l2|l0/22/1:

national Bureau of Standards

Library, H.W. Bldg

APR 8 1963

^ecknlccil rlote 172

PRACTICAL METHODS FOR

CALIBRATION OF POTENTIOMETERS

DAVID RAMALEY

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS

wecAmca( ^^cte 172

ISSUED MARCH 25, 1963

PRACTICAL METHODS FOR

CALIBRATION OF POTENTIOMETERS

David Ramaley

Radio Standards Laboratory

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 30 cents

Contents

Page

1. o JjLlX jrOCLU.C LXOXio •a»o»ott«oooaoooooaoooooe»«*os««ooooooooo««o«e -^ ^« U nX'Vo ]7 S 3.x X\.3.LlO o6L5o o*«oa<ioo«aeo*e««oo»eooo«»o»oeooooo««* Ct ^o -L • K^ 2.1l C\Ji±LJL 'Y OX xvH'^lO OcLOo o0O*ooao*«oo»««oo«o*oaoo*oao*« ^

2, 2. Operation of the Universal Ratio Set as a

Calibrating Instrument , , 4

3. Constant Current Multipurpose Potentiometers 7

3. 1, The Basic Potentiometer Concept 7

3. 2. Modifications to the Basic Idea 8

3. 3, Compensation Considerations , 10

3. 4. Range or Factor Arrangements, ,,,, .o». 12

4, Calibration of Constant- Current Potentiometers , 16

4, 1, Necessary Calibrations and Corrections 16

4, 2. Calibration of the Maximum Range with the Universal

Ratio Set and Calibration of the Standard Cell Circuit. ... 18

4. 3, Calibration of Additional Ranges or Factors with the

Universal Ratio Set 26

a. Factors for Potentiometers Designed for

Standardization on All Ranges 28

b. Factors for Potentiometers Standardizing on a

Single Range 29

c. Other Factor Circuits 32

4, 4. Examples of Factor Measurement. 32

a. Measurements on an Instrument that Standardizes

on all Ranges 32

b. Measurements on an Instrument that Standardizes

on a Single Range 33

4. 5, Working Test for Factors 36

4. 6. Comparison with Another Potentiometer as a Method

of Calibration 37

4.7. Calibration of Constant- Current Potentiometers

Designed to Measure Small EMF's and of Modified

Constant- Current Potentiometers 38

5. Potentiometers of the Constant Resistaince or Lindeck

Variety and Combination Types 39

5. 1. Principles of Circuitry 39

5. 2. Calibration of Lindeck and Combination Potentiometers. 41

6, References 44

111
Practical Methods for Calibration of Potentiometers

David Ramaley

Potentiometer circuitry, particularly as related to

calibration, is discussed with the primary consideration

given to the required circuit measurements. The more

feasible means of calibrating potentiometers are described

in considerable detail. Emphasis is placed upon the use

of the Universal Ratio Set as the basic implement for

accomplishing the major portion of potentiometer calibrations.

IV
1, Introduction

This paper is concerned primarily with calibration of potentiometers of precision quality, including both the multipurpose types

and somewhat specialized types. A presentation of the methods involved and enough detailed descriptive material are included to enable

the reader to grasp the fundamentals. Minutely detailed instructions

are omitted. It is anticipated that this manner of presentation will

fulfill the requirements of one who wishes to understand the principles

without the necessity of becoming involved in procedural details.

Calibration procedures or instructions of the "cook book" type also

are needed. This latter need now is becoming more nearly fulfilled

by maniifacturers' instructions and recently available procedures

written up by various standardizing laboratories. For example, the

Division of Electricity of the National Bureau of Standards is compiling calibration procedures for several types of potentiometers. These

procedures are available to other standards laboratories upon request

to the Resistance and Reactance Section of the Division of Electricity,

NBS.

Examples of potentiometer circuits given in this paper are

chosen to demonstrate the diversity of circuit arrangements and in

several cases are not taken from actual existing instruments. Good

explanations of principles involved in the circuitry of various types of

manufactured potentiometers can be found in texts on electrical measurements such as that of Harris [ 1] . In this paper the more complicated calibration methods are not discussed where simpler raethods

are available. Generally, instead of calibrating potentiometers by

means of potential differences, the appropriate resistors in the instrument are compared or measured by means of Wheatstone net circuits

incorporating the Universal Ratio Set [2, 3, 4] . A brief review of

the Universal Ratio Set follows.

^Figures in brackets indicate the literature references at the end of

this paper.
2. Universal Ratio Sets

2. 1. Circuitry of Ratio Sets

II

Practically all ratio sets and resistive voltage dividers contain

a resistance circuit terrainated on each end by a binding post connector.

A simple slide-wire represents the most readily visualized ratio set or voltage divider. The sliding contact is free to travel from one end

of the wire to the other. The ratio of the resistance of the wire on

one side of the sliding contact to the resistance on the other side can

be varied continuously as the slider is moved along the resistance

wire. These two resistances, one on either side of the slider, can be

used to form two arms of a Wheatstone net or bridge circuit. It is

such a circuit that is used to calibrate potentiometers. At least one

and commonly two of the other bridge arms consist of selected portions

of the potentiometer under calibration. We may also think of the slide

wire as a ratio set giving the ratio of resistance of either arm of the

slide-wire to the total slide-wire resistance. Likewise, the slidewire may be considered as a voltage divider. A fraction of the voltage

impressed between the two slide-wire ends appears between the slider

and one end, while the remainder appears between the slider and the

other end. These concepts facilitate the visualizing of the operation

of a ratio set.

It is not practical, physically, to construct a very long, accurately graduated slide-wire of extremely uniforra cross section such

that the resistance per unit length is sufficiently constant. Such a slide-wire would offer an infinite nuinber of ratios of resistance,

limited only by the fineness of adjustment possible with the slider.

The resolution of such a slide-wire would be exceptional. As an

approach to this ideal, substitute circuits containing many intermediate
3

steps have been developed. In the case of commercial voltage dividers, the well known Kelvin-Varley circuit [ 1] usually is utilized.

Such a circuit makes possible a large nuraber o£ ratios and can be

used to calibrate potentiometers. However, the overall resistance

of most commercial voltage dividers is usually soraewhat excessive

for many potentiometer calibrations.

