By the ratio of the turns of the voltmeter exciting coil, and of the high potential circuit, 1÷150 vs. 1300, from the effective voltmeter reading, the effective potential at the discharge plates was found, and by assuming the sine law of E. M. F. wave, that is, by multiplication with 2, the maximum potential at the electrodes or discharge plates calculated.

The connection between electrodes and secondary coils consisted of two short pieces of rubber insulated wire, which were carried through the air, so that practically no escape of current could take place from them.

The application of the potential always lasted but a short time -not over 15 seconds. Still, all the materials became more or less heated before breaking down.

The exactness of this method of testing is necessarily limited, and the results may possibly contain a constant-error due to the deviation of the E. M. F. from sine shape-so that the maximum E. M. F. is not exactly equal 2 x effective E. M. F.-and an error in the counting of the secondary turns, which, though done very carefully, is unavoidable with such a large number as 6,000 turns. This possible constant-error, however, can amount to a very small percentage only, probably not exceeding two per cent.

Where several tests were made with the same thickness of material, and gave nearly the same result, the average of the readings was taken, and the number of readings marked in the table.

In the following tables, in the first column, the maximum difference of potential where the dielectric broke down, is given in kilo-volts or thousands of volts, as V.

In the second column, the thickness of the dielectric, or the sparking distance, is given in milli-centimetres, or thousandths of centimetres, as ò.

obs.

From these two observed quantities, in the third column, the electrostatic gradient g = is calculated, in kilo-volts per

centimetre.

V

obs.

From these tests, empirical formulas, expressing the interdependence of V and ò̟, were calculated, and the values of ò calculated by means of these formulas, given in the fourth column as

d.

calc.

calc.

The fifth and sixth columns give the difference between and in milli-centimetres and in percentages of 8.

obs.

First I tried the equation of the hyperbola,

calc.

=

which would give a finite value V b, where ò becomes infinite, that is, discharge takes place into the air. This function did not satisfy the results at all, as seen from the last column of Table I., and within the range of observation, no tendency to electrostatic saturation was noticed. It would give a limiting value of Vat about 79 kilo-volts.

With some materials, the tests agreed fairly well with the linear function,

d = a V,

a

showing that at a definite electrostatic gradient, g = the dielectric breaks down, independent of its thickness.

Other materials did not follow this equation at all, but the sparking distance increased quicker than the E. M. F. The addition of a quadratic term,

δ = a V + b V2,

gave fair agreement with the tests.

A remarkable behavior was noticed with air. For higher E. M. F.'s, the sparking distance in air agreed fairly well with this quadratic law; but even better still with a formula, where the parabola did not start at the origin, but from an E. M. F. of about 650 volts, so that these tests were expressed by

Consequently, to express the tests over the whole range, a further term has to be added, which disappears for values of V beyond 1,500 2,000 volts.

acter is the exponential e el

The simplest function of this char

-dV, and, indeed, the tests made with

air, over the whole range, were fairly well-that is, within the errors of observation-expressed by the equation,

This equation is merely empirical and can consequently be expected to hold only within the range covered by the tests. Still. the terms of this equation may have some theoretical foundation. The term a V gives the electrostatic gradient g = 1, at which

1

a

the air while at rest under ordinary pressure breaks down.

Mechanical or other changes taking place in the air under the electrostatic stress (for instance, air currents), and being proportional to the E. M. F., may justify the introduction of the quadratic term, b V2

As known, all the solid materials are covered-by molecular attraction-with a thin film of compressed air. The disruptive strength of compressed air is greater than that of air of ordinary pressure. Consequently, these two films of compressed air must behave like an increase of the distance of the electrodes, by that length, e, which is equivalent to the greater disruptive strength of the two films of compressed air covering the electrodes. Hence, the theoretical sparking distance, a+b, has to be decreased by a constant e, giving

But when approaching the electrodes so closely that the two films of compressed air unite more or less, the constant term e will be more or less decreased. Now, the density of the air near the surface of an attracting body is represented by an exponential function of the form el

dx

Hence, it is possible that this exponential term, which I noticed only in air, e (e-dv_ 1), has a physical meaning.

