FALL OF

POTENTIAL

ONY (3)

E. M. F.

(Eo)

the corresponding current is nearly half an ampere. All these curves are seen to be special forms of the type curve g, and all are capable of representation by the function e(2) above constructed.

Given the characteristic curve for a gas under given conditions, then by means of the Kaufmann diagram (fig. 2) we may find what the current will be in a circuit containing an e. m. f. E, and an ohmic resistance R. The diagram is drawn for a circuit containing a gas at rather low pressure, with a moderately large e. m. f. controlled by considerable resistance. Keeping the e. m. f. E, constant, if the external resistance be increased, the line E-R will take a greater and greater slope and intersect the e() curve farther and farther to the left. At a certain slope it will intersect the curve in three places and the current may become intermittent. Finally

it will become tangent to the under side of the gas curve and the heavy current will cease abruptly, leaving only the brush discharge corresponding to the upper intersection. Diminishing the external resistance, the current will not start again where it ended so abruptly, but only when the resistance line becomes tangent to the curve on its upper side. By taking a higher e. m. f., only single intersections will occur as the resistance is varied, hence the current will never become intermittent and the whole e() curve may be followed through experimentally, as it can not be when the e. m. f. used is just sufficient to break down the gas. Stark" has worked out the relation between the critical minimum current for the arc (when the

a Ann. d. Phys. 12, pp. 694–699; 1903.

arc breaks) and e. m. f. and electrode metal. The relation to the density of the surrounding atmosphere may be seen from figs. 1 and 2, since as the pressure is diminished, curve a, fig. 1, is deformed into

curve g.

When a spark or Plücker tube is excited by an induction coil or transformer, it is the e. m. f. E, that is variable, while the resistance remains constant. In this case the E-IR line moves parallel to itself, and the resultant current flowing through the gas has quite a different wave form from what it would have if the current were controlled by varying the resistance alone. Fig. 3, taken from the author's paper on Rectifying Effects, shows a typical curve for the current through a

gas upon which a sine alternating e. m. f. E(t) is impressed. Starting with the point a on the curve E(t) giving the e. m. f. as a function of time, the point c on the curve i(t) giving current as a function of time is obtained by means of the intermediate points E and b, assuming that the characteristic curve e() for the gas is of the form shown and that sufficient ohmic resistance has been used to give the line E-iRthe slope indicated. Fig. 3 of course represents the current only in the ideal case of a circuit containing neither inductance nor capacity. When inductance (L) is added, instead of E-IR we must use the line di

di E-IR-L (a line in three dimensions E, i, to find the current

3

graphically. Without constructing this three dimensional diagram it is easy to see that the general effect of adding inductance is to increase the slope of the E-iR line while the current is starting and to decrease the slope when the current is decreasing. Hence the vertical portions of the current curve ¿ (t), fig. 3, will be replaced by sloping lines which will always be convex toward the axis of abscissæ and sharp corners will all be rounded off.

When a low voltage transformer (say 1,000 volts) is used to excite a Plücker tube with but little resistance or inductance in series, the current, if it pass at all beyond a mere brush discharge, will pass with brilliant flashes of light. This sudden and very great increase in the current is what we should expect, since in this case in the Kaufmann diagram the line E-iR is nearly horizontal and after it has once passed over the crest of the e() curve, intersects the latter only at a very large value of the current.

But it is only after capacity has been added that sufficient quantity of electricity can be supplied to actually attain the enormous currents predicted by the Kaufmann diagram for circuits of low resistance and inductance. The spark with capacity runs through the characteristic e(i) curve for a gas up to large values of i; without capacity, an intermittent or alternating current runs over the small current end of the curve only. When the spark passes several times during each alternation, all discharges after the first are made over a modified and much lower characteristic curve. The effect of capacity on the form of the current curve, i(t), fig. 3, is the opposite of the inductance effect, it sharpens the corners and increases the discontinuities. But

di

quantity not being independent of the current, like we can not

dt'

