The mean value is 1 / 381,100,000, with a probable error of 10.36 per cent of the quantity involved. Upon other occasions I have obtained exhaustions of 1 / 373,134,000 and 1 / 388,200,000. Of course in these cases a gauge-correction was applied; the highest vacuum that I have ever obtained irrespective of a gauge-correction was 1 / 190,392,150. In these cases and in general, potash was employed as the drying material; I have found it practical, however, to attain vacua as high as 1 / 50,000,000 in the total absence of all such substances. The vapor of water which collects in bends must be removed from time to time with a Bunsen burner while the pump is in action. It is evident that the final condition of the pump is reached when as much air leaks in per unit of time as can be removed in the same interval. The total average leakage per ten minutes in the pump used by me, when at rest, was 0.000211 cubic millimeter at press. 760 mm. Let us assume that the leakage when the pump is in action is four times as great as when at rest; then in each ten minutes 0.000844 cubic millimeter press., 760 mm., would enter; this corresponds in the pump used by me to an exhaustion of 1 / 124,000,000; if the rate of the pump is such as to remove one-half of the air present in ten minutes, then the highest attainable exhaustion would be 1 / 248,000,000. In the same way it may be shown that if six minutes are required for the removal of half the air the highest vacuum would be 1 / 413,000,000 nearly, and rates even higher than this have been observed in my experiments. An arrangement of the vacuum-bulb whereby the entering drops of mercury would be exposed to the vacuum in an isolated condition for a somewhat longer time would doubtless enable the experimenter to obtain considerably higher vacua than those above given. _Exhaustion obtained with a plain Sprengel Pump._--I made a series of experiments with a plain Sprengel pump without stopcocks, and arranged, as far as possible, like the instrument just described. The leakage per hour was as follows: Duration of the Leakage per hour in experiment. cubic mm. at press. 760 mm. 22 hours 0.04563 2 days 0.04520 2 days 0.09210 4 days 0.06428 ------- Mean 0.06180 Using the same reasoning as above we obtain the following table Time necessary for removal Greatest attainable of half the air. exhaustion. 10 minutes 1 / 5,000,000 7.5 minutes 1 / 7,000,000 6.6 minutes 1 / 12,000,000