Properties of 

Thermistors Used in 

Geothermal Investigations 

and

Preparation of 

Thermistor Cables Used in 

Geothermal Investigations

GEOLOGICAL SURVEY BULLETIN 1203-B, C

.

loo)

Properties of 

Thermistors Used in 

Geothermal Investigations

By EUGENE C. ROBERTSON, RUDOLPH RASPET, JOEL H. SWARTZ, and MAJOR E. 

LILLARD

Preparation of 

Thermistor Cables Used in 

Geothermal Investigations

By RUDOLPH RASPET, JOEL H. SWARTZ, MAJOR E. LILLARD, and EUGENE C. 

ROBERTSON

EXPERIMENTAL AND THEORETICAL GEOPHYSICS

GEOLOGICAL SURVEY BULLETIN 1203-B,C

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1966
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 25 cents (paper cover)
Properties of 

Thermistors Used in 

Geothermal Investigations

By EUGENE C. ROBERTSON, RUDOLPH RASPET, JOEL H. SWARTZ, and MAJOR E. 

LILLARD

EXPERIMENTAL AND THEORETICAL GEOPHYSICS 

GEOLOGICAL SURVEY BULLETIN 1203-B

A study of the precision, 

sensitivity, and stability 

of thermistors in temperature 

measurement

CONTENTS

Page

Abstract_ ________-________-___-___________________--__---_--___- Bl

Introduction. _____________________________________________________ 2

Characteristics of thermistors_____________---______----_--------__-- 4

Manufacture. _________________________________________________ 4

Dependence of resistance on temperature.________________________ 6

Dependence of resistance on pressure___________________________ 9

Temperature measurements with thermistors________________________ 10

Precision of measurement_____________________________________ 10

Temperature of ice baths for thermistor cables____________________ 12

Thermistor stability.______________________________________________ 14

Drift of thermistors in cables_________________________-_--_------ 14

Laboratory studies of thermistor drift___-___________-----_-_---_- 19

Drift of thermistors held at constant temperature ___-_____---__-- 21

Drift rates at various temperatures_________________---------___- 22

Possible explanations of thermistor drift.__________________---__-- 23

Simplified method for conversion of resistance to temperature.__________ 26

References _ _____________________________________________________ 32

ILLUSTRATIONS

FIGURE 1. Log resistance versus temperature for a thermistor of No. 1

2. Graph of change in mean apparent temperature of thermistor 

cables against time between ice-point calibrations.-- ______

3. Histogram of thermistor drift. ____________________________

4. Graph of drift rates of seven thermistors. __________________

5. Graph showing parallelism and approximate range of curves of 

log resistance versus reciprocal temperature for type-17A 

thermistors. __________________________________________

Page 

B8

15

18

24

27

TABLES

Page 

TABLE 1. Interpolation errors in four equations for temperature-resistance

relations of thermistors.________________________________ B7

2. Pressure coefficients of resistance of thermistors at several temperatures______________________________________________ 9

3. Statistical summary of resistances at the ice point of five thermistors and a platinum thermometer_______________________ 11

m
IV CONTENTS

Page

TABLE 4. Temperature of ice baths measured with a platinum thermometer, and pertinent data for 28 thermistor cables-________ B13

5. Drift at the ice point of 411 thermistors in 15 cables._________ 16

6. Summary of nine thermistor-stability studies.--_____________ 20

7. Mean drift rates of seven thermistors at five temperatures over

a 13-year period_________________________________ _ 23

8. Master table for conversion of thermistor resistance to temperature.._______________ ______________________ 28

9. Determination of temperature corrections for thermistor 4550__ 31
EXPERIMENTAL AND THEORETICAL GEOPHYSICS

PROPERTIES OF THERMISTORS USED IN GEOTHERMAL

INVESTIGATIONS

By EUGENE C. KOBERTSON, KUDOLPH KASPET, JOEL H. SWARTZ, and

MAJOR E. LILLARD

ABSTRACT

Thermistors are small rugged beads, disks, or rods of sintered oxides, which 

can be used to measure temperature with a precision of ±0.01°C with a simple 

four-dial Wheatstone bridge. Thermistors of number 1 material have a spinel 

crystal structure, the approximate formula being Ni0 .6Mn^4Mn+2O4. Thermistors 

of this material generally are used in temperature sensing, and those with a nominal 

resistance of 1,000 ohms at 20°C have a negative temperature coefficient of resistance of about 5 percent per deg C at that temperature. Most thermistors differ 

in resistance and in change of resistance with temperature and so are not interchangeable.

An empirical adaptation of the equation for electrical resistivity of semiconductors fits the resistance-temperature data for thermistors very well:

R=A exp

where R is resistance, in ohms; Tis temperature, in degrees Celsius; and A, B, and 

C are constants. For this equation, interpolations between 15°C intervals are 

good to ±0.01°C. The effect of pressure on thermistor resistance is negative 

and very small, about 10~7 bar"1 ; at the bottom of a 3,000-meter hole, in a 

logging cable, a thermistor (nominally 50,000 ohms at 20°C) would have a change 

of resistance of 0.1 ohm, equivalent to + 0.0002°C, due to the pressure of the 

water column in the hole.

In a separate study of precision of measurement, a platinum thermometer was 

used to determine the absolute temperature of 23 carefully made ice baths (nominally at 0°C), and the mean was + 0.0004° C, the standard deviation being 

0.0014°C. These values constitute, respectively, the systematic and the random 

errors of both the thermometer measurements and the bath temperatures. Five 

thermistors in the same baths showed a standard deviation of temperature measurement of 0.003°C; however, the coherent variation of the resistances of all five 

thermistors from bath to bath shows that relative-temperature measurements 

with thermistors can inherently be as precise as ± 0.0001° C.

In the calibrations of 41 thermistor cables at the ice point (0°C) in a large box, 

the mean temperature as measured by the platinum thermometer was 0.0018° C, 

and the standard deviation was 0.0031°C. Thermistors in cables can be accurately calibrated in such baths.

Bl
B2 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

During 15 years of geothermal studies by the Geological Survey, many multithermistor cables have been recalibrated two or three times at the ice point. 

These fairly precise data give a quantitative measure of thermistor drift, observed as a secular increase of resistance, which is equivalent to a decrease in 

apparent temperature: the mean drift for 613 pairs of readings of disk thermistors 

in 15 cables was 3.8X10"3 deg C per mo, and the standard deviation was 

5.1X10~3 deg C per mo; 32 aberrant readings were excluded. The results of 

nine studies, by other men, of the stability of bead and disk thermistors show 

in general a similar increase of resistance with time; heating to 150° or 200°C 

shocks thermistors badly, and cooling to 79° C disturbs them beyond further 

usefulness. Thermistors held within 0.5°C of a constant temperature drift very 

little; two separate studies for 8- and 9-year periods show a drift <0.3X10~3 

deg C per mo. The drift rate varies with temperature; the mean rate for seven 

disk thermistors over a 13-year period at 30°C was found to be 2.5XKT3 

deg C per mo, and at +30°C the rate was 4.2X10"3 deg C per mo.

Thermistor drift is ascribed principally to diffusion of impurity ions resulting 

from passage of the electric measuring current; other causes may be change in 

the oxidation state of some of the manganese atoms, mechanical shock, thermal 

shock, or disordering of atoms in the crystal structure.

A simplified method for converting resistance to temperature is described; it 

utilizes a master table and individual thermistor correction tables; the method 

is easy to use in the field, inasmuch as the arithmetical calculations are simply 

made.

INTRODUCTION

Temperature measurement with semiconducting, thermally sensitive resistors, or thermistors, has become increasingly widespread 

since 1950, although thermistors have been used since 1940 for temperature compensation in telephone and other electrical circuits (Sillars, 

1942). The results of 15 years experience in the use of thermistors 

as temperature-sensing elements in geophysical work of the Geological 

Survey are analyzed in this report. The physical properties, precision, 

and stability, and the installation, use, and reliability of thermistors 

are discussed in the light of this experience.

The use of thermistors in cables for measuring temperatures in 

drill holes was initiated and developed in 1949 by J. H. Swartz (1954). 

Since then, thermistor cables have been used in many places to measure subsurface temperatures: MacCarthy (1952), Brewer (1958), 

Lachenbruch and Brewer (1959), and Greene, Lachenbruch, and 

Brewer (1960) studied temperature problems due to permafrost at 

several locations on the Arctic Slope; Swartz (1958) used thermistor 

cables to determine temperatures in deep drill holes on Eniwetok 

and Bikini atolls and Kilauea volcano in Hawaii; Miller (1958) 

studied ice temperature and glacier flow in southeastern Alaska. 

LaFond (1962) used thermistors to determine temperatures of the 

sea near the surface; Kevelle and Maxwell (1952) measured heat flow 

through the ocean floor; Von Herzen (1962) measured ocean-floor
PROPERTIES OF THERMISTORS B3

temperature gradients with four thermistors in a Wheatstone bridge; 

Lachenbruch (1957) used a thermistor probe to measure thermal 

conductivity. Other applications of thermistor cables to determine 

terrestrial heat flow were described by Misener, Thompson, and Uffen 

(1951),Misener,Bremner,and Hodgson (1956), Horai (1959),Chadwick 

(1956), Newstead and Beck (1953), Cooper and Jones (1959), Bullard 

(I960), Garland and Lennox (1962), Beck (1962), Saull, Clark, Doig, 

and Butler (1962), Diment and Robertson (1963), Sass and LeMarne 

(1963), Diment and Werre (1964), and Diment and Weaver (1964).

Measurement of thermal conductivity of rock in place with a 

thermistor cable in a borehole was described by Beck, Jaeger, and 

Newstead (1956). Techniques of temperature measurement in 

boreholes with thermistor cables and cable fabrication were described 

by Lachenbruch, Brewer, Greene, and Marshall (1962), Misener and 

Beck (1960), and Beck (1963). Comprehensive discussions of the 

characteristics of thermistors were given by Becker, Green, and 

Pearson (1946) and Nielsen (1959). The electrical circuits used with 

thermistors in measuring temperature were described by Swartz 

(1954) and Droms (1962); use of thermistors for measurement of 

very low temperatures was discussed by Sachse (1962).

The principal advantages of using thermistors in measuring 

temperatures in the earth are that (1) they have a large change of 

resistance with temperature (ohms per ohm per deg C), 10 times that 

of metals; (2) they are available in a wide range of resistances, from 

10 to 107 ohms at 25°C, for optimum matching to the measuring 

circuit to eliminate large corrections for lead or contact resistances;

(3) their resistance is a function of the absolute temperature, and 

thus the need for a junction at a reference temperature is eliminated;

(4) they are little affected by the usual chemical and physical conditions of the environment; (5) they are small; (6) they are mechanically 

rugged.

A primary consideration of this paper is the stability of thermistors, 

that is, the change of the temperature-resistance relation with time. 

In ordinary use, thermistors are subject to an inherent, apparently 

unavoidable, secular drift, although if they are held at a constant 

temperature, the drift seems to be very greatly reduced. Calibration 

and ice-point recalibration data are the basis for discussion of this 

drift.

We are grateful to A. H. Lachenbruch and W. H. Diment for many 

helpful additions and improvements on techniques, data, and interpretations, and we appreciate the skillful preparation of thermistor 

assemblies and careful assistance of Everett Saunders in many parts 

of this investigation.

781-990 66 2
B4 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

CHARACTERISTICS OF THERMISTORS

MANUFACTURE

The manufacture of thermistors was observed in five commercial 

plants by one of the authors (Raspet), and the conclusion was reached 

that the fabrication of thermistor bodies is about the same in each. 

Therefore, the following description of processing may be considered 

as generally applicable.

The raw material for thermistor bodies is prepared by calcining 

at 800°C the chemically pure carbonates of nickel, manganese, and 

cobalt. Thermistors of No. 1 material are made by mixing 20 percent (by weight) nickel oxide with 80 percent manganese oxide, and 

adding a small amount of a volatile binder; No. 2 material contains 

67 percent No. 1 material and 33 percent cobalt oxide. Inasmuch 

as the No. 2 material is less sensitive to temperature change than the 

No. 1, few thermistors of No. 2 composition are used. Hereafter, 

the characteristics of thermistors made from No. 1 material only 

are described.

The mixed calcined powder is compacted under high pressure into 

a pellet of disk or ball shape, and the pellet is then fired at 1,300°C 

for 10 hours. Before sintering, when the pellet is in the green state, 

it has a density of about 3.0 g per cm3 and a porosity of about 20 

percent; after sintering it has a density of 4.95 ±0.05 g per cm3 

and a porosity of about 3.0 percent. The grain size of the finished 

thermistor is 0.1 to 10 microns.

As a result of solid diffusion during the sintering process, the 

thermistor material acquires the crystal structure of spinel with a 

cell size close to that of magnetite (Mary E. Mrose, unpub. data, 1960). 

The resulting thermistor compound has a calculated composition 

of Nio.6Mn+2o.4Mn2+304 . The sintering is a complex process and must 

be done in an oxidizing atmosphere to obtain both valence states 

of manganese and thereby to obtain the stable spinel compound.

Three types of thermistors are commercially available: beads, 

disks, and rods. In bead thermistors, two separated platinum wire 

leads are fabricated directly through the bead by sintering the calcined oxides around them; bead thermistors are usually finished by 

coating with glass. Electrical connections are made to the flat ends 

of the disk and rod thermistors by first painting them with a silverand-glass paste and firing at 800°C for 1 hour. A spot of low-melting 

silver-alloy solder is alloyed to the paste, and then tin-coated copper 

wire leads are inserted into the molten solder. The bond of the wire 

leads and solder to the thermistor body will withstand a pull of 500
PROPERTIES OF THERMISTORS B5

psi. The cylindrical surfaces are cleaned of paste in a centerless 

grinder by a very fine abrasive.

Preliminary stabilization of the thermistors is accomplished at 

the factory by aging at 110° to 150°C for 1 to 4 weeks, or by selfheating with a low electric current for 1 week. This aging tends to 

reduce subsequent increase of resistance (secular drift).

The type-17A thermistor, manufactured by Western Electric Co. 

was used by the Geological Survey in the present investigation, and 

most of the data were taken on thermistors of this type. Equivalent 

thermistors of similar size and characteristics are made by other companies, such as General Electric Co. (Metallurgical Products Dept.), 

Fenwal, Inc., Victory Engineering Corp., Gulton Industries, Inc., and 

Yellow Springs Instrument Co. The 17A is a disk, 5mm in diameter 

and 1 mm thick; it is large enough to manipulate easily without being 

too bulky after installation inside a cable. The 17A has worked well 

in cables, withstanding the mechanical handling of the cable when 

stretched in a hole and when flexed in coiling on a reel.

