Humboldt State University ® Department of Chemistry

Robert A. Paselk Scientific Instrument Museum

The following instructions have been taken, with minor editing, from: Minor, Ralph S. Physical Measurements: A Laboratory Manual in General Physics for Colleges. Part II: Heat, Mechanics and Properties of Matter. Berkeley, Calif. (1919) pp. 26-30.
Copyright © 1998 Richard A. Paselk
Prior to modern manufacturing methods uniform tubing (todays precision bore tubing) was not generally available. Thus the following proceedures for calibration in which determining the uniformity of the tubing is a major portion.

To plot a curve from which the true temperature may be obtained corresponding to each scale-reading of a given mercurial thermometer.
Such a curve is called the calibration curve of the thermometer. The process of obtaining it is absolute since it does not involve comparison with a standard thermometer. This process consists, first, in determining the absolute corrections for two separate scale-readings on the thermometer, preferably near its fixed points, that is, the points on its scale corresponding to the temperature of melting ice and the temperature of water boiling under standard pressure. The thermometer tube between the two points is then calibrated because of the possibility that its bore may not be uniform, and the relative corrections thus determined are superimposed graphically upon the correction curve resulting from the absolute corrections at or near the two fixed points.
(a) Calibration of the Tube.--Break off a portion of the thread of mercury about ten degrees in length. For this purpose, first invert the thermometer and let enough mercury flow into the small cistern to fill it about half full; then, holding the thermometer in a horizontal position, tap or jar it lightly lengthways to break the mercury in the small cistern loose from the rest. The mercury in the stem will now flow back into the bulb and leave the stem free for the thread of mercury which must be jarred loose from the mercury in the small cistern.
Ask for assistance, if necessary. Jar the lower end of the thread to the zero-point of the scale and read the position of the upper end (which will be near the 10° mark) to tenths of a degree. Then jar the lower end of the thread to the 10° mark and read the upper end. Repeat with the lower end at the successive points 20°, 30°, 40°, etc., up to 90°. Then take the readings in the reverse order, setting the upper end of the thread successively at 100°, 90°, etc., down to 10°, and reading the position of the lower end each time. The object of these readings is to find the length of the thread in each of the ten intervals between 0° and 100°; by means of the two series it is possible to find the average value of the length of the thread for each interval.
(b) Correction at the Lower Fixed Point.--Put the thermometer through the cork in a test-tube, having filled the latter about half full of distilled water. Place the tube in a freezing mixture of shaved ice and salt, and stir the water around the thermometer until it begins to freeze. Read the thermometer. By warming the tube in the hand and repeating the freezing process, obtain several readings.
(c) Correction Near the Upper Fixed Point.--Place the thermometer through the cork in the tube at the top of the boiler, with the bulb well above the surface of the water. Boil the water so that the steam issues freely, but not with any perceptible pressure, from the vent. Read the thermometer when it becomes steady. Allow the boiler to cool slightly, and repeat, making three readings in all. If the instrument be provided with a water-manometer, take the manometer-reading simultaneously with the temperature-reading. Read the barometer.
(d) Let the thermometer cool slowly to about the temperature of the room, and repeat (b). If the freezing point observed now is different from that observed in (b), use the mean of the two values in the calibration that follows.
(e) Assume that the temperature of freezing water is O°C. From the Tables take the true boiling-point temperature for the pressure observed in (c), find the corrections of the thermometer for the scale-readings observed in (b) and (c). Record these two corrections by points on coordinate paper, having as abscissae the
scale-readings of the given thermometer in degrees, and as ordinates the corresponding corrections in tenths of a degree but on a magnified scale. (See Fig. 2). Corrections should be plus (+) if they are to be added to the observed to give the true temperatures, minus (-) if they are to be subtracted.
Connect these two points by a straight line. The ordinate of this straight line at any point gives the correction of the thermometer at that scale-reading on the assumption that the bore of the thermometer is uniform throughout the whole range. In general this assumption is not justified, and there must be added to this correction at each point another correction due to the inequalities of the diameter of the bore. In order to find the bore correction, proceed as follows. Determine the mean length of the thread in all of its different positions. If the bore were uniform, each of the observed lengths would equal this mean value. From the deviation between the observed and mean thread lengths, calculate the length which a thread whose mean length was exactly ten degrees would have when placed in the first interval. This would be in the same ratio to the observed thread length as ten degrees is to the mean thread length. We will call this the reduced thread length. An actual rise of exactly ten degrees in temperature will produce an apparent rise equal to this amount. The difference between this reduced thread length and ten degrees when the sign is reversed, gives the bore correction for a temperature of approximately ten degrees. Proceed similarly with each interval. The total correction which must be applied at any point of the scale is found, by adding together the corrections for all the intervals below that point. Since, by definition, the mean thread length is one tenth the sum of all the observed thread lengths, the total bore correction at 100° will necessarily be zero. The sample set of data given below will illustrate the method. l is the observed thread length in a given interval, which may be an average of several determinations. L is its mean value for all intervals; r is the reduced thread length in a given interval. Its mean value is ten degrees. 10 - r gives the correction for each interval, and the sum of all such corrections gives the total at a certain point of the scale.
Intervals Average l r Dif.(10-r) Bore-Corrections
1st 14.16 10.01° -0.01° At 0°= .00°
2nd 14.25 10.07 -.07° " 10°=-.010
3rd 14.27 10.09° -.09° " 20°=-.O8°
4th 14.42 10.19° -.19° " 30°=-.17°
5th 14.27 10.09° -.09° " 40°=-.36°
6th 14.13 9.99° +.01° " 50°=-.45°
7th 14.13 9.99° +.01° " 60°-.44°
8th 14 9.89 +.11° " 70°=-.43°
9th 14 9.89 +.11° " 80°=-.32°
10th 13.85 9.79° +.21° " 90°=-.21°
Mean = 14.15°= L 10.00° " 100° = .00°
The curve showing the resultant corrections for all scale-readings from 0 to 100 can therefore be obtained by super-imposing the bore-corrections just found upon the line drawn to show the corrections due to the errors in the fixed points. For this purpose plot points whose abscissae are 10°, 20°, 30°, etc., and whose corresponding ordinates are found by measuring from the slanting line, already drawn, distances equal to the corresponding bore- corrections--measuring up or down from this line according as the corrections are plus or minus. The smooth curve, which should now be drawn through these plotted points, is the calibration curve of the thermometer.
What are the true temperatures corresponding to the scale-readings 0°, 25°, 50°, 75° and 100° on the given thermometer ?

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Last modified 22 July 2000