Universal Ratio Sets are designed for calibrating most types

of potentiometers. In function, the six-dial URS is actually the equivalent of a calibrated slide-wire potentiometer with an extremely high

resolution. It is identical in operation to a slide -wire of total resistance 2111. 110 ohms graduated in equal divisions of 0. 001 ohm. Actually, the URS utilizes separate resistance coils, and the position of

the adjustable contact is varied by raeans of dial switches. The first

dial is associated with 20 equal 100-ohm steps, and the other dials

control decade resistances ranging frora 10 ohms per step to 0. 001

ohm per step in the case of a six-dial ratio set. A schematic diagrara

of a URS is shown in figure 1. All of the ten-step dials are of the

same type construction. One switch handle operates both the switches

to the upper and to the lower resistance sections simultaneously. If resistance is added by the upper switch, an equivalent resistance is

reraoved frora the circuit by the lower switch. (This technique will

be referred to as "compensation" of the device. ) The use of this type

of decade enables one to establish a potential difference in the resistance netw^ork corresponding to any of the various step points. Furtherraore, when several decades of this type are connected together as is

done in the URS or in the Feussner potentiometer [5] , the potential

connections can be made corresponding to any step on the interconnected dials. The total overall resistance of the ratio set is held constant

by raeans of these compensating switching dials. The resistance
4 ' between A and C increases from 0. 000 to 2111. 110 ohras as the dials

are advanced frora their minimum, to their maximum readings. At ^11

the same time the resistance between B and C decreases from 2111. 110

ohms to 0. 000 as the dials are advanced. The URS can thus be represented schematically by a simple, graduated slide -wire.

2. 2. Operation of the Universal Ratio Set as a Calibrating Instrument

To illustrate determination of ratios of resistances by means

of a Universal Ratio Set, variable resistive voltage divider, or a uniformly graduated slide-wire, the resistances for comparison are all

connected in series and the whole series then shunted by the Universal

Ratio Set, divider, or slide -wire as shown in figure 2.

With currents I 12and I^ as shown, balances are made on the

calibrated slide-wire corresponding to connections to the resistance

elements a, b, and c. Therefore, R is at the same potential as P , the terrainal at the left end of a, and R is at the same potential as

P , the ternainal at the right end of a. The potential drop across

these two resistance segments is equal.

Likewise,

Dividing (1) by (2),

Likewise,

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R., - R, — =-• (3)

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Because each balance point R , R , R , etc. , is naade in a Wheatstone bridge circuit, the positions R , R , R , etc. , are not

dependent upon the constancy of current in the circuit. Furthermore,

the connections to the power source and galvanometer can be interchanged without affecting the balance points R , R , R , etc. Under

some conditions this interchange is advantageous from the standpoints

of power dissipation in the circuit and suitable galvanometer damping.

It is desirable to use a source of power which is reversible in polarity,

thus affording increased sensitivity and reduction of effects of thermoelectromotive forces.

Most Universal Ratio Sets are closely adjusted to the design

specifications. However, a URS should be calibrated to determine

any corrections which should be applied when the instrument is used.

Hereafter in this paper when we refer to URS readings, we are referring to corrected URS readings.

3. Constant Current Multipurpose Potentiometers

3. 1. The Basic Potentiometer Concept

A simplified schematic diagram demonstrating the principles

of a constant current potentiometer is shown in figure 3. In this

figure, BA is a supply battery which furnishes a current that is controlled by the variable resistor R. R is a uniform or linear graduated slide -wire which may be adjusted over the entire graduated scale.

With this arrangement, two sources of ennf , E and E , can be comX s pared, with no appreciable current being drawn from either souice.

The actual current drawn causes only slight deflections of the galvanometer as the operator is adjusting for a null condition. With the

standard source E (e. g. , a standard cell) in the circuit, the adjustable slider is set to a reference position R such that the scale will be

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direct reading in terms of the voltage of the standard cell. The current

through the potentiometer is adjusted by means of R until the galvanometer indicates a null. The potentiometer is then said to be standardized. The unknown emf E can then be measured by connecting the

X

unknown source in place of the standard and adjusting the slider on

R to the position R such that a null is indicated by the galvanometer.

If the scale of the slide -wire is calibrated in units of potential difference, the value of E can be read directly in the same units. Other

X

wise E can be determined relative to E by the ratio of resistance of

X s that portion of R, to the left of R to that portion of R. to the left of

1 X 1 R . s Obviously, the only calibration needed for such a simple instrument would be a determination of the linearity of the resistor R corresponding to various settings of the adjustable slider.

3. 2. Modifications to the Basic Idea

Potentiometers are rarely as simple as the one described

above. The modifications are usually either for the purpose of adding

to the convenience of operation or for extending the range of measurements, for example, measurements in the microvolt region.

In order to facilitate more rapid measurements and easier

standardization, the circuit employed in standardizing the instrument

comraonly is terminated by specially designated SC terminals. The

SC circuit may or may not be a part of the measuring or EMF circuit

with terminals marked EMF. In many potentiometers the two circuits

may employ certain resistance portions of the same circuit jointly.

Potentiometers are generally so constructed that, by means of switches,

a single galvanometer and a single set of keys for several degrees of
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sensitivity can be switched conveniently from the standardizing circuit

to the measuring circuit, thereby elirainating the need for duplicate

galvanometers and keys.

The incorporation of a separate standard cell dial or dials

apart from the EMF or measuring circuit, although adding to the

convenience, detracts somewhat from the accuracy of operation. The

use of a dial and slide -wire instead of the single slide -wire adds to

convenience of taking readings. Calibration of a potentiometer of this

type requires additional measurements. Both the measuring and the

standard cell circuits need to be checked for linearity. The ratio of

resistance of the EMF circuit to the resistance of the SC circuit must

be established. As before, no absolute standards of resistance are

required for calibration because only the ratios of resistances need be

determined.

Instruments with additional ranges will be considered next;

how^ever, these utilize compensating resistors, and a brief consideration of compensated circuits is appropriate.

3. 3. Compensation Considerations

The term compensation as applied to potentiometers refers to

the adjustment of circuit resistances for various settings of dial

switches, range switches, and EMF-SC circuit switches in respect to

the constancy of overall resistance between the BA+ and BA- terminals,

If the overall resistance is constant for all such switch settings, the

instrument is said to be perfectly compensated.

In case the overall resistance of the instrument when the

instrument is standardized is slightly different from the overall

resistance of the instrument when the unknown E is being measured,

X

the current drawn from the supply battery will be different for the two

conditions. This circumstance is not encountered in single-range
11

potentiometers but may occur in multiple -range instruments as demonstrated later. In the discussion that follows we shall assume that

the pow^er supply has negligible internal resistance and a constant

electromotive force.