In measuring resistance of the 17 A, a portable four-dial Wheats tone 

bridge is ordinarily used in the range 10,000 to 1,000 ohms, (equivalent to 20° to +25°C); current in the bridge circuit is limited to 

150 jua to minimize self-heating in the thermistor; about 1 milliwatt 

of power must be dissipated. With the usual self-contained galvanometer (sensitivity of 4 /xa per mm), the precision is about 1 ohm 

(equivalent to 0.02°C at +25°C). An improved precision to 0.1 ohm 

(0.002°C) can be attained with a five-dial Wheatstone bridge by using 

(1) an amplifier ahead of a low-sensitivity galvanometer, (2) a sensitive 

null indicator, or (3) an external galvanometer having a sensitivity of 

0.05 /xa per mm.

As with most other semiconductors, thermistors have a large negative temperature coefficient of resistance. For the 17A thermistor, 

made of No. 1 material, the coefficient is 4.4 percent per deg C at 

+30°C (total resistance, 800 ohms), and is 6.5 percent per deg C 

at 30°C (total resistance, 18,000 ohms).

The resistances of the 17A thermistors may differ considerably at 

the same temperature. For example, two thermistors might differ by 

1,000 ohms at 30°C and 50 ohms at +30°C, each resistance equivalent to >1°C; also, their changes of resistance with temperature would 

differ widely. Therefore, each thermistor requires a separate calibration. It is possible to obtain two or more thermistors with nearly 

matching resistance-to-temperature conversions (matching to ±0.1°C) 

at a somewhat greater cost, and for many purposes these are useful, 

especially if separate calibrations need not be made.
B6 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

DEPENDENCE OF RESISTANCE ON TEMPERATURE

Thermistors, like other semiconductors, have an electrical conductivity approaching that of a metal at high temperatures and are nearly 

insulating at low temperatures. The dependence of conductivity a-, 

(ohm-cm)"1 , on absolute temperature Tin degrees Kelvin, is commonly 

expressed by

<r=A(T) exp (-AE/2kT) (1)

in which A(T) is a slowly varying function of temperature, AE is an 

energy term, and k is the Boltzmann constant (8.625X10" 5 ev per 

deg K). This relation is explained for elements like Si and Ge and 

for compounds like InSb, GaAs, and A1P in terms of their band structure, that is, their electron energy spectrum. The valence band is 

separated from the conduction band by an energy gap AE; the number 

of electrons excited across the gap AE is proportional to the exponential term in equation 1. The electrical conductivity of these semiconductors is equal to the number of free electrons and holes times their 

mobilities and times their charges.

Unfortunately, the spinel semiconductors, including thermistors, do 

not have the simple band structure of the metallic semiconductors, 

and furthermore the intrinsic electrical properties of the spinels are 

difficult to measure accurately; their theoretical characteristics are 

therefore not so well understood. A review of the theory on semiconducting compounds was given by Mooser (1960). Sillars (1942) 

discussed the use of some semiconducting ionic and electronic metallic 

oxides as temperature-sensing elements; Becker, Green, and Pearson 

(1946) discussed the properties and uses of semiconductors and 

thermistors.

The following empirical equations, modeled after equation 1, have 

been found to fit the measurements made on thermistors. Because 

the resistance, rather than the conductivity or resistivity, is measured, 

the expressions are inverted and multiplied by a form factor to relate 

resistance to temperature for any given thermistor. The logarithmic 

form is also given because it is commonly used in calculations.

Exponential form Logarithmic form

R=Aexp(BT-1 ) log R=A'+B' T~l (2)

R=AT~C exp (BT~1} log R=A'-C\og T+B'T'1 (3)

R=A exp [B(T+C)-1} log R=Af +Bf (T+0)~l (4)

£=exp (AT+BT- 1) log B=Af T+Bf T~1 (5)

where A, A', B, B', and (7 are constants; R is resistance, in ohms; T is 

temperature, in degrees Kelvin. Equation 2 is merely equation 1 

inverted, assuming A(T) to be a constant. Equation 3, containing 

three constants, was proposed by Becker, Green, and Pearson (1946).
PROPERTIES OF THERMISTORS B7

Equation 5 is the result of an empirical search for a two-constant 

relation by William H. Diment (unpub. data, 1962). Equation 4 

was developed in 1949 by one of the authors (J. H. Swartz, 1954), and 

independently by Bosson, Gutmann, and Simmons (1950); in this 

equation, T may be measured in degrees Celsius with no difference 

from measurements in degrees Kelvin except in the numerical value of C.

The measured value for the resistance of a thermistor is compared 

in table 1 with the values calculated according to equations 2 through 

5. These data are from 21 calibrations quoted by Bosson, Gutmann, and 

Simmons (1950) and are used because they permit a severe test of the 

relative accuracy of the four equations to be made for the rather large 

temperature interval of 200°C. The large change of resistance in 

this interval is shown by the curve in figure 1.

As shown in table 1, equation 4 fits the calibration data best, and 

has been used by the Geological Survey in preparing temperatureresistance conversion tables. In general, interpolations by equation 

4 are made at 1° intervals between calibrations at 30°, 15°, 0°, 

+ 15°, and +30°C. A comparison between resistances interpolated 

by equation 4 and observations at the midtemperatures, 22.5°, 

 7.5°, +7.5°, and +22.5°C, was made for 30 calibrations; the mean 

interpolation error of resistance (calibrated calculated) converted 

to equivalent temperature was 0.031°C, and the standard deviation 

was 0.017°C. Inasmuch as this error includes errors of measurement, 

the deviation of calculated from observed values may be somewhat 

less. The curve of equation 4 deviates from a straight line by about 

0.01°C as a maximum for 1° intervals; therefore, linear interpolation 

in 1° intervals is generally acceptable.

TABLE 1. Interpolation errors in four equations for temperature-resistance relations

of thermistors

Equation

2 _ ............

3. -. 

4 _ _ ....... __ ...

5 _ _ ___ .....

Resistance « at 296.35°K 

(ohms)

Calculated

36, 771 

44,276 

45,142 

41,432

Observed

45,383 

45,383 

45,383 

45,383

Equation error

Resistance 

error 

(observed 

minus calculated value, 

in ohms)

+8,612 

+1, 107 

+241 

+3,951

Equivalent 

temperature 

error 

(observed 

minus calculated value, 

in°C)

-4.4 

-.57 

-.12 -2.0

i Calculated and observed resistances at 296.35°K are based on data on a thermistor of No. 1 material from 

Bosson, Qutmann, and Simmons (1950, table 1); the calculated resistances were obtained from the equations 

whose constants were determined from the following observations: 10,558,700 ohms at 204.71°K, 4,761.1 ohms 

at 357.16°K, and 1,177.6 ohms at 407.17°K.
B8 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

10 7

10'

o

z

ul 

O

z 

<

- 10 5 v> 1U

LU

ce

10'

 50 0 +50 +100 + 150

TEMPERATURE, IN DEGREES C

FIGURE 1. Log resistance versus temperature for a thermistor of No. 1 material. 

After Bosson, Gutmann, and Simmons (1950, table 1).

Temperature versus resistance curves for many thermistors were 

observed to be enough alike in shape and absolute values of coordinates to suggest that a calibration curve for one thermistor might 

serve as a master curve from which resistance-temperature conversions
PROPERTIES OF THERMISTORS B9

for other thermistors might be obtained. A simplified method for 

conversion of resistance to temperature is described on page B26. 

Table 8 is useful for thermistors (like the 17A) whose resistance at 

0°C is about 3,000 ohms; with carefully determined corrections, conversions made by use of the table, especially in measuring temperature 

differences over a few degrees, are accurate to ±0.01°C in the temperature range 30° to +30°C.

DEPENDENCE OF RESISTANCE ON PRESSURE

Thermistors may be used to measure temperatures in deep drill 

holes, where the water pressure may be high, and so the effect of 

pressure on the resistance of thermistors must be considered. If the 

pressure coefficient of resistance were high enough, the resistance 

measurements would have to be corrected before conversion to 

temperature. Three studies indicate, however, that the pressure 

effect is negligible.

The pressure effect on thermistor resistance was described by 

Tavernier and Prache (1952) and Misener and Thompson (1952); a 

brief discussion by Diment and Robertson (1963) is amplified here. 

In each study, the pressure chamber was placed in a constant-temperature bath, controlled to ±0.01°C; the absolute value of the bath 

temperature was less important than its constancy. In these studies, 

the thermistors were not jacketed but were compressed directly by 

the pressure fluid. The range of pressures applied and the temperatures of the test baths for the three studies are given in table 2.

The tests summarized in table 2 revealed that the slope of resistance 

with pressure is approximately linear to the limits of pressure attained, 

and hence that the pressure coefficient of resistance (1/JS0) (A5/AP) 

can be assumed to be constant over the pressure range for the given 

thermistor and temperature. The high values of the pressure coefficient of Tavernier and Prache are probably due to a difference in the

TABLE 2. Pressure coefficients of resistance of thermistors at several temperatures

Thermistor

1000B ___ . __

1000B -.... _ . __ .

64. ....................

64.....................

64 ___ . _______ ....

67..... _ .. _ ..... _

67.. ___ ..............

FB311...... _ ........

4589.... _ . ___ .....

Temperature

CO)

31.3

69.7

0

25.0

50.0

25.0

50.0

0

0

Maximum

pressure

(bars)

4,400

4,500

100

130

130

120

100

1,300

1,300

Thermistor

resistance,

at zero

pressure

(ohms)

856.2

196.2

17, 112

8,730

4,928

8,686

4,902

5, 518. 5

3, 410. 9

Pressure

coefficient of

resistance (10-" bar-»)

-47

-46

-.9

-1.2

 9

-1.4

-1.4

-.8

-.2

Reference

Tavernier and Prache

(1952).

Do.

Misener and Thompson (1952).

Do.

Do.

Do.

Do.

Present investigation.

Do.
BIO EXPERIMENTAL AND THEORETICAL GEOPHYSICS

physical characteristics of their thermistor, which was manufactured 

in France; it may have been somewhat less dense, that is, less compacted in the processing, than the American-made thermistors of the 

other two studies, and therefore may have been more susceptible to a 

pressure effect. (Misener and Thompson used type-12A rod thermistors made by Western Electric Co. The present authors used a 

glass-enclosed bead thermistor, serial No. FB311, type GB32P22, 

made by Fenwal Co., and a disk thermistor, serial No. 4589, type 17A, 

made by Western Electric Co.) The broad differences in the pressure 

coefficients probably reflect differences in manufacture, but the small 

differences, as between runs of thermistors 64 and 67, may be due to 

the unsteady thermal condition inside the pressure chamber when 

resistances were measured: at least 2 hours are required for the adiabatic heat produced by raising (or lowering) the pressure 500 bars to 

be dissipated and for the temperature to return to within 0.02°C of 

a steady state. There is a suggestion from the results of Tavernier 

and Prache and of Misener and Thompson that for a given thermistor, 

the pressure coefficient is nearly constant over a temperature range 

of 50°C.

It is apparent that the pressure effect on the resistance of a thermistor 

is very small. For example, at the bottom of a 3,000-meter hole in 

the earth, the water pressure would be about 300 bars and the 

temperature about 85°C; a thermistor with a nominal resistance of 

50,000 ohms at 20°C would therefore have a change of resistance due 

to the pressure of 0.1 ohms, or an equivalent temperature change 

of +0.0002°C. The following changes in resistance permit a comparison of the temperature effect with the pressure effect, between 

3,000 and 3,001 meters depth: the resistance of this thermistor would 

decrease 3.2 ohms owing to an assumed geothermal gradient of 20°C 

per km, and would decrease 10~ 5 ohm owing to the pressure gradient 

of 100 bars per km.

TEMPERATURE MEASUREMENTS WITH THERMISTORS 

PRECISION OF MEASUREMENT

A special study was made of the precision of temperature measurements by thermistors and by the platinum thermometer used in ail 

calibrations; the electrical circuits are described in Raspet, Swartz, 

Lillard, and Robertson (1966). The measurements, hi turn, depend 

on the reliability of the operating procedures and the precision of the 

Wheatstone and Mueller bridges, and these methods and characteristics also were evaluated.

The resistance of the platinum thermometer and the resistances of 

five thermistors were examined in replicate ice baths, made in a 

Dewar flask, and carefully prepared with shaved ice and distilled
PROPERTIES OF THERMISTORS Bll

water. Observations were made each working day, 5 days per week, 

for 6 weeks, from April 14 to May 25, 1960; 30 sets of measurements 

in all were taken. The platinum thermometer was calibrated by the 

National Bureau of Standards on June 24, 1960, and by the Geological 

Survey in a triple-point cell on August 17, 1963.

The five thermistors chosen were placed in glass tubes, which were 

partly filled with kerosene and closed with sealing wax. Four were 

type 17A thermistors: two of these, serial Nos. 154 and 1421, had 

been well calibrated and used as secondary standards; one of the 

other two, serial No. 20, was old, and the second one, serial No. 4151, 

was new. A small glass-enclosed bead thermistor, type 23A, serial 

No. B36, was also used.

Instruments were cleaned and standard procedures were arranged 

before the study began. In the operation of the Wheatstone bridge, 

the bridge current was allowed to pass continuously through the 

thermistor circuit while the bridge was being balanced, to avoid 

operator differences and to insure that any static charges would leak 

off. A careful manipulation procedure for the Mueller bridge was 

worked out. All contacts in the bridges and at the connections were 

cleaned.

A statistical summary of the observations is given in table 3. The 

range of fluctuation of thermistor resistances is less than 0.1 percent 

of the total, which although not large, is significant in many uses of 

thermistors. The question arises, then, whether the fluctuations are 

inherent in the thermistors themselves or in the measurements. 

Although the resistance of a given thermistor varies randomly from 

bath to bath, all the thermistors in a given bath on a given day showed 

concordant departures in direction and amount from those of the 

preceding or succeeding days. It thus appears that the variation is 

in large part in the instrumentation and the human operations, and 

is external to the thermistors.

TABLE 3. Statistical summary of resistances at the ice point of five thermistors and

a platinum thermometer

Thermistor: 

154-.. ____ .....

1421--. ___ .. ......

20-. . 

4151-- 

B36- 

Platinum thermometer: 

231... __ ... __ ..

Observations

30 

30 

30 

30 

30

23

Resistance (ohms)

Eange

3, 327. 6 to 3, 329. 7 

3, 247. 6 to 3, 250. 4 

3, 226. 7 to 3, 230. 1 

3,390.9 to 3, 393.1 

4, 618. 1 to 4, 620. 6

25. 4689 to 25. 4694

Mean

3, 329. 0 

3, 249. 3 

3, 228. 8 

3,392.2 

4, 619. 1

2 25. 46924

Standard 

deviation

0.40 

.48 

.57 

.58 

.76

.00014

Temperature 

equivalent 

to standard 

deviation 

(°C)i

0.0024 

.0029 

.0034 

.0035 

.0029

.0014

1 An approximate conversion factor for thermistors at 0°C is 170 ohms per deg C, and for the platinum 

thermometer the conversion factor is 0.1015 ohms per deg O.

