## Abstract

The most satisfactory primary pressure gauge for measuring low pressures is the open mercury column, but, for pressures above about 30b, the practical difficulties caused by the great height of such a column preclude its use (1 bar, abbreviated b = 10$^{6}$ dyn/cm$^{2}$). In order to calibrate free-piston gauges at higher pressures, a column of 'reduced height' has been designed and constructed which will measure static pressures up to 2500b with an accuracy of $\pm $0$\cdot $15 b at the maximum pressure. This consists of a mercury-in-steel column about 900 cm tall, connected to steel end-blocks at both extremities. Two oil lines containing liquid paraffin are used to transmit pressure to the top and the bottom of the column, the position of the mercury-oil interfaces being located by electrical contacts fixed in the end-blocks. The vertical distance between the two mercury menisci is obtained from the distance between the exposed ends of the insulated plugs which obturate the contacts. This height is measured to $\pm $0$\cdot $013 cm by a calibrated Invar tape, with the aid of suitable levels for making a horizontal transfer from each reference point to the tape. The mercury column and the oil line connected to the upper end-block are enclosed in a well-lagged jacket, through which water is circulated from a thermostatically controlled tank maintained at 25 degrees C. The mean temperature of the column which is known to $\pm $0$\cdot $02 degrees C is estimated from the temperature of the water, measured by mercury-in-glass thermometers as it enters and leaves the jacket. A high-pressure valve manifold connected to the two oil lines enables the pressure at the top or the bottom of the column to be transmitted to one or other of two sensitive free-piston gauges. In operation, the pipe line connected to the top of the column is first opened to atmospheric pressure, and a free piston gauge is connected to the foot of the column. The pressure balanced by this gauge, which may be calculated from the hydrostatics of the system, is then reproduced at the top of the column by oil pressure, with the same free-piston gauge now connected to the top oil line. The second free-piston gauge is then connected to the foot of the column, and the pressure at which it is balanced is equivalent to the pressure at the foot during the first operation, plus the pressure due to the mercury column itself. By repeated interchanges of the two free-piston gauges, the pressure is increased to 2500b in increments of pressure equivalent to the pressure drop across the column, which is about 11$\cdot $5 b. The accurate calculation of the pressure drop across the column, as a function of pressure, requires a knowledge of the compressibility of mercury and of the liquid paraffin. The results for the compressibility of mercury obtained previously by both static and dynamic measurements are compared, and it is shown that there are large discrepancies between the results obtained by various authors. Possible sources of error in the experimental methods are briefly discussed, and by correlating the most reliable results an equation is developed which expresses the compression of mercury at 25 degrees C as a function of pressure up to 3000b. Measurements of the compressibility of liquid paraffin with a re-entrant type Pyrex glass piezometer are described and values of the compression are tabulated at 15, 20 and 25 degrees C, and pressures up to 2500b. The compression of pure benzene was also measured at 25 and 40 degrees C, and pressures up to 1000b, using the same apparatus, in order to ensure that there were no large systematic errors in the method. The average difference between these values and those obtained by previous workers is about 0$\cdot $7%. Since benzene readily absorbs moisture from the air, it was distilled into the piezometers under vacuum using an apparatus which is briefly described. Detailed consideration is given to the random experimental errors and to possible systematic errors in the measurement of the pressure drop across the column, and in the determination of an absolute pressure using the primary pressure gauge. It is shown that the standard deviation of the pressure drop, 1$\cdot $1 $\times $ 10$^{-3}$ b at 2000b, arises principally from the uncertainty in the compressibility of liquid paraffin and mercury. On the other hand, the accuracy of the absolute pressure measurements depends in part on the error in the measurement of the pressure drop, but chiefly on the accuracy with which the pressures can be transferred from the bottom to the top of the column. The transfer error arises from uncertainty as to the temperature of the piston and the sensitivity of the free-piston gauges. With the gauges described, it is shown that the standard deviation of the pressure measurement at 500b should be about $\pm $0$\cdot $015 b (one part in 34000), and at 2500 b $\pm $ 0$\cdot $14 b (one part in 18000).