Thus, the purer the platinum the greater will be the coefficient C.
As examples of the values of the above constants we give the fol-
lowing data taken from tests* made by the National Bureau of
Standards upon two platinum-resistance thermometers, called A
#0 = 21.3476
Diameter of wire = 0.01 cm.
Ro= 3. 48779
5 = 1.504
Diameter of wire =
and B. The current thru the thermometers in the above test
was 0.004 ampere and 0.010 ampere respectively.
If we plot resistance as ordinates and gas thermometer degrees
'as abscissae, the curve obtained for platinum is always slightly
concave toward the axis of X and is parabolic in form.f
When pure nickel is used for resistance thermometers, the re-
sistance variation obeys another law. Prof. C. F. Marvin has
* Bulletin of the Bureau of Standards, Vol. 6, page 156, 1909.
t For a more extended discussion of formula (2) and for a description
of methods for reducing platinum temperatures to the gas scale, consult
"Measurement of High Temperatures," Burgess and Le Chatelier, 1912 edi-
tion, Chapter V.
300 MEASURING ELECTRICAL RESISTANCE [ART. 1301
shown * that the nickel-resistance curve is very closely represented
by the equation
Log e R = a + ml, (4)
where R is resistance of thermometer in ohms, t the temperature
in degrees C., and m and a are constants. In some particular cases
this equation became
Log e R = 1.0854 + 0.001699 1,
Log e R = 1.9004 + 0.001818 1,
Log e R = 0.9614 + 0.001450*.
These equations were tested in the range 25 C. to 75 C. with
an error never greater than 0.1 C. and again in the range C.
to 375 C. with an error not exceeding 0.9 C.
The simple meaning of the above relation [Eq. (4)] is that pure
nickel wire increases in resistance by the same per cent of its re-
sistance at the beginning of an increment of temperature for every
equal increment in temperature anywhere in the range 25 C.
to 350 C.
The law is sufficiently accurate to be relied upon for work not
requiring a precision greater than 1 C. over the range mentioned
above, and for short ranges of 50 C., or less, reliance may be
placed upon the law to 0.1 C., or better.
As far as known, no other metal obeys the law of nickel. Be-
cause of this law for nickel the temperature-resistance curve may
be located by observing the resistance at only two temperatures,
say C. and 100 C. When resistance is plotted as ordinates
and temperature as abscissae the curve will always be convex
toward the axis of X. It follows that, if a certain length of nickel
wire is joined in series with a certain length of platinum wire, a
combination resistance thermometer may be made which, over
short ranges, will have a change with temperature which is prac-
To engineers and those who make industrial uses of resistance
thermometers the theoretical side of the subject is of minor
interest. There is a practical procedure which may be adopted
that makes it unnecessary for manufacturers or users to give
consideration to these methods of standardization of resistance
* Physical Review, April, 1910, pages 522-528.
ART. 1301] MEASUREMENT OF TEMPERATURE 301
thermometers. The instrument maker may carefully construct a
resistance thermometer to serve as a standard and send this from
time to time to the National Bureau of Standards at Washington.
The Bureau will measure the resistance of this thermometer
over a wide range, at several known temperatures given by
their standard resistance thermometers, and furnish a certificate
giving the relations which are found between temperature and
resistance of the thermometer submitted for calibration. The
instrument maker may then use this thermometer as a standard
with which other thermometers are easily calibrated. This is
done by direct comparison in an oil bath for medium temperatures,
and in a specially constructed electric furnace for high tempera-
tures. Cold brine, or liquid air, or other means may be used for
making the comparison at low temperatures.
The feature of paramount importance in the use of electrical
resistance thermometers is the constancy with which they main-
tain their calibration. This subject has received considerable
attention, especially in the case of thermometers made of platinum
wire, and the results observed have proved the entire reliability
of this material for temperatures not exceeding 1000 C. It is
highly probable that other materials will behave in an entirely
regular manner if not subjected to too high temperatures.
