September 1942 RadioCraft
[Table
of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from RadioCraft,
published 1929  1953. All copyrights are hereby acknowledged.

Buckle your mental seatbelt before
reading this fastmoving rundown of the origins of many measurement standards used in
the cgs (centimetergramsecond) system. It reminds me of a video you might see of a
physics dude 'wowing' an audience of science laymen as he rolls through one topic after
another, among them being mass, acceleration, time, electricity, magnetism, solenoids,
pendulums, inertia, and gravity. There's nothing you haven't seen and heard before in
the first couple chapters of Physics 101 class in the way of equations and drawings,
but you'll probably enjoy the review.
Standards of Measurement
By Willard Moody
If you go back and try to find out what an ampere, volt or ohm really is, you will
; find that electrical and mechanical units of energy, or work, are defined in terms
of the fundamental quantities, distance, mass and time. Work will be done by the moving
of a mass in a unit of time. A gram moved a distance of one centimeter in one second
is a definite amount of work done, equal to the basic unit of work; the erg. This represents
the centimetergramsecond system of measurement, abbreviated c.g.s.
Time is determined by astronomical observations. The sidereal day is reckoned by the
interval of time between successive meridian passages of the same star. This is the time
required for earth rotation of one cycle. The solar day is reckoned by the motion of
the sun. When the sun is on the meridian, it is said to be solar or apparent noon. The
interval of time between two successive noons represents the solar day. The average length
of the solar day over a. period of one year is the mean solar day. The second will be
1/86,400th part of this day.
Fig. 1  Helmholtz coil.

The centimeter is 1/100th part of the meter. In 1799 a platinum bar was constructed
by Borda for the French Government which had a length of 1 meter, the meter being taken
as 1/10,000,000th part of the meridian line from equator to the pole. It is now known
that this distance is 10,000,856 meters, but the original bar serves as the standard.
The gram, unit of mass, is 1/1,000th part of the kilogram, The gram is equal to the
mass of a cubic centimeter of pure water at 4 degrees Centigrade. The standard kilogram
is a bar of platinum kept at Paris and is the real standard on which all metric weights
are based. The unit of mass in engineering is the pound, which is equal to 453.59 grams.
The gram has been defined in terms of the centimeter, gram and second. The centimeter
and second have been explained in detail. The remaining factor is the 4 degrees Centigrade
specification. Melting ice will represent 0 degrees on the Centigrade scale, and the
temperature at which water boils under standard atmospheric pressure will be 100 degrees
on the Centigrade scale. Now, what is standard atmospheric pressure? It is the pressure
of one atmosphere, derived from a column of mercury 76 centimeters high at zero degrees
Centigrade. In sound measurements, of radio engineering, the bar is occasionally used.
A bar is 1/1,000,000th part of the pressure corresponding to 75 cm. of mercury at zero
degrees Centigrade.
Now we come to the unit of force. The Greek word for force is dyne. A force of one
dyne acting on a mass of one gram will change the mass velocity by one centimeter per
second. In other words, the force required to
move [accelerate*] 1 gram a: distance of 1 cm. in 1 second is 1 dyne. The work that
is done and the energy used up or expended is 1 erg.
In magnetism, a unit pole is one which if placed 1 cm. from an equal pole in vacuum
will repel it with a force of 1 dyne. The relation, stated mathematically, is
where m is the magnetic strength
of the first pole and m' is the magnetic strength of the second pole. The factor r_{p}
is the distance between poles in centimeters. The strength of the magnetic field at any
point is the force in dynes on a unit magnetic pole placed at that point. When a pole
of strength m is placed at a point where the field intensity is H, the pole is acted
on by a force Hm dynes. In any field of force, the two poles of a magnetic needle are
urged in opposite directions. The direction in which the north pole tends to move is
known as the positive direction of the line of force at that point.
In electrostatics, unit charge or unit quantity of electricity is defined as that
quantity which when placed 1 cm. from an equal charge in vacuum repels it with a force
of 1 dyne. Stated mathematically, where q is the first electrostatic
unit and q' is the second electrostatic unit. The factor r is the distance between the
charges, measured in centimeters.
Fig. 2  .

