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Part 1. Geometrical and Mechanical Units

Part 1. Geometrical and Mechanical Units

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Dalton (atomic inass unit R/I,).--Unit of mass, 1/16 inass of oxygen (801e)

g (Phys. scale). (See Table 26.)

atom, 1.66080 x

Density.-The mass per unit volume. The specific gravity of a body is the

ratio of a density to the density of a standard substance. Water and air are

commonly used as the standard substance.

in. ; 1/12 the apparent diameter of the sun or moon.


of “power of a lens.” The diopter = the reciprocal of the

focal length in meters.


Dyne.-The cgs, unit of force = that unbalanced force which acting for

1 second on body of 1 gram mass produces a velocity change of 1 cm/sec.

Energy.-The work done by a force produces either a change in the velocity

of a body or a change of its shape or position or both. In the first case it produces a change of kinetic energy, in the second, of potential energy.

Erg.-The cgs unit of work and energy = the work done by 1 dyne acting

through 1 centimeter.



standard g.

of viscosity.

work which will raise 1 pound. body 1 foot high for


1 foot.

work done when a force of 1 poundal acts through

Force ( f ) .-Force is the agent that changes the motion of bodies and is

measured by the rate of change of momentum it produces on a free body.

Gal = gravity standard = an acceleration of 1 cm set?.

Giga = lo9.


standard of mass in the metric system. (See Table 31.)



its molecular weight.

Gravitation constant.-(

cm2 g-2.

cgs gravitation unit of work.

mass in grams of a substance numerically equal to

G, in formula F = Gnz,wz2/rZ) = 6 . 6 7 0 ~lo-*dyne

Gravity (g).-The attraction of the earth for any mass. It is measured by

the acceleration produced on the mass under standard conditions. This acceleration g equals 980.665 cm sec-* or 32.17 ft sec-*.


unit of mechanical power. The English and American

horsepower is defined by some authorities as 550 foot-pounds/sec and by

others as 746 watts. The continental horsepower is defined by some authorities as 75 kgm/sec and by others as 736 watts.


of work (energy) = lo7 ergs. Joules = (volts2 x sec)/

ohms = watts x sec = amperes2 x ohms x sec = volts x amperes x sec.


,OOO dynes. About 0.980 gram weight.




energy associated with the motion = - in ergs if


m i s in grams and v in cni/sec.

Kinetic energy.-The


Linear acceleration

a= $).-The

rate of change of velocity.

Table 32.


Loschmidt number.-The

number of molecules per cm3 of an ideal gas at

0°C and normal pressure = 2.6S70 x 10l9molecules/cm3.


of pressure = 1,000,000 baryes = 1 bar = 0.957 atmosphere.

Meter.-See Table 31.



prefix indicating the millionth part. (See Table 901.)


= one-millionth of a meter = one-thousandth of a millimeter.




of an inch.

= 5,280 feet; nautical or geographical = 6,050.20 feet.

prefix denoting the thousandth part.

Modulus of elasticity.-Ratio of stress to strain. The dimension of strain,

a change of length divided by a length, or change of volume divided by a

volume, is unity.

Mole or mo1.-Mass

equal numerically to molecular weight of substance.

Momentum ( M = mv) .-The quantity of motion in the Newtonian sense ;

the product of the mass and velocity of the body.

Moment of inertia ( I ) of a body about an axis is the 2mr2,where m is

the mass of a particle of the body and r its distance from the axis.


3, part 2.)

unit of force in the MKS system = lo5 dynes. (See Table

Pound weight.-A

force equal to the earth's attraction for a mass of 1

pound. This force, acting on 1 lb mass, will produce an acceleration of 32.17


Pounda1.-The ft-lb sec unit of force. That unbalanced force which acting

on a body of 1 lb mass produces an acceleration of 1 ft/sec2.

Pi (~)=3.1416. (See Table 11.)


(p ="d) is the time rate of doing work.


angle subtended by an arc equal to the radius. This angle

equals 180°/r= 57.29578" = 57" 17'45" =206265'!

Resilience.-The work done per unit volume of a body in distorting it to

the elastic limit or in producing rupture,

(32.17 lb) acquiring acceleration 1 ft s e P when continuously


acted upon by force of 1 lb weight.





deformation produced by a stress divided by the original di-



force per unit area of a body that tends to produce a deforma-


meter = 1 angstrom.

Torque, moment of a couple, about an axis is the product of a force and the

distance of its line of action from the axis.

Volume.-Extent of space. Unit, a cube whose edge is the unit of length.

The volume of a body is expressed as V = CL8. The constant C depends on

the shape of the bounding surfaces.

