mann, which, as it seems to me, pretty well elucidate the phenomena in question. The tube used for these experiments had a uniform diameter of 2 centims., the points of the electrodes being 8 centims. distant from each other. Besides the tube, a Riess sparkmicrometer was placed in the circuit, by which such spark-distances as I pleased could be inserted. The method of conducting the observations was that which I had previously employed, and is described in Pogg. Ann. vol. cxlvii. If the exhaustion of the tube was a minimum, with a long spark-distance the discharge passed only in the same rhythm as in the spark, but it filled the entire tube; the spectrum is not the line-spectrum, but the band-spectrum not sharply shaded. If the spark-distance be diminished, there follows upon the first momentary discharge a positive luminous tuft showing stratification (that described in the Jubelband of Poggendorff's Annalen). The number of strata increases as the spark-distance decreases; when the distance is short, but still just sufficient to exclude the closing-current, four strata are visible. At about 1 millim. pressure, if a spark-distance of 30 millims. be inserted, the discharge commences with a momentary partial discharge which fills the tube, followed immediately by a positive luminous tuft with stratification. The spectrum is the bandspectrum. With decreasing spark-distance the stratification becomes sharper, and in the spectrum the shadings appear more distinct. With an air-pressure of 4 millims. and without a sparkdistance the positive tuft, completely filling half of the tube, appears as a perfectly continuous field of light; but when a spark-distance is inserted, first the momentarily passing bluish discharge shows itself, and the positive tuft takes the form of a cloud (described by P. A. in the Jubelband). Band-spectrum. Pressure 25 millims. A small spark-distance gives at the commencement a partial discharge, visible in the rotating mirror as an unspread image of the tube; then follows a luminous tuft at the positive electrode in the form of two clouds. If the sparkdistance is taken very great, only the momentary partial discharges appear, which fill the tube each time with whitish blue light. In the spectrum the shadings are no longer distinctly recognizable; but not a line of the line-spectrum is to be seen. Pressure 45 millims. Without a spark-distance the light divides in the rotating mirror into four clouds. With a sparkdistance of 30 millims. the clouds have nearly vanished, and the current passes only in 3-4 discharges, which in the rotating mirror give unspread images of the tube; but the spectrum is still the band-spectrum, only not so sharply shaded. On shortening the spark-distance the clouds gradually develop; and when it is reduced to 20 millims. they are already completely formed, but are of shorter duration than when there is no sparkdistance. With 65 millims. pressure the number of clouds rises to five or six; in other respects the appearance is substantially as before. Pressure 100 millims. Without a spark-distance, essentially a positive luminous tuft, in the shape of a great number of clouds, which give the band-spectrum. When a spark-distance of 10 millims. is interpolated, there appears a small and feeble spark, in the rotating mirror as a fine line of white light opening the discharge; but it reaches only about 1 centim. below the positive electrode, and is there lost in the diffused discharge, as before described in the case of hydrogen. On increasing the spark-distance inserted, the spark extends further; with one of 30 millims. it sometimes goes quite over from one electrode to the other. When the spark enters, the green lines of the line-spectrum immediately appear in the band-spectrum otherwise furnished by the tube, and exactly as far as the spark extends; so that in the spectrum the length of the spark can be accurately ascertained, even without the aid of the rotating mirror. Pressure 145 millims. Without the interpolation of a sparkdistance the current passes at first in the form of a partial discharge; then follows a positive tuft which appears in the rotating mirror as flickering clouds. The insertion of a spark-distance of 12 millims. sometimes produces in the tube a very peculiar spark-discharge from the positive electrode springs a spark to about the distance of 1 centim. in the tube, and is there lost, but reappears 1 centim. lower down, looking again like a sparkline 1 centim. in length. Sometimes the spark is present as a line along this whole distance; but it never goes further than about half the distance between the two electrodes. Only with the external interpolation of a greater spark-distance does the spark in the tube become longer; and when the former amounts to 30 millims. the latter sometimes extends the whole distance from one electrode to the other. The spectrum of the spark shows, besides the green, even the yellow and red lines of the nitrogen line-spectrum. The lines, however, are to be seen in the spectrum only just as far as the spark extends (here, as before, I copy, word for word, the note made at the time); hence we can recognize in the spectrum precisely to what distance the spark reaches. The above-related series of experiments consequently shows unequivocally that a spark-distance interpolated in the circuit of the induction-current by no means always calls forth sparks in spaces filled with rarefied gases, even with uniform rhythm of the discharge, but that the occurrence of sparks depends much more on the pressure of the enclosed gas and on the length of the interpolated spark-distance. As long as, in the space filled with rarefied air, the discharge does not pass in a proper spark, only the band-spectrum appears; when the spark enters, the lines of the line-spectrum also are seen. With respect to the formation of the spark and with it the appearance of the line-spectrum under circumstances otherwise the same, viz. equal pressure and equal spark-distance, I have as yet not been able to verify in air any perceptible influence of the dimensions of the tube in which the air is enclosed; according to M. Goldstein's observations, such an influence seems to be present, just as I have observed it in hydrogen. In reference to this, I take leave to quote a sentence or two from the forth-coming new edition of the 2nd volume of my