theory leads-as previously shown by Mr. Drude *-to the equation †

where g is the coefficient of extinction, v the index of refraction of the metals for normal incidence. This equation, which is only approximately correct, shows that the index of refraction and the extinction coefficient are numerically equal for long waves.

Besides

R=100(1–3)=100(1 —

therefore

g=v=

200 100-R'

Consequently both values are definable from the emissionpower alone.

7. A further consequence, resulting from the agreement of our researches with the electromagnetic theory of light, deserves special mention. Besides abstract numbers, the theoretical computation of the constant C contains only the velocity of light and the wave-length, both of which can be determined by experiments on radiation. By dividing the emission-power of a metal for the wave-length λ (the emission of the black body being rated at 100) by the constant C, and by squaring the ratio, we obtain the electrical resistance in ohms of a wire of the respective metal (1 m. length and 1 mm. cross-section). So it is now possible to undertake absolute determinations of electrical resistances solely by the aid of measurements on radiation.

* P. Drude, Physik des Aethers, p. 575 formula (68), 1894; and M. Planck, l. c. In the footnote p. 166 of this paper we have given Planck's enunciation of formula (6).*

It follows from formula (6) that the extinction-coefficient (g) increases, for long waves, with the square-root of the wave-length. The Ang absorption-coefficient a= which characterizes the real absorption λ of the metals, consequently diminishes proportionally to the square-root of the wave-length. Nevertheless the absorption of the metals remains very considerable, even for waves longer than one metre. A metal layer of about 10 mm. thickness must necessarily absorb the whole infra-red spectrum. It is therefore impossible that infra-red rays of great wave-length pass through layers of aluminium half a millimetre thick, and it follows that M. Blondlot's so-called "Rayons N" cannot possibly be infra-red rays.

XVII. On the Relation of the Electric Charges transported by Cathode and Canal Rays to the Exciting Current. By FRANZ LEININGER *.

SINCE the time are

NINCE the time when W. Wien, in the course of his research on electric discharge in rarefied gases †, showed that a splitting off of positive and negative particles took place at both electrodes, the anode as well as the cathode, the particles being projected in opposite directions by the two electrodes, it has been a problem of outstanding interest to determine the dependence of these showers of positive and negative particles, the so-called canal and cathode rays, on the intensity of the corresponding exciting current. Stimulated by a problem propounded in this sense by the philosophical faculty of Würzburg University, I have endeavoured to offer some small contributions towards it.

The phenomena of cathode and canal rays take place most readily at perforated cathodes. Hence the main attention. was to be given to the occurrences at the cathode, the anode being always earthed. I set myself the problem of determining the ratio of the electric convection-currents due to the cathode and canal rays to the exciting current. At first the currents corresponding to the rays and the main current were measured by means of galvanometers of the Kohlrausch and Wiedemann types, and later by moving-coil galvanometers of the Siemens & Halske and Hartmann & Braun patterns.

In making the arrangements, I asked myself whether it might be a matter of indifference whether the galvanometer was connected on the high- or low-potential side of the tube. In order to clear up this point, I made use of a differentially-connected Wiedemann's reflecting galvanometer for the current measurement. If, then, the currents flowing towards and leaving the tube were the same, no deflexion could be obtained on the galvanometer so connected. Now I found the following characteristic result in the case of all the tubes employed :

1. The galvanometer gave no deflexion when the collecting electrode AE was in connexion with the neighbouring discharge electrode.

2. The galvanometer gave a deflexion when the collecting electrode AE was connected to earth.

This result I interpreted as follows:-The current supplies the electric charges for the cathode and canal rays, and that Communicated by the Author.

† W. Wien, Wied. Ann. lxv. pp. 440–452 (1899).

part of it which is used up in producing the rays falling on AE is diverted when the collecting electrode is connected to earth. The decrease of current must therefore be proportional to the quantity of diverted cathode or canal rays. This inference was confirmed by the experiments, and furnished me with a second though difficult check method, for determining the relation of the convection-currents represented by the cathode and canal rays to the exciting current. Thereby I was put in possession of two mutually independent modes of investigation.