The following equations represent the relationships existing

at the time of measurement and the time of standardization:

E =R I , (5) X XX

E = R I . (6)

s s s

I is the current drawn when the emf E is being measured

X X

and I is the current when the standardization occurs. Dividing (5)

s by (6), gives

S ^ S ^ S'

In w^ell compensated potentiometers the current through the

potentiometer will be practically independent of the positions of the

EMF dials when making measurements and independent of the settings

of the standard cell dials when the SC-EMF switch is set to SC. Consequently, the ratio I /I usually will be a constant and needs to be

measured only once for any given range. , However, this ratio may be variable in a potentiometer having

double decade -switching dials of the Feussner variety exemplified by

the ten-step dials of a URS in figure 1. Here the resistance between

points A and B is the same for various settings of the ten-step switches, provided the various sections of the double decades are completely compensating. If the sections are sufficiently different in resistance,

the current will depend upon the switch positioning.
12

For the situation where I and I are independent of standard

s X

cell dial positioning and EMF dial positioning, for a given factor or range,

X

E

s (Mrxrn^)- ^ s

T is the total overall potentiometer resistance when the instrument

s is being standardized, and T is the total overall potentiometer resistance when measurements are being made.

3. 4. Range or Factor Arrangements

Extra ranges in potentioraeters are usually 0. 1 and 0. 01 of the

primary range. Switching arrangements in the circuits usually change

the ranges by changing the ratios of resistance of the EMF circuit to

the SC circuit by the appropriate amounts.

Figure 4 illustrates a potentiometer circuit in which the range

change is accomplished by changing the resistance of the EMF or

measuring circuit. When the plug is placed in the 0. 1 -range position,

a shunt reduces the resistance of the EMF circuit by a factor of ten.

At the same time, the reinoval of the plug from the 1 -range position

inserts a series resistor of proper raagnitude to maintain a constant

overall resistance for the potentiometer.

For an arrangement such as this, where the instrument can be

standardized on both ranges and where the standard cell circuit resistance is identical for both ranges, the currents I and I will be equal,

s X

and there is no need to make measurements of the overall resistance.

If the standardizing circuit is combined with the measuring

circuit as in figure 5, it will be irapossible to standardize the instrument on more than one range since the standard cell circuit is shunted
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along with the EMF circuit when the range is changed. Therefore if the range resistors are not perfectly compensating, I for the 0. 1 X

range w^ill differ slightly from I which is determined on the 1. 0-range.

Consequently, a calibration of the potentiometer for the 0. 1 -range

must take into consideration the ratio of I on the 1. -range to I on

s ^ X

the 0. 1 -range or T to T . ^ X s In order to calculate the factor or range correction, it is necessary to determine the factor compensation of the instrument. The

factor compensation refers to the ratio of currents through the potentiometer corresponding to the various factor or range switch positions.

In turn, the current ratios are determined by the ratios of the overall

resistances between supply battery terrainals of the potentiometer for

the various ranges.

Some of the potentiometers in which the balance for the standard cell circuit is made on a single range include the Rubicon Type B,

and Leeds and Northrup Type K-1 [6] , and the Wenner Standardizing

Leeds and Northrup potentiometers. The Rubicon Type B is so arranged that whenever the SC-EMF selector switch is set to the SC position,

the highest voltage range is in the circuit. If potentiometers of these

several types are inadequately compensated, the correction to the

factor or range multiplier may vary with the emf of the supply battery

when batteries furnishing voltages of different magnitudes are used.

The overall resistance of such a potentiometer is different for different

factor positions and results in a current difference in the instrument

when the factor is changed. If another supply battery of twice the voltage were to be substituted, and additional amount of resistance equal

to that of the overall resistance for the first condition would be required

in the adjusting rheostat R. For this modified situation, when the

factor is changed the total change in current is only about one -half as
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much as for the original situation. Therefore the factor value can be

seen to be a function of the supply battery voltage. Most multipurpose

potentiometers are constructed to perrait standardization on all ranges,

and for this type of instrum.ent the current can be properly readjusted

when a change in range is raade.

The factor calibration for the circuit of figure 4 is determined

as a ratio of the resistances of the two EMF circuit arrangements

considered as four -terminal resistors.

The calibration of ranges or factors will be considered in some

detail later. For the more coraplicated circuit arrangeraents , range

or factor determinations may be soraewhat intricate.

4. Calibration of Constant -Current Potentiometers

4. 1. Necessary Calibrations and Corrections

In general, the calibration of a multirange constant-current

type potentiometer will require measurements on the standard cell

circuit to deterinine its linearity. Perfect linearity implies that the

standard cell circuit resistance varies directly with the setting of the

standard cell dial or dials. Calibrations are needed for the individual

dials in the EMF circuit and also for the ranges or factors for instruments with multiple ranges. The ratio of resistance of the EMF circuit to the SC circuit is established for the appropriate range at the

tirae the EMF dials are calibrated by the manner in which this calibration is performed. The calibration data on a simple potentiometer in

which the standard cell circuit is linear, usually can be applied to a convenient equation similar in form to the following:

E = F (1 + f) (D^ + d^ + D^ + d^ + D^ + d^, etc. ). (9)
17

In this equation E is the EMF or potential difference being

measured expressed in the same unit as the emf of the standard cell

used in standardizing the instrument. F is the multiplying factor for

the range in use, and D, , D , D , etc. , are the readings of the several EMF dials obtained by the observer after he has positioned the

dials so that a null is indicated by the galvanoraeter when the potential

difference is being measured. The terras f, d , d , d , etc. , are

calibration corrections to be applied to F, D , D , D , etc. If the

SC circuit is not adequately linear, a table can be prepared giving

corrected settings for the standard cell dials for various standard

cell voltages. The corrections f, d , d , etc. , can be arranged

conveniently in tabular form.

The correction to the high range or factor 1 is normally given

as zero because the calibration of the instrument is performed for

this range. The factor corrections for the other ranges will not be

zero if the instrument is not in perfect adjustment in respect to factor

switching resistors. Usually in the case of universal or multipurpose

type of potentiometers, the correction for the 0. 1 factor is given to

0. 001 percent and for the 0. 01 factor to 0. 01 percent on documents

issued by the National Bureau of Standards.