Experimentalphysik, because it at the same time explains the fact that, of two tubes simultaneously inserted in the circuit, with a capillary intervening portion, the one tube containing air, and the other hydrogen, the former shows the band-spectrum, the other the line-spectrum. After giving the explanation deduced by me from the observations on wide tubes, I say (p. 252):-"The same difference in the thickness of the luminous layer is also present in tubes with an intervening capillary piece, as appears from the course of the phenomena being the same in my experiments on the nitrogen-spectrum (Pogg. Ann. vol. cxxxvii.); there also the thickness of the layer of gas which fills the capillary tube is still very great in comparison with the fine line of the proper spark. That some gases, rendered incandescent by the induction-current, give only the line-spectrum depends on this, that the current can only pass through them in sparks. It is worthy of note that in narrow tubes, even with hydrogen, in slight pressures the spark-discharge appears together with the sparkless one; in a tube of 1 centim. diameter I almost constantly saw the sparkdischarge; and in tubes with a capillary between them, in slight pressures the spark-discharge often came alone, without that luminous tuft. This circumstance accounts for the fact that, in Geissler tubes with a capillary between-piece, we often obtain only the line-spectrum, and often the same accompanied by the band-spectrum." Hereby, probably, the most important of M. Goldstein's objections are answered. With respect to the thick sparks giving the line-spectrum (p. 340), I only add that, leaving out of view the fact that it is very difficult to give a definite judgment on the thickness of a spark, every spark (if we designate as such an entire discharge apparently taking place in one spark) consists of a great number of partial discharges following one another in very rapid succession. On this account we cannot expect the band-spectrum even with apparently very thick sparks, as, even when the quantity of electricity passing in the spark was rising, I constantly obtained only the unshaded continuous spectrum in addition to the line-spectrum or developed out of it. After the foregoing, it is unnecessary at present to go into M. Goldstein's further experiments, some of them very interesting; closer consideration shows that not one of them contains any contradiction of my explanation of spectra. I reserve to myself a more detailed examination of them when I have opportunity to finish and communicate the above-mentioned experiments on the forms of the discharges in spaces filled with rarefied gases. LIII. On the Flow of Electricity in a uniform plane conducting Surface. Part I. By G. CAREY FOSTER, F.R.S., and OLIVER J. LODGE. [Concluded from p. 400.] [With a Plate.] 22. RESISTANCE.-The resistance, in the direction of the flow, of the part of the sheet extending between two given equipotential circles follows directly from equation (4) (in §19). Thus for the potentials of the circles characterized by the ratios r1r and re: respectively, where r, and r2 are distances from the source, and and r', the corresponding distances from the sink, we have whence Q 1 2 U1= log and U-log Q πκδ Τι Consequently the resistance of the part of the sheet between these circles is 2пкб 2 If Pi is the radius of the circle which has the greater absolute potential, or the one nearest the source, and P2 is the radius of the circle nearest the sink, the similarity of the triangles APC and BPC in fig. 2, Plate IX., gives P1 a+d1 discharge, but that the occurrence of sparks depends much more on the pressure of the enclosed gas and on the length of the interpolated spark-distance. As long as, in the space filled with rarefied air, the discharge does not pass in a proper spark, only the band-spectrum appears; when the spark enters, the lines of the line-spectrum also are seen. With respect to the formation of the spark and with it the appearance of the line-spectrum under circumstances otherwise the same, viz. equal pressure and equal spark-distance, I have as yet not been able to verify in air any perceptible influence of the dimensions of the tube in which the air is enclosed; according to M. Goldstein's observations, such an influence seems to be present, just as I have observed it in hydrogen. In reference to this, I take leave to quote a sentence or two from the forth-coming new edition of the 2nd volume of my Experimentalphysik, because it at the same time explains the fact that, of two tubes simultaneously inserted in the circuit, with a capillary intervening portion, the one tube containing air, and the other hydrogen, the former shows the band-spectrum, the other the line-spectrum. very After giving the explanation deduced by me from the observations on wide tubes, I say (p. 252):-"The same difference in the thickness of the luminous layer is also present in tubes with an intervening capillary piece, as appears from the course of the phenomena being the same in my experiments on the nitrogen-spectrum (Pogg. Ann. vol. cxxxvii.); there also the thickness of the layer of gas which fills the capillary tube is still great in comparison with the fine line of the proper spark. That some gases, rendered incandescent by the induction-current, give only the line-spectrum depends on this, that the current can only pass through them in sparks. It is worthy of note that in narrow tubes, even with hydrogen, in slight pressures the spark-discharge appears together with the sparkless one; in a tube of 1 centim. diameter I almost constantly saw the sparkdischarge; and in tubes with a capillary between them, in slight pressures the spark-discharge often came alone, without that luminous tuft. This circumstance accounts for the fact that, in Geissler tubes with a capillary between-piece, we often obtain only the line-spectrum, and often the same accompanied by the band-spectrum." Hereby, probably, the most important of M. Goldstein's objections are answered. With respect to the thick sparks giving the line-spectrum (p. 340), I only add that, leaving out of view the fact that it is very difficult to give a definite judgment on the thickness of a spark, every spark (if we designate as such an entire discharge apparently taking place in one spark) consists of a great number of partial discharges following one another in |