Thermometry

Correction of the Fundamental In

terval.—The thermometer to be tested is exposed to steam condensing at atmos pheric pressure in an apparatus which is often called a "hypsometer," constructed with double walls to protect the inner tube containing the thermometer from any cooling by radiation. The standard atmos pheric pressure at which the temperature of the steam is by definition equal to oo° C is equivalent to that produced by a column of mercury 76o millimetres high, having a density of 13.5951 at a place where the acceleration of gravity is 980.665 giving a pressure equal to 1,013,250 The atmospheric pressure at the time of observation is reduced to these units by applying the usual corrections for temperature and gravitation. If the pressure is near 76o mm., the temperature of the steam may be deduced by assuming that it increases at the rate of I° C for 27.2 mm. of pressure. The following approximate formula for the temperature t of steam in terms of pressure p in inm. has been adopted for the range between 68o and 78o mm.

t= ioo+ 0.0367(p-76o) (4) A convenient type of hypsometer is shown in fig. 1. The boiler B is separate from the steam-jacket A surrounding the thermom eter. A gauge G is provided for indicating the steam pressure (difference from atmospheric) and a condenser C for returning the condensed steam to the boiler. The thermometer is observed by the microscope M.

If the barometer has a brass scale correct at o° C, and p be the reading in millimetres, the correction for temperature is made approximately by subtracting 0.00163 p mm.

If L is the latitude and M the height of the station in metres above the sea-level, the correction for gravitation is approximately made by subtracting (0.0026 cos 2L-Po.0000002M) p.

The zero of the thermometer is observed immediately after the steam point. If n be the interval in degrees of the scale between the two observations, and if be the temperature of the steam, the fundamental interval of the thermometer may be as Ioo provided that is nearly ioo° C. Since all the readings of a thermometer have to be corrected for the error of the funda mental interval, by dividing by the fundamental interval thus observed and multiplying by i oo, it is a matter of some con venience in practice to have the instrument graduated so that the difference between the readings in ice and at oo° C is very nearly Ioo° of the stem. The correction can then be applied as a small percentage independently of the other corrections. The method of determining the fundamental interval above described applies to all other kinds of thermometers, except that it is not generally necessary to observe the zero after the steam point. The tempera ture of the steam should be expressed in the scale of the ther mometer tested, if the scale differs appreciably from that of Regnault.

Pressure Correction.

The corrections for variations of in ternal and external pressure on the bulb are of some importance in accurate thermometry, but can be applied with considerable certainty at moderate temperatures. The correction for external pressure is assumed to be proportional to the change of pressure, and to be independent of the temperature. It is generally deter mined by enclosing the thermometer to be tested in a vessel of water, and observing the change of reading produced by varying the pressure. The correction is generally between one and two thousandths of a degree per centimetre of mercury change of pressure, but must be determined for each thermometer, as it depends on the nature of the glass and on the form and thickness of the walls of the bulb. The coefficient of the correction for internal pressure is greater than that for external pressure by the difference between the compressibility of mercury and that of glass, and may be calculated from it by assuming _ this relation. If b1, are the external and internal coefficients, expressed in degrees of temperature per centimetre of mercury, we have the relation bi=b0+0.00015, degrees per cm. of mercury. (5) The coefficient of internal pressure can also be determined by taking readings in the horizontal and vertical positions when the thermometer is at some steady temperature such as that of ice or steam. The reading of the thermometer is generally reduced to an external pressure of one standard atmosphere, and to an internal pressure corresponding to the horizontal position. It is also

possible to include the internal pressure correction in the scale correction, if the thermometer is always read in the vertical posi tion. In addition to the variations of internal pressure due to the column of mercury in the stem, there are variations due to capil larity. The internal pressure is greater when the mercury is rising than when it is falling, and the reading is depressed to an extent depending on the fineness of the bore and the thinness of the walls of the bulb. The capillary pressure does not depend Only on the bore of the tube, but also apparently to an even greater extent on the state of the walls of the tube. The least trace of dirt on the glass or on the mercury is capable of producing capillary pressures much greater than would be calculated from the diameter of the tube. Even in the best thermometers, when there are no in equalities of bore sufficient to account for the observed variations, it is seldom found that the mercury runs equally easily in all parts of the stem. These variations of capillary pressure are somewhat capricious, and set a limit to the order of accuracy attainable with the mercury thermometer. It appears that the difference of read ing of a good thermometer between a rising and falling meniscus may amount to five or ten thousandths of a degree. The difference may be reduced by continuous tapping, but it is generally best to take readings always on a rising column, especially as the varia tions in the angle of contact, and therefore in the capillary pres sure, appear to be much smaller for the rising meniscus. In ordinary work the zero reading and the steam reading would both generally correspond to a falling meniscus ; the former necessarily, the latter on account of the phenomenon of the temporary de pression of zero, which causes the thermometer to read higher during the first moments of its exposure to steam than it does when the expansion of the bulb has reached its limit. It is easy to secure a rising meniscus at the steam point by momentarily cool ing the thermometer. At the zero point the meniscus generally begins to rise after five or ten minutes. The question, however, is not of much importance, as the error, if any, is regular, and the correction for capillarity is necessarily uncertain.

Stem-exposure Correction.—When the bulb of a mercury thermometer is immersed in a bath at a temperature t, and a part of the column of mercury having a length of n degrees is exposed to a lower temperature t2, the reading of the thermometer will be lower by aXnX (t—t2) degrees (nearly) than it would have been if the whole of the mercury and stem had been at the temperature t. The factor a in this expression is the apparent coefficient of ex pansion of mercury in glass, and varies from .000150 to .000165 for different kinds of glass. In order to apply this correction, it is usual to observe t2 by means of an auxiliary "stem-thermometer" with its bulb placed near the middle of the emergent column n. Occasionally stem-thermometers with long thin bulbs are em ployed to give more nearly the average temperature of the whole emergent column. Owing to conduction along the stem of the thermometer, and to heated vapours near the bath, the mean temperature determined in this manner is generally too low. To allow for this empirically, an arbitrary reduction is often made in the value taken for n or a, but this cannot be regarded as satis factory for work of precision. The only practical method of re ducing the correction is to limit the number of degrees n exposed, or, in other words, to work with thermometers of "limited range." Each of these thermometers must then be corrected by comparison with a standard thermometer free from stem-exposure correction, such as a platinum-resistance thermometer. To secure results of any value the correction must be determined at each point under the actual conditions of observation under which the thermometer is to be used. In work of precision it is necessary to use ten or twenty thermometers to cover a range of 300°, as this is the only method of securing an open scale and reasonable accuracy as regards stem-exposure.