the readings were reduced to comparable measure by comparison with a long-range electrometer which I had made for the most part according to Thomson's description.

It was found that 6 of the units in which in the following the differences of potential are expressed correspond to a potential-difference of about 5 Daniells. I would not, however, lay too much stress upon these data, since the battery at my disposal was too small to enable me to accomplish a more accurate determination.

Now, if we assume that the Holtz-machine electrode which is connected with the gas-pipes conducts away negative electricity, the positive electricity issuing from the other electrode finds two paths-the first through the rheostat to the gaspipes, and the second through the discharge-apparatus and the galvanometer, likewise to the gas-pipes. The quantity of electricity which passes through the discharge-apparatus can now be varied within wide limits by altering the resistance of the rheostat. The galvanometer indicates this quantity; and the electrometer measures the difference of potential between the point and the plate.

=

I soon observed that the discharge does not take place with every difference of potential, but that rather a perfectly fixed difference is always necessary in order to induce it. If at the commencement of the experiment the resistance of the rheostat has been made nearly 0 (when of course the deflections of the galvanometer and electrometer are likewise = 0), and if now the resistance be gradually increased, on the electrometer indeed a steady rise of the potential will be observed, but the potential must have reached a certain value before the galvanometer will show, by a sudden, proportionally great, and constant deflection (if the resistance of the rheostat remains invariable), that the discharge has commenced. When once the discharge is present the resistance of the rheostat and consequently the potential can be again diminished, through which the discharge, it is true, steadily decreases, but does not at once sink to zero. Only with a considerably less potentialdifference than that with which the discharge commenced does it again entirely cease.

I found, further, that the commencement of the discharge was dependent on many collateral circumstances, e. g. whether a discharge had taken place a shorter or a longer time previously; unavoidable dust particles, too, have probably an influence. On the other hand, determinations of the difference of potential at which the discharge ceases, derived from different experiments separated from one another by considerable

intervals of time, gave values which agreed excellently with each other. I resolved on this account, at least preliminarily, to direct my attention chiefly to the determination of this difference of potential, which we will name the minimum potential-difference, and, for brevity, denote by M. P.

The moment when the discharge ceases is, for the most part, characterized by this-that the already much diminished galvanometer-deflection (amounting to only 2-4 scale divisions), after a further very slight lessening of the resistance in the rheostat, suddenly becomes zero. At this instant the M. P. is read off at the electrometer. I am inclined to account for this phenomenon by the small variations which the potential undergoes notwithstanding the insertion of the Leyden jars. The electrometer, which is provided with a powerful damper, gives the mean value of the variations of the potential. The fact that the discharge had now really ceased I verified also in another way: that is to say, if the galvanometer was made considerably more sensitive by being rendered more perfectly astatic, its deflection vanished at exactly the same difference of potential as before; in like manner an electroscope, which instead of the galvanometer was connected with the plate in the discharge-apparatus, was not charged, and the characteristic star-shaped luminous appearance visible in the dark, which was present during the discharge, disappeared when the M.P. was attained.

In all the following experiments the distance of the point from the plate remained the same. Further, the temperature was constant, at least in those experiments which were to be compared with one another; and, lastly, it is to be noticed that the point was always positive when the contrary is not expressly stated.

Unfortunately, the investigation had to be interrupted, first because the seasons of spring and summer are very unsuitable for working with static electricity, and secondly because for its continuation the reconstruction of some of the apparatus, especially of the electrometer, had become absolutely necessary. Consequently, of the many questions which might be put, only a few can be answered. The results are given below.

1. How does the M. P. in a gas depend on the pressure? The question was repeatedly answered for dry air free from carbonic acid. Fig. 1 represents the result of one experiment: the pressures in millims. of mercury were laid down as abscissæ, and the M. P. as ordinates. The unit in which the latter are expressed is not directly comparable with that mentioned above.

Pressure in millims.
of mercury
M. P.....

615 544 499 445 385 266 198 138 68 29 10-9 7-1 639 602 577 547 503 439 402 361 301 258 198 189

It follows from these experiments that with pressures above 200 millims. the increase of the pressure is at least nearly pro

portional to the increase of the M. P.; below that limit the M. P. diminishes much more quickly in proportion. Similar ratios were found with other gases.

2. How, in a gas which is subjected to a fixed pressure, is the quantity of electricity discharged connected with the difference of potential between the point and the plate?

=

Dry air, free from carbonic acid, was tried with the pressures 391, 294, 203.4, 109.7, and 51.8 millims. mercury. The highest difference of potential which could be determined with my electrometer was 3684 units (6 units 5 Daniells); the greatest quantity of electricity that could be measured amounted to something over 500 arbitrarily chosen units. The following Tables contain in the first column the differences of potential, in the second the corresponding amounts of electricity discharged; and in the third I have given, under the name of "disposable potential-differences," the differences between the numbers in the first column and the M. P. corresponding to each pressure, the quantity of electricity discharged being of course 0. I have calculated these differences, and given them the name above mentioned, because possibly the view is

=

correct that the M.P. is compelled to overcome a certain transitional resistance, and that only the disposable potential-difference measures the quantity discharged. The latter shall, for shortness, be denoted by D. P.

The first of these Tables, corresponding to the pressure 51.8, is graphically represented in fig. 2; the abscissæ denote the quantities discharged, the ordinates the D. P. The curves for the other pressures have a similar form.

3. In a gas with a determined difference of potential, in what manner does the amount of electricity discharged depend upon the pressure? Dry air, free from carbonic acid, with the potential-difference 3684, was examined in detail.

Pressure in millims. of mercury 641-2 466-4 391-0 294-0 203-4 109-7 Amount of electricity discharged 0 41.5 65 105 192 522

This Table is graphically represented in fig. 3; the abscissæ denote the amounts of electricity discharged, the ordinates the pressures. Other gases behaved similarly.

In these experiments, as already mentioned, the difference of potential was constant. But as, according to No. 1, with different pressures the discharge ceases and commences respec

tively at different potential-differences, the D. P. were not the same; it was consequently still questionable whether any

simple relation subsisted between pressure and electricity discharged, if with different pressures not the absolute but the disposable potential-difference was found constant. The question can be answered from the data of No. 2. I have extracted from the Tables the following comparison, valid for the D. P. =1000:

391 294 203-4 109-7 51.8 71 79 106 194 450

In fig. 4 will be found the graphic representation. A simple relation is not perceptible. To be sure the product of the pressure into the quantity of electricity for the last four pressures is nearly constant; but with the pressure 391 there is a considerable deviation from this rule. For the purpose of fully answering questions 2 and 3, experiments with different gases, between wider limits of the potential-differences, the pressures, and the quantities of electricity discharged, will be absolutely necessary.

4. Does an expressible relation exist between the minimum difference of potential and the nature of the various gases in which the discharge takes place ?

The gases were all tried at two pressures, approximately 205 and 110 millims. mercury; experiments with higher pressures