2 Equivalent temperature, +0.0004°C.

781-990 66 3
B12 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

The temperatures of small ice baths can be duplicated to ±0.0002°C, 

if prepared correctly (Thomas, 1941), but the platinum-thermometer 

results showed a larger variation in this study. To test whether this 

variation was due to use of tap water for the ice in the first baths, the 

ice in later baths was made from distilled water; however, the same 

fluctuations occurred both in the platinum-thermometer measurements and in the concordant departures of resistance of all the thermistors. A systematic error of +0.0004°C and a random error of 

0.0014°C are implied by the results. These errors can be assigned as 

the accuracy and the precision of the platinum thermometer and the 

ice bath as a combined system.

The possibility was also considered that variation of the ambient 

room temperature might affect the resistances of the lead wires and 

resistors in the bridges, so the temperature fluctuations in the room 

and inside the Mueller bridge were recorded; however, they could not 

be correlated with the thermistor fluctuations. Apparently, the 

observed variation of resistance of the thermistors is due to instrumental and operator error, and, being random errors, the standard 

deviations in table 3 represent the precision of measurement. It 

appears that the thermistors are inherently very good relative-temperature sensing elements, probably precise to ± 0.0001°C, although 

such precision would require considerable improvement in measurement techniques.

TEMPERATURE OF ICE BATHS FOR THERMISTOR CABLES

After installation of thermistors in a multiconductor cable, it is 

standard practice by the Geological Survey to recalibrate the thermistors by placing the thermistor-bearing part of the cable in an ice 

bath made in a 6-cubic-foot box. The calibration procedure is described by Raspet, Swartz, Lillard, and Robertson (1966).

After the cable in an ice bath reaches a thermal steady state, the 

temperature is found to be surprisingly constant, both at different 

places in the same bath and in successive baths. This constancy is 

shown in any one bath by placing the platinum thermometer in several 

locations in it, after first inserting an aluminum probe in the ice to 

make a hole for the glass tube of the thermometer. Temperatures 

taken at different locations vary by <0.002°C.

The temperatures of 41 different ice baths, as determined with a 

platinum thermometer, are given in table 4. Bath temperatures 

frequently are slightly below 0°C, probably because of salt, dissolved 

air, or other contamination in the ice, despite the great care in preparation. The standard deviation for the bath temperatures would be 

only 0.0012°C if two seemingly anomalous low temperatures, 0.008° 

and 0.011°C, are omitted. It is apparent from the mean and stand-
PROPERTIES OF THERMISTORS B13

ard deviation in table 4 that the ice baths are accurate and very 

uniform, and are therefore quite suitable for calibration of thermistors 

in cables. Moreover, as shown by the range in size and lengths of 

cables listed in table 4, the ice-bath method of recalibrating a large 

variety of cables is technically feasible.

A notable trend is indicated in table 4 by the occurrence of minus 

temperatures for measurements made from 1957 to 1959 and plus 

temperatures for measurements made from 1959 to 1962. A plot of 

these data shows an increase of temperature from the oldest to the 

youngest baths. The increase is larger than the measurement error, 

which is about ±0.001°C, and would thus appear to be real. The 

cause of this apparent increase in bath temperature is probably a 

secular increase in resistance of the platinum thermometer. Even

TABLE 4. Temperature of ice baths measured with a platinum thermometer, and 

pertinent data for 28 thermistor cables

Date

July 13, 1962.....................

Apr. 9, 1962 ___ . __ . _ . .....

Dec. 13, 1961 ____________

Dec. 9, 1960 __________ ....

June 1, 1960 ____________

Do............ ...........

Do.... ...................

Do....... .... ...............

Do.... ............. ......

Feb. 5, 1960 ___________ ..

Feb. 2, 1960 __ . _______ . ...

July 24, 1959 .....................

July 22, 1959 ________ ......

June 23, 1959 __ . _______ ..

June 24, 1959 __________ ..

June 4, 1959 ____________

June 8, 1959 ____________

Apr. 13, 1959 .....................

Do.... ...................

Feb. 9, 1959 ..._..................

Jan. 29, 1959 _________ . ...

Oct. 23, 1958 -.--_ . - ._._-.

Aug. 28, 1958... .................

Aug. 12, 1958...... ..... ......

Do __________ . __ ..

July 2, 1958. __ . _____ ... ...

Do.... ...... ...........

June 30, 1958 ____________

Do-. . --_ ......

Do....... ...................

May 15, 1958... _________

Do. 

Do. ....... ... .......

Do.. .................

Apr. 30, 1958 ......... .........

Apr. 8, 1958 ____________

Feb. 25, 1958 __ . _________._..._

Dec. 17, 1957 ______ . _ ... ...

Dec. 19, 1957 _________ _________

Dec. 16, 1957 ._..................

Ice-bath 

temperature (°C)

+0.003

+.002

+.002

+.002

i.OOO

+.002

-.008

-.003

-.002

+.001

-.011

+.001

+.001

} » -. 002

-.003

-.003

-.002

-.005

} ' -. 001

1 UU*

} 1 -.002

} i.OOO

1-.004

-.001

-.003

-.003

-.004

-.004

-.004

-.0018

.0031

Cable No.

346

315

315

341

194

198

I 328

334

335 »116

3117

337

337 ^336

*336

8249

*249

f 334

\ 335

321

324

314

324

f 149

\ 150

f 330

1 333

331

332

323

329

198

194

327

328

326

320

321 8325

*325

325

Cable 

diameter 

(in)

H

Me 7A,

1342

04.

Vi 'Me

ILf.

'Me

m

m'Me

'He

'Me

»H«

'Me

%'Me

'Me

WK

Me

Me

Me 'Me

%'Me

ILf.

'Me

'Me

'Me

H

Me 'Me

'Me

'Me

Me

Me

lLf ft

lVf«

'Me

Length of 

cable in bath 

(ft)

450

520

520

603

9

11

24

23

23

8

8

550

570

550

570

550

570

23

23

850

1,030

530

1,030

38

53

57

209

58

158

53

58

11

9

24

24

410

810

850

350

440

640

Thermistors 

in bath

5

11

11

6

28

28

11

17

17

96

96

10

10

10

9

10

9

17

17

17

21

11

21

19

9

10

18

10

15

28

10

28

28

11

11

17

17

17

13

7

18

' Cables marked off by a brace were calibrated in the same ice bath.

2 Special ice baths.

3 Calibration of upper half only of cables and thermistors.

4 Calibration of lower half only of cables and thermistors.
B14 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

with gentle handling, there is some shaking of the delicate wire coil of 

the thermometer, a very small cold working, and a consequent very 

slight increase of resistance (J. L. Riddle, National Bureau of Standards, oral commun., 1960). The slope of the regression line fitted to 

the data in table 4 is -f0.0014°C per yr, or + 1.4X10"4 ohms per yr 

if converted to thermometer resistance. This value is corroborated 

over the same 5-year period by two calibrations of the thermometer 

by the National Bureau of Standards in 1956 and 1960 and by one 

made by the Geological Survey in 1962 using a triple-point cell. If 

the bath-temperature data were corrected for this effect, the standard 

deviation would be greatly decreased.

THERMISTOR STABILITY

DRIFT OF THERMISTORS IN CABLES

Thermistors of all makes and types are well known to have a secular 

increase of resistance, which results in a decrease of apparent temperature with time. As this apparent temperature drift affects all readings, it is important to determine how large this drift is, so that it can 

be recognized and corrected for where necessary. Successive calibrations of thermistor cables by the Geological Survey over a 10-year 

period permit estimates to be made of the rate of thermistor drift.

The absolute temperature of each ice bath in which cables are 

placed is within ±0.005°C of 0°C, as shown in table 4; hence it is 

feasible to find the change in resistance between two ice-point calibrations for each thermistor in a cable, and thereby learn the amount of 

drift over the period between calibrations. A summary of such data, 

together with pertinent information on the cables, is given in table 5. 

All thermistors were type 17A. There were 32 usable pairs of icepoint determinations and 645 pairs of thermistor readings for these 

cables. The time interval between ice points ranged from 1 month 

to 4% years, the mean being 21 months.

The resistance changes of the thermistors from one ice-point calibration to the next have been converted to equivalent changes of 

temperature in table 5 in order to put all thermistors on a similar 

and more understandable basis. However, it should be remembered 

that it is the change in absolute resistance at the ice-point that is 

observed. (An approximate conversion factor at 0°C for 17A thermistors is 170 ohms per deg C.) Thermistor resistance which becomes higher, upon conversion, will show a change to a lower temperature because of the inverse relationship; this change is seen as 

a fall in the converted temperature from the first ice-point to the 

second. For each cable listed in table 5, the mean drift per month 

and the standard deviation were calculated for the thermistors in 

each cable; 32 aberrant changes were discarded. The mean tern-
PROPERTIES OF THERMISTORS B15

perature change of all the thermistors in each cable is plotted in 

figure 2 against the number of months between ice-points. There 

is an obvious decrease in the observed apparent temperature with 

time, although the points have a wide scatter.

The data for each thermistor were reduced to temperature drift 

per month, classified at intervals of 5X10~3 deg C per mo, and then 

plotted as the histogram of figure 3. The class of 0 to 5X10~3 

deg C per mo includes 480 values, or 75 percent of the total 645. 

The preponderance of values in this range indicates that the drift 

of 17A thermistors in cables in ordinary use is very uniform. Excluding 32 aberrant pairs, the mean drift for 613 pairs of thermistor

o -l

CO

LU 

LU 

CC

LU

Q

I2-2

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2-4 

<

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10 20 30 40 

TIME, IN MONTHS

50 60

FIGURE 2. Change in mean apparent temperature of thermistor cables against 

time between ice-point calibrations.
B16 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

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PROPERTIES OF THERMISTORS B17

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B18 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

500

400

300

o 200

100

I I I I I I I I I I I I I I I I I I I I I I I I 1 M I I I I I I I II II I I I

ThiiiDipiiiiiinp

<-100 -50 0 +50 > + 100 

RATE OF TEMPERATURE CHANGE, IN 10~ 3 DEGREES C PER MONTH

FIGURE 3. Thermistor drift for 645 pairs of thermistor readings classified statistically at intervals of 5X10~3 deg C per mo.

readings is 3.8X1CT3 deg C per mo, and the standard deviation 

is 5.1X10"3 deg C per mo. This mean drift, which is equivalent to 

about 0.05°C per yr, or +8 ohms per yr, is plotted as the dashed 

line on figure 2.

In a large majority of the determinations reported in table 5 the 

secular drift of thermistors was observed to be an increase in resistance, 

equivalent to a decrease in apparent temperature. In figure 3, most 

of the 21 small thermistor changes, <15X10~3 deg C per mo, on the 

positive side of the histogram can be discounted because the change 

was near the limit of measurement error, although a few of the changes 

cannot be so explained. Two large changes, +37X10"3 and
PROPERTIES OF THERMISTORS B19

+ 50X10"3 deg C per mo (fig. 3), are for thermistors in cable 321, 

which was roughly handled in the field; moderate-resistance electrical 

shorts in the lead wires probably developed owing to moisture and 

abrasion of the insulation of the copper leads. A defective thermistor 

in cable 314 is assumed to be the reason for the +100X10"3 deg 

C per mo drift observed. The large negative values do not have 

obvious explanations. The high positive drift values of other investigators (table 6) seem to be caused by subjecting the thermistors to high 

temperatures or to rough handling. Therefore, it appears that in 

ordinary use, thermistor drift usually occurs as an increase in resistance between calibrations at a given temperature.

LABORATORY STUDIES OF THERMISTOR DRIFT

The results of some previous laboratory investigations of thermistor 

stability are listed in table 6. They agree with the general conclusions 

found in our study of thermistors in cables (table 5; figs. 2, 3) that 

thermistors of all types show some drift, and that usually the drift is toward a higher resistance, or equivalently toward a lower temperature.

Thermistor drift can be greatly reduced by annealing at about 

100°C. Becker, Green, and Pearson (1946, p. 717-718) showed that 

after 2 weeks of aging at 105°C, %-inch disk thermistors of both 

material No. 1 and material No. 2 were stablized and had a drift of 

about 4X10~3 deg C per mo thereafter. This effect of annealing 

was corroborated by Nielsen (1959, p. 22-28). Several manufacturers 

now anneal or preage their thermistors as a general procedure to 

improve their drift characteristics.

On the other hand, the results of an investigation by Droms (1962, 

table 2) show that annealing at a temperature >100°C can disturb 

thermistors; for 3 months, he held half of his laboratory study group 

of eight types of thermistors at 100°C and the other half at 200°C; 

both groups changed, but the latter group had much larger resistance 

changes. Similar results were found by Swartz and Raspet (1961, 

figs. 2, 3) for thermistors subjected to 130°C for 1 hour; they found 

that from an initial drift of 70X10"3 deg C per mo, the rate after 

1 year had slowed to 10X10~3 deg C per mo, after 2 years to 

 4X10~3 deg C per mo, and after 4 years to 3X10~3 deg C per mo. 

They found also that cold shock at 79°C disturbs thermistors very 

badly, sometimes beyond further use.

Bead thermistors are protected by a glass coating, so they might be 

expected to have a lower drift rate than the unprotected disk thermistors, both in the field and in the laboratory; apparently, however, the 

glass makes only a small difference, if any. Two bead thermistors 

studied by Beck (1956, fig. 1) were used in the field for borehole 

logging and their average drift rates were 140X10"3 and 210X10"3

781-99$ 66 4
B20 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

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PROPERTIES OF THERMISTORS B21

deg C per mo; the higher rate apparently was caused by an exposure 

to sunlight. Two bead thermistors studied by Diment (unpub. data, 

1964) had drift rates of 11X10~3 and 3X10~3 deg C per mo after

8- and 11-months field use in logging cables.

In his laboratory study, Nielsen (1959, fig. 10) found that his bead 

thermistors were well stabilized by heat treating; the drift rate was 

between 1X10~3 and 5X10~3 deg C per mo after 1 year. Comparisons of these data with those in table 5 suggest that glass-covered 

bead and the unprotected disk thermistors have similar drift rates, 

although some bead thermistors seem to have lower rates.

DRIFT OF THERMISTORS HELD AT CONSTANT TEMPERATURE

As described above, thermistors subjected to the ambient temperatures and mechanical flexing undergone by cables in logging exhibit a 

perceptible drift. Therefore, it is of interest to observe that thermistors held at a nearly constant temperature and in a relatively fixed 

position apparently drift very little.