Some manufacturers have provided their instruments with socalled self -checking facilities. Switching arrangeraents may be provided to intercompare the various steps and ranges in order to determine circuit linearity and correctness of adjustment. Instruction

sheets or booklets should be consulted to check the instruraent in this

manner.
18

4. 2. Calibration of the Maximum Range with the Universal

Ratio Set and Calibration of the Standard Cell Circuit

Normally, multipurpose potentiometers can be calibrated most

simply with a Universal Ratio Set. These include the following: Leeds

and Northrup Type K varieties and Wenner Standardizing model,

Rubicon Type B and Bonn Five -Dial type, Otto Wolff Feussner varieties, and counterparts raade by other raanufacturers. A detailed set

of instructions for calibrating a potentioraeter of the Crompton type is

available [7] , We shall consider the calibration of the potentiometer shown

in figure 6 as an example of the method of calibrating a single -range

potentiometer or the maximum range of a multirange instrument. The

potentiometer circuit is a hypothetical single -range potentiometer consisting of an EMF circuit with two associated dials. Each step of the

first dial is 0. 1 volt. The second dial is a slide-wire with a total

range of 0. 11 volt which is graduated in finer steps. The standard

cell circuit consists of a fixed resistance including part of the EMF

circuit (steps 2 to 12) and an adjustable SC slide-wire. Standardization is accoraplished by adjusting the battery rheostat, R.

In this circuit the measureraents to be made for a complete

calibration include (1) a comparison of the resistances of all steps on

the first dial, (2) a deter imination of the linearity of the second dial at

frequent intervals such as 0. 1 -volt steps, (3) a determination of the

linearity of the standard cell circuit, and (4) the ratio of the resistance of the SC circuit to the EMF circuit. If we take these measurements, the corrections designated as d and d in (9) will be determined. Because this is a single-range potentiometer there is no

factor correction f.
19

The left terminal of the URS is connected to the BA+ terminal

of the potentiometer. The right URS terminal is connected to the BA-#

terminal. Leads from the URS to the BA+ and BA-# terminals of the

potentiometer may be reversed if desired. If so, readings on the URS

will be symmetrically arranged in respect to the first set of readings

about the midpoint of the URSo If a second calibration of a potentiometer is desired, a good procedure is to perform the second calibration

with reversed leads. The galvanometer or null detector is across the

URS also. Power is supplied at the center terminal of the URS and to

the selected one of four connecting paths to the potentiometer circuit,

namely the SC4-, SC-, ZMF+, and EMF-# binding posts.

Balance is obtained for each connection selected by adjusting

the dials of the URS until a position is obtained such that there is a minimum of galvanometer deflection upon reversal of the current from

the power source.

The differences between URS readings for selected positions

of the SC and EMF dials and slide-wires serve to indicate the linearity of the SC and EMF circuits and also the ratio of resistance in

the EMF circuit to the resistance of the SC circuit. Differences between balance -point readings on the Universal Ratio Set are directly

proportional to the resistances of the respective portions of the circuits involved when these balances are made as previously described.

The comparisons of the various portions of the circuits are thus computed by ratio and proportion.

A convenient method of making the computations is to assume

that a standard cell of 1. 01900 volts is to be used with the instrument.

Then the difference between the URS readings for the SC+ and SC-#

connections would correspond to 1. 01900 volts. The differences between SC+ and SC-# readings for other settings of the standard cell
20

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dial would then yield figures expressable as voltages, which would

determine just how linear the standard cell dial actually might be.

The differences between the URS readings for EMF-f and EMF- connections will yield the voltages which will appear across these terminals when a standard cell of 1. 01900 volts is used with the potentioraeter. With the actual voltages corresponding to the various settings

of the EMF dials thus determined, the corrections d and d for the

various dial positions are obtained by simple inspection. If a standard

cell of other voltage is to be used we can use the same computation

procedure based on the other standard cell voltages. This calibration

procedure actually gives the calibration of the EMF dials in terms of

the SC dial and establishes the relationship between the two circuits.

A method of reducing the computations to a minimum is afforded by making the URS direct reading in terras of a desired portion of

the circuit under calibration. Usually the portion of the circuit selected is that part of the standard cell circuit corresponding to a voltage

typical of the majority of standard cells. If the potentiometer is to be

used with unsaturated cells at room temperatures, a setting of standard cell dial or dials at 1. 01900 volts would be convenient. To raake

the ratio set direct reading in terms of this selection, the difference

in readings for balances of the URS when connected to SC-H and SCterminals respectively should be 1019. 000 ohms, if the ratio set is

calibrated in ohms. To achieve this difference the first time a new

type instrument is calibrated, a system of trial and error is necessary

using different settings of the battery adjusting rheostat R. In achieving the correct setting of R for other instruments of the same type,

the SC+ and SC- readings will usually be found to be in the same general range on the URS. Thus, previous experience with a given type

of potentiometer helps to shorten the time used in setting the battery

circuit rheostats.
22

Let us assume that the URS has been made direct reading for

the SC circuit and that the readings for the circuit in figure 6 are as shown in table 1. By taking the series of SC+ readings, we have determined the uniformity or linearity of the standard cell circuit for points

1. 01800, 1. 01850, and 1. 01950. The uniformity at other points could

be determined similarly. The resistance of the standard cell circuit

at 1. 01800 setting is about 6 parts in a million lower than it should be.

The resistance of the standard cell circuit at point 1. 01850 is low by

3 parts per million and at point 1. 01950 is high by about 30 parts per

million. If we wish to achieve the maximum accuracy with a 1. 01950-

volt cell, we should set the standard cell circuit dial at point 1. 019469

instead of 1. 019500.

The EMF circuit is calibrated in a similar manner. Let it be

assumed we obtain the URS readings at balance for various settings

of the potentiometer as shown in table 2. In following this procedure

again we have actually established the relationship between the EMF

circuit and the SC circuit because the EMF circuit measurements were

taken after the circuit was adjusted to correspond to a specified standard cell potential.

The corrections are computed on the assumption that the potential of the EMF+ terminal is zero when the 0. 1 -volt-per -step dial

is set on zero. The EMF-# terminal could have been chosen just as conveniently for the reference terminal.

In the course of performing such a calibration, any instability

in the potentiometer circuit will be evident as non-reproducibility of

URS readings. Consequently, the URS readings for the SC+ and SCconnections should be checked as often as necessary to insure that the

