . *Wied. Ann.* 1897 Alternating Currents 3.015 × 10^{10}

In connexion with the numerical values in the above definitions much work has been done. The electrochemical equivalent of silver or the weight in grammes deposited per second by 1 C.G.S. electromagnetic unit of current has been the subject of much research. The following determinations of it have been given by various observers:—

Name. Value. I Reference.

E. E. N. Mascart . 0.011156 ]oZ4r§ t. de ghysigue, 1884, 2 3 2 3.

F. and W. Kohlrausch 0.011183 Wiedl Afnn., 1886, 27, 1. Lord Rayleigh and Mrs 0.011179 Phtl. Trans. Roy. Soc., Sedgwick 1884, 2, 411.

J. S. H. Pellat and 0.0I1192 Jonrn. de Phys., 1890, (2), A. Potier 9, 381.

Karl Kahle . 0.011183 Wzcd, Ann., '1899, 67, 1.

G. W. Patterson and 0.011192 Physical Review, 1898, 7, K. E. Guthe 251.

J. S. H. Pellat and S. A. 0.011195 *Comptes rendus*, 1903,
Leduc 136. 1649.

Although some observers have urged that the 0.01119 is nearer
to the true value than 0.01118, the preponderance of the evidence
seems in favour of this latter number and hence the value per ampere second
is taken as 0.0011800 gramme. The exact value of the
electromotive force of a Clark cell has also been the subject of
much research. Two forms of cell are in use, the simple tubular
form and the H-form introduced by Lord Rayleigh. The Berlin
Reichsanstalt has issued a specification for a particular H-form of
Clark cell, and its E.M.F. at 15° C. is taken as 1-4328 international
volts. The E.M.F. of the cell set up in accordance with the British
Board of Trade specification is taken as 1.434 international volts
at 15° C. The detailed specifications are given in Fleming's *Handbook*
*for the Electrical Laboratory and Testing Room* (1901), vol. i.
chap. 1; in the same book will be found copious references to the
scientific literature of the Clark cell. One objection to the Clark
cell as a concrete standard of electromotive force is its variation
with temperature and with slight impurities in the mercurous
sulphate used in its construction. The Clark cell is a voltaic cell
made with mercury, mercurous sulphate, zinc sulphate, and zinc
as elements, and its E.M.F. decreases 0.08% per degree Centigrade
with rise of temperature. In 1891 Mr Weston proposed to
employ cadmium and cadmium sulphate in place of zinc and
zinc sulphate and found that the temperature coefficient for the
cadmium cell might be made as low as 0.004 % per degree
Centigrade. Its E.M.F. is, however, 1.0184 international volts
at 20, C. For details of construction and the literature of the
subject see Fleming's *Handbook for the Electrical Laboratory*, vol. i.
chap. 1.

In the British Board of Trade laboratory the ampere and the
volt are not recovered by immediate reference to the electrochemical
equivalent of silver or the Clark cell, but by means of instruments
called a standard ampere balance and a standard 100-volt electrostatic
voltmeter. In the standard ampere balance the current is
determined by weighing the attraction between two coils traversed
by the current, and the ampere is defined to be the current
which causes a certain attraction between the coils of this
standard form of ampere balance. The form of ampere balance in
use at the British Board of Trade electrical standards office is
described in Fleming's *Handbook for the Electrical Laboratory*, vol. i.,
and that constructed for the British National Physical Laboratory
in the report of the Committee on Electrical Standards (*Brit. Assoc.*
*Rep.*, 1905). This latter instrument will recover the ampere within
one-thousandth part. For a further description of it and for full
discussion of the present position of knowledge respecting the
values of the international practical units the reader is referred to
a paper by Dr F. A. Wolff read before the International Electrical
Congress at St Louis Exhibition, U.S.A., in 1904, and the subsequent
dispassion (see *Journ. Inst. Elec. Eng. Lond.*, 1904–5, 34, 190,
and 35, 3.