An impressive example of the stability of thermistors held undisturbed at constant temperature is given by the data for a cable 

frozen in place in the South Barrow well 3, near the Arctic coast at 

Barrow, Alaska (Lachenbruch and others, 1962, fig. 12). The temperature of each thermistor in the cable changed <0.5°C during a

9-year period of observation at depths having temperatures ranging 

from 6° to 10°C. The drift rate for each of 16 type-17A thermistors was determined to be < 0.3X10"3 deg C per mo; this limiting 

rate was fixed by the precision of measurement, and may well have 

been much smaller. Time between measurements was > 1 month.

Another example of stability is a single 17A thermistor, number 

823, which has been held for 8 years at 31.5°±0.3°C in a thermostatcontrolled container for standard voltage cells in a Geological Survey 

laboratory. A mercury thermoregulator cycles the heater at a 5- 

minute period. Inside the insulated box, thermistor 823 registers 

each cycle as a temperature fluctuation of ±0.002°C. The absolute 

temperature in the box was measured with a platinum thermometer 

in 1960, 1963, and 1964, and from these measurements the drift rate 

of thermistor 823 was found to be < 0.2X10"" deg3 C per mo; this 

upper limit was determined by the precision of measurement. From 

absolute temperature measurements made with a mercury thermometer to ±0.05°C in 1956, 1958, 1960, 1963, and 1964, nearly the same 

drift rate was calculated for thermistor 823 in each period.

Bead thermistors left on the shelf also show a reduced drift rate. 

One thermistor (Beck, 1956, p. 17) had an average drift of about 

 50X10"3 deg C per mo for an initial 8 months, but for 8 months on 

the shelf thereafter, the rate was only about 2X10~3 deg C per mo.
B22 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

Two bead thermistors (Diment, unpub. data, 1964) drifted at 

 0.3X.10"3 and 1.1X10"3 deg C per mo for a 2-year period on 

the shelf.

Apparently, if a thermistor is held practically undisturbed and at 

a nearly constant temperature, there will be only a very small drift 

of the resistance of the thermistor with time, a characteristic worth 

consideration if a thermistor is to be used under such conditions.

DRIFT BATES AT VARIOUS TEMPERATURES

The drift rate of thermistors as a function of temperature was 

studied for one thermistor by Beck (1956, table 2) over the temperature range 5° to 32°C. For a given time lapse, the drift rate is higher 

for the higher temperature, although the temperature effect is small 

compared to the total drift rate:

Thermistor drift rate 

Time period (mo) Temperature (°C) (10~3 deg Cper mo)

5_____.___._____.__.____.. 5.27 -134.0

5______.___.___________ 18.31 -138.0

!!___________________________ 14.09 -140.0

!!_______________________ 30.89 -142.7

15_________________________ 14.22 -120.0

15._________________________ 30.84 -122.7

17_ _____ ________________ 11.71 -142.4

17_________________.____ 32.24 -147.6

In the study by Droms (1962, table 2), 19 thermistors were held 

at 100°C and 19 at 200°C, and both sets were recalibrated at 0°C 

and at 50°C after 51 days and after 91 days. The thermistors 

drifted at widely varying rates, both positive and negative, from 

very little to highs of 0.6°C per mo at 50°C and 1.8°C per mo at 0°C. 

The scatter is too great for any uniformity to be discerned. A group 

of thermistors held at the temperatures 0°, 10°, 20°, 30°, and 40°C 

by Staley (1952, table 4) exhibited such a wide and random scatter, 

from 54X10"3 to +28X10~3 deg C per mo, that no conclusion on 

the dependence of drift rate on temperature is feasible; no explanation 

is available for the high drift rates, unusual in the 0° to 40 °C range.

When thermistors were first used by the Geological Survey in 1949, 

seven were set aside and calibrated carefully for use as secondary 

standards, in lieu of a platinum thermometer, and the calibration 

data on these is pertinent. Four of them, Nos. 124, 125, 127, and 

128, were installed in the bath in which all cable thermistors have 

since been calibrated, and they have been cycled between 30°C 

and +30°C in about 250 calibration runs during the last 15 years. 

Three other thermistors, Nos. 154, 1421, and 1422, were put in 

glass tubes, which were partly filled with kerosene and closed with 

sealing wax; these thermistors were set aside for use in occasional 

ice baths and for other purposes.
PROPERTIES OF THERMISTORS B23

Each of these seven thermistors was calibrated by the National 

Bureau of Standards, on October 26, 1951, at five temperatures, 

 30°, 15°, 0°, +15°, and +30°C; two later calibrations were 

made on six of these thermistors by the Geological Survey at the same 

temperatures on October 27, 1956, and on July 8, 1964. During the 

intervals between calibrations the thermistors changed in resistance by 

amounts which on the average increased with increasing temperature. 

Resistances were converted to temperature in order to have a uniform basis for comparison among the data. The two sets of drift 

rates calculated for the two periods between the three calibrations are 

plotted separately in figure 4. The magnitude of the drift rate tends 

to increase with increasing temperature, but there is considerable 

variation among the thermistors, one even taking on a slightly positive drift rate. Neither the continued temperature cycling of the 

bath thermistors nor the desultory temperature cycling of the tubed 

thermistors seem to have widely differing effects on the drift rates.

The mean drift rate and standard deviation at each temperature 

for the seven thermistors for the 13-year period is given in table 7; 

these mean drift rates are also plotted at the bottom in figure 4. 

Although the trend to larger drift rates with higher temperature is 

evident, the difference over the 60° temperature range is not great 

on the average. The temperature effect on the drift rate should be 

recognized and taken into account, however, because the effect on 

some thermistors can be large.

TABLE 7. Mean drift rates of seven thermistors 

at five temperatures over a 13-year period 

(Oct. 26, 1951-July 8, 1964)

Temperature (°C)

-30 

-15 

0 

+15 

+30

Mean drift rate Standard deviation

(10~3 deg C per mo)

-2.52 

-3.05 

-3.32 

-3.76 

-4.22

1.26 

1.88 

2.19 

2.63 

2.92

POSSIBLE EXPLANATIONS OF THERMISTOR DRIFT

Causes of thermistor drift may be chemical attack from a potting 

compound, mechanical shock, thermal shock, chemical deterioration 

by oxidation by diffusion or by electrolysis, and combinations of these 

causes. Although thermistors have been on the market a long time, 

their manufacture and, presumably, their composition and physical 

properties have not been changed during this period (G. L. Oddy, 

Western Electric Co., oral commun., 1959), Therefore, the reasons
B24 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

0

-5 

0

-5

cr

UJ 1 /-, o_ 10

UJ Q c

-5

m +1

o -5

o

tr

<

Q_

Q- _ i

-5

No 124

No 125

No 127

No 128

No 154

No 1422

Mean 

I I I I I

-30 -15 0 +15 +30 

CALIBRATION TEMPERATURE, IN DEGREES C

FIGURE 4. Drift rates of seven thermistors at five temperatures between 30° 

and +30°C from 1951 to 1956 (solid lines) and from 1956 to 1964 (dashed 

lines).
PROPERTIES OF THERMISTORS B25

for secular drift of resistance should be the same in all thermistors, 

and comparisons may logically be made between them.

Direct chemical attack may be considered first. Fluids such as 

kerosene, which contains 0.1 to 1 percent sulfur, could permeate and 

attack the silver flash coating, because the porosity of a thermistor 

body is about 3 percent; or a chemical curing agent in the potting 

compound could attack the silver. Neither of these possibilities, 

however, explains the drift of the glass-coated bead thermistors 

immersed in such fluids (table 6). Staley (1952, p. 70) found that the 

drift of laboratory thermistors was the same as that of thermistors 

exposed to the weather, and concluded that weathering was not a 

cause of drift in his rod thermistors.

The five thermistors used in the study of precision of measurement 

(table 3) were tested for possible effects of mechanical shock. While 

in their glass tubes, each was tapped sharply 20 times against the edge 

of a table, almost hard enough to break the glass, but there was no 

measureable effect on their resistances. Inasmuch as a force of several 

hundred pounds per square inch is required to pull the copper wire 

leads from a thermistor, the mechanical bonding is good. Cables 315 

and 321 were both subjected to rough handling in the field, and the 

insulation was abraded in many places, but despite this, the resulting 

drift of then* thermistors is not excessive. It thus appears that 

mechanical shock alone causes only a small part of the drift.

The effects of shock from heating or cooling on thermistor stability 

were demonstrated by Swartz and Raspet (1961) and by others (table 

6). The very low drift rate in thermistors held at constant temperature and measured at >1-month intervals is discussed an page B21.

It is possible that the original sintering in each thermistor does not 

oxidize the manganese to the exact stoichiometric proportions of atoms 

with +2 and +3 valence; passage of electric current or heating imposed later would tend to stabilize the oxidation states and, presumably, to produce a lower conductivity. The passage of the electric 

current or heating might cause some disordering of atoms in the crystal 

grains and possibly produce a higher resistance.

Removal of impurity atoms by electrolysis could affect the resistivity. The conduction of an electric current by a semiconducting 

material is presumed to occur by migration of electrons, holes, and 

ions, depending on the impurity content and type and on the temperature. An irreversible change of the crystal structural arrangement of 

atoms to a higher resistance state might be the cause of the thermistor 

drift. Thermistor raw materials are not highly purified, and one 

mechanism for rearrangement of atoms is the lattice diffusion of 

impurity ions, mobilized by direct electric current passing through the 

material.
B26 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

Wenden (1957), in a study of this diffusion phenomenon in singlecrystal quartz, found that there is a logarithmic change of resistivity 

with time, in which a rapid initial change is followed by a long-term 

(Yt to 40 days) decelerating increase of resistivity (amounting commonly to two orders of magnitude); Wenden attributed this conduction change to an electrolysis of impurity ions in the quartz. (There 

is a succeeding long-term steady-state conduction arising from electrolysis of the silicon and oxygen atoms in the quartz.) He suggested 

that the impurity ions become irreversibly trapped in lattice defects or 

migrate to the sample surface, plate out, and thus become unavailable 

to act as charge carriers. A similar mechanism of impurity conduction 

could be the cause of the increase in resistivity of thermistors with 

time. This explanation tends to be supported in that thermistors 

which are not subjected very often to electric current have a low drift 

rate compared with that of thermistors in cables, which are subjected 

quite often to electric current.

As the resistance change per unit time (that is, the drift) is very small 

in proportion to the total resistance of the thermistor, the processes 

causing drift, whether electrolysis, oxidation, ordering, diffusion, or 

something else, seem to affect only a small proportion of atoms in the 

whole thermistor body. Electrolysis (Wenden, 1957), oxidation, 

disordering, and diffusion are accelerated by an increase in temperature, so the annealing heat treatment given to thermistors to age and 

stabilize them would speed up these processes.

SIMPLIFIED METHOD FOR CONVERSION OF RESISTANCE 

TO TEMPERATURE

The calibration curves of reciprocal temperature versus log resistance for different 17A thermistors are very similar in curvature and 

not very different in magnitude, as shown in figure 5. Most curves for 

17A thermistors fall within the upper and lower curves shown in the 

figure. Coordinate differences are small and change smoothly and 

slowly with temperature. Because of this close parallelism, a simple 

master table for all thermistors can be used to convert resistance to 

temperature instead of a separate table for each thermistor. The 

conversion of the resistance reading to temperature for a given 

thermistor can be easily accomplished by obtaining a trial temperature 

value from the master table and then correcting this value to the 

actual temperature of the thermistor.

The resistance-to-temperature calibrations, at 30°, 15°, 0°, 

+ 15°, and +30°C, of thermistor 4249 were found to vary uniformly and were used to construct a master table. The calibration
PROPERTIES OF THERMISTORS B27

3X104

o 

<3X10 3

4X10 2

I I

+ 30°C 

I

+ 15"C 0°C -15°C I -30°C

3.3 3.4 3.5 3.6 3.7 3.8 3.9 

RECIPROCAL TEMPERATURE, IN 10" 3 DEGREES

4.0 

KELVIN

4.1

FIGURE 5. Parallelism and approximate range of curves of log resistance versus 

reciprocal temperature for type-l7A thermistors.

technique is described by Raspet, Swartz, Lillard, and Robertson 

(1966); temperatures are accurate to ±0.005°C, and relative resistances are accurate to 1 part in 10s. The calibration data for thermistor 

4249 were fitted to Swartz's (1954) equation, log R=A+B(T+(T)-1 ) 

where R is resistance, in ohms; Tis temperature, in degrees Celsius; and 

A, B, and C are constants. Using the proper constants in the equation, 

resistance-temperature values were calculated for integral degrees 

between 30° and +40°C; the values were then smoothed by the 

difference method. Linear interpolations to 0.1°C were made and 

proportional parts to 0.01°C were calculated throughout; the results 

are given in table 8. In determining temperature differences <C5°C, 

the uncertainty inherent in the table is estimated to be ±0.01°C.
B28 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

TABLE 8. Master table for conversion of thermistor resistance to temperature

&.R 

(0)

96

86

75

64

53

43

32

21

11

90

80

70

60

50

40

30

20

10

83.7

74.4

65.1

55.8

46.5

37.2

27.9

18.6

9.3

78.1

69.4

60.7

52.1

43.4

34.7

26.0

17.4

8.7

72.9

64.8

56.7

48.6

40.5

32.4

24.3

16.2

8.1

68.1

60.6

53.0

45.4

37.9

30.3

22.7

15.1

7.6

63.6

57.6

49.5

42.4

35.4

28.2

21.2

14.1

7.1

E

(a)

17, 516. 0

17,409.0

17, 302. 0

17, 195. 0

17, 088. 0

16,982.0

16, 875. 0

16,768.0

16, 661. 0

16, 554. 0

16, 447. 0

16,347.0

16, 248. 0

16, 148. 0

16,049.0

15,949.0

15,849.0

15, 750. 0

15, 650. 0

15, 551. 0

15, 451. 0

15,358.0

15, 265. 0

15, 172. 0

15, 079. 0

14,986.0

14, 893. 0

14, 800. 0

14, 707. 0

14, 614. 0

14, 521. 0

14, 434. 0

14,347.0

14,261.0

14, 174. 0

14, 087. 0

14,000.0

13, 913. 0

13, 827. 0

13,740.0

13, 653. 0

13,572.0

13, 491. 0

13, 410. 0

13,329.0

13,248.0

13, 167. 0

13, 086. 0

13, 005. 0

12, 924. 0

12,843.0

12, 768. 0

12, 692. 0

12, 616. 0

12, 540. 0

12, 465. 0

12, 389. 0

12,313.0

12, 238. 0

12, 162. 0

12, 086. 0

12, 016. 0

11,945.0

11, 874. 0

11,803.0

11, 733. 0

11, 662. 0

11,591.0

11, 521. 0

11, 450. 0

11, 379. 0

T (°C)