Careful investigations of the constancy of other materials
than platinum that are suitable for resistance thermometers are
needed. But the investigations so far made show that where
permanent alterations in resistance occur these may usually be
traced to causes which proper precautions may avoid. Thus, the
material selected for the thermometer may be by nature of an
unstable character. Iron, for example, is an unsuitable metal to
use. The material may contain impurities which by vaporization,
crystallization, or otherwise, cause the resistance to alter gradually.
The wire of which the thermometer is made may have been sub-
jected to mechanical strains which gradually work out with re-
peated heatings, thus altering the resistance. If the material is
one which does not oxidize, it may still be greatly affected at high
temperatures by absorbing gaseous impurities. Thus, a nickel-wire
or a platinum-wire thermometer heated to 400 C. in a brass tube
is ruined by absorbing the metallic vapors given off. For the
same reason all metal solderings near the resistance wire are liable
at high temperatures to give off vapors which affect the permanent
302 MEASURING ELECTRICAL RESISTANCE [ART. 1302
resistance, besides making liable the formation of local resistance
at the joints.
Proper construction and choice of materials can remove all the
above causes of permanent alterations. It may be that in the
case of platinum, to some extent at least, and more so in other
materials, slow permanent alterations in resistance occur, the
cause of which is not known. Only extended investigations can
give the limits of these possible alterations. Enough work has
been done, however, to show that for even very refined work the
reliability of platinum and some other materials is sufficient if
temperatures too high are not exceeded.
In resistance thermometry practical details of construction are
all important. The chief of these will now be considered.
1302. Construction of Resistance Thermometers. The best
material of which to construct a resistance thermometer depends
upon the temperature range to be measured, as well as upon the
physical qualities of the available materials.
Constancy of composition and other practical considerations
seem to limit the choice to a few of the pure metals, usually in the
form of wire. The metal which has received the most study is
platinum. It can be used over a very wide temperature range,
and can be obtained under the name of Herseus platinum in a state
of great purity. This material answers every requirement of re-
sistance thermometry, except that it is very costly. A substitute
for platinum should, therefore, be sought and used wherever it
will serve as well. This substitute should be inexpensive and
obtainable in a pure state. It is desirable that it should have a
high specific resistance, combined with a large temperature coeffi-
cient. It should be unoxidizable under usable conditions, and
withstand a high temperature without deterioration or permanent
alteration in resistance.-
An examination of the pure metals shows that these conditions
are best met by nickel. The author has had many thermometers
constructed of this wire for temperatures ranging from 40 C.
to 300 C., and has found it reliable in this range. It has a higher
coefficient than the purest platinum, that of nickel being about
0.0041 per degree between C. and 100 C., pure platinum being
0.0039, and commercial platinum but about 0.002. The specific
resistance of pure nickel and pure platinum is in the ratio of about
933 to 1000.
ART. 1302] MEASUREMENT OF TEMPERATURE 303
It may here be remarked that a determination of the tempera-
ture coefficient of the metallic elements offers usually a very deli-
cate test of their purity, and specimens of nickel and platinum
which show a low temperature coefficient can positively be con-
sidered as impure and inferior for use in resistance thermometers.
Another test of interest, especially on wires intended for use
in thermocouples, is to attach the two ends of a short length to
the terminals of a very sensitive galvanometer, and to pass a
flame along the wire. If the galvanometer gives positive and
negative deflections of considerable magnitude, the wire may be
known to be unhomogeneous, and liable to have parasitic currents
set up in it when exposed to high temperatures. A pure nickel
and a pure platinum wire should show little of this effect.
The particular purpose for which a resistance thermometer is
to Be used largely determines its special features of construction.
Broadly classified, resistance thermometers are particularly useful
in the following cases:
1. Measurement of all temperatures below 40 C., the freez-
ing point of mercury.
2. Measurement of all temperatures up to 1000 C., when the
temperature is to be taken at a place where it cannot be directly
3. Measurement of temperatures below 1000 C., and above
the range of the mercury thermometer.
4. Measurement of all temperatures below 1000 C., which
must be photographically or otherwise recorded.