Velocity (v=

%) is distance traversed per unit time.

Viscosity.-The property of a liquid by virtue of which it offers resistance

to flow. The coefficient of viscosity is the tangential force that must be applied

to the upper surface of a 1-cni cube of the liquid on an edge to produce a

velocity of 1 cm/sec in the face when the lower face is at rest.

W o r k (W).-The work done by an unbalanced force is the product of the

force by the component of the resulting displacement produced in the direction

of the force.

Young's modulus.-Ratio of longitudinal stress within the proportional

limit to the corresponding longitudinal strain.

Part P.-Hert


Blackbody.-A body that absorbs all the radiation that falls upon it. From

this definition and certain assumptions it can be shown that its total radiation =

uT' (Stefan-Boltzmann Law) and that the spectral distribution of the radiation is given by the Planck Law : 5a

Brightness temperature (S).-The temperature of a non-blackbody determined from its brightness (with an optical pyrometer, see Table 77) as rf

it were a blackbody. Such temperatures are always less than the true temperatures.

British thermal unit (Btu).-The

amount of heat required to raise 1

pound of water at 60"F,1°F. This unit is defined for various temperatures,

but the general usage seems to be to take the Btu as equal to 252 calories. (See

calorie. See Table 7.)

Calorie.-The amount of heat necessary to raise 1 gram of water at 15"C,

1o r

I L.


For dimensional formulas see Table 30, part 2.

m An

easier way to write this exponential term is:

This form will be used hereafter.



There are various calories depending upon the interval chosen. Sometimes

the unit is written as the gram-calorie or the kilogram-calorie, the meaning of

which is evident. There is some tendency to define the calorie in terms of its

mechanical equivalent. Thus the National Bureau of Standards defines the

calorie as 4.18400 joules. At the International Steam Table Conference held

in London in 1929 the international calorie was defined as 1/860 of the international watt hour (see Table 7), which made it equal to 4.1860 international

joules. With the adoption of the absolute system of electrical units, this becomes 1/859.858 watt hours or 4.18674 joules. The Btu was defined at the

same time as 251.996 international calories. Thus, until such a time as these

differences are taken care of, there will be some confusion.

Celsius temperature scale.-The

present-day designation of the scale

formerly known as the Centigrade scale.

C entigrade temperature scale.-The

temperature scale that divides the

interval between the ice point, taken as O'C, and the boiling point of water

with 100".

Coefficient of thermal expansion.-Ratio

of the change of length per

unit length (linear), or change of volume per unit volume (voluminal), to the

change of temperature.

Color temperature ( T s ).-The color temperature of a non-blackbody is

the temperature at which it is necessary to operate the blackbody so that the

color of its emitted light will match that of the source studied.

Emissivity.-Ratio of the energy radiated at any temperature by a nonblackbody to that radiated by a blackbody at the s a n e temperature. The

spectral emissivity is for a definite wavelength, and the total emissivity is

for all wavelengths.

Entha1py.-Total energy that a system possesses by virtue of its temperature. Thus, where U is the internal energy, then the enthalpy = U PV where

PV represents the external work.




measure of the extent to which the energy of the system is

Fahrenheit temperature scale.-A scale based on the freezing point .of

water taken as 32" and the boiling point of water taken as 212".


body that has a constant emissivity for all wavelengths.

Heat.-Energy transferred by a thermal process. Heat can be measured

in terms of the dynamical units of energy, as the erg, joule, etc., or in terms of

the amount of energy required to produce a definite thermal change in some

substance, as for example the energy required per degree to raise the temperature of a unit miLss of water at some temperature. The mechanical unit of

heat has the dimensional formula of energy ( M L 2 T 2 ) .The thermal unit

( H ) ,as used in many of these tables, is ( M e ) where 0 denotes a temperature


Joule's equivalent (J) o r the mechanical equivaient of heat.-Conversion factor for changing an expression of mechanical energy into an expression of thermal energy or vice versa (4.1855 J/cal).

6Gen. Electr. Rev., vol. 47, p. 26, 1944.



Kelvin temperature scale.-Scale of temperature based on equal work for

equal temperatures for a working substance in a carnot cycle = Celsius (Centigrade) scale



Langley (ly).-A

new unit of radiation, surface density, has been suggested which equals 1 calorie ( lS°C) per cm?.

L a t e n t heat.-Quantity

of matter.


of heat required to change the state of a unit mass

unit of radiant intensity = 1 cal cniP inin-l.

Radiant energy.-Energy

traveling in the form of electromagnetic waves.

Radiant temperature.-The

temperature obtained by use of a total radiation pyrometer when sighted upon a non-blackbody. This is always less than

the true temperature.

