The first observations are the ice points of the thermometers under test. The test thermometers are then mounted in the comparison bath between the two standards. It is preferable to have two observers (A and B). Observer A reads in the order left to right as the thermometers appear in the table, and immediately repeats the observations in the order right to left, while observer B records the data. Observer B promptly reads in the same manner while observer A records. The bath temperature is increasing linearly with time and the observations are spaced uniformly in time. For this reason the mean of the observations with any one thermometer will correspond to the mean temperature value of the comparison bath medium during the observations of all of the thermometers. Immediately after the comparison observations, ice points of the two standards are observed and recorded. With the ice point data and the adjusted scale corrections for the standards, the temperatures indicated by the standards are calculated, and an overall mean temperature for the observations is obtained. This mean temperature is compared with the mean of the observations for each thermometer to

obtain a correction to the scale of the thermometers. The thermometer comparisons are repeated in the same manner at the next higher test point until the calibration is completed.

When a platinum resistance thermometer is used as a standard, the sequence of observations is the same, except that the one resistance thermometer is read in place of the separate observations of two liquidin-glass standards. For more information on platinum. resistance thermometers refer to NBS Monograph 126, Platinum Resistance Thermometry, available from the Superintendent of Documents, U. S. Government Printing Office, Washington, D. C. 20402.

5.3. Corrections for Emergent Stem

When a thermometer is calibrated and used under conditions of total immersion, no difficulty is encountered when the reported scale corrections are to be applied. The temperature of the thermometer bulb and the portion of the stem containing the mercury is definitely defined as the temperature of the bath medium. The corrections apply as given on the report, when this thermometer is used at total immersion.

Occasionally it becomes necessary to use a totalimmersion thermometer with a portion of the stem emergent from the bath medium. The temperature of the environment above the bath, or apparatus containing the thermometer, may differ markedly from the temperature of the thermometer bulb. It is also possible to have pronounced temperature gradients along the length of exposed mercury column. A correction can be calculated to account for the difference in temperature between the bulb and the emergent stem. A reliable estimate of the mean temperature of the emergent stem is required and should actually be measured. The determination of the stem temperature should be repeated each time the thermometer is used in this way, or the accuracy of the correction will depend upon the constancy of the environmental temperature over a period of time. Significant variations in the temperature of the emergent stem may occur due to air circulation and variations in ambient temperature, even though the location of the thermometer does not change.

The same situation occurs in the case of partialimmersion thermometers. The reported scale corrections apply only for the indicated depth of immersion and a particular stem temperature. If the thermometer is used under conditions other than specified, the reported scale corrections are no longer applicable, and a stem temperature correction is required.

The following paragraphs describe methods for determining stem temperatures and calculating corrections. It will be seen how important the stem temperature correction is in relation to a desired accuracy.

a. Measurement of Emergent-Stem Temperature

There are two methods available for measuring the approximate mean temperature of the emergent stem. The first method consists of placing one or more small

shown in figure 8(c). For a more accurate measurement faden or thread thermometers [8, 9] can be used. These thermometers have long bulbs measuring variously 5 to 20 cm, with wall thicknesses and bore sizes nearly the same as the stem of an ordinary thermometer. The bulb length is selected to approximate that of the emergent stem whose temperature is to be measured. The stem of the faden thermometer has a finer capillary than the bulb and is usually graduated in intervals of 2, 5, or 10 degrees Celsius. Stem temperature measurements taken at NBS are based upon the use of faden thermometers whenever possible.

A convenient method for measuring the emergentstem temperature of a total-immersion thermometer that is used at partial immersion involves the use of a faden thermometer. The top of the faden thermometer bulb is placed on a horizontal plane with the top of the mercury column of the thermometer whose stem temperature is being measured. The faden thermometer chosen must have a bulb which is long enough to cover the vertical area of unknown temperature gradient necessary to be measured. This sometimes involves placing part of the faden thermometer bulb in the bath medium, since the top portion of the medium can be at a temperature different from the temperature of the total-immersion thermometer bulb. (This is especially true for measurements above 150 °C). The reading of the faden thermometer will indicate the mean temperature value of the area surrounding the bulb, which is also the mean temperature value of the adjacent portion of the total-immersion thermometer stem. A faden thermometer used in this manner is illustrated in figure 8(a).

If the stem temperature of a partial-immersion thermometer is to be measured, a similar approach is followed. In this case it is necessary to measure the mean temperature from the immersion line to the top of the mercury column of the partial-immersion thermometer. One or more faden thermometers with appropriate bulb lengths are chosen to accomplish this measurement. This procedure is shown in figure 8(b).

convenient to express the length of the thermometer stem adjacent to the faden bulb in terms of degrees on the thermometer scale. If a faden thermometer, having a bulb which is 10 cm long, is used for a stem temperature measurement, then the number of degrees corresponding to the 10 cm length must be found by measuring a portion of the thermometer scale. This measurement should be made over the portion of the graduated scale which was adjacent to the faden thermometer bulb. This is particularly important with high-temperature thermometers, where the length of a degree is generally not the same throughout the entire length of the scale. In some instances the adjacent portion of the thermometer stem is not graduated. This is especially true with partial-immersion thermometers in the area above the immersion line. This ungraduated length between the immersion line and the first graduation must be evaluated in terms of scale degrees and included as part of the distance covered.