5. Determinations of small temperature differences or varia-
tions for which the mercury thermometer is not sufficiently
It is evident from the above classification that there can be no
general form or type of construction of a resistance thermometer.
Each special requirement must be met by the instrument maker,
who should be guided in his designs by experience and a study of
the conditions. The form of thermometer having been chosen,
the particular method of reading the resistance variations and of
expressing them in degrees should have particular care, for in
nearly every case which arises different requirements must be met.
Resistance thermometers for use below 140 C. are of relatively
simple construction, for in this case silk-insulated nickel wire may
be used. Certain precautions, nevertheless, need attention. The
304 MEASURING ELECTRICAL RESISTANCE [ART. 1302
mass of the wire used and that of the body on which it is wound
should be small, or the temperature of the resistance wire will lag
behind any changing temperatures which are being measured,
and lead to erroneous indications. The wire must be so chosen
in respect to size and resistance that the heating of the wire by the
measuring current shall be negligible.
The constancy of any wound resistance depends largely upon
the treatment to which it is subjected after being wound. The
winding of the wire introduces strains, which gradually work out,
causing variations in the permanent resistance. This certain
result is avoided by an artificial " aging," which consists in main-
taining the wire for several hours or days, before the thermometer
is calibrated, at a temperature higher than that at which it will
Insulating Rod holding Mica Winding Form.
Platinum Winding on Mica Form.
, Metal Case.
Lead Wires in Grooves
in Insulating Rod.
It is needful to finish the terminals of the wire, especially if
short, in such a manner that no local variations in resistance can
occur at the joints. As a rule the terminals should be hard silver
soldered for low-temperature thermometers, and for high-tem-
perature thermometers all joints exposed to the high temperature
must be welded joints.
Generally, the resistance wire should be protected by a casing.
When, however, as in the measurement of moderate temperatures
of gases or insulating fluids, the wire can be directly in contact
with whatever is to have its temperature determined, the resist-
ance thermometer assumes the surrounding temperature very
quickly, far surpassing the mercury thermometer in this respect.
If a casing must be used, it should be so shaped that the ratio of
its surface to its volume is large, and the construction should aim
to reduce to a minimum the heat which is conducted along the
case or which is distributed by air convection within it. Repro-
ductions are here given of two types of resistance thermometers
designed for the measurement of low or moderate temperatures.
The thermometer shown in Fig. 1302a was constructed for use
ART. 1302] MEASUREMENT OF TEMPERATURE 305
in measuring and recording with great precision the temperature
differences between two brine mains. The average temperature
of the brine was about 37 C. and the average difference of
temperature between the two mains was about 1.5 C. The
allowable error was 0.01 C., and hence great care in the construc-
tion of the thermometers, as well as in the rest of the apparatus,
was required. This thermometer was wound with No. 35 platinum
wire, of great purity. Its resistance at room temperature was
about 80 ohms. It is probable that nickel wire would have served
as well, but because of the better known properties of platinum
and the importance of the experiment platinum was selected.
No.32 B. & S. Nickel Wire. (Silk Insulation)
/ Silk Insulation
It should be noted that the steel case is long and small in
diameter, that the winding ends well below the nut which screws
into the brine main, and that the wire is wound on a light frame
of mica, having a minimum of mass. A small sudden change
in the temperature of the brine was followed by the thermometer
to within about 0.005 C. within two minutes.
Fig. 1302b is a sectional view of a form of resistance thermometer
made for the purpose of measuring the temperature of the soil
at different depths where the thermometers are permanently
buried. The winding is in the form of a skein, and No. 32 silk-
insulated nickel wire is used. To insure permanency the wire
should be kept immersed, after winding, in hot paraffin for three
or four days. The changes in the temperature of the soil are very
slow, and hence there is no need to provide against a temperature
lag of the thermometer winding.