In electromagnetics, unit current is that current flowing in a circular coil of 1 centimeter
(cm.) radius which will act on a magnetic pole at its center with a force of 1 dyne for
every centimeter of wire in the coil.
The practical unit of electricity is the Ampere, named in honor of the French physicist
who investigated current. The quantity of charge transmitted by 1 ampere in 1 second
is called a coulomb. One coulomb is equal to 3,000,000,000 units of electrostatic charge,
as defined previous to the definition of electromagnetic charge.
In electromagnetics, 1 volt potential difference exists between two points when unit
current is moved between the two points by energy equal to 1 erg. The volt is 100,000,000
electromagnetic units of potential. The practical unit of resistance is equal to 1 volt
divided by 1 ampere.
Electromagnetic field strength is measured by force per unit pole and is a vector
quantity having both magnitude and direction. The magnetic field is indicated by drawing
as many lines of force per sq. cm. as the field has units of intensity. The magnetic
flux is equal to the magnetomotive force divided by the reluctance. If in a magnetic
circuit there are 1,000 lines of flux, there are 1,000 maxwells. The Maxwell was named
in honor of Clerk Maxwell, English physicist. In a moving conductor which has induced
in it 1 electromagnetic unit of potential, the flux cut per second is 1 maxwell. The
unit of induction is the Gauss and is equal to Maxwells/cm.^{2} In other words,
in a magnetic field having 1 line per square centimeter, or 1 maxwell per cm.^{2},
there is 1 gauss or unit induction.
Magnetic intensity induction or flux density B is measured in lines of magnetic induction
per square centimeter (gauss). If the substance in which the field exists is nonmagnetic,
B is the equal of H and the ratio B/H or permeability is μ. = 1. When the substance
through which the field passes is magnetic (say iron core placed inside of an air core
solenoid) B becomes much greater than H, in a relationship which seldom is linear and
must be determined experimentally for a given material. The number of flux lines of force
will be equal to
The reluctance of an iron ring may be calculated:
where 1 is the length of the ring A the cross sectional area and μ the permeability
constant of the iron.
The French physicist Arago, in 1820, demonstrated electromagnetism. The attraction
of the armature to the magnet poles, expressed in dynes, is:
(pull per sq. cm. of
pole area)
The energy of a magnetic field is
Fig. 3  Tangent Galvanometer
Fig. 4  The Pendulum