The coefficient k varies for different kinds of glass, or for different temperature intervals, i.e., different values of (t,t). For purposes of computing the emergent-stem correction, the value of k may be considered as depending on the average of t1 and t. Values of k as the function of (t, + t) /2 for two widely used thermometric glasses are given in table 4. If the kind of glass is not known, it is acceptable to use 0.00016 for mercury thermometers graduated in degrees Celsius and k 0.00009 for mercury thermometers graduated in degrees Fahrenheit.

k

The expansions of liquids such as alcohol, toluene, etc., vary quite rapidly with the temperature causing k to vary considerably for different temperature intervals. An approximate stem correction for such thermometers may be calculated by setting the value of k in the above equation as equal to 0.001 for Celsius thermometers or 0.0006 for Fahrenheit thermometers. Calculation of the stem correction may be illustrated by the following example: A total-immersion thermometer indicates a reading of 90 °C in a bath when

This correction is added to the corrected thermometer reading to obtain the actual temperature of the bath medium. Note that when the temperature of the emergent stem is lower than the bath temperature, the sign of the correction is +, since the thermometer would indicate a higher temperature reading if immersed properly.

If a faden thermometer was not available in the above example, the emergent-stem temperature could be estimated by suspending a small auxiliary thermometer above the bath adjacent to the thermometer. The bulb of the auxiliary thermometer would be placed at the center of the emergent stem or at the 85 °C graduation. The reading of the auxiliary thermometer will indicate the approximate mean temperature of the 10 degrees (80° to 90 °C) emergent from the bath. For this correction the value for n would be 10. If the auxiliary thermometer indicates a reading of 60 °C, the stem correction would be:

c. Formula for Partial-Immersion Thermometers The scale corrections for partial-immersion thermometers calibrated at NBS are applicable when the thermometer is immersed to the immersion mark and, unless otherwise requested, for the unspecified stem temperatures which prevailed over the comparison baths at the time of calibration. Frequently it is necessary to report scale corrections which are applicable when specified mean temperatures of the emergent stem are requested. In such cases the emergent stem temperatures are measured during calibration and the observations are corrected as necessary to account for any differences found between the specified stem temperatures and the stem temperatures observed during test. The magnitude of the stem correction will be proportional to the difference between the specified and observed stem temperatures, and may be calculated for Celsius mercurial thermometers by using the following formula:

n

tobs),

specified mean temperature of the emergent stem (for which reported scale corrections apply),

observed mean temperature of the emergent stem (faden thermometer reading),

= number of scale degrees equivalent to the length of emergent stem (including the evaluated area above the immersion line).

This correction must be applied (added if positive, subtracted if negative) to the difference of the readings to give the actual temperature difference.

Example: The thermometer was immersed to the 20° mark; the initial reading, ti, was 25 °C; the final reading, tr, was 30 °C; and the stem temperature was 20 °C. The correction is:

0.00016 x 5 (25 +30-20-20) = +0.012 °C. Since the difference between ti and tr was 5°, the actual difference between the initial and final temperature readings was:

any part of the lower portion of the stem exposed to ambient temperature. Since this part may contain 5 to 10 times more mercury per centimeter than the graduated portion, a large and uncertain error will be introduced if this section is not in the bath medium. If it is unavoidable, and such a thermometer must be used in this way, the necessary correction may be computed from the above formula, provided S in the formula is replaced by S+m, where m is the number of degrees the temperature of the thermometer must be lowered to bring the meniscus from the zero mark on the scale to the point of immersion.

If the thermometer is immersed to some point other than the zero mark, as would ordinarily be the case with thermometers having the zero graduation at the top of the scale, the differential stem correction may be calculated from the above formula if S is replaced by Sm. The formula is applicable whether the point of immersion is on the scale or below it, provided the points at which readings are made are above the point to which the thermometer is immersed.

5.4. Number and Choice of Test Points

A thermometer is usually calibrated at points spaced uniformly over the entire range of the main scale. The number of calibration points chosen depends on the range of scale, graduation interval, and accuracy desired. The interval between the calibration points should not be unnecessarily small, nor should it be so large as to destroy confidence in interpolated corrections for temperature values between the calibration points.