arrangeraent remains sufficiently stable. Changes of a few parts per

million would not be excessive for normally expected precision of
23

Table 1

Typical Calibration Data for the Standard Cell Dial Circuit of Figure 6

Power Applied Potentiometer

to Terminal Setting,

Indicated Volts

SC- 1. 0190

SC+ 1. 0190

SC+ 1.01800

SC+ 1. 01850

SC + 1. 01900

SC + 1. 01950

URS

Reading,

Ohms

1023. 363

4. 363

5. 369

4.866

4. 363

3. 832

Reading

Difference

1019. 000

1017. 994

1018. 497

1019. 000

1019. 531
24

Table 2

Calibration Data and Computed Corrections

for a Simplified Two-Dial Potentiometer

Power Positons of Corrections to

Applied to Potent:IOmeter URS be Applied to the

Terminal D:Lais URS Reading Potentiometer

Indicated (Volts) Reading

23. 397

Differences

1199. 972

in Volts

Firsit Dial

EMF+ 1. 2 -0. 000028

1. 1 123. 394 1099. 975 -0. 000025

1. 223. 381 999.988 -0, 000012

0. 9 323. 375 899.994 -0. 000006

0. 8 423. 359 800. 010 + 0. 000010

0. 7 523. 345 700. 024 + 0. 000024

0. 6 623. 338 600. 031 -HO. 000031

0. 5 723. 336 500. 033 + 0. 000033

0. 4 823. 342 400. 027 + 0. 000027

0. 3 923. 354 300, 015 + 0. 000015

0. 2 1023. 363 200. 006 + 0. 000006

0. 1 1123. 365 100. 004 + 0. 000004

0. 1223. 369 0. 000 0. 000000

Second Dial

EMF- 0. 00 1223. 373 0. 004 + 0. 000004

0. 01 1233. 373 10. 004 + 0. 000004

0. 02 1243. 370 20. 001 + 0. 000001

0. 03 1253. 367 29.998 -0. 000002

0. 04 1263. 362 39.993 -0. 000007

0. 05 1273. 351 49. 982 -0. 000018

0. 06 1283. 359 59.990 -0. 000010

0. 07 1293. 366 69.997 -0. 000003

0. 08 1303. 372 80. 003 + 0. 000003

0. 09 1313. 379 90. 010 + 0, 000010

0, 10 1323. 382 100. 013 + 0. 000013

0. 11 1333. 391 110. 022 + 0. 000022
25

measurement. Instability, when present, usually results from poor

contacts in the battery rheostat. It is advisable to clean these as well as possible.

Another but more precise method of calibrating this potentiometer with a URS would be to set the EMF dials at the voltage of the standard cell to be used with the instrument. The potentiometer battery

rheostats are then adjusted so that the URS reading difference at balance points between EMF+ and EMF- terminals corresponds to the

voltage of the standard cell. The URS would then be direct reading

for calibrating the EMF dials at all desired points.

By switching the URS connection to the standard cell circuit,

the correct setting could be obtained that would correspond to the

potential of the standard cell. After this correct setting is known,

the user can standardize the instrument with the usual standard cell

circuit if the standard cell dial is set to this point. This same point

can be obtained by the user without a URS, simply by first standardizing the instrument with the standard cell connected to the EMF circuit and quickly switching the standard cell to the standard cell circuit

and obtaining a balance by adjusting the standard cell dial. A repetition may be necessary to assure the user of the correctness of the

setting.

This same technique can be used for spot checking the adjustment of any potentiometer having an emf range covering that of the

standard cell dial.

The URS can be connected so that readings are spread out

over the range of the set more effectively in many situations. Let us

assume that we have a potentiometer with considerable resistance in

one end and no measurements to be taken on this portion of the circuit.

If we connect the variable resistance box, H, in series with the URS
26

as shown in figure 7, the readings on the portion of the circuit in which

we are interested can be spread out more effectively and thereby provide better resolution.

This arrangement, shown in figure 7, is the equivalent of adding an extra range, H, to the URS although no readings can be taken

over the range H. This imposes no restrictions, however, if there

are no readings to be taken corresponding to resistors K, L, and M

which would be those that would fall on the added range H. Consequently, we have been able to spread out the EMF and SC readings so that

more of the URS range is utilized.

4. 3. Calibration of Additional Ranges or Factors

with the Universal Ratio Set

The procedure for calibration of factors depends upon the circuitry of the potentiometer. It is best for the person performing the

calibration to be familiar with the circuit and to derive his own expressions for the factor determination in terms of resistance ratios

of the various circuit components.

Methods described here for calibration of factors of multipurpose potentiometers are the simpler ones but not necessarily the most

precise. If we choose to solder special connecting leads into the circuits and in some instances use calibrated standard resistors, usually

it is possible to attain better precision and accuracy on factor measure'

ments.

Let us now consider the factor for some range, Y, other than

the 1 range and designate this factor as F . This generalized expression can be used to represent either the 0. 1 range or the 0. 01 range.

We shall designate the potential difference developed at the EMF terminals corresponding to the Y range as V and the potential difference
27

COo<

UJ

a:

UJ

COo<

CO

q:

LlI >

I-O

C9Q<

IjJ cr

Q.

CO

u.oooXo<

CD<

S2

U-
28

at the EMF terminals for the 1 range as V . In both situations the

potentiometer is assumed to have been properly standardized. F is

thus the ratio of V to V .

a. Factors for Potentiometers Designed for

Standardization on All Ranges

For potentiometers which actually standardize on all ranges

regardless of circuit details, we can develop a factor expression. We

shall use the following terminology:

I^ is the current supplied to the potentiometer by the

battery when the factor is set at 1.

I is the current when the factor is set at Y.

R , is the four -terminal resistance of the EMF circuit

considering the EMF terminals as potential terminals

with the EMF dials set to a maximum position and

the factor set on 1. R is the corresponding four -terminal resistance with

the factor set on Y.

R . is the four -terminal resistance of the standard cell

circuit considering the SC terminals as potential

terminals and the standard cell dial set to a convenient position.

R is the corresponding four -terminal resistance with

the factor set on Y.

It should be noted that figure 4 is a special case of the following

derivation in which R = -^cv ^^^ "'•i ~ ^v' The factor F for the Y

o i o Y i Y Y range is obtained frora the following expression:

^Y ^EY^Y ^_JL^ iLY Y ^ ^1 ^El^l
29

For the corresponding standardization for each range, the

potential difference developed across the standard cell circuit is the

same and is

^Sl^l^^SY^Y- '11'

Consequently,

(12)

Substituting (12) into (10), gives

^EY^ /^Sl \ ^^EY\ ^^Sl

The ratio R / R^v ^® readily measured on the URS by connecting one end of the URS to BA+ and the other end to BA-# terminals

of the potentiometer. The battery-adjusting rheostat should be set to

its minimum and the factor switch set on Y. The ratio R_ , / R„ , is

SI El

obtained in a similar manner with the factor switch set on 1. F can be obtained from (13) by actually raeasuring, as fourterminal resistances, the four resistances on the right of the equation.

These can be measured in terms of known standards using the URS,

by means of a Kelvin or Thomson double bridge or any other convenient and acceptable method. The factor F can be expressed as

F( 1 + f ) where F is the nominal factor and f the correction. For

example, a factor of 0. 100006 would represent the nominal 0. 1 factor

with a correction of +0. 006 percent.

b. Factors for Potentiometers Standardizing on a Single Range

For the potentiometer which standardizes on the highest range

only, such as shown in figure 5, the method will be somewhat modified. The current I may differ from I because the overall resistance
30

of the potentiometer T for the Y factor differs from the overall

resistance for the 1 factor T .

