Average.................... 0.001266 I endeavored to locate this leakage, and proved that one-quarter of it is due to air that enters the gauge from the top of its column of mercury, thus: Duration of the Gauge-leakage per hour experiment. in cubic mm., press. 760 mm. 18 hours.................................0.0002299 7 days..................................0.0004093 7 days..................................0.0003464 Average.......................0.0003285 This renders it very probable that the remaining three quarters are due to air given off from the mercury at B, Fig. 4, from that in the bends and at the entrance of the fall-tube, _o_, Fig. 3. Further on some evidence will be given that renders it probable that the leakage of the pump when in action is about four times as great as the total leakage in a state of rest. The gauge, when arranged for measurement of gauge-leakage, really constitutes a barometer, and a calculation shows that the leakage would amount to 2.877 cubic millimeters per year, press. 760 mm. If this air were contained in a cylinder 90 mm. long and 15 mm. in diameter it would exert a pressure of 0.14 mm. To this I may add that in one experiment I allowed the gauge for seven days to remain completely filled with mercury and then measured the leakage into it. This was such as would in a year amount to 0.488 cubic millimeter, press. 760 mm., and in a cylinder of the above dimensions would exert a pressure of 0.0233 mm. _Reliability of the results: highest vacuum._ The following are samples of the results obtained. In one case sixteen readings were taken in groups of four with the following result: Exhaustion. 1 / 74,219,139 1 / 78,533,454 1 / 79,017,272 1 / 68,503,182 Mean 1 / 74,853,449 Calculating the probable error of the mean with reference to the above four results it is found to be 2.28 per cent of the quantity involved. A higher vacuum measured in the same way gave the following results: 1 / 146,198,800 1 / 175,131,300 1 / 204,081,600 1 / 201,207,200 The mean is 1 / 178,411,934, with a probable error of 5.42 per cent of the quantity involved. I give now an extreme case; only five single readings were taken; these corresponded to the following exhaustions: 1 / 379,219,500 1 / 371,057,265 1 / 250,941,040 1 / 424,088,232 1 / 691,082,540