The construction of the international ohm or practical unit of
resistance involves a knowledge of the specific resistance of mercury.
Numerous determinations of this constant have been made. The
results are expressed either in terms .of the length in cm. of the
column of pure mercury of 1 sq. mm. in section which at 0° C. has a
resistance of 109 C.G.S. electromagnetic units, or else in terms of
the weight of mercury in grammes for a column of constant cross sectional
area and length of 100.3 cm. The latter method was
adopted at the British Association Meeting at Edinburgh in 1892,
but there is some uncertainty as to the value of the density of
mercury at 0° C. which was then adopted. Hence it was proposed
by Professor J. Viriamu [ones that the re determination of the ohm
should be made when required by means of the'Lorentz method
(see J. V. Jones, “The Absolute Measurement of Electrical Resistance,”
*Proc. Roy. Inst.* vol. 14, part iii. p. 601). For the length of
the mercury column defining the ohm as above, Lord Rayleigh in
1882 found the value 106.27 cm., and R. T. Glazebrook in the same
year the value 106.28 cm. by a different method, while another
determination by Lord Rayleigh and Mrs Sedgwick in 1883 gave
106.22 cm. Viriamu ]ones in 1891 gave the value 106-30 cm., and
one by W. E. Ayrton in 1897 by the same method obtained the value
106.27 to 106.28 cm. Hence the specific resistance of mercury
cannot be said to be known to 1 part in 10,000, and the absolute
value of the ohm in centimetres per second is uncertain to at least
that amount. (See also J. Viriamu Jones, “On a Determination
of the International Ohm in Absolute Measure,” *Brit; Assoc.*
*Report*, 1894.)

The above-described practical system based on the C.G.S.
double system of theoretical units labours under several very
great disadvantages. The practical system is derived
from and connected with an abnormally large unit of Rational system of electrical units.
length (the earth quadrant) and an absurdly small
unit of mass. Also in consequence of the manner in
which the unit electric quantity and magnetic pole strength are
defined, a coefficient, 4π, makes its appearance in many practical
equations. For example, on the present system the magnetic
force H in the interior of a long spiral wire of N turns per centimetre
of length when a current of A amperes circulates in the
wire is 4π AN/10. Again, the electric displacement or induction
D through a unit of area is connected with the electric force E
and the dielectric constant K by the equation- D=KE/4π. In
numerous electric and magnetic equations the constant 4π makes
its appearance where it is apparently meaningless. A system of
units in which this constant is put into its right place by appropriate
definitions is called a rational system of electric units.
Several physicists have proposed such systems. Amongst others
that of Professor G. Giorgi especially deserves mention.Giorgi's system of electrical units.
We have seen that in expressing the dimensions of
electric and magnetic qualities we cannot do so simply
by reference to the units of length, mass and time,
but must introduce a fourth fundamental quantity. This
we may take to be the dielectric constant of the ether or its
magnetic permeability, and thus we obtain two systems of
measurement. Professor Giorgi proposes that the four fundamental
quantities shall be the units of length, mass, time and
electrical resistance, and takes as the concrete units or standards
the metre, kilogramme, second and ohm. Now this proposal
not only has the advantage that the theoretical units are
identical with the actual practical concrete units, but it is also
a rational system. Moreover, the present practical units are
unaltered; the ampere, volt, coulomb, weber, joule and watt
remain the actual as well as theoretical units of current, electromotive
force, quantity, magnetic flux, work and power. But
the unit of magnetic force becomes the ampere-turn per metre,
and the unit of electric force the volt per metre; thus the
magnetic units are measured in terms of electric units. The
numerical value of the permeability of ether or air becomes
4π×10^{−7} and the dielectric constant of the ether or air becomes
1/4π×9×10^{9} their product is therefore 1/(3×10^{8})^{2}, which is
the reciprocal of the square of the velocity of light in metres
per second.

For a discussion of the Giorgi proposals, see a paper by Professor
M. Ascoli, read before the International Electrical Congress at St
Louis, 1904 (*Journ. Inst. Elect. Eng. Lond.*, 1904, 34, 176).

It can hardly be said that the present system of electrical units is entirely satisfactory in all respects. Great difficulty would of course be experienced in again altering the accepted practical concrete units, but if at any future time a reformation should be possible, it would be desirable to bear in mind the recommendations made by Oliver Heaviside with regard to their rationalization. The British Association Committee defined the strength of a magnetic pole by reference to the mechanical stress between it and another equal pole: hence the British Association unit magnetic pole is a pole which at a distance of one centimetre attracts or repels another equal pole with a force of one dyne. This, we have seen, is an imperfect definition, because it omits all reference to the permeability of the medium in which the experiment takes place; but it is also unsatisfactory as a starting-point for a system of units for another reason. The important quantity in connexion with polar magnets is not a mechanical stress between the free poles of different magnets, but the magnetic flux emanating from, or associating with, them. From a technical point of view this latter quality is far more important than the mechanical stress between the magnetic poles, because we mostly employ magnets to create induced electromotive force, and the quantity we are then mostly concerned with is the magnetic flux proceeding from the poles. Hence the most natural definition of a unit magnet pole is that pole from which proceeds a total magnetic flux of one unit. The definition of one unit of magnetic iiux must then be that flux which, when inserted into or withdrawn from a conducting circuit of one turn having unit area and unit conductivity, creates in it a flow or circulation of one unit of electric quantity. T he definition of a unit magnetic pole ought, therefore, to have been approached from the definition of a unit of electric quantity.