Description of Apparatus.

Altogether five different forms of discharge-tube were used. Here I shall, however, describe only two of the most important. For one series of experiments I used the tube shown in fig. 1. This was quite symmetrical with respect to both electrodes. These latter consisted of two exactly equal brass tubes 3 ems. long, with a piece of gauze, forming a "net" electrode, soldered to each. The distance between the pieces of gauze was 6.5 cms. The three component glass portions of the tube fitted tightly into the brass tubes just mentioned, and were cemented to them by means of sealingwax. The collecting electrode AE was provided with the following arrangement for displacing it without altering the vacuum. The collector was attached by means of two thick copper wires to a nut which moved between two guides, the latter being soldered to a springy ring of brass which pressed tightly against the glass walls of the tube. By means of a long screw passing through the nut and cemented to an easily rotating stopper, the electrode could be displaced to and fro by simply turning the stopper.

The experiments with other gases required a different form of tube, in which all bodies capable of giving off gases, such as greased stoppers, cemented joints, &c. had to be avoided. For this reason in such experiments the tube shown in fig. 2 was mostly used. It consisted of a glass tube about 35 cms. long and having an internal diameter of 3.2 cms. It was used in a vertical position, the upper end being closed and the lower one continued into a barometer-tube. The two perfectly symmetrical net-electrodes consisted of "nets of the second kind." It should be explained that in order to determine the effect of different nets, two kinds were used. The small-meshed nets, or nets of the first kind, were such that their wires covered 64.67 per cent. of the total area; the openings were square. In the wide-meshed nets, or nets of the second kind, the wires covered 48.37 per cent. of the

The arrangement for displacing the collecting electrode is shown in perspective, the rest in cross-section.

area. From this I concluded that nets of the first kind absorbed 35-33 per cent. of the rays, and those of the second kind 51.6 per cent. In the tube, fig. 2, the net-electrodes were soldered to springy brass rings, 8 mms. wide, which pressed firmly against the walls of the tube. The distance apart of the rings amounted to 2.9 cms. By means of these tubes, the values given in Tables I. to VIII. were obtained. The collecting electrode consisted of a disk of aluminium which fitted the tube exactly. The thick iron connecting wire passed through the mercury of the barometer. Thus the collecting electrode could be pushed up and down inside the barometer-tube, and moved up to a distance of 11 cms. away from the nearest net-electrode. The amount of this displacement could be read off on a scale running along the tube. In the case of the electrode nearest the collecting electrode, it was necessary to observe that the ring fitted the wall of the tube closely, so as to leave no open space; as otherwise with a high vacuum a secondary discharge passed to the collecting electrode, causing considerable disturbance and rendering observations impossible.

For exhausting the tubes, a Töpler mercury hand-pump was used, and in order to save labour arrangements were made for a preliminary exhaustion down to a pressure of a few millimetres by means of a water-jet pump.

For measuring the pressure inside the tube, a McLeod precision-gauge by Rich. Müller Uri of Brunswick was at first used. As, however, this gave incorrect results with high pressures, and as I wished to avoid the use of all greased stoppers in the experiments with other gases, instead of the pressures the potential-differences were noted in this case.

These were measured by a Thomson electrostatic voltmeter by Siemens & Halske, which enabled the potentialdifferences to be read off directly on a scale extending up to 15,000 volts.

For the measurement of the current as well as of the rate at which electric charges were picked up by the collecting electrode, a Kohlrausch galvanometer was at first employed. Later on, the current was measured with a Wiedemann's galvanometer, and the radiated electricity with the Kohlrausch instrument.

The Kohlrausch galvanometer had a resistance of 952.8 ohms, and a sensitiveness of 8.7 x 10-9 ampere per scaledivision with a scale distance of 2 metres.

The front coil of the Wiedemann's galvanometer had a resistance of 3354·7 ohms, and the back coil a resistance of 2933 ohms.