The resistance is made large, about 100 ohms at 20 C., and
the winding is encased in a brass tube filled with paraffin. The
lead-covered leads are soldered with a wiped joint to the brass
tube, thus preventing the entrance of moisture, which has to be
carefully avoided. The resistance of the thermometer being high,
the change in the resistance of the leads is entirely negligible.
A somewhat similar construction would be suitable for measur-
MEASURING ELECTRICAL RESISTANCE [ART. 1302
ing the temperature of the interior of stored material, such as
grain, tobacco, hay, wheat, etc., also for measuring the temperature
of cold-storage rooms. Any number of such thermometers can be
located at different places and be connected by a switch, one at a
time, to a single reading device which reads directly in degrees
Fahrenheit or Centigrade. The methods of reading these and
other resistance thermometers will be presently described.
Tube Platinum T ube
Resistance thermometers give often the most accurate and con-
venient means of measuring high temperatures up to 1000 C. or
possibly more. It is stated by Le Chatelier* that experiments
carried out at the National Physical Laboratory, England, showed
that throughout the temperature range of 1000 C. the agreement
between the scales of the platinum-resistance and the thermo-
electric pyrometers tested was within 0.5 C.
Such statements as the above, however, are true only when
the resistance thermometers have been constructed in a particular
manner to avoid alterations and deteriorations in the wire that
are sure to result at high temperatures with improper construction.
Platinum heated red hot and exposed to certain gases, as hydrogen
or metallic fumes, absorbs impurities which permanently alter its
resistance and often render it extremely brittle.
Accumulated experience has shown that for temperatures above
a red heat (525 C. to 600 C. for all materials) the design of the
thermometer should embody the general features shown in the
illustration, Fig. 1302c, I and II.
In the thermometer here illustrated, the winding is a pure
* "High Temperature Measurements," page 105, 1904 edition.
ART. 1302] MEASUREMENT OF TEMPERATURE 307
Harseus wire, its purity being shown by its temperature coefficient,
which is about 0.0039 at 100 C. This wire, No. 35 B. & S., is
wound bare, on a frame of thin mica, in such a manner as to touch
only the edges of the mica. The winding is 36 turns to the inch.
The mica frame is made by matching together at right angles two
pieces of mica sheet, of the shape shown in Fig. 1302d.
As the winding touches only at the edges of the mica, only a
small percentage of its length can become contaminated by any
possible action of a solid material. The lead wires, by a method
of compensation to be later described, do not enter into the resist-
ance which is measured, and may be of a less pure platinum
than the resistance winding. These lead wires are either three
or four in number, according to the method of compensation
adopted. They are insulated from each other by being passed
through tubes of porcelain.
For temperatures above the fusion point of hard glass, porcelain
tubes especially constructed for this work by the Royal Berlin
Porcelain Works are the most satisfactory material for a casing.
The interior parts of the thermometer shown in Fig. 1302c, II,
are designed to be easily withdrawn from the tube for examination,
and again replaced. In the particular case shown, the winding
was made 13 cms long, to give the thermometer a high resistance.
This is generally an advantage, where the conditions permit, as
the contact resistances in the measuring device are then small in
comparison, and greater sensibility is more easily obtained.
It was legitimate to make the winding long for the case shown,
as this thermometer was designed to measure the temperature of
hot gases which would surround the porcelain tube more than, half
way to its head. If, however, the temperature of the place to be
measured is uniform over a small space only, then the winding
should be as short and as much concentrated at the end of the
tube as possible, and so permit of placing the entire winding in
the hot place, the temperature of which is to be measured.
308 MEASURING ELECTRICAL RESISTANCE [ART. 1303
Thermocouples have in this respect an advantage over a resist-
ance thermometer as above designed, for the end of the thermo-
couple is a very small body, that may be closely located at the
place, where the temperature is to be observed. This consideration
led the author to design another form of resistance thermometer
which will be shown to combine the advantages of both. A de-
scription of this is best given, however, under methods of reading
resistance thermometers, which we shall now consider.