For thermometers not graduated above approximately 200 °C, it is generally accepted that the interval between test points should not exceed 100 scale divisions, if the corrected temperature values between the calibration points are to have an expected accuracy of approximately one-half of one scale division. If accuracies of one or two-tenths of a scale division are desired, it will be necessary to reduce the calibration interval to every 40 or 50 scale divisions. If a thermometer is graduated above 200 °C, a 40 to 50 scale division calibration interval is required to produce corrected temperature values with expected accuracies of approximately one-half of a scale division, and a 20 to 25 scale division calibration interval is necessary for expected accuracies to be approximately one or two-tenths of a scale division.

The above results were derived from analysis of calibration data taken on more than 50 thermometers purchased from 1930 through 1956 for use as laboratory standards. The data indicated that there was considerable variation between individual thermometers and that scale corrections obtained over a given interval for a particular thermometer were not sufficient to predict whether or not more calibration points were required. The above studies were made with only a few of the many types of thermometers submitted to NBS for calibration, and may not necessarily be

applicable to other types. Experience with a particular type of thermometer seems to be the most reliable guide in the choice of its calibration points.

If a thermometer is submitted to NBS for calibration and the calibration points are not specified on

the purchase order, it will be tested at a reference point and at intervals of approximately every 100 scale divisions. A calibration should never consist of fewer than two points on the main scale, and should always be tested at a reference point, whether on the main scale or on an auxiliary scale.

A listing of tolerances and expected accuracies for common types of liquid-in-glass thermometers, which are accepted for calibration, are given in tables 5 through 12. The scale tolerances shown are chosen to be indicative of good manufacturing practice. When a thermometer is manufactured, small errors in pointing (marks placed on a blank thermometer at various temperatures to be used as guides for the placement of the graduation lines) and graduating are inevitable. These graduation marks are also subject to variations due to the inherent properties of the glass. The tolerances must be sufficiently restrictive to insure a satisfactory high-grade thermometer, and at the same time not cause undue manufacturing difficulties.

In addition to the scale tolerance limit, the error in any temperature interval should not exceed 5 percent of the nominal value of the interval. The purpose of this requirement is to eliminate thermometers having large corrections of alternating signs, which lead to uncertainties in the interpolation of scale corrections. between the calibration points.

The word "accuracy" used in these tables refers to the best values attainable in the use of thermometers when all corrections are applied. The accuracy bounds may seem broad in some instances, but the definite limitations of liquid-in-glass thermometry become ap parent when all factors are considered. For example, if the scale is expanded by reducing the diameter of the capillary, a practical limit is reached beyond which capillary forces, in combination with the elasticity of the thermometer bulb, will prevent a smooth advance or retreat of the mercury column. The movement of the mercury meniscus may be erratic and occur in steps appreciably large in comparison to the graduation interval. This is particularly true when the temperature of the medium is decreasing. Less rigid bulbs (relatively large diameters and/or thin walls), as well as capillaries of small diameters, may cause large "meniscus jumps." Excessively elliptical ⠀ or flattened bores are not recommended for the same reason. Therefore, increasing the length of a degree on the scale, for practical bulb sizes, improves thermometric performance only to a certain point. Beyond this point precision of reading may readily be mistaken for accuracy in temperature measurement. A study of the effects of bulb and capillary dimensions on thermometer performance, made by Hall and Leaver [10], provides valuable guidelines for design purposes.

Other factors such as ice-point changes, unless exactly accounted for, and differences in external pressure may also account for inaccuracies much greater than the imprecision with which a scale having 0.1 or 0.2 degree graduations may be read.

6.1. Total-Immersion Thermometers Thermometers pointed and graduated by the manufacturer to indicate correct temperatures when the bulb and the portion of the stem containing the thermometric liquid are subjected to the temperature being measured are known as total-immersion thermometers. While these thermometers are designed for immersion of all the mercury, it is not desirable to immerse the portion of the stem above the meniscus. The heating of this portion to high temperatures could cause excessive gas pressures resulting in erroneous readings and possibly permanent damage to the bulb.

In practice, a short length of the mercury column often must be left emergent from the bath or medium being measured so that the meniscus is visible. If the temperature difference between the bath medium and its surroundings is large, an appreciable temperature gradient may exist around the thermometer stem near the surface of the bath. This condition becomes more serious when a total-immersion thermometer is intentionally used at partial immersion. If either situation exists, an emergent stem correction, as explained in section 5.3b, will be necessary. The correction may be as large as 20 Celsius degrees (36 Fahrenheit degrees) if the length of the emergent liquid column and the difference in temperature between the bath and the space above it are large. Tolerances and accuracies expected of total-immersion thermometers are given in tables 5 and 6.

6.2. Partial-Immersion Thermometers

In many instances the use of a total-immersion liquid-in-glass thermometer for temperature measurements is inconvenient or impossible. For this reason partial-immersion thermometers are designed with scales graduated to indicate correct temperatures when the thermometers are immersed to specified depths. Unless otherwise stated, each Report of Calibration issued by NBS gives corrections which are applicable for temperatures prevailing above the comparison baths. No stem temperature correction is necessary when