R a n k i n temperature scale.-Absolute




Fahrenheit scale = Fahrenheit

R e a u m u r temperature scale.-A

scale based upon the freezing point of

water taken as 0"R and the boiling point of water taken as SOOR.

Specific heat.-Ratio of the heat capacity of a substance to the heat capacity

of an equal mass of water. When so expressed, the specific heat is a diniensionless number.

Standard temperature.-A

temperature that depends upon some characteristic of some substance, such as the melting, boiling, or freezing point, that

is used as a reference standard of temperature.

T h e r m a l capacitance.-The

heat capacity of a hody is the limiting value,

as T approaches zero, of the ratio

A 0


where A T is the rise in temperature


resulting from the addition to the body of a quantity of heat equal to A Q .

T h e r m a l conductivity.-Quantity of heat, Q , which flows normally across

a surface of unit area per unit of time and per unit of temperature gradient

normal to the surface. In thermal units it has the tliinensional forinula

( HO-lL-lT-l)or (ML-'T-'), in mechanical units ( I I ~ L T - ~ O P ) .

Thermodynamic temperature.-See


Kelvin teinperature scale.

of the flow of heat.

Thermodynamic laws : Zeroth ln.iu.-Two systems that are in thermal

equilibrium with a third are in thermal equilibrium with each other. First low:

When equal quantities of niechanical effect are produced by any means whatever from purely thermal effects, equal quantities of heat are put out of

existence or are created. S'ccoizd lnzw: It is impossible to transfer heat from

a cold body to a hot body without the perfornlance of mechanical work. Third

lnzv: I t is impossible by any means whatever to superpose only the images of

several light sources to obtain an image brighter than the brightest of the



Aldrich et al., Science, vol. 106, p. 225, 1947.



Part 3.-Electric

and Magnetic Units

A system of units of electric and magnetic quantities requires four fundamental quantities. A system in which length, mass, and time constitute three

of the fundamental quantities is known as an “absolute” system. There are

two abso1u:e systems of electric and magnetic units. One is called the electrostatic, in which the fourth fundamental quantity is the dielectric constant, and

one is called the electromagnetic, in which the fourth fundamental quantity is

magnetic permeability. Besides these two systems there will be described a

third, to be known as the absolute system, that was introduced January 1, 1948.

(See Table 4.)

I n the electrostatic system, unit quantity of electricity, Q, is the quantity

which exerts unit mechanical force upon an equal quantity a unit distance from

it in a vacuum. From this definition the dimensions and the units of all the

other electric and magnetic quantities follow through the equations of the

mathematical theory of electromagnetism. The mechanical force between two

quantities of electricity in any medium is

Q Q’

F= -

KrZ ’

where K is the dielectric constant, characteristic of the medium, and r the distance between the two points at which the quantities Q and Q‘ are located. K

is the fourth quantity entering into dimensional expressions in the electrostatic

system. Since the dimensional formula for force is [ M L T 2 ] ,that for Q is

[M’LZ T ’ K ’ ] .

The electroinagnetic system is based upon the unit of the magnetic pole

strength (see Table 466). The dimensions and the units of the other quantities

are built up from this in the same manner as for the electrostatic system. The

mechanical force between two magnetic poles in any medium is

m d

F= pr2 ’

in which p is the permeability of the medium and Y is the distance between two

poles having the strengths m and m‘. p is the fourth quantity entering into

dimensional expressions in the electromagnetic system. I t follows that the

dimensional expression for magnetic pole strength is [M’L:T 1 p * ] .

The symbols K and p are sometimes omitted in tlie dimensional formulae so

that only three fundamental quantities appear. There are a number of objections to this. Such formulae give no information as to the relative magnitudes

of the units i n the two systems. The omission is equivalent to assuming some

relation between mechanical and electrical quantities, or to a nlechanical explanation of electricity. Such a relation or explanation is not known.

The properties I< and p are connected by the equation I / V / K p = v , where v

is the velocity of an electromagnetic wave. For empty space or for air, K and

p being measnred in tlie same units, 1VKp=c, where c is the velocity of

light in vacuo, 2 . 9 9 7 7 6 ~10’O cni per sec. It is sometimes forgotten that the

omission of the dimensions of K or p is merely conventional. For instance,

magnetic field intensity and magnetic induction apparently have the same dimensions when p is omitted. This results in confusion and difficulty in understantling the theory of magnetism. The suppression of p has also led to the use

of the “centimeter” as a unit of capacity and of inductance ; neither is physically

the same as length.




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

shown above.

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.



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Part 1. Geometrical and Mechanical Units

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