-30.00

-29.90

-29.80

-29. 70

-29.60

-29.50

-29.40

-29.30

-29.20

-29. 10

-29.00

-28.90

-28.80

-28.70

-28.60

-28.50

-28.40

-28.30

-28.20

-28.10

-28.00

-27.90

-27.80

-27. 70

-27.60

-27.50

-27.40

-27. 30

-27. 20

-27. 10

-27.00

-26.90

-26. 80

-26.70

-26.60

-26. 50

-26.40

-26.30

-26. 20

-26. 10

-26.00

-25. 90

-25.80

-25.70

-25.60

-25. 50

-25.40

-25.30

-25. 20

-25. 10

-25.00

-24.90

-24.80

-24. 70

-24.60

-24.50

-24.40

-24.30

-24.20

-24.10

-24.00

-23.90

-23.80

-23.70

-23.60

-23.50

-23.40

-23.30

-23.20

-23.10

-23.00

AR(Q)

59.5

52.9

46.3

39.7

33.1

26.4

19.8

13.2

6.6

55.7

49.5

43.3

37.1

31.0

24.8

18.6

12.4

6.2

52.1

46.3

40.5

34.7

28.9

23.2

17.4

11.6

5.8

48.8

43.4

37.9

32.5

27.1

21.7

16.3

10.8

5.4

45.7

40.6

35.6

30.5

25.4

20.3

15.2

10.2

5.1

42.8

38.1

33.3

28.6

23.8

19.0

14.3

9.5

4.7

40.2

35.7

31.3

26.8

22.3

17.8

13.4

8.9

4.5

R 

(Q)

11,379.0

11,313.0

11,247.0

11, 181. 0

11, 115. 0

11, 049. 0

10, 982. 0

10,917.0

10, 850. 0

10, 784. 0

10, 718. 0

10, 656. 0

10, 594. 0

10, 533. 0

10,471.0

10, 408. 0

10,347.0

10, 285. 0

10, 223. 0

10, 161. 0

10, 099. 0

10, 041. 0

9,983.0

9,926.0

9, 868. 0

9, 810. 0

9, 752. 0

9, 694. 0

9, 636. 0

9, 578. 0

9, 520. 2

9,466.0

9, 411. 8

9,357.6

9, 303. 4

9, 249. 2

9, 195. 0

9, 140. 8

9, 086. 6

9, 032. 4

8,978.1

8,927.3

8, 876. 5

8, 825. 7

8, 774. 9

8, 724. 1

8,673.3

8, 622. 5

8, 671. 1

8,520.9

8,470.2

8,422.6

8, 375. 0

8,327.4

8, 279. 8

8, 232. 2

8, 184. 6

8, 137. 0

8, 089. 4

8, 041. 8

7,994.1

7,949.4

7,904.7

7,860.0

7,815.3

7,770.6

7, 725. 9

7, 681. 2

7,636.5

7, 591. 8

7, 547. 5

T

(°C)

-23.00

-22.90

-22.80

-22. 70

-22.60

-22.50

-22. 40

-22. 30

-22.20

-22. 10

-22.00

-21.90

-21.80

-21.70

-21.60

-21.50

-21.40

-21. 30

-21.20

-21. 10

-21. 00

-20.90

-20.80

-20.70

-20.60

-20.50

-20.40

-20.30

-20.20

-20. 10

-20.00

-19.90

-19.80

-19.70

-19.60

-19.50

-19.40

-19.30

-19.20

-19. 10

-19.00

-18. 90

-18.80

-18. 70

-18.60

-18.50

-18,40

-18.30

-18.20

-18. 10

-18.00

-17.90

-17. 80

-17. 70

-17.60

-17.50

-17.40

-17.30

-17.20

-17. 10

-17.00

-16. 90

-16.80

-16. 70

-16.60

-16.50

-16.40

-16. 30

-16.20

-16. 10

-16.00

AJJ

(Q)

37.7

33.5

29.3

25.1

21.0

16.8

12.6

8.4

4.2

35.4

31.5

27.5

23.6

19.7

15.7

11.8

7.9

3.9

33.2

29.6

25.6

22.2

18.5

14.8

11.1

7.4

3.7

31.2

27.8

24.3

20.8

17.4

13.9

10.4

6.9

3.5

29.3

26.1

22.8

19.6

16.3

13.0

9.8

6.5

3.3

27.6

24.5

21.5

18.4

15.3

12.3

9.2

6.1

3.1

25.9

33.1

20.2

17.3

14.4

11.5

8.6

5.8

2.9

R

(Q)

7,547.5

7,505.6

7, 463. 7

7, 421. 8

7, 379. 9

7,338.0

7, 296. 1

7, 254. 2

7,212.3

7, 170. 4

7, 128. 5

7, 089. 2

7,049.8

7, 010. 5

6, 971. 2

6,931.9

6, 892. 5

6, 853. 2

6, 813. 9

6, 774. 5

6, 735. 2

6, 698. 3

6, 661. 4

6,624,5

6, 587. 6

6, 550. 7

6, 513. 8

6, 476. 9

6,440.0

6, 403. 1

6, 365. 8

6, 331. 1

6, 296. 4

6. 261. 7

6, 227. 0

6, 192. 3

6,157.6

6, 122. 9

6, 088. 2

6, 053. 5

6, 018. 7

5,986.1

5, 953. 5

5, 920. 9

5,888.3

5, 855. 7

5, 823. 1

5, 790. 5

5, 757. 9

5, 725. 3

5,692.6

5,661.9

5, 631. 3

5,600.6

5, 570. 0

5, 539. 3

5, 508. 6

5,478.0

5, 447. 3

5, 416. 7

5,386.0

5,357.2

5, 328. 3

5, 299. 5

5, 270. 7

5, 241. 9

5, 213. 0

5, 184. 2

5, 155. 4

5, 126. 5

5,097.7

T (°C)

-16.00

-15.90

-15.80

-15. 70

-15.60

-15. 50

-15.40

-15.30

-15.20

-15. 10

-15.00

-14. 90

-14. 80

-14. 70

-14.60

-14.50

-14. 40

-14.30

-14.20

-14. 10

-14.00

-13.90

-13. 80

-13. 70

-13. 60

-13.50

-13. 40

-13.30

-13. 20

-13. 10

-13.00

-12.90

-12.80

-12. 70

-12.60

-12.50

-12.40

-12.30

-12. 20

-12. 10

-12.00

-11.90

-11.80

-11.70

-11.60

-11. 50

-11.40

-11.30

-11.20

-11. 10

-11.00

-10. 90

-10.80

-10.70

-10.60

-10.50

-10.40

-10. 30

-10. 20

-10. 10

-10.00

-9.90

-9.80

-9.70

-9.60

-9.50

-9.40

-9.30

-9.20

-9.10

-9.00

AR

(Q)

24.4

27.4

19.0

16.3

13.6

10.9

8.1

5.4

2.7

23.0

20.4

17.9

15.3

12.8

10.2

7.7

5.1

2.6

21.6

19.2

16.8

14.4

12.0

9.6

7.2

4.8

2.4

20.4

18.1

15.8

13.6

11.3

9.0

6.8

4.5

2.3

19.2

17.0

14.9

12.8

10.7

8.5

6.4

4.3

2.1

20.1

18.1

16.0

14.0

12.0

10.0

8.0

4.0

2.0

17.0

15.1

13.2

11.3

9.5

7.6

5.7

3.8

1.9

R

(Q)

5,097.7

5, 070. 6

5, 043. 4

5, 016. 3

4, 989. 2

4, 962. 1

4,934.9

4,907.8

4,880.7

4, 853. 5

4,826.4

4,800.9

4,775.4

4, 749. 8

4, 724. 3

4, 698. 8

4,673.3

4, 647. 8

4,622.2

4, 596. 7

4, 571. 2

4, 547. 2

4, 523. 2

4, 499. 1

4, 475. 1

4, 451. 1

4, 427. 1

4,403.1

4, 379. 0

4, 355. 0

4, 331. 0

4, 308. 4

4, 285. 8

4, 263. 1

4, 240. 5

4, 217. 9

4, 195. 3

4, 172. 7

4, 150. 0

4, 127. 4

4,104.8

4, 083. 5

4, 062. 2

4, 040. 9

4, 019. 6

3, 998. 3

3, 977. 0

3, 955. 7

3,934.4

3, 913. 1

3, 891. 8

3, 871. 7

3, 851. 7

3,831.6

3, 811. 6

3, 791. 5

3, 771. 4

3, 751. 4

3, 731. 3

3, 711. 3

3,691.2

3, 672. 3

3, 653. 4

3,634.3

3, 615. 6

3,596.7

3, 577. 8

3,558.9

3,540.0

3, 521. 1

3, 502. 2

T

(°C)

-9.00

-8.90

-8.80

-8.70

-8.60

-8.50

-8.40

-8.30

-8.20

-8.10

-8.00

-7.90

-7.80

-7.70

-7.60

-7.50

-7.40

-7.30

-7.20

-7.10

-7.00

-6.90

-6.80

-6.70

-6.60

-6.50

-6.40

-6.30

-6.20

-6.10

-6.00

-5.90

-5.80

-5.70

-5.60

-5.50

-5.40

-5.30

-5.20

-5.10

-5.00

-4.90

-4.80

-4.70

-4.60

-4.50

-4.40

-4.30

-4.20

-4.10

-4.00

-3.90

-3.80

-3.70

-3.60

-3.50

-3.40

-3.30

-3.20

-3.10

-3.00

-2.90

-2.80

-2.70

-2.60

-2.50

-2.40

-2.30

-2.20

-2.10

-2.00
PROPERTIES OF THERMISTORS B29

TABLE 8. Master table for conversion of thermistor resistance to temperature 

Continued

AR 

(0)

16.0

14.2

12.5

10..7

8.9

7.1

5.3

3.6

1.8

15.1

13.4

11.8

10.1

8.4

6.7

5.0

3.4

1.7

1.6

3.2

4.8

6.3

7.9

9.5

11.1

12.7

14.3

1.5

3.0

4.5

5.6

7.5

9.0

10.5

12.0

13.5

1.4

2.8

4.2

5.6

7.1

8.5

9.9

11.3

12.7

1.3

2.7

4.0

5.3

6.7

8.0

9.3

10.7

12.0

1.3

2.5

3.8

5.0

6. 3

7.6

8.8

11.3

12.6

R

(0)

3,502.2

3, 484. 4

3, 466. 6

3,448.7

3, 430. 9

3, 413. 1

3, 395. 3

3, 377. 5

3,359.6

3, 341. 8

3, 324. 0

3, 307. 2

3, 290. 4

3, 273. 6

3,256.8

3, 240. 0

3,223.2

3,206.4

3, 189. 6

3, 172. 8

3, 156. 0

3, 140. 2

3, 124. 3

3, 108. 5

3, 092. 6

3, 076. 8

3, 060. 9

3, 045. 1

3, 029. 2

3, 013. 4

2, 997. 5

2,982.6

2,967.6

2, 952. 7

2, 937. 7

2, 922. 8

2,907.8

2, 892. 9

2, 877. 9

2, 863. 0

2, 848. 0

2, 833. 9

2, 819. 8

2, 805. 7

2,791.6

2, 777. 5

2, 763. 3

2, 749. 2

2, 735. 1

2, 721. 0

2,706.9

2, 693. 6

2, 680. 2

2, 666. 9

2,653.6

2,640.3

2,626.9

2, 613. 6

2,600.3

2,586.9

2, 573. 6

2, 561. 0

2,548.4

2, 535. 8

2, 523. 2

2,510.6

2, 498. 0

2, 485. 4

2, 472. 8

2,460.2

2,447.6

T

(°C)

-2.00

-1.90

-1.80

-1.70

-1.60

-1.50

-1.40

-1.30

-1.20

-1.10

-1.00

-0.90

-0.80

-0.70

-0.60

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

+0.10

+0.20

+0.30

+0.40

+0.50

+0.60

+0.70

+0.80

+0.90

+1.00

+1.10

+1.20

+1.30

+1.40

+1.50

+1.60

+1.70

+1.80

+1.90

+2.00

+2.10

+2.20

+2.30

+2.40

+2.50

+2.60

+2.70

+2.80

+2.90

+3.00

+3.10

+3.20

+3.30

+3.40

+3.50

+3.60

+3.70

+3.80

+3.90

+4.00

+4.10 --4. 20

--4. 30

--4. 40

--4. 50

--4. 60

--4. 70

--4. 80

--4. 90

--5. 00

AR

(0)

1.2

2.4

3.6

4.8

6.0

7.1

8.3

9.5

10.7

1.1

2.3

3.4

4.5

5.6

6.8

7.9

9.0

10.1

1.1

2.1

3.2

4.3

5.3

6.4

7.5

8.5

9.6

1.0

2.0

3.0

4.0

5.0

6.0

7.1

8.1

9.1

1.0

1.9

2.9

3.8

4.8

5.7

6.7

7.6

8.6

0.9

1.8

2.7

3.6

4.5

5.4

6.3

7.2

8.1

0.9

1.7

2.6

3.4

4.3

5.1

6.0

6.8

7.7

R

(S3)

2,447.6

2,435.7

2, 423. 8

2, 411. 9

2, 400. 0

2, 388. 1

2,376.1

2, 364. 2

2, 352. 3

2, 340. 4

2, 328. 5

2, 317. 2

2, 306. 0

2, 294. 7

2,283.5

2, 272. 2

2, 260. 9

2, 249. 7

2, 238. 4

2,227.2

2, 215. 9

2, 205. 3

2, 194. 6

2, 184. 0

2, 173. 3

2, 162. 7

2, 152. 0

2, 141. 4

2, 130. 7

2, 120. 1

2,109.4

2,099.3

2, 089. 2

2, 079. 2

2, 069. 1

2, 059. 0

2, 048. 9

2, 038. 8

2, 028. 8

2,018.7

2,008.6

1,999.1

1, 989. 5

1, 978. 0

1,970.4

1,960.9

1, 951. 4

1,941.8

1,932.3

1, 922. 7

1, 913. 2

1,904.2

1, 895. 1

1, 886. 1

1, 877. 0

1, 868. 0

1,859.0

1, 849. 9

1,840.9

1, 831. 8

1, 822. 8

1,814.3

1,805.7

1, 797. 2

1, 788. 6

1,780.1

1, 771. 5

1,763.0

1,754.4

1,745.9

1,737.3

T

(°C)