On the C.G.S. or British Association system, if a magnetic filament
has a pole strength *m*—that is to say, if it has a magnetization
I, and a section *s*, such that I*s* equals *m*—then it can be shown
that the total flux emanating from the pole is . The factor ,
in consequence of this definition, makes its appearance in many
practically important expressions. For instance, in the well-known
magnetic equation connecting the vector values of magnetization
, magnetic force and magnetic flux density , where we have
the equation

the appearance of the quantity disguises the real physical meaning of the equation.

The true remedy for this difficulty has been suggested by Heaviside
to be the substitution of rational for irrational formulae and definitions.
He proposes to restate the definition of a unit magnetic
pole in such a manner as to remove this constant Heaviside’s rational system.
rational from the most frequently employed equations. His start system
mg-point IS a new definition according to which a unit
magnetic pole is said to have a strength of in units if
it attracts or repels another equal pole placed at a distance of
d centimetres with a force of *m* ^{2}4π*d* ^{2} dynes. It follows from this
definition that a rational unit magnetic pole is weaker or smaller
than the irrational or British Association unit pole in the- ratio of
1/√4π to 1, or 0.28205 to 1. The magnetic force due to a rational
pole of strength m at a distance of *d* centimetres being *m*/4π*d* ^{2} units,
if we suppose a magnetic filament having a pole of strength m in
rational units to have a smaller sphere of radius *r* described round
its pole, the magnetic force on the surface of this sphere is *m*/4π*r* ^{2}
units, and this is therefore also the numerical value of the flux
density. Hence the total magnetic flux through the surface of
the sphere is

and therefore the number which denotes the total magnetic flux coming out of the pole of strength in in rational units is also in.

The Heaviside system thus gives us an obvious and natural
definition of a unit magnetic pole, namely, that it is a pole through
which proceeds the unit of magnetic flux. It follows, therefore,
that if the intensity of magnetization of the magnetic filament is
I and the section is *s*, the total flux traversing the centre of the
magnet is I*s* units; and that if the filament is an endless or poleless
iron filament magnetized uniformly by a resultant external magnetic
force H, the flux density will be expressed in rational units by the
equation B =I+H. The physical meaning of this equation is that
the Hux per square centimetre in the iron is simply obtained by
adding together the flux per square centimetre, if the iron is supposed
to be removed, and the magnetization of the iron at that place.
On the rational system, sinceihe unit pole strength has been
decreased in the ratio of I to 1/√4π, or of 3.5441 to 1, when compared
with the magnitude of the present irrational unit pole, and since
the unit of magnetic flux is the total flux proceed in from a magnetic
pole, it follows that Heaviside's unit of magnetic flux is larger than
the C.G.S. unit of magnetic flux in the ratio of 3.5441 to 1.

It will be seen, therefore, that the Heaviside rational units are
all incommensurable with the practical units. This is a great
barrier to their adoption in practice, because it is impossible to
discard all the existing resistance coils, ammeters, voltmeters, &c.,
and equally impossible to recalibrate or readjust them to read in
Heaviside units. A suggestion has been made, in modification of
the Heaviside system, which would provide a system of rational
practical units not impossible of adoption. It has been pointed out
by J. A. Fleming that if in place of the ampere, ohm, watt, joule,
farad and coulomb, we employ the dekampere, dekohm, the
dekawatt, the dekajoule, the dekafarad and the dekacoulomb, we
have a system of practical units such thatirneasurements made in
these units are equal to measurements made in Heaviside rational
units when multiplied by some power of 4π. Moreover, he has shown
that this power of 4π, in the case of most units, varies inversely
as the power under which, μ appears in the complete dimensional
expression for the quantity in electromagnetic measurement.
Thus a current measured in Heaviside rational units is numerically
equal to (4π)^{1/2} times the same current measured in dekamperes, and
in the electromagnetic dimensional expression for current, namely,
L^{1/2}M^{1/2}T^{−1}μ^{−1/2}, μ appears as μ^{−1/2}. If, then, we consider the permeability
of the ether to be numerically 4π instead of unity, the
measurement of a current in dekamperes will be a number which is
the same as that given by reckoning in Heaviside rational units.
In this way a system of *Rational Practical Units* (R.P. Units) might
be constructed as follows:—