^Y ^1

1 Y

Substituting (14) into (10), gives

R

^Y= (a(4)- . _ Y

It should be emphasized that T /T is the ratio of total resistances for the potentiometer when in use with a battery of a specified

voltage. If a battery of a different voltage is used with the potentiometer, a corresponding change in the battery rheostat must be made in

which case T,/T may be appreciably different if T and T are not

close to equality (the condition of poor factor compensation). For this

situation the factor for range Y will be a function of the supply battery

voltage and will have to be calculated for whatever voltage is furnished

by the supply battery.

The expression R^ /R^, can be measured readily by connect- EY El

ing a URS across the BA+ and BA- terminals. After EMF and SC dials

have been calibrated, the EMF dials are set to a maximum and readings

at balance taken on the URS for potential connections EMF+ and EMF-.

The same procedure is repeated with the factor switch in the Y position.

The URS reading differences AE for the 1 factor and AE for the Y

factor are given by the following equations:

(16)

(17)

AEj ^El

2111. 11 "^IC

AE^ ^EY

2111. 11 "^YC
31

The term 2111. 11 represents the overall resistance, in ohms, of

conventional Universal Ratio Sets. The term T is the total resistance of the potentiometer on the 1 factor as the instrument is being

calibrated, and T is the total resistance of the potentiometer on the

Y factor as the instrument is being calibrated.

Conabining (16) and (17) and rearranging terms gives

R_„ .AE,. ,T

^<^)(^y

Substituting (18) in (15) gives

AE..X .T„„x ,T

'y -(^)(^)(i)^

Equation (19) is used to compute the factor. The term AE /AE is

obtained directly from differences of URS readings. The term

T /T is obtained by comparing the total resistances with the

factor set at 1 and at Y with the battery rheostat in the position used

when the EMF dials are calibrated. This comparison can be made

with a precise Wheatstone bridge but is obtained more conveniently

with a Direct Reading Ratio Set (Wenner Ratio Set) [2, 4] . The term

T / T is obtained in similar fashion except that the total resistance

in the potentiometer is that in the circuit when the potentionaeter is in

use.

If the potentiometer is to be used with a battery such that the

overall potentiometer resistance is close to that at which calibration

is performed, the expression

.T,_x .T

YIC^ V-^y/

reduces to unity for practical purposes. This is frequently the situation. One manufacturer, however, provides for choice of either three
32

or six-volt supply by providing the instrument with an added resistor

to be inserted in series with the battery-adjusting rheostat. The

factor corrections for instruments of this type frequently are different

for use with three and six-volt batteries. If an extremely high voltage

supply were used with the correspondingly high dropping resistance,

the term T /T practically would be unity. If the term T /T is

unity, so also is T /T unity.

c. Other Factor Circuits

Other factor arrangements for constant current potentiometers

can be treated in a similar manner to determine just what measurements are necessary and to what precision. The examples given are

illustrative of the type of measurement capabilities of the URS. These

methods may be extended with slight modifications to such specialized

varieties as microvolt potentiometers and others where the range of

potential measured differs considerably from that of a standard cell.

4. 4. Examples of Factor Measurement

a. Measurements on an Instrument that Standardizes on All Ranges

Typical data are shown in table 3 for factor determiniation on

a potentiometer that standardizes on all ranges.

We have shown that the ratios of URS reading differences are

proportional to the ratios of the corresponding resistances. Equation

(13) may be restated in terms of URS reading differences. For the

0. 1 factor.

F„ = ^^v^M=r,,^;^V.c^V (20) ^ ^^SY^ V^Ei^ v^scg_jy ;aEj

f

197.518 \ / 1Z51.Z48 \ _ ^Y - ' 1251. 246 ) \ 1975. 317 j

" °- O'^''''''^- '2''
33

This can be expressed in terms of the nominal factor ratio 0. 1 and a correction. Using the same reasoning for the 0. 01 factor,

_ /^^O. 01 \ / ^^^1\ ^ / 19.751 \ / 1251.248\

Y \ASC^^^^J \ AE^ J

f^ 1251. 2397 \l915.3nj

= 0. 009999 = 0. 01(1 - 0. 0001). (22)

b. Measurements on an Instrument

that Standardizes on a Single Range

Typical data are shown in table 4 for factor deter raination on

one type of potentiometer that standardizes on a single range. Potentiometer dials are set at 1. 600 volts. When the instrument is calibrated by the URS and also when it is used as a potentiometer with a 3-volt battery, the overall resistance is about 27 2 ohms. When the

instrument is used as a potentiometer with a 6 -volt battery, the overall resistance is about 545 ohms.

The following measurements were taken with a high-resolution

Wheatstone bridge on overall resistances for use in (19). The circuit

was adjusted for calibration or for use with a 3-volt power supply.

For 1 factor, T = T = 271.990 ohms.

-I- V—

i For 0. 1 factor, T = T = 27 1. 984 ohms.

For 0. 01 factor, T = T = 271. 996 ohms.

Y K^ 1 The following terms were computed for a 6-volt power source

requiring an added resistance of about 27 3 ohms.

For 1 factor, T = 544.990 ohms.

For 0. 1 factor, T = 544.984 ohms.

For 0,01 factor, T = 544.996 ohms.
34

Table 3

Typical Factor Measurement Data for an Instrument

That Standardizes on All Ranges

Potential Factor

Connection to or URS Reading

Potentiometer Range

1

1

Reading

859. 4521

2110. 700j

Differences

SC+

SC- 1251. 248 = ASC

EMFEMF+

1

1 1976. 472'!

1. 155J

1975. 317 = AE

SC+

sc0. 1 0. 1 859. 4541

2110. 700J

1251.246 = ASC^^

^ EMFEMF+

0. 1 0. 1 2037.891)

1840. 373 J

197. 518. AE^^^

SC+

sc0. 01

0. 01

859.4611

2110.700 J

1251. 239 = ASCq^^j

EMFEMF+

0. 01

0. 01

2044. 032 1 2024. 281 1 ^9-^^1-AE^.Ol
35

Table 4

Typical Factor Measurement Data For an Instrument

that Standardizes on a Single Range

Potential Factor

Connection to or URS Reading

Potentionrieter Range Reading Differences

EMF+ 1 71.2281 ,,^„ ^^^ _

T->xT^ 1 1/^1 oon r 1600. 002 = AE, EMF- 1 1671. 2 30 j

1

» EMF+ 0.1 1511.1391 1/^ n^c

EMF- 0.1 1671.144; 160. 005 = AE^^

^ EMF+ 0.01 1655.0051 w nn-> _ ir EMF- 0.01 1671.007/ ^^- °^^ = ^^0. 01
36

When these values are substituted in (19), the following results

are obtained.

