This section is from "Scientific American Supplement Volumes 275, 286, 288, 299, 303, 312, 315, 324, 344 and 358". Also available from Amazon: Scientific American Reference Book.
The cylinder into which the gauge-tube dips is first elevated by a box sufficiently thick merely to close the gauge, afterwards boxes are placed under it sufficient to elevate the mercury to the base of the measuring tube; when the mercury has reached this point, thin boards and card-boards are added till a suitable pressure is obtained. The length of the inclosed cylinder of air is then measured with the cathetometer, also the height of the mercurial "meniscus," and the difference of the heights of the mercurial columns in A and B, figure 4. To obtain a second measure an assistant removes some of the boxes and the cylinder is lowered by hand three or four centimeters and then replaced in its original position. In measuring really high vacua, it is well to begin with this process of lowering and raising the cylinder, and to repeat it five or six times before taking readings. It seems as though the mercury in the tube, B, supplies to the glass a coating of air that allows it to move more freely; at all events it is certain that ordinarily the readings of B become regular, only after the mercury has been allowed to play up and down the tube a number of times. This applies particularly to vacua as high 1/50,000,000 and to pressures of five millimeters and under. It is advantageous in making measurements to employ large pressures and small volumes; the correct working of the gauge can from time to time be tested by varying the relations of these to each other. This I did quite elaborately, and proved that such constant errors as exist are small compared with inevitable accidental errors, as, for example, that there was no measurable correction for capillarity, that the calculated volume of the "meniscus" was correct, etc. It is essential in making a measurement that the temperature of the room should change as little as possible, and that the temperature of the mercury in the cylinder should be at least nearly that of the air near the gauge-sphere. The computation is made as follows
n = height of the cylinder inclosing the air; c = a factor which, multiplied by n, converts it into cubic millimeters; S = cubic contents of the meniscus; d = difference of level between A and B, fig. 4; = the pressure the air is under; N = the cubic contents of the gauge in millimeters; x = a fraction expressing the degree of exhaustion obtained; then
x=1/([N (760/d)]/[nc - S])
It will be noticed that the measurements are independent of the actual height of the barometer, and if several readings are taken continuously, the result will not be sensibly affected by a simultaneous change of the barometer. Almost all the readings were taken at a temperature of about 20° C., and in the present state of the work corrections for temperature may be considered a superfluous refinement.
It is necessary to apply to the results thus obtained a correction which becomes very important when high vacua are measured. It was found in an early stage of the experiments that the mercury, in the act of entering the highly exhausted gauge, gave out invariably a certain amount of air which of course was measured along with the residuum that properly belonged there; hence to obtain the true vacuum it is necessary to subtract the volume of this air from nc. By a series of experiments I ascertained that the amount of air introduced by the mercury in the acts of entering and leaving the gauge was sensibly constant for six of these single operations (or for three of these double operations), when they followed each other immediately. The correction accordingly is made as follows: the vacuum is first measured as described above, then by withdrawing all the boxes except the lowest, the mercury is allowed to fall so as nearly to empty the gauge; it is then made again to fill the gauge, and these operations are repeated until they amount in all to six; finally the volume and pressure are a second time measured. Assuming the pressure to remain constant, or that the volumes are reduced to the same pressure,
v = the original volume; v' = the final volume; V' = volume of air introduced by the first entry of the mercury; V = corrected volume; then
V' = (v'-v)/6 V = v - [(v'-v)/6]
It will be noticed that it is assumed in this formula that the same amount of air is introduced into the gauge in the acts of entry and exit; in the act of entering in point of fact more fresh mercury is exposed to the action of the vacuum than in the act exit, which might possibly make the true gauge-correction rather larger than that given by the formula. It has been found that when the pump is in constant use the gauge-correction gradually diminishes from day to day; in other words, the air is gradually pumped out of the gauge-mercury. Thus on December 21, the amount of air entering with the mercury corresponded to an exhaustion of
1/27,308,805 .......Dec. 21.
1/38,806,688 ...... Dec. 29.
1/78,125,000 .......Jan. 15.
1/83,333,333 .......Jan. 23
1/128,834,063 ......Feb. 1.
1/226,757,400 ..... Feb. 9.
1/232,828,800 ..... Feb. 19.
1/388,200,000 ......March 7.
That this diminution is not due to the air being gradually withdrawn from the walls of the gauge or from the gauge-tube, is shown by the fact that during its progress the pump was several times taken to pieces, and the portions in question exposed to the atmosphere without affecting the nature or extent of the change that was going on. I also made one experiment which proves that the gauge-correction does not increase sensibly, when the exhausted pump and gauge are allowed to stand unused for twenty days.