This is corroborated by the numerical values of a, c and d. For, calculating the electrostatic gradient of air for extremely small distances,

we get 139 kilo-volts per cm. Dry fibre, a porous material. gives almost the same value, 130 kilo-volts per cm.

Very interesting luminous effects take place when a thin sheet of good insulating material, as mica, is placed between the electrodes. At a difference of potential of 830 volts and a thickness of mica of 1.8 milli-centimetres, in darkness, a

faint bluish glow becomes visible between the mica and the electrodes. This glow is very perceptible at 970 volts, and faintly visible in broad daylight at 1,560 volts. With increasing difference of potential, this bluish glow increases in intensity, forming a sharply defined, smooth, blue line around the electrodes at their point of contact with the mica.

At a difference of potential of 4.5 kilo-volts-thickness of mica of 2.3 milli-centimetres-violet creepers of about 2 mm. length break here and there out of the line of bluish glow. These creepers are distinctly different from the blue glow surrounding the electrodes and increase in number and length with increasing potential, until they form a broad electrostatic aurora surrounding the electrodes on either surface of the mica-sheet, consisting of an infinite number of small violet streamers, rushing with a hissing noise over the mica. This corona increases rapidly in width until it reaches the edges of the mica-sheet. Then white sparks of intense brightness pass from electrode to electrode over the surface of the mica, first few in number, then with increasing potential, covering the whole sheet with an infinite number of streaks of lightning, with a roaring noise. The amount of current passing through these sparks is exceedingly small, for no perceptible reaction upon the primary circuit was noticed. The length of these sparks is many times larger than the sparking distance in air, being tenfold at 17 kilo-volts. They are intensely hot, and leave whitish marks, due to calcination, on the mica when passing over it. The sheet of mica and, especially, the electrodes become heated very rapidly, the mica twists and begins to splinter, to separate into sheets, until finally it breaks down.

To determine the difference of potential required for the production of these sparks, a circular disk of mica, of 7" diameter and 19 milli-centimetres thickness, was inserted between the electrodes, the E. M. F. increased until the first sparks passed over the edge of the mica, the voltmeter read-then the mica disk cut down to 6" diameter and the test repeated, etc. These tests are given in Table XIII. and Fig. 8.

The width of the electrostatic corona is half the length of these sparks. The length of these sparks depends somewhat upon frequency and the thickness of the mica-sheet, being greater for higher frequency and thinner mica disk, but apparently only inso-far as the capacity, or, rather, the charging current of the condenser, represented by the mica disk as dielectric, is increased thereby.

Since these sparks behave entirely different from an are passing between the electrodes, and are usually unable to start an arc, I believe they are merely a condenser phenomenon. That is, I explain it so, that the corona is the charging current of the condenser formed by the mica disk as dielectric, and the whole surface covered by the corona as condenser plate, while, when the corona reaches the edge of the dielectric, disruptive discharge of the condenser takes place, by these sparks passing over the edge of the dielectric.

I do not know whether this explanation really covers the phenomenon, but merely offer it as a suggestion. Of all the highpotential phenomena, this is undoubtedly the most brilliant

Referring now to the tables and figures:

Table I., Fig. 4, Disruptive Discharge Through Air.

XIII., Fig. 8, Luminous Effects and Creeping Discharge.

XIV., Electrostatic Gradients and Specific Electric Resistances.

In Figs. 6 and 8, the air-curves, and

In Fig. 7, the air and the mica-curves are drawn in dotted lines for comparison.

As seen from Table XIV., the electrostatic gradients and the specific electric resistances have no relation with each other. As a curiosity, it may be remarked that by extrapolating the sparking distance by means of the empirical formula of Table I.,

we would get for 100,000 volts, a sparking distance of about 7"; for a quarter-million volts, a sparking distance of 3 feet; for one million volts, 40 feet sparking distance; while a lightning stroke of one mile in length would require 11,000,000 volts.