For 0. 1 factor and a 3-volt battery,

/ 160. 005\ /271.984\ /271.990\ ^ , ^Y - (16007002 ; (271:990; {wTw) - ^' ^°«°^^-

For 0. 1 factor and a 6-volt battery,

/ 160. 005 \ /271.984\ /544. 990\

^Y = (

1600.002 ) (27r9?o) (l44:?84 J

= °- l""""^-

For 0. 01 factor and a 3-volt battery.

/ 16. 002 \ /271.996\ , .,„ , ^Y - (

1600.002 ) (271:990) ^ ^^^-^ ' = '• ^l^^OlFor 0. 01 factor and a 6-volt battery.

/ 271.990

\ 271. 996

/ 271.996\ / 544. 990

^Y- ( 1600:002 ; V(I7i:l9^; 271.990y \ 544.996 f^^^^^:^) =0.010001.

Because the 0. 01 factor ordinarily is computed with no more

precision than 0. 01 percent, the 0. 01 factor would be the same for

either a 3-volt or a 6-volt power source.

4. 5. Working Test for Factors

In addition to the spot check mentioned on page 25 for checking

the EMF range corresponding to the SC range, a simple working test

for three factors can be arranged. The test requires three accurately

known resistors in ratios 1 to 10 to 100. The lowest resistor can be

of any value from 1 to 100 ohms. These resistors are connected in

series to a suitable battery of constant voltage and thus provide three

stable sources of potential difference with nonninal ratios of 0. 01 and

0. 1. The actual ratios of potential are the same as the accurately

known ratios of the three resistors. A suitable, stable current is

established in the resistors so that the potential difference across the

highest resistor falls near the upper linnit of the highest range of the

potentiometer. The potential differences across the three resistors
37

are measured on the three respective ranges of the potentiometer.

The factors can be checked by comparing the measured potential

ratios against the actual potential ratios. This same technique is

applicable to other types of potentiometers also.

4. 6. Comparison with Another Potentiometer

as a Method of Calibration

Perhaps the most straightforward method of calibrating a potentiometer is to compare it directly with a potentiometer of similar

range which previously has been calibrated accurately. However, this

method usually is not as accurate as the bridge circuit URS methods.

It has the advantage of calibration under actual operating conditions

and is suitable for portable instruments of moderate accuracy.

In comparing a potentiometer with another calibrated one, the

instrument under calibration can be used to furnish potential differences at desired calibration points. These potential differences are

measured by the calibrated potentiometer. The functions of the two

instruments may be interchanged. It is essential that the currents in

both potentiometers be held as constant as possible. This requirement demands the utmost in stability of power sources. Furthermore,

the presence of thermal electromotive forces constitutes possible

sources of calibration errors. If two observers work together and

standardize the instruments as frequently as required, the errors due

to drift with time may be minimized. A single standard cell with

appropriate switching arrangements may be used to standardize both

instruments. If separate standard cells are used, emf' s of both must

be known accurately or the difference known accurately.

If standard cell circuits are compared with each other for

linearity, a switching arrangement should be used that avoids the

possibility of accidently discharging the standard cells. During this
38

comparison, the standard cell terminals of both instruments will be

connected to each other, and the standard cells must not be connected

to either potentiometer while the potentiometers are interconnected.

The standard cell circuit linearity can be evaluated by using the EMF

circuit of a calibrated potentiometer, if switching arrangements are

provided to protect the standard cell frora accidental discharge.

To deterraine the factor corrections of a potentiometer by

comparison, it is not necessary to make measurements on all positions

of the dials. A check on two or three of the highest settings of the

first dial should be adequate to furnish the ratios of the factors.

4.7. Calibration of Constant-Current Potentiometers

Designed to Measure Small EMF' s and of

Modified Constant-Current Potentioraeters

Typical of the group are such types as the Diesselhorst potentiometer, the Wenner Low-Range potentiometer, the White Double

potentiometer, and the Rubicon Six-Dial Thermofree potentiometer.

Most of these are described by Harris [8] . Specialized circuits are

incorporated in these instruments necessitating individual circuit

analysis for each variety before a definite calibration procedure can

be established. Some of these varieties can be calibrated by a number

of methods. Details of the calibration by means of another potentiometer, outlined previously, are applicable here. The URS is useful in

calibrating all of these instruments. However, because of the extensive range in magnitude of component circuit resistors, resultant high

or low resistance ratios cannot be obtained with the required measurement accuracy by direct comparison of URS reading differences. In

these circurastances the comparison of the coraponents with calibrated

standard resistors of approximately the same magnitude as the components usually is required. Thus, an added step is introduced in

determination of resistance ratios.
39

5. Potentioraeters of the Constant -Resistance

or Lindeck Variety and Combination Types

5. 1, Principles of Circuitry

Figure 8 is a schematic diagram of a simple potentiometer

illustrating this principle. The source of unknown potential difference

is connected in series with a galvanometer G and a tapping key, all

connected across a calibrated resistance R^. R„ may be a single E E

resistor, a multiple resistor, or a combination of resistors. Current

is supplied to this resistor by a battery, and its magnitude is controlled by the adjustable rheostat R, A meter, M, usually a milliammeter

or microammeter , is inserted in this circuit.

When the tapping key is closed and the galvanometer indicates

a null condition, the EMF or potential difference at the EMF terminals

equals the four -terminal resistance of R times the current in this

resistor. The current is indicated by the meter. The meter scale

usually is graduated to read the potential difference present across

the EMF terminals of the instrument.

Several types of potentiometers in use incorporate in their

circuits a combination of a constant-current potentiometer and a constant-resistance potentiometer. Each unit measures a portion of

the unknown emf. Figure 9 is the schematic diagram of such a combination.

This instrument has two ranges, and both the constant-current

portion of the circuit and the Lindeck portion of the circuit have separate factor plug switches to accomplish this change in range. That

portion of the unknown EMF measured by the constant -current method

is equal to the potential drop across resistors S + S ; the portion

measured by the Lindeck potentiometer is equal to the drop across S .
40

>-O

LUO

UJ

-I

Q.1

in<O<

cr

LU

GO
41

Dials D and D adjust the potential drop across S and S , whereas

dials D and D adjust the potential drop across S . Each potentiometer unit uses a separate battery.