extend the Kaufmann diagram to cover the case of capacity as was possible with inductance, nor do the equations appear to admit of other than a graphical solution. Aside from making a very heavy maximum current possible, adding capacity has another very important effect generally overlooked, namely, that of reducing the potential of the discharge, or more strictly speaking the maximum e. m. f. of the spark circuit. If the supply of energy is limited, as it is in an induction coil or small transformer, the voltage may be cut down to 10 or 20 per cent of its value when no capacity is in circuit, and cutting down the voltage nearly to that necessary to just cause a spark to pass, increases the discontinuities in the current curve, and hence may actually strengthen the metallic spectrum. I have succeeded in showing this in a very striking manner. A 2-mm spark in hydrogen at about

atmospheric pressure was produced by a 300-watt 5,000-volt transformer controlled by noninductive resistance in its 100-volt side. With only 50 watts supplied, capacity was introduced until the spark barely passed, and thus a brilliant metallic spectrum, sharing the spectral energy about equally with the hydrogen, was obtained. But when the energy supply was increased from 50 to 200 watts the metallic spectrum was weakened to less than one-fourth of the total energy. Introducing inductance did not appear to alter this voltage effect.

Another aspect of the effect of capacity on the spark should be mentioned here. If a spark with large capacity in parallel and fed with a steady supply of current is examined with a rotating mirror, bright sparks appear at regular intervals. On decreasing the capacity gradually the sparks appear smaller and nearer together, until at a capacity of a few centimeters they are no longer distinguishable. The spark has now become an arc, and from this point of view an arc may be regarded as a rapid succession of very minute sparks.

Hartmann," working with a magnesium arc carrying a current of 4 amperes, found that the line Mg 4481 appeared much brighter with only 20 volts e. m. f. than it did on a 120-volt circuit. A Kaufmann dia gram (see fig. 2) indicates a very plausible explanation. The 20-volt current is just on the point of breaking, hence the E-R line will cut the characteristic gas curve in three points, while the 120-volt line cuts it but once. The 20-volt arc should then be of the nature of a rapid succession of very short sparks, and might well show spark lines in its spectrum.

EXPERIMENTAL RESULTS.

Experimental work was undertaken chiefly with the object of providing a wide range of homogeneous data relating to the conditions. governing the relative intensity of the spectrum of the electrodes to the spectrum of the intervening gas in arc, spark, and discharge tube. Spectra of 21 different metals were photographed with a large spectrograph, all under a uniform schedule of 81 different conditions. Three different gases were used as atmospheres; pure hydrogen, pure oxygen, and air, each being used at three different pressures, namely, 760 mm, 380 mm, and 100 mm, a considerable number of metals being tried at 4 mm as well. On each plate nine spectra were taken with the same metal in the same gas at the same pressure, but with nine different modes of excitation, thus making 81 different spectra of each metal.

a Astroph. J. 17, p. 145; 1903.

5. Series spark with small capacity-0.006 mf-over both sparks.
6. Same as (1), but with large inductance added-0.9 millihenry.

7. Same as (2), with same inductance as (6).

8. Same as (3), with same inductance as (6).

9. Same as (5), with same inductance as (6).

In the last four cases capacity was varied rather than inductance, because the inductance effect is sharply marked and persistent, while the capacity effects are more varied. These nine spectra, each about 15 cm long and 4 mm wide, were photographed side by side on the same plate, so that very slight variations could easily be traced.

A spark about 2 mm in length was used. This was excited usually by a 5,000-volt, 300 watt transformer, but sometimes a 5,000-volt continuous current from a generator set was used instead. The condenser consisted of large glass plates in air and had a capacity of about 0.15 microfarad, variable in steps of 0.006 mf. The inductance spool had an inductance of about 0.9 millihenry, variable in 0.009 millihenry steps. The series spark used was between 15 mm brass balls in air and was lengthened out to nearly its maximum before an exposure was made. The tube for holding the electrodes and inclosing the spark is shown in fig. 4. It was designed so that it could easily be opened for cleaning and interchanging electrodes and yet withstand a powerful and long-continued discharge. Electrodes E, 2 mm in diameter and 20 mm long, were slipped into a roll of platinum foil P, which was inclosed in a small glass tube sealed off at S except for a wire leading to the outside. The ground joint permitted easy removal of the whole. The design prevented conduction of heat to the joint to such an extent that stopcock grease could be used (this contained 1 part rubber, 1 part vaseline, part paraffin). A bulb B proved useful at low pressures as an auxiliary gas reservoir in keeping the pressure constant. A quartz window W, 40 mm in diameter and 40 mm. away from the spark, was attached with a hard grade of fusible cement.