+5.00

+5.10

+5.20

+5.30

+5.40

+5.50

+5.60

+5.70

+5.80

+5.90

+6.00

+6.10

K

.20

.30

+6.40

+6.50

+6.60

+6.70

+6.80

+6.90

+7.00

+7.10

+7.20

+7.30

+7.40

+7.50

+7.60

+7.70

+7.80

+7.90

+8.00

+8.10

+8.20

+8.30

+8.40

+8.50

+8.60

+8.70

+8.80

+8.90

+9.00

+9.10

+9.20

+9.30

+9.40

+9.50

+9.60

+9.70

+9.80

+9.90

+10.00

+10. 10

- -10. 20 --10.30

--10.40

- -10. 50 --10.60

- -10. 70

+10.80

+10.90

+11.00

+11. 10 --11.20

--11.30

- -11. 40 --11.50

--11.60

--11.70

+11.80

+11.90

+12.00

AR

(Q)

0.8

1.6

2.4

3.2

4.1

4.9

5.7

6.5

7.3

0.8

1.5

2.3

3.1

3.8

4.6

5.4

6.1

6.9

0.7

1.5

2.2

2.9

3.6

4.4

5.1

5.8

6.5

0.7

1.4

2.1

2.8

3.4

4.1

4.8

5.5

6.2

0.7

1.3

2.0

2.6

3.3

3.9

4.6

5.2

5.9

0.6

1.2

1.9

2.5

3.1

3.7

4.3

5.0

5.6

0.6

1.1

1.8

2.4

2.9

3.5

4.1

4.7

5.3

R

(Q)

1,737.3

1,729.2

1, 721. 1

1,713.0

1, 704. 9

1, 696. 8

1,688.7

1, 680. 6

1, 672. 5

1, 664. 4

1, 656. 3

1,648.6

1,640.9

1, 633. 3

1, 625. 6

1,617.9

1, 610. 2

1,602.5

1, 594. 9

1, 587. 2

1, 579. 5

1, 572. 2

1, 565. 0

1,557.7

1,550.4

1, 543. 2

1,535.9

1, 528. 6

1, 521. 3

1, 514. 1

1, 506. 76

1, 499. 87

1, 492. 97

1, 486. 08

1, 479. 19

1,472.30

1, 465. 40

1, 458. 51

1, 451. 62

1, 444. 72

1, 437. 83

1, 431. 29

1, 424. 76

1, 418. 22

1, 411. 68

1, 405. 15

1, 398. 61

1, 392. 07

1,385.53

1,379.00

1,372.46

1, 366. 26

1,360.06

1,353.86

1,347.66

1,341.46

1,335.26

1, 329. 06

1, 322. 86

1, 316. 66

1, 310. 46

1,304.58

1,298.69

1, 292. 81

1, 286. 93

1, 281. 05

1, 275. 16

1,269.28

1,263.40

1,257.51

1, 251. 63

T

(°C)

+12. 00

+12. 10

+12. 20

+12.30

+12.40

+12. 50

+12.60

+12.70

+12. 80

+12. 90

+13.00

+13. 10

+13.20

+13.30

+13.40

+13.50

+13.60

+13. 70

+13.80

+13.90

+14.00

+14. 10

+14.20

+14.30

+14. 40

+14. 50

+14.60

+14. 70

+14. 80

+14. 90

+15. 00

+15. 10

+15.20

+15.30

+15.40

+15. 50

4-15.60

+15. 70

+15. 80

+15.90

+16.00

+16. 10

+16.20

+16. 30

+16.40

+16.50

+16. 60

+16.70

+16. 80

+16.90

+17.00

+17. 10

+17.20

+17.30

+17.40

+17. 50

+17.60

+17.70

+17. 80

4-17. 90

+18.00

+18. 10

+18.20

+18. 30

4-18. 40

+18. 50

+18.60

+18.70

hl8. 80

+18.90

K9.00

AR

(Q)

0.6

1.1

1.7

2.2

2.8

3.4

3.9

4.5

5.0

0.5

1.1

1.6

2.1

2.7

3.2

3.7

4.2

4.8

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.5

1.0

1.4

1.9

2.4

2.9

3.4

3.8

4.3

0.5

0.9

1.4

1.8

2.3

2.7

3.2

3.6

4.1

0.43

0.87

1.30

1.73

2.17

2.60

3.03

3.47

3.90

0.41

0.82

1.23

1.65

2.06

2.47

2.89

3.30

3.71

R

(Q)

1,251.63

1,246.04

1,240.46

1,234.87

1, 229. 29

1, 223. 70

1, 218. 11

1, 212. 53

1,206.94

1, 201. 36

1, 195. 77

1, 190. 47

1, 185. 16

1, 179. 86

1,174.55

1, 169. 25

1, 163. 95

1, 158. 64

1,153.34

1, 148. 03

1, 142. 73

1, 137. 69

1, 132. 64

1, 127. 61

1, 122. 57

1,117.53

1, 112. 48

1, 107. 44

1, 102. 40

1,097.36

1, 092. 32

1, 087. 53

1,082.74

1, 077. 95

1,073.16

1, 068. 37

1, 063. 57

1,058.78

1, 053. 99

1, 049. 20

1,044.41

1, 039. 85

1, 035. 30

1, 030. 74

1,026.19

1, 021. 63

1,017.07

1, 012. 52

1, 007. 96

1,003.41

998.85

994.52

990.18

985.85

981.51

977.18

972.85

968.51

964.18

959.84

955:51

951. 39

947.26

943.14

939. 01

934.89

930.76

926.64

922.51

918. 39

914.26

T

(°C)

+19.00

+19. 10

- -19. 20 --19.30

--19.40

--19.50

--19.60

+19. 70

+19.80

+19.90

+20.00

+20.10

+20.20

+20.30

+20.40

+20.50

+20.60

+20. 70

+20. 80

+20.90

+21.00

+21. 10

+21.20

+21.30

+21.40

+21. 50

+21. 60

+21.70

+21. 80

+21.90

+22.00

+22.10

4-22.20

+22.30

+22.40

+22. 50

+22.60

+22.70

+22.80

+22.90

+23.00

+23.10

4-23.20

+23.30

+23.40

+23.50

+23.60 J-23.70

J-23.80

+23.90

+24.00

+24.10

+24.20 --24.30

--24.40

--24.50

-24.60

--24.70

-24.80

--24.90

-25.00

+25.10

+25.20

+25.30 J-25.40

+25.50

+25.60

+25. 70

+25.80

+25.90

+26.00
B30 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

TABLE 8. Master table for conversion of thermistor resistance to temperature 

Continued

A.R 

(0)

0.39

0.79

1.18

1.57

1.96

2.36

2.75

3.14

3.54

0.37

0.75

1.12

1.50

1.87

2.25

2.62

2.99

3.37

0.36

0.71

1.07

1.43

1.78

2.14

2.50

2.85

3.21

0.34

0.68

1.02

1.36

1.70

2.04

2.38

2.72

3.06

R

W

914. 26

910. 33

906.40

902. 47

898.54

894. 62

890. 69

886.76

882.83

878. 90

874.97

871. 23

867.49

863.74

860.00

856. 26

852. 52

848.78

845.03

841.29

837. 55

833. 98

830. 42

826.85

823. 29

819. 72

816. 15

812. 59

809.02

805.46

801.89

798. 49

795. 05

791. 69

788.29

784.89

781. 48

778. 08

774.68

771.28

767. 88

T

(°C)

+26. 00

+26.10

+26. 20

+26.30

+26.40

+26.50

+26.60

+26.70

+26.80

+26.90

+27.00

+27.10

+27.20

+27. 30

+27. 40

+27.50

+27.60

+27. 70

+17.80

+27.90

+28.00

+28. 10

+28.20

+28.30

+28.40

+28. 50

+28.60

+28.70

+28.80

+28.90

+29.00

+29.10

+29.20

+29.30

+29.40

+29.50

+29.60

+28.70

+29.80

+29.90

+30.00

A.R

(n)

0.32

0.65

0.97

1.30

1.62

1.95

2.27

2.59

2.92

0.31

0.62

0.93

1.24

1.55

1.86

2.17

2.48

2.79

0.30

0.59

0.87

1.18

1.48

1.77

2.07

2.36

2.66

0.28

0.56

0.85

1.13

1.41

1.69

1.98

2.26

2.54

R

(S3)

767. 88

764.64

761.39

758. 15

754.91

751. 67

748. 42

745. 18

741.94

738. 69

735. 45

732.35

729.26

726. 16

723.07

719.97

716. 87

713. 78

710. 68

707. 59

704.49

701.53

698. 58

695. 62

692. 67

689.71

686.75

683.80

680.84

677. 89

674.93

672. 11

669.28

666.46

663.63

660.81

657.99

655. 16

652.34

649.51

646.69

T

(°C)

+30. 00

+30.10

+30.20

+30. 30

+30. 40

+30. 50

+30. 60

+30. 70

+30. 80

+30. 90

+31.00

+31. 10

+31.20

+31.30

+31.40

+31.50

+31.60

+31. 70

+31.80

+31. 90

+32.00

+32. 10

+32.20

+32.30

+32.40

+32. 50

+32.60

+32. 70

+32.80

+32. 90

+33. 00

+33. 10

+33. 20

+33.30

+33. 40

+33.50

+33.60

+33. 70

+33.80

+33.90

+34.00

A.R

(n)

0.27

0.54

0.81

1.08

1.35

1.62

1.89

2.16

2.43

0.26

0.52

0.77

1.03

1.29

1.55

1.81

2.06

2.32

0.25

0.49

0.74

0.99

1.23

1.48

1.73

1.98

2.22

0.24

0.47

0.71

0.95

1.18

1.42

1.65

1.89

2.13

R

(0)

646.69

643.99

641.29

638.59

635.89

633.20

630. 50

627.80

625. 10

622.40

619. 70

617. 12

614. 54

611. 96

609.38

606.80

604.21

601.63

599. 05

596.47

593. 89

591. 42

588.95

586.48

584. 01

581.55

579. 08

576. 61

574. 14

571. 67

569.20

566.84

564.47

562. 11

559. 74

557.38

555. 02

552.65

550. 29

547.92

545.56

T

(°C)

+34. 00

+34. 10

+34. 20

+34.30

+34. 40

+34. 50

+34. 60

+34. 70

+34.80

+34.90

+35.00

+35. 10

+35.20

+35.30

+35.40

+35. 50

+35.60

+35. 70

+35.80

+35.90

+36.00

+36. 10

+36.20

+36. 30

+36.40

+36.50

+36.60

+36. 70

+36.80

+36.90

+37. 00

+37. 10

+37. 20

+37. 30

+37. 40

+37. 50

+37.60

+37. 70

+37.80

+37.90

+38.00

Atf

(0)

0.23

0.45

0.68

0.91

1.13

1.36

1.58

1.81

2.04

0.22

0.43

0.65

0.87

1.08

1.30

1.52

1.74

1.95

R

(Q)

545. 56

543.30

541. 03

538.77

536.51

534.25

531.98

529.72

527.46

525. 19

522.93

520.76

518.59

516.42

514. 25

512. 09

509.92

507. 75

505. 58

503.41

501.24

T

(°C)

+38.00

+38. 10

+38.20

+38.30

+38.40

+38.50

+38.60

+38.70

+38.80

+38.90

+39. 00

+39. 10

+39. 20

+39.30

+39. 40

+39.50

+39.60

+39. 70

+39.80

+39.90

+40.00

A correction table for a given thermistor can be determined from 

its calibration data and the master table as follows: The resistance 

of the thermistor at each calibration point is converted to a trial 

temperature from the master table, and the difference of this trial 

temperature from the thermistor's calibration temperature (measured 

with the platinum thermometer) is calculated. A smooth curve is 

drawn through values of this difference plotted against the calibration 

temperature; the corrections can be taken from the curve. The 

corrections rarely change more than 0.01°C over 1° intervals, hence 

corrections in a temperature range of a few degrees are easily tabulated and applied.

As an example to clarify the calculation procedure, observations 

and calculations on thermistor 4550 can be examined. The pertinent 

data are listed hi table 9. Calibration measurements are tabulated 

in columns 1 and 2; trial conversions of thermistor resistance to
PROPERTIES OF THERMISTORS B31

temperature are in column 3; temperature differences between data 

in columns 1 and 3 are given in column 4. Data in column 4 were 

plotted, and the smoothed data from the curve are given in column 5 

for the nominal temperatures in column 6; corrections would be 

closer if listed at 1° intervals of nominal temperature.

TABLE 9. Determination of temperature corrections for thermistor 4650

(I)

Platinumthermometer

temperature (°C)

-30.31

-14.99

-.01

+15. 07

+30.04

(2) 

Thermistor 

resistance

(ohms)

18,214

7, 258. 9

3, 219. 1

1, 531. 1

781. 79

(3) 

Temperature 

from master table

(°C)

-30. 61

-15.32

-.38

+14. 66

+29. 58

m (4) Temperature 

difference

(D-(3) (°C)

+0.30

.33

.37

.41

.46

m (5) * Temperature 

correction

(°C)

+0.30

.31

.32

.33

.34

.35

.37

.38

.39

.41

.43

.44

.46

(6) 

Nominal 

temperature

(°C)

-30

-25

-20

-15

-10

 5

0

+5

+10

+15

+20

+25

+30

As an example of the use of the data in table 9, let us assume that 

thermistor 4550 has been installed in a cable and has been lowered to 

some depth in a drill hole, at which the resistance is measured to be 

3,991.7 ohms. This resistance includes of course that of both the 

thermistor and its circuit. If the lead wire resistance is 2.3 ohms, 

then the thermistor resistance will be 3,989.4 ohms. For this resistance, the trial temperature from the master table, table 8, will 

be between 4.40° and 4.50°C. The thermistor resistance is 

12.4 ohms greater than that for 4.40°C, and in the AR column, 

this difference is nearest that corresponding to 0.06°C; the trial 

temperature therefore is 4.46°C. Note that the hundredth digit, 

the 6, is determined by inspection of the one-tenth digit in the T 

column; thus the space of another column is saved. The applicable 

correction from column 5 of table 9 is +0.35°C; adding algebraically, 

the temperature equivalent to the hypothetical resistance reading is 

-4.11°C.

As another example, if the thermistor resistance reading (corrected 

for lead resistance) were 2,051.5 ohms, the corresponding trial temperature from table 8 would be between +8.50° and +8.60°C. 

The thermistor resistance is 7.5 ohms less than that for +8.50°C, 

and this difference is near the &R value for 0.07°C. The trial temperature then is +8.57°C. Applying the correction of +0.39°C 

from table 9, the actual temperature is +8.96°C.
B32 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

REFERENCES

Beck, A. E., 1956, The stability of thermistors: Jour. Sci. Instruments, v. 33,

p. 16-17. 

 1962, Terrestrial flow of heat near Flin Flon, Manitoba: Nature, v. 195,

no. 4839, p. 368-369.

1963, Lightweight borehole temperature measuring equipment for resistance thermometers: Jour. Sci. Instruments, v. 40, no. 9, p. 452-454.

Beck, A. E., Jaeger, J. C., and Newstead, G., 1956, The measurement of the thermal conductivities of rocks by observations in boreholes: Australian Jour. 