1303. Methods of Reading 'Resistance Thermometers. As
previously stated, the National Bureau of Standards at Washington
will furnish the instrument maker with a certificate giving the con-
nection between the electrical resistance and the temperature of a
selected standard resistance thermometer, and the calibration of
other thermometers is reduced to comparing their resistances with
that of the standard when all are brought to equal temperatures,
In the case of high temperatures, a specially constructed electric
furnace is used for the purpose. The problem, then, of reading
temperatures with thermometers thus calibrated resolves itself into
measuring their resistance in a simple manner when subjected to
The resistance being known, the temperature may be taken
from a previously plotted curve, or the resistance-measuring
device may be constructed to read directly in degrees Centigrade
or Fahrenheit. The convenience, simplicity, precision, and re-
liability with which these measurements can be made largely
determine the practical and commercial usefulness of resistance
thermometers. The continuous recording of temperatures given by
resistance thermometers is another, but closely related, problem,
but one which cannot here receive our attention.
The available and useful methods of determining resistances for
measuring temperatures may be classified as follows :
Slide- wire bridge method.
Differential galvanometer method.
By resistance-thermometer bridge with two traveling contacts.
By use of dial bridges.
Kelvin-double-bridge method of reading temperatures.
Direct-deflection method of reading temperatures.
1304. Slide-wire Bridge Method. This is a very convenient
zero method to employ, especially when the reading instrument
has a scale calibrated to read directly in degrees. The slide-wire
MEASUREMENT OF TEMPERATURE
bridge may have its connections arranged in either of two useful
ways. The first is less precise, but more convenient. The connec-
tions are given diagrammatically in Fig. 1304a.
jPi, Tz, T 3 , etc., represent any number of resistance thermom-
eters; y, y are the thermometer leads, which should be alike but
may be of any length. Contact can be made with any ther-
mometer by means of a simple sliding switch S. The resistances r,
ri, r 2 , should be about equal to each other and to the resistance of
the thermometer when at a mean temperature. The resistance of
the slide wire I should be such as will take care of only the variation
in resistance of the thermometers.
In an actual construction, the contact p would move over a
circularly disposed wire and scale. This scale may be divided
into arbitrary divisions, and reference be made to a curve, to
obtain the temperature of any thermometer corresponding to a
given setting for a balance. In this case, the different thermom-
eters need to be made of only approximately the same resistance.
The scale may, however, without great difficulty, be graduated
to read directly in degrees when used with a thermometer of a
particular resistance and temperature coefficient.
If, however, many thermometers are to be read on the same
scale, they must be adjusted to exact equality both in respect to
resistance and temperature coefficient. This last adjustment can
MEASURING ELECTRICAL RESISTANCE [ART. 1304
be made by using a certain resistance of manganin in series with
those thermometers which have too high a coefficient.
The arrangement of connections shown does not entirely com-
pensate for changes in the resistance of the leads. The error,
however, would not exceed from this cause 0.1 C. in an ordinary
case. The obvious advantage of making the connections in this
way is that while nearly complete compensation is obtained, each
thermometer has only two lead wires and one common terminal
connecting all the thermometers to the galvanometer. The man-
ner of making the bridge connections according to the second
arrangement is shown in Fig. 1304b.
By connecting the bridge in this manner and choosing the ratio
arms equal, the resistance of the leads y, y, entirely eliminate.
Thus, the value of any resistance Xi, X^ etc., is
X = R-(l-2a)=a constant + 2 a.
This method, while perfectly compensating, requires that two
pairs of leads shall be carried to each thermometer. This is a
decided disadvantage where many thermometers are to be read
at a distance on one bridge. The method recommends itself when
the highest possible precision is required. In this method also
the scale may be calibrated in degrees, if desired.
The balance point on the wire in either of the above methods
may be found with a telephone, but preferably with a galvanometer.
MEASUREMENT OF TEMPERATURE
A pointer galvanometer of portable type, such as that described
in par. 1501, is amply sensitive for the purpose.
The illustration, Fig. 1304c, shows a completed instrument,
designed for portability.
A temperature measurement is made by slightly depressing the
button, which closes the battery circuit, and then rotating the