The intensity of a magnetic field H at a point is equal to the magnetic potential
gradient at that point. The average intensity of field between two points may be considered
the average fall of magnetic potential all along the path and is expressed in oersteds
or gilberts/cm^{2}. In a long straight solenoid with length 25 times the diameter.
where H = oersteds, field intensity ( vicinity of center)
l = centimeters, coil winding length
N = number of turns in coil
I = current, amperes
A Helmholtz coil may be used for determining field intensity in a certain plane, as
illustrated in Fig. 1.
The magnetic force of the solenoid, at any point inside of it, is for Fig. 1 expressed
by the relation:
The intensity of the horizontal component of the earth's magnetic force may be measured
by the following method due to Gauss. A small steel bar magnet is suspended horizontally
by a fine silk thread in a closed box which protects it from air currents. It is then
set to oscillate through a 5 degree arc or swing and the period of oscillation is carefully
determined by using a stop watch. This period depends on M, the magnetic moment of the
magnet and on H the horizontal component of the earth's magnetic force. This is expressed
by the relation,
where k = is the moment of inertia of the magnet, which depends upon the size, mass
and shape.
To determine the relation of H and M, a second procedure is necessary. Suppose that
(in Fig. 2) P is the point where the magnetic intensity H is to be determined. A short
magnetic needle is placed at P, while the magnet bar is placed exactly east or west of
P, and with its axis on the eastwest line. If r is the distance from the center of the
bar to P, the force at P due to the bar is,
Then at P the force due to earth and the force due to the magnet bar are represented
vectorially. The tangent of the angle will be F/H or 2M/r^{3}H and H/M then equals
2/r^{3}tanθ. M may also be determined by the Helmholtz coil. But, since
F/tanθ = H, knowing the product of H and M, the quantity H can be divided into
that product to get M. The Helmholtz coil or the magnetic needle and bar methods are
used for determining H. The moment of inertia k is given by:
Moment of inertia =
where M is the mass in grams and 1 the length in centimeters of the magnet bar.
The tangent galvanometer shown in Fig. 3 can be used for determining absolute electromagnetic
unit current. The coil is large compared with the magnet needle, so that the poles of
the needle are considered as being at the center of the coil. The cross section of the
coil must be of large enough mean radius so that all turns bear essentially the same
relation to the needle.
The pendulum may be used for the establishment of frequency. The action is shown in
Fig. 4. We may assume the whole mass of the pendulum to be concentrated at B, the mass
of the silk cord being so small as to be negligible. The forces acting on the mass m
are its weight mg and the tension P of the suspending cord. The weight mg may be resolved
into two components, one in line with the cord and opposing its tension and one at right
angles to the cord and in the direction in which the mass m moves. The latter component
F, gives the mass a motion through the arc. The force diagram is then BCO, and
F/mg = BC/BO
As BO = 1, the length of the cord, and the angle through which the pendulum swings
is quite small, BC is practically equal to arc BA. The arc length of BA may be represented
as x. Approximately,
F/mg = x/1 and
F = mgx/1
Therefore the force F persuading m along the arc toward A is proportional to the displacement
x measured along the arc. This is a simple, harmonic vibration expressed by the relation
of force to period of vibration in the equation,
substituting, we have:
and
(g = acceleration due to gravity)
The period of vibration is dependent only on length of the pendulum and acceleration
due to gravity at the place the pendulum is swung, and is independent of its mass and
length of arc if the length of arc is small (say 5 degrees). A more exact formula is:
Where the arc is measured in radians, between points A and B.
The values of gravitational constant for various locations are given in the following
table. The height is assumed as being at sea level.
Pole 983.1 cm.^{2} sec." or 32.25 ft./sec.^{2}
London ............ 981.2
32.19 Paris ................ 980.9
32.18 New York ......... 980.2
32.16 Washington ..... 980.0
32.15 Equator ........... 978.1
32.09
An approximate formula due to Clairaut gives the gravitational constant at n latitude
and h height above sea level.
g = 980.60562.5028 cos 2n0.000003h
The force urging downward a freely falling m is shown by the equation,
F = mg
where F is force in dynes, m mass in grams and g the gravitational constant in centimeters/sec.^{2}.
The force unit in poundals, weight of 1 pound falling, is 32.16 poundals at New York
latitude. The standard force of a pound may be stated as the weight of a pound mass at
New York, where the acceleration due to gravity happens to be 32.16 ft./sec.^{2}.
The acceleration due to a constant force acting on a mass moving in a single direction
is constant and is related as in the equation,
Length of Pendulum Which Beats Seconds

It should be realized that mass and weight are not identical. The unit of mass is
a physical quantity of arbitrary size, chosen as a constant. One c.c. of water at 4 decrees
Centigrade represents one gram of mass. The engineering pound is 453.59 grams. If we
take a mass of one gram, raise it to a height of n centimeters above ground level, and
then allow the mass to fall freely taking the time with a stop watch for the fall to
be completed, we have a means of determining the velocity constant of gravity at the
point on the earth where the experiment is conducted. Speed is the ratio of unit length
to time. We have miles/hour, ft./sec. and cm./sec., etc., so that if. S = 1/2 gt^{2}
and we know the speed and time, we can compute readily the gravitational constant. Conversely,
knowing the gravitational constant, we may figure the speed of a falling object.
If we have a standard of mass and time and know the height above sea level we can
determine the latitude. If we have an accurate standard of height above ground, such
as a fine rule or scale graduated in inches we can measure the time required for an object
to fall a certain distance and the gravitational constant will then be 2s/t^{2}
where s is the speed.
* Thanks to RF Cafe visitor Marek Klemes, Ph.D., for catching this error in
the original article!
Posted October 28, 2014