The R.P. Unit of | Magnetic Force = 4π | × | the | C.G.S. Unit. |

,,,, | Magnetic Polarity = 1/4π | × | ,, | ,, |

,,,, | Magnetic Flux | = | 1 | ,, |

,,,, | Magnetomotive Force | = | 1 | ,, |

,,,, | Electric Current | = | 1 | ,, |

,,,, | Electric Quantity | = | 1 | ,, |

,,,, | Electromotive Force | = | 10^{9} |
,, |

,,,, | Resistance | = | 10^{8} |
,, |

,,,, | Inductance | = | 10^{8} |
,, |

,,,, | Power | = | 10^{8} |
,, |

,,,, | Work | = | 10^{8} |
,, |

,,,, | Capacity | = | 10^{−8} |
,, |

All except the unit of magnetic force and magnetic polarity are commensurable with the corresponding C.G.S. units, and in multiples which form a convenient practical system.

Even the rational systems already mentioned do not entirely
fulfil the ideal of a system of physical units. There are certain
constants of nature which are fundamental, invariable, and, as far
as we know, of the same magnitude in all parts of the universe.
One of these is the *mass* of the atom, say of hydrogen. Another
is the *length* of a wave of light of particular refrangibility emitted
by some atom, say one of the two yellow lines in the spectrum
of sodium or one of the hydrogen lines. Also a time is fixed by
the velocity of light in space which is according to the best
measurement very close to 3×10^{10} cms. per sec. Another
natural unit is the so-called *constant of gravitation*, or the force
in dynes due to the attraction of two spherical masses each of
1 gramme with centres at a distance of 1 cm. Very approximately
this is equal to 648×10^{10} dynes. Another natural electrical unit of great importance is the electric charge represented by
1 electron (see Electricity). This according to the latest
determination is nearly 3.4×10^{−10} electrostatic units of quantity
on the C.G.S. system. Hence, 2930 million electrons are equal to
1 E.S. unit of quantity on the C.G.S. system, and the quantity
called 1 coulomb is equal to 879×10^{16} electrons. In round
numbers 9×10^{18} electrons make 1 coulomb. The electron is
nature’s unit of electricity and is the charge carried by 1 hydrogen
ion in electrolysis (see Conduction, Electric, § Liquids). Accordingly
a truly natural system of physical units would be one
which was based upon the electron, or a multiple of it, as a unit
of electric quantity, the velocity of light or fraction of it as a
unit of velocity, and the mass of an atom of hydrogen or multiple
of it as a unit of mass. An approximation to such a natural
system of electric units will be found discussed in chap. 17 of a
book on *The Electron Theory*, by E.E. Fournier d’Albe (London,
1906), to which the reader is referred.

See J. Clerk Maxwell, *Treatise on Electricity and Magnetism*,
vol. ii. chap. x. (3rd ed., Oxford, 1892); E. E. N. Mascart and J.
Joubert, *Treatise on Electricity and Magnetism*, translation by
E. Atkinson, vol. i. chap. xi. (London, 1883); J. D. Everett, *Illustrations*
*of the C.G.S. System of Units* (London, 1891); Magnus Maclean,
*Physical Units* (London, 1896); Fleeming Jenkin, *Reports on*
*Electrical Standards* (London, 1873); *Reports* of the British Association
Committee on Electrical Units from 1862 to present date;
J. A. Fleming, *A Handbook for the Electrical Laboratory and Testing-Room*
(2 vols., London, 1901); Lord Rayleigh, *Collected Scientific*
*Papers*, vol. ii. (1881-87); A. Grey, *Absolute Measurements in*
*Electricity and Magnetism*, vol. ii. part ii. chap. ix. p. 150 (London,
1893); Oliver Heaviside, *Electromagnetic Theory*, i. 116 (London,
1893); Sir A. W. Rücker, “On the Suppressed Dimensions
of Physical Quantities,” *Proc. Phys. Soc. Lond.* (1888), 10 37;
W. Williams, “On the Relation of the Dimensions of Physical
Quantities to Directions in Space,” *Proc. Phys. Soc. Lond.* (1892),
11, 257; R. A. Fessenden, “On the Nature of the Electric and
Magnetic Quantities,” *Physical Review* (January 1900). (J. A. F.)

- ↑
^{1.0}^{1.1}Neither the Weber nor the gauss has received adoption, although recommended by the Committee very general of the British Association on Electrical Units. Many different suggestions have been made as to the meaning to be applied to the word “gauss.” The practical electrical engineer, up to the present, prefers to use*one ampere-turn*as his unit of magneto motive force, and*one line of force*as the unit of magnetic flux, equal respectively to 10/4π times and 1 times the C.G.S. absolute units. Very frequently the “kiloline,” equal to 1000 lines of force, is now used as a unit of magnetic flux.