Physics, v. 9, no. 2, p. 286-296.

Becker, J. A., Green, C. B., and Pearson, G. L., 1946, Properties and uses of thermistors thermally sensitive resistors: Am. Inst. Elec. Engineers Trans., 

v. 65, p. 711-725.

Bosson, G., Gutmann, F., and Simmons, L. M., 1950, A relationship between 

resistance and temperature of thermistors: Jour. Applied Physics, v. 21, p. 

1267-1268.

Brewer, M. C., 1958, Some results of geothermal investigations of permafrost in 

northern Alaska: Am. Geophys. Union Trans., v. 39, no. 1, p. 19-26.

Bullard, E. C., 1960, Measurement of temperature gradient in the earth, in 

Runcorn, S. K., ed., Methods and techniques in geophysics: New York, Interscience Publishers, v. 1, p. 1-9.

Chadwick, P., 1956, Heat flow from the earth at Cambridge: Nature, v. 178, no. 

4524, p. 105-106.

Cooper, L. R., and Jones, C., 1959, The determination of virgin strata temperatures from observations in deep survey boreholes: Royal Astron. Soc. Geophys. Jour., v. 2, p. 116-131.

Diment, W. H., and Robertson, E. C., 1963, Temperature, thermal conductivity, 

and heat flow in a drilled hole near Oak Ridge, Tennessee: Jour. Geophys. 

Research, v. 68, no. 17, p. 5035-5047.

Diment, W. H., and Weaver, J. D., 1964, Subsurface temperatures and heat flow 

in the AMSOC core hole near Mayaguez, Puerto Rico, in Burk, C. A., ed., 

A study of serpentinite: The AMSOC core hole near Mayaguez, Puerto Rico: 

Natl. Acad. Sci.-Natl. Research Council Pub. 1188, p. 75-91.

Diment, W. H., and Werre, R. W., 1964, Terrestrial heat flow near Washington: 

Jour. Geophys. Research, v. 69, no. 10, p. 2143-2149.

Droms, C. R., 1962, Thermistors for temperature measurements, in Am. Inst. 

Physics, Temperature, its measurement and control in science and industry: 

New York, Reinhold Publishing Corp., v. 3, pt. 1, p. 339-346.

Garland, G. D., and Lennox, D. H., 1962, Heat flow in western Canada: Royal 

Astron. Soc. Geophys. Jour., v. 6, p. 245-262.

Greene, G. W., Lachenbruch, A. H., and Brewer, M. C., 1960, Some thermal effects 

of a roadway on permafrost, in Short papers in the geological sciences: U.S. 

Geol. Survey Prof. Paper 400-B, p. B141-B144.

Horai, Ki-iti, 1959, Terrestrial heat flow at Hitachi, Ibaraki Prefecture, Japan: 

Earthquake Research Institute Bull., v. 37, p. 571-592.

Lachenbruch, A. H., 1957, A probe for measurement of thermal conductivity of 

frozen soils in place: Am. Geophys. Union Trans., v. 38, no. 5, p. 691-697.

Lachenbruch, A. H., and Brewer, M. C., 1959, Dissipation of the temperature 

effect of drilling a well in Arctic Alaska: U.S. Geol. Survey Bull. 1083-C, 

p. 73-109.
PROPERTIES OF THERMISTORS B33

Lachenbruch, A. H., Brewer, M. C., Greene, G. W., and Marshall, B. V., 1962, 

Temperatures in permafrost, in Am. Inst. Physics, Temperature, its measurement and control in science and industry: New York, Reinhold Publishing 

Corp., v. 3, pt. 1, p. 791-803.

LaFond, E. C., 1962, Temperature structure of the upper layer of the sea and its 

variation with tune, in Am. Inst. Physics, Temperature, its measurement and 

control in science and industry: New York, Reinhold Publishing Corp., v. 3, 

pt. 1, p. 751-767.

MacCarthy, G. R., 1952, Geothermal investigations on the Arctic slope of Alaska: 

Am. Geophys. Union Trans., v. 33, no. 4, p, 589-593.

Miller, Maynard M., 1958, Phenomena associated with the deformation of a 

glacier bore-hole: Internat. Geod. Geophys. Union, Assoc. Sci. Hydrology 

Assembly, Toronto, 1957, v. 4, p. 437-452.

Misener, A. D., and Beck, A. E., 1960, The measurement of heat flow over land, 

in Runcorn, S. K., ed., Methods and techniques in geophysics: New York, 

Interscience Publishers, v. 1, p. 10-61.

Misener, A. D., Bremner, P. C., and Hodgson, J. H., 1956, Heat flow measurements in permafrost at Resolute Bay, Northwest Territories: Royal Astron. 

Soc. Canada Jour., v. 50, no. 1, p. 14-24.

Misener, A. D., and Thompson, L. G. D., 1952, The pressure coefficient of resistance of thermistors: Canadian Jour. Technology, v. 30, p. 89-94.

Misener, A. D., Thompson, L. G. D., and Uffen, R. J., 1951, Terrestrial heat flow 

in Ontario and Quebec: Am. Geophys. Union Trans., v. 32, no. 5, p. 729-738.

Mooser, E., 1960, Semiconducting compounds: Science, v. 132, no. 3436, p. 1285- 

1291.

Muller, R. H., and Stolten, H. J., 1953, Use of thermistors in precise measurement of small temperature differences: Anal. Chemistry, v. 25, no. 7, p. 1103- 

1106.

Newstead, G., and Beck, A. E., 1953, Borehole temperature measuring equipment and the geothermal flux in Tasmania: Australian Jour. Physics, v. 6, 

p. 480-489.

Nielsen, K. E. C., 1959, Temperature measurements with thermistors in concrete: 

Swedish Cement and Concrete Research Inst. Bull., no. 34, 44p.

Raspet, Rudolph, Swartz, J. H., Lillard, M. E., and Robertson, E. C., 1966, 

Preparation of thermistor cables used in geothermal investigations: U.S. 

Geol. Survey Bull. 1203-C, p. C1-C11.

Revelle, R. R. D., and Maxwell, A. E., 1952, Heat flow through the floor of the 

eastern North Pacific Ocean: Nature, v. 170, no. 4318, p. 199-202.

Sachse, H. B., 1962, Measurement of low temperatures with thermistors, in Am. 

Inst. Physics, Temperature, its measurement and control in science and 

industry: New York, Reinhold Publishing Corp., v. 3, pt. 2, p. 347-359.

Sass, J. H., and LeMarne, A. E., 1963, Heat flow at Broken Hill, New South 

Wales: Royal Astron. Soc. Geophys. Jour., v. 7, no. 4, p. 477-489.

Saull, V. A., Clark, T. H., Doig, R. P., and Butler, R. B., 1962, Terrestrial heat 

flow in the St. Lawrence Lowland of Quebec: Canadian Inst. Mining Metallurgy Trans., v* 65, p. 63-66.

Sillars, R. W., 1942, Materials and devices of falling resistance-temperature 

characteristic: Jour. Sci. Instruments, v. 19, no. 6, p. 81-84.

Staley, R. C., 1952, Performance characteristics of Sanborn rod thermistors: 

Am. Meteorol. Soc. Bull., v. 33, no. 2, p. 67-72.
B34 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

Swartz, J. H., 1954, A geothermal measuring circuit: Science, v. 120, no. 3119,

p. 573-574. 

 1958, Geothermal measurements on Eniwetok and Bikini Atolls, U.S. Geol.

Survey Prof. Paper, 260-U, p. 711-739. 

Swartz, J. H., and Raspet, R., 1961, Thermal shock and its effect on thermistor

drift: Nature, v. 190, no. 4779, p. 875-878. 

Tavernier, Paul, and Prache, Pierre, 1952, Influence de la pression sur la re'sistivite'

d'une thermistance: Jour. Physique et Radium, v. 13, p. 423-426. 

Thomas, James L., 1941, Reproducibility of the ice point, in Am. Inst. Physics,

Temperature, its measurement and control in science and industry: New

York, Reinhold Publishing Corp., p. 159-161. 

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Am. Inst. Physics, Temperature, its measurement and control in science and

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Wenden, H. E., 1957, Ionic diffusion and the properties of quartz, the direct

current resistivity: Am. Mineralogist, v. 42, no. 11-12, p. 859-888.
Preparation of 

Thermistor Cables Used in 

Geothermal Investigations

By RUDOLPH RASPET, JOEL H. SWARTZ, MAJOR E. LILLARD, and EUGENE C. 

ROBERTSON

EXPERIMENTAL AND THEORETICAL GEOPHYSICS 

GEOLOGICAL SURVEY BULLETIN 1203-C

Thermistor calibration 

and fabrication of 

multithermistor cables 

for temperature logging

CONTENTS

Page

Abstract .-__-___-_.___________________________._ Cl

Introduction-- _-.______________________________.__ 1

Calibration. __________._____.__________________ 2

Constant-temperature bath for thermistors_______________________ 2

Ice-point calibrations of thermistor cables________________________ 5

Thermistor cables.________________________________________________ 7

Construction ________________________________________________ 7

Use and care._______________________________________________ 10

References _____________________________________________________ 11

ILLUSTRATIONS

Page 

FIGURE 1. Sketch of bath for calibration of thermistors in the range 30°

to +70°C___-__-_-________-_______ ______________-__--. C3

2. Diagram of thermistor and platinum-thermometer circuits.. __ 4

3. Diagrammatic cut-away section of a thermistor installation in

a multiconductor cable________________________________ 8

in

EXPERIMENTAL AND THEORETICAL GEOPHYSICS

PREPARATION OF THERMISTOR CABLES USED IN 

GEOTHERMAL INVESTIGATIONS

By RUDOLPH RASPET, JOEL H. SWARTZ, MAJOR E. LILLARD, and 

EUGENE C. ROBERTSON

ABSTRACT

Each thermistor that is used for temperature measurement must be calibrated 

in the temperature range of interest because the resistances of thermistors and 

their rates of change with temperature vary, and they are not interchangeable for 

precise measurements. In the calibration procedure used by the Geological 

Survey, the resistance of each thermistor is measured in a bath controlled to 

±0.002°C, at temperatures of 30°, -15°, 0°, +15°, and +30°C, which are 

determined to 0.001°C with a platinum thermometer. The resistance bridges 

and the platinum thermometer used in the calibration have been calibrated by 

the National Bureau of Standards.

Useful procedures for installation and later recalibration of thermistors in 

multiconductor cables, used in logging temperatures of drill holes, have been 

developed by the Geological Survey. Installation of thermistors in cables 

requires care in each operation: opening the insulation, proper identification 

of conductors, making the electrical connections, potting the thermistors, and 

sealing the cable opening and ends against moisture. Alternatively, individual 

metallic or plastic pods may be built into the cable to contain the thermistors.

Calibrations of thermistors in a cable are checked after installation by putting 

the whole cable in an ice bath, a fairly easy way to attain a fixed temperature, 

reliably found to be within ± 0.01° C of 0°C.

Determinations of temperature in boreholes can be made quickly and inexpensively with thermistors because their resistances are measured easily with a 

portable resistance bridge, and their small size permits easy and effective installation in a cable. Fabrication procedures of the Geological Survey for mounting 

and inserting thermistors at intervals in a multiconductor cable have been used 

successfully for thermistor logging cables as much as 5,000 feet long.

INTRODUCTION

In general, no two commercial thermistors of any particular type 

have the same resistance at a given temperature nor do they have the 

same change of resistance with temperature. Therefore, each 

thermistor should be calibrated before it is put in a cable, and the 

Geological Survey, has developed a procedure for the calibration of

Cl
C2 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

thermistors at five temperatures. After the thermistors are installed 

in a cable, a fairly easy calibration check can be made at the ice 

point (0°C) by immersing the thermistors and the adjacent length of 

cable in a box of shaved melting ice. Details of this procedure are 

described herein.

Details of installing thermistors in multiconductor cables are not 

widely known and are given here. Such cables can sometimes be 

more useful than single thermistor cables, especially for dry holes 

where measurement of the steady-state temperature requires a long 

wait. The methods of handling, shipping, and care of thermistor 

cables are listed also.

The authors express their deep appreciation for the assistance with 

their problems in thermometry received from J. L. Riddle, R. E. 

Wilson, and H. F. Stimson of the National Bureau of Standards.

CALIBRATION

CONSTANT-TEMPERATURE BATH FOR THERMISTORS

Each thermistor is in general calibrated, in a Geological Survey 

laboratory, at five temperatures: 30°, 15°, 0°, +15°, and +30°C. 

This calibration is done in a precisely controlled temperature bath, a 

drawing of which is shown in figure 1. The bath is patterned after 

one used by the National Bureau of Standards (Scott, 1941). A 1-gallon 

Dewar flask with a 6-inch mouth is mounted inside an insulated plywood and aluminum box. During each calibration, the space between 

the inner and outer aluminum containers is filled with pieces of dry 

ice (solid CO2) to attain temperatures below 0°C and to provide a 

steady heat sink at all calibration temperatures. To improve thermal 

coupling, the space between the flask and the dry-ice chamber is 

filled with isopropyl alcohol.

Inside the flask and suspended from the laminated-plastic-board 

cover are the thermistor mounting frame and the stirring mechanism 

(fig. 1). Each thermistor is mounted between an outer laminatedplastic ring, 3 inches in diameter, and the middle ring of brass, which 

serves as the common electrical return. One blank circuit affords a 

lead correction. The frame has a capacity of 56 thermistors; identification control is maintained by assigning a serial number to each 

thermistor and coding the positions on the rings. The thermistors 

are connected to the measuring circuits through a 58-conductor cable 

The Dewar flask is filled with silicone fluid (Dow Corning 200), which 

has high resistivity and low viscosity (10 centistokes) over a wide 

temperature range. The impeller which stirs the silicone fluid is 

externally driven through a belt and pulley system.

Two heater coils are wound on laminated-plastic webs attached to 

a 4 ^-inch-diameter hollow aluminum cylinder (fig. 1), which is sus-
PREPARATION OF THERMISTOR CABLES C3

58-conductor 

cable

0-ring

Temperature 

controlling 

thermistor

Laminatedplastic- board 

rings havingbinding posts 

connected to 

58-conductor 

cable

Hollow

aluminum

cylinder

Laminatedplastic-board 

webs

Dewar flask

Aluminum 

divider

Aluminum 

tank

Styrofoam 

insulation

Thermistor

Brass ring 

serving as 

common 

electrical 

return

Thermistor

Heater 

wires

Dry ice

Plywood 

box

Isopropyl 

alcohol

FIGURE 1. Bath for calibration of thermistors in the range 30° to -f 70°C.

pended from the cover. The temperature of the bath is held constant 

by heating the coils enough to counter the cooling of the dry ice 

outside the Dewar flask. To steady the overall heat exchange further, the interwall space of the flask is evacuated to 0.1 mm of mercury. 

