where P1 is the pressure at t°; P0 the pressure at 0°; and b the coefficient of pressure; that is, the increase in unit pressure at 0° for a rise in temperature of 1°. Thus if P0 = 76 cms.; b = 0·00367; height of mercury in cistern above A = 55·8 cms.; then
P1 = (76 + 55·8) = 131·8 cms.,
and by inserting these values in the above equation t is found to be 200°. In the instrument described, P0 is equal to the height of the barometer, since the tap C is open whilst the bulb is immersed in ice. The coefficient of pressure may be determined by placing the bulb in steam at a known temperature, and noting the increased pressure. In the equation given, P1, P0, and t are then known, and the value of b may be calculated.
Fig. 1.—Constant Volume Air Thermometer.
In using this instrument for exact determinations of temperature, allowance must be made for the expansion of the bulb, which causes a lower pressure to be registered than would be noted if the bulb were non-expansive. Again, the gas in the connecting tube is not at the same temperature as that in the bulb; an error which may be practically eliminated by making the bulb large and the bore of the tube small. The temperature of the mercury column must also be allowed for, as the density varies with the temperature. When the various corrections have been made, readings of great accuracy may be secured.
When applied to the measurement of high temperatures, the bulb must be made of a more infusible material than glass. Gold, porcelain, platinum, and quartz have been used by different investigators, but the most reliable material for temperatures exceeding 900° C. has been found to be an alloy of platinum with 20 per cent. of rhodium. The most suitable gas to use inside the bulb is nitrogen, which is chemically inert towards the materials of the bulb, and is not absorbed by the metals mechanically. When measuring high temperatures with this instrument, a considerable pressure, amounting to 1 atmosphere for every increase of 273 degrees above the ice point, is requisite to prevent expansion of the nitrogen; and this pressure tends to distort the bulb and so to falsify the indications. This trouble has been overcome by Day, who surrounded the bulb by a second larger bulb, and forced air or nitrogen into the intervening space until the pressure on the exterior of the thermometer bulb was equal to that prevailing in the interior. Even then it was not found possible to secure higher readings than 1550° C., as the bulb commenced to alter in shape owing to the softening of the material. This temperature represents the highest yet measured on the gas scale; but by using a more refractory material, such as fused zirconia, it may be found possible to extend this range to 2000° C. or more. Experiments in this direction are very desirable, in order that high-reading pyrometers may be checked directly against the gas scale.
Fixed Points for Calibration of Pyrometers.—It is evident that the gas thermometer is totally unsuited for use in workshops or laboratories when a rapid determination of a high temperature is required. Its function is to establish fixed points or temperature standards, by means of which other instruments, more convenient to use, may be graduated so as to agree with each other and with the gas scale itself. The temperature scales of all modern pyrometers are thus derived, directly or indirectly, from the gas thermometer. In the table on next page, a number of fixed points, determined by various observers, is given; the error, even at the highest temperatures, probably not exceeding ±2° C.