September 1942 Radio-Craft
Wax nostalgic about and learn from the history of early electronics.
See articles from Radio-Craft,
published 1929 - 1953. All copyrights are hereby acknowledged.
Buckle your mental seatbelt before reading this fast-moving rundown
of the origins of many measurement standards used in the cgs
(centimeter-gram-second) 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 centimeter-gram-second
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
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 rp 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 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.
Fig. 2 - .
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 non-magnetic, 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
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
(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/cm2. 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 east-west 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/r3H and H/M then equals 2/r3tanθ.
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:
(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
Pole 983.1 cm.2 sec." or 32.25 ft./sec.2
London ............ 981.2
Paris ................ 980.9
New York ......... 980.2
Washington ..... 980.0
Equator ........... 978.1
An approximate formula due to Clairaut gives the gravitational
constant at n latitude and h height above sea level.
g = 980.6056-2.5028 cos 2n-0.000003h
The force urging downward a freely falling m is shown by the
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 gt2 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
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/t2
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