All openings are gasketed, like the 0-ring seal between the cover and 

the Dewar flask; the gaskets prevent the entrance of moisture, which 

could cause an electrical short circuit.

The bath temperature is kept constant to ±0.002°C. Coarse 

adjustments of the heater current are made manually. The fine 

control is done automatically by an electronic circuit: a thermistor in 

the bath, connected to one arm of a direct-current bridge, senses the 

temperature, and a manually adjustable arm of the bridge permits
C4 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

close selection of the calibration temperature. A temperature drop 

caused by the absorption of heat by the dry ice is sensed by the control 

thermistor, which causes an unbalance in the bridge. This unbalance 

is fed through an amplifier to a sensitive relay which closes a power 

relay allowing current to flow through the fine-control heater coil to 

counter the temperature drop. The bath temperature is monitored 

precisely by use of a platinum thermometer, which is inserted into 

the bath through a gasketed hole in the cover.

A diagram of the circuits used to measure the resistances of the 

thermistors being calibrated and of the platinum thermometer is given 

in figure 2. A five-dial Wheats tone bridge and a null indicator are 

used to measure the resistances of the thermistors with a precision of 

±0.1 ohm in 3,000 ohms at 0°C. The current through 17A thermistors is kept <O50/za to minimize the effects of self-heating. A sixtr

58-conductor 

cable

Ti

^~

^

^,-^-Platinum 

thermometer

 Constanttemperature 

bath

Null indicator 

sensitivity 0.005j*a 

mm

Galvanometer 

sensitivity 0.082jxy_ 

mm

Wheatstone 

bridge

FIGURE 2. Thermistor and platinum-thermometer circuits.
PREPARATION OF THERMISTOR CABLES C5

dial Mueller bridge and a sensitive galvanometer are used to measure 

the platinum-thermometer resistance, from which the bath temperature can be determined with an accuracy of ±0.001°C. Both bridges 

and the platinum thermometer have been calibrated by the National 

Bureau of Standards. A description of the precision of the platinum 

thermometer is given by Robertson, Raspet, Swartz, and Lillard 

(1966).

The thermistor resistances, bath temperature, time, and pertinent 

remarks are recorded during each calibration. Two calibrations of 

each thermistor are made, at least 1 month apart; the second calibration makes it possible to cull out an abnormal thermistor (one having 

large calibration resistance changes), of which there is about 1 in 

every 50.

ICE-POINT CALIBRATIONS OF THERMISTOR CABLES

It can be expected that each thermistor's individual calibration is 

valid after installation in a cable, but a check calibration is advisable. 

Single-thermistor probes can be recalibrated at various temperatures 

in a suitable bath, but multithermistor cables are usually recalibrated at 0°C in a large ice bath. It is standard practice in the 

Geological Survey that cables be recalibrated after field use; aberrant 

or damaged thermistors can thus be located and replaced.

Multiconductor thermistor cables are calibrated most easily and 

accurately in a bath of melting ice, at 0°C, the ice point, for the following reasons: (1) Preparation of the ice bath is inexpensive, (2) 

the ice bath is easily prepared with only a few necessary precautions, 

and (3) the ice point is constant and closely reproducible if the bath 

is properly prepared. By this calibration, the thermistor resistances 

reveal any installation or handling damage and should corroborate 

the preinstallation calibration at 0°C, usually within ±0.01°C.

The method recommended for making an ice bath is that used by 

the National Bureau of Standards, described by Busse (1941, p. 241). 

A large clear block of ice is obtained from a commercial ice company 

and cut into hand-size chunks to fit into a commercial ice shaver. 

Ice containing impurities, mostly dissolved air which is indicated by 

a frosted appearance, is chipped off to leave only clear ice; each chunk 

is then washed in tapwater and in distilled water. Before use, the 

ice shaver, trays, and the ice-bath box are rinsed with distilled water 

also. Before being placed in the bath, the cable should be carefully 

cleaned by scrubbing with detergent and water, rinsing with a stream 

of tapwater, and then rinsing with distilled water. As a further 

precaution, rubber gloves may be used in handling ice and cable to 

prevent contamination with salt from the hands, but this precaution 

probably is unnecessary.
C6 EXPERIMENTAL AND THEORETICAL GEOPHYSICS

A bath container, \% by \% by 3 feet, is big enough to contain 

about 500 feet of )2-inch cable and the ice. It can be made of wood, 

which gives better thermal insulation than metal; it is made watertight by calking and coating inside with heavy asphalt paint. If the 

part of the cable containing thermistors is too long or too bulky, 

half of the thermistor section can be calibrated on one day, and the 

remaining half on the following day.

In preparing the bath, a 3-inch layer of shaved ice is packed on the 

bottom of the box, and the cable is coiled on the ice layer in such a 

way that the thermistors are placed near the center area and the 

remainder of the cable is along the sides of the box. The thermistor 

sections should be at least 3 inches away from any other part of the 

cable; usually, a length of cable containing three thermistors can be 

suitably coiled on one ice layer. Shaved ice is packed around and 

between coils of the cable, a new 3-inch layer of ice is put in, and the 

same procedure is repeated until a length of cable well beyond the 

last thermistor is in the box.

Shaved ice alone does not maintain a uniform temperature; the 

ice particles must be thermally coupled, and therefore two or three 

times during the bath preparation a small amount of distilled water 

must be sprayed in. The proper water saturation is determined by a 

simple empirical test: a rod is pressed with only forearm leverage into 

the shaved ice, and at proper saturation, a bluish color appears in the 

compressed ice.

After the ice bath is prepared, 2 hours are allowed to elapse before 

the first set of measurements is made; at this time, generally, the 

cable temperature is within 0.01°C of that of the bath. The bath 

and cable arrive within 0.001 °C of a thermal steady state after 4 to 6 

hours, for a K-inch cable. Excess water may need to be drawn off 

and melted ice replaced after 4 hours.

Measurements of the thermistor and platinum-thermometer resistances are made with the same bridge circuits shown in figure 3; use 

of the platinum thermometer is described below. The bridge current 

for 17A thermistors should be limited to 150 /za both in the laboratory 

and in the field to minimize self-heatine. Lead-wire resistances 

must be subtracted from the total resistance of each thermistor before 

converting resistance to temperature; for this purpose the test lead 

wire resistance is used to determine the correction for each thermistor 

lead. (See Swartz, 1954, for description of the circuit and the testlead correction.)

For multithermistor cables in the field, a method devised by Diment 

(in Diment and Kobertson, 1963, p. 5039-5040) provides calibrations 

of thermistors relative to each other over the temperature range of 

interest. The resistance of each thermistor can be read at the same
PREPARATION OF THERMISTOR CABLES C7

depth in a thermally stable drill hole, and the converted temperatures 

can be compared; if the thermistors are evenly spaced, by moving the 

cable one interval, measurements can be made for all but one thermistor at depth positions previously occupied by other thermistors. 

The process may be repeated to get several duplicate measurements, 

which can be analyzed for the best correlations and appropriate 

corrections. Another method is to compare the temperatures measured at specific depths with two cables. For many heat-flow studies, 

such relative calibrations are adequate.

THERMISTOR CABLES

CONSTRUCTION

The fabrication of a cable with only one thermistor is usually done 

by placing the thermistor in one end of a short metal probe. The 

probe may be attached to the cable by vulcanizing a shoulder onto the 

insulation and clamping the probe on the shoulder; for short cables, 

the probe may be clamped directly onto the cable. The probe is 

sealed with 0-rings or tape. Construction details of such a singlethermistor probe were given by Misener and Beck (1960).

The installation of thermistors in a multiconductor cable is not 

difficult, but it is tune consuming because the thermistors must be 

handled carefully to avoid detaching their copper lead wires and must 

be installed properly to cushion them and to seal them off from water 

when the cable is used. In Geological Survey practice, in a 30-conductor cable, 28 thermistors would be installed; two conductors 

are needed for a common lead and for measuring a typical lead resistance. (See Swartz, 1954.) The conductors of the cable are all 

soldered together at the bottom end, covered, and a 30-contact connector 

is wired to the top end. A watertight metallic cover should be fitted 

over the top connector to protect it against the entrance of moisture 

and dirt during use in the field.

Before installation, positions for the thermistors should be measured 

off and marked on the cable. A short slit is then cut in the cable 

jacket at each desired location, and a piece of the jacket is cut away 

to make room for the thermistor, as shown in figure 3. The proper 

conductor under the insulation is located (usually by a color code) 

and cut, and the thermistor leads are attached to the conductor ends 

with squeeze-type, solderless connectors. Solder is avoided because 

it strain hardens easily and breaks quickly on flexing. Insulating 

tubing, an inner length of glass-fiber tubing and an outer one of plastic 

tubing, is slipped over the thermistor and the leads before the second 

joint is made, and is used to cushion and insulate the thermistor. The 

tubing then is filled with silicone rubber or some other insulating
Silicone-rubber 

P° tting Com| nd

Insulating 

Thermistor / 

Plastic or self-vulcanizingrubber sealing tape

Linen 

Cable jacket' Conductors 

FIGURE 3. Cut-away section of a thermistor installation i
PREPARATION OF THERMISTOR CABLES C9

flexible potting compound, and the whole is tied with linen cord into 

a compact joint.

The joint is pushed down inside the cable, and the opening is 

covered by wrapping with tape. If the cable jacket is natural rubber, 

two layers of self-vulcanizing cold-setting rubber tape are wrapped 

on, and after setting, several layers of rubber tape are wound over 

it. If the cable jacket is plastic, five to seven layers of plastic tape 

are wound tightly over the joint. Such a cold-sealed joint does not 

disturb the thermistor calibration and is adequate for most uses, but 

if the joint may be subjected to high water pressure or to heavy 

abrasive wear, a vulcanized-rubber joint should be considered. The 

principal disadvantage is that the temperature of vulcanization (about 

130°C) is so high that the thermistor calibration may be considerably 

disturbed. Swartz and Easpet (1961) found that the disturbance 

took the form of an initial offset of about -f 0.2°C in the apparent 

temperature at the ice point, with an increase in the rate of thermistor 

drift. After 4 months, the apparent ice-point temperature had 

returned to 0°C, but the drift rate continued to be greater than normal 

though gradually decreasing for 1^ years, after which the drift continued at the normal rate, about 4X10~3 deg C per mo.

The resistance of each conductor is measured before the thermistors 

are installed to obtain the basis for the lead-resistance correction. 

The lead resistance must be subtracted from the total measured 

resistance to obtain the resistance of the thermistor. Swartz (1954) 

showed that for any temperature of the lead, the lead correction is 

simply the ratio of the given thermistor-lead resistance to the test-lead 

resistance, as measured before thermistor installation, multiplied by 

the test-lead resistance observed in the field.

To check each thermistor circuit, that is, to identify the conductor 

and thermistor, each joint can be chilled through the cable with ice 

and the deflection of the galvanometer in the thermistor bridge circuit 

observed. Watertightness in a cable can be tested by inspecting for 

bubbles when it is subjected to an internal pressure of air at about 20 

psi while it is under water; alternatively, a high-voltage spark tester 

can be used.

Another method of installing thermistors in a multiconductor cable 

(Lachenbruch and others, 1962, p. 793) is to put each one in a stainlesssteel or plastic pod, installed by the cable manufacturer. This 

method has the advantage that the thermistors can be removed 

fairly easily for recalibration in the temperature range of interest, 

although the bulk of the pods may prove troublesome in getting the 

cable in and out of a hole.
CIO EXPERIMENTAL AND THEORETICAL GEOPHYSICS

USE AND CARE

Certain precautions in the preparation and handling of a completed 

cable should be taken to insure best results. For example, the connector at the end of the cable which plugs into the measurement 

circuit should be protected from moisture and dust; otherwise highresistance short circuits may develop. It is helpful to have a multilead connector of the Military Specification (MS) type, which has a 

packing gland at the cable entrance. A dust cover for the connector 

can be made with an 0-ring seal; one design is a long aluminum cup 

with two outer rods to clamp it in place.

For shipping or for use as a reel, a wooden spool may need to be 

constructed. The core diameter of the spool should not be so small 

that the thermistor installations are flexed too sharply; a 14-inchdiameter core seems to provide good rigidity and is not too large for 

short cables. The capacity (O) of the reel, in feet, can be calculated 

quite closely by the following formula:

where, d is the cable diameter, L is the inside distance between spool 

ends, RI is the core radius, and Rz is the outside-spool radius, all 

dimensions in inches. In shipping a spool by commercial carrier 

a layer of cardboard should be wrapped over the top cable layers 

and the whole finished with a wood cover nailed to the spool ends, 

to protect the cable adequately.

At the well site, a pulley of a maximum practicable diameter should 

be used in lowering the cable into the well to prevent undue flexing 

of the thermistor pods as they ride over the pulley; most thermistor 

pods and taped installations are about 6 inches long, so a 12-inchdiameter pulley is adequate. Mechanical damage to the jacket can 

be avoided by covering or smoothing sharp ends of well casings, 

sharp pulley edges, or any sharp corners. The cable should not be 

left lying on the ground where it can be damaged by traffic or can 

be exposed to the hot sun (which changes the resistance-to-temperature calibration).

For measurements in the field, the current passing through the 

thermistor should be held at 150 /ia to keep self -heating to a minimum. 

In using a portable four-dial Wheatstone bridge, a 1%-volt cell with 

a 1000-ohm resistor in series provides an acceptable current under 

normal conditions of measurement. A simple test for self-heating 

can be made by balancing the bridge, opening the current circuit 

for a short time, and closing the bridge circuit again; if the galvanometer deflects and then slowly returns to balance, some self-heating 

is occurring.
PREPARATION OF THERMISTOR CABLES Cll

Despite care in handling, a few thermistors of the group in a multiconductor cable occasionally experience a small upset of the temperature-to-resistance calibration. It is possible not only to identify 

anomalous thermistor data but to retrieve most of the measurements 

despite such upsets by using Diment's method of in-hole calibration 

(Diment and Eobertson, 1963, p. 5039-5040).

Normally, the equation of Swartz (1954) equation 4 of Robertson, 

Easpet, Swartz, and Lillard (1966) is used for converting resistance 

to temperature. In the field, the method of master and correction 

tables (Robertson and others, 1966) for conversion of resistance to 

temperature is easily used; fewer reference tables are needed and no 

calculator is required as when separate conversion tables are compiled 

for each thermistor. Another simplification to speed up conversions 

can be used for long-term cable installations in which the resistances 

measured are in a small range; conversion tables can be calculated 

listing the resistances at 1-ohm intervals and the corresponding temperatures opposite; such a table is useful for a single-thermistor cable, 

also.

REFERENCES

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