5. 2. Calibration of Lindeck and Combination Potentiometers

A simple Lindeck unit such as shown in figure 8, merely

requires four -terminal resistance determinations on the resistor R^E

for all ranges, and also a calibration of the meter. The resistance

measurements do not require extreme precision and may be accomplished by a number of methods. One method is the comparison of

the potential difference across R with the corresponding potential E

difference across a known standard resistor connected in series with

R when the circuit is energized with a steady direct current. Like- E

wise, any suitable bridge method of making moderately accurate fourterminal resistance measurements is acceptable.

The meter can be calibrated by any suitable method of calibrating sensitive, dc, low-current meters. In combination instruments,

provision may be made for calibrating the meter directly against steps

on the constant-current portion of the circuit.

In figure 9, EMF dials D and D , as well as the standard cell

circuit, are calibrated against standard resistors of appropriate magnitudes by' means of a URS. Furthermore, the dials D,12and D^ must

be checked to insure that the circuits are so compensated that the

current in the potentiometer is independent of the positions of dials

D and D . The range or factor measurements on the meter factors, as well as the factors for the constant -current portion of the circuit, can

be accomplished by methods previously outlined. However, the procedure is somewhat more complicated and may require the soldering

of some lead connections into various portions of the circuit for best
42

DIAL FACTOR^ . RANGE ^ ^ /

EMF

FIG. 9 SIMPLIFIED SCHEMATIC DIAGRAM OF COMBINATION OF CONSTANT

CURRENT AND CONSTANT RESISTANCE POTENTIOMETER
43

results. In figure 9, leads may be soldered at the points indicated byarrows 1 and 2. These leads are then connected to the battery terminals as shown by the dashed lines in order to short out both the battery

rheostat R and the standard cell circuit. Potential connections are

obtained by clips on the shafts on the dials as indicated by arrows 3

and 4. The A and B terminals of the URS are connected to the special

leads at points 1 and 2 or to the BA terminals. Readings are taken

on the URS corresponding to connections made at potential points 3 and

4 for both of the dial factor positions. In addition, a determination is

made on the ratio of the overall resistances of the circuit between

points 1 and 2, corresponding to the two positions of the dial factor

switch. These measurements provide the data necessary to compute

the factor.

The same factor can be measured without any checks on overall resistances or any extra leads soldered in if we simply connect the

BA^ terminals to the A and B terminals of the URS and then follow the

procedure outlined in the section on potentiometers which standardize

on all ranges. The points which should be used in place of the EMF

terminals are the connections to the dial shafts. The precision of this

method will be somewhat limited by the smaller difference obtainable

in URS readings between the potential points 3 and 4 in the EMF circuit.

This is because the ratio of the EMF circuit resistance to the total

resistance of the standard cell circuit and the battery rheostat is small.

However, the spread of readings on the URS for the EMF

potential points can be increased by shorting out the standard cell

circuit and the battery adjusting rheostat R, and making the following

raodification. A high-quality resistor of a suitable magnitude about

the same as that of the EMF circuit resistance between points 3 and 4

can be connected in place of the standard cell circuit. The connections
44

to the resistor potential terminals R and R will then serve as substitutes for the SC-f and SC-# terminals when taking URS readings. In

effect, a dummy standard cell circuit has been created to substitute

for the original. URS reading differences for the EMF circuit and the

dunnmy standard cell circuit are the same order of magnitude, and the

accuracy of the measurement is thereby improved appreciably.

The meter factor in figure 9 can be measured by identical

methods when the meter is disconnected from the circuit. The meter

itself can be calibrated against the dials D and D by a so-called

"self -checking" method.

The above exaraples serve to show some of the means of calibrating the factors of Lindeck-type potentiometers. However, these

factors can be calibrated by measuring resistances of individual components. In general, each circuit should be carefully studied to determine the most appropriate calibration method.

6, References

[1

[3

[4

[5

[6

[7

[8

F. K. Harris, Electrical measurements, pp 144-185, John

Wiley and Sons, Inc., New York, N. Y. (1952).

F. Wenner and E. Weibel, The testing of potentiometers. Bulletin Bureau of Standards BSU, 27 (1914), S223.

J. L,. Thomas, Precision resistors and their measurement,

NBS Circ. 470 (1948).

P. P. B. Brooks, Calibration procedures for direct current

resistance apparatus, NBS Monograph 39.

F. K. Harris, op. cit. , p. 157.

F. K. Harris, op. cit., pp. 150-153, 155-156.

NBS Monograph, op. cit., pp. 40-53.

F. K. Harris, op. cit., pp. 172-176.

« U.S. GOVERNMENT PRINTING OFFICE: 1963 O - 678083
U. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineering] in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the

front cover. WASHINGTON, I). C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurement&

Dielectrics. High Voltage.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology.

Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Piwe Substances. Spectrochemistry. Solution Chemistry. Standard Refer- ence Materials. Applied Analytical Research, Crystal Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Polymers. Macromolecules: Synthesis and Structure. Polymer Chemistry. Polymer Physics. Polymer Characterization. Polymer Evaluation and Testing. Applied Polymer Standards and Research. Dental Research.

Metallurgy. Engineering Metallurgy. Microscopy and Diffraction. Metal Reactions. Metal Physics. Electrolysis

and Metal Deposition.

Inorganic Solids. Engineering Ceramics. Glass. Solid State Chemistry. Crystal Growth. Physical Properties.

Crystallography.

Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Stand^ds. Heat Transfer. Inorganic Building Materials. Metallic BuUding Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. Operations Reseeuch. Data Rrocessing Systems. Components and Techniques. Computer Technology. Measurements Automation.

Engineering Applications. Systems Analysis.

Atomic Physics. Spectroscopv. Infrared Spectroscopy. Far Ultraviolet Physics. Solid State Physics. Electron Physics. Atomic Physics. Plasma Spectroscopy.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. Ele- mentary Processes. Mass Spectrometry. Photochemistry and Radiation Chemistry.

Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering Laboratory. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Cryogenic Technical Services. CENTRAL RADIO PROPAGATION LABORATORY

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services, Vertical Soundings Research.

Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Systems. Applied Electromagnetic Theory. High Frequency and Very High Frequency Research. Fre- quency Utilization. Modulation Research. Antenna Research. Radiodetermination.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. High Latitude Ionosphere

Physics. Ionosphere and Exosphere Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.

RADIO STANDARDS LABORATORY

Radio Physics. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency and Time-Interval

Standards. Radio Plasma. Millimeter-Wave Research.

Circuit Standards. High Frequency Electrical Standards. High Frequency Calibration Services. High Frequency

Impedance Standards. Microwave Calibration Services. Microwave Circuit Standards. Low Frequency Csdibration

Services.
~ '-MNBS

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