kilowatt-seconds, the duration of the discharge would be: 10/5 X 10 = 2 X 10 seconds, or two-millionths of a second.

The discharge is probably oscillatory. In view of the high resistance of the discharge path, the damping effect must be very great; that is, a very large part or nearly all the energy expended in the first half wave; that is, the discharge consists of only one or very few half waves. With a duration of the discharge of 2 X 10-6 seconds, assuming two half waves as average, gives 500,000 cycles.

The frequency of oscillation of the lightning flash thus appears as of the magnitude of half a million cycles.

Since the velocity of propagation of electric disturbances is the velocity of light, or 188,000 miles per second, the wave

length of a discharge of 500,000 cycles is

miles, or about 2000 feet.

188,000 3 8

500,000

=

A wave-length of 2000 feet means that the current in the discharge flows in one direction for 1000 feet, in the opposite direction that is, with opposite potential gradient-in the next thousand feet, and so on. That is, in our former discussion, the average distance through which the potential gradient has the same direction, or the distance between maximum and minimum, between densest of lightest parts of the cloud, is about 1000 feet. This agrees fairly well with the appearance of the clouds to the eye, and it also agrees in magnitude with the distance over which the wind velocity varies, in gusts, as shown by Professor Langley in his investigation on the "internal energy of the wind."

It appears herefrom that the varying wind velocity as measured by Professor Langley, that is, the gusty character of the air currents, results not only in an internal mechanical energy— which the bird utilizes for soaring-but also results in unequal moisture distribution, and so, when condensation occurs, in an internal electrostatic energy of the thunder cloud, which discharges as lightning.

With an average length of the half wave of 1000 feet, and 50,000 volts per foot as potential gradient, the potential differences in the clouds would be of the magnitude of 50 million volts. These are values that appear reasonable.

Assuming that a lightning flash drains the electric energy of the cloud within a radius of about 100 to 200 feet from the path of the discharge, this affords a different method of estimating the magnitude of the energy of the lightning flash: Assuming, for instance, saturated air at 40 degrees centigrade mixing with air at o degree centigrade, condensation of a part of the moisture occurs which can easily be calculated. Assuming that this moisture has conglomerated to rain-drops of 0.1 to 0.2 inch diameter, the number of such drops in a space of two miles length and 200 to 400 feet diameter can be calculated, also their electrostatic capacity. With a wave-length of 2000 feet, and a potential gradient of 50,000 volts per foot, from the capacity follows the energy of the electrostatic charge, which discharges as lightning flash. This is found, under above assumption, as of the magnitude of 10,000 kilowatt-seconds, so agrees with the results derived from the photometric considerations.

To conclude, then, as approximate values of magnitude of the electric quantities in a lightning flash may be estimated: Average potential gradient: 50,000 volts per foot at the moment of discharge.

Average potential difference between different points of the cloud: 50 million volts.

Average current in the discharge: 10,000 amperes.

I

Average duration of the discharge:

second.

500,000

Average frequency of discharge: 500,000 cycles. Average energy of the discharge: 10,000 kilowatt-seconds, or 7 million foot-pounds.

LIGHTNING IN ELECTRIC CIRCUITS

Of greatest importance to an electrical engineer are the high-potential phenomena produced in electric circuits by atmospheric lightning as well as by other causes, frequently internal to the circuit, which gives similar or the same effects to such an extent that it has become customary when dealing with electric. circuits to distinguish between external or atmospheric lightning and internal lightning, as caused by electric-circuit disturbances or defects, such as sudden changes of load, or arcing grounds, and so forth.

While a very large amount of data on high-potential

phenomena in electric circuits has accumulated, the possible variety of phenomena is so great that an intelligent understanding of the phenomena, as it is required for effective protection of the circuits, is feasible only by a theoretical investigation of the high-potential phenomena that may be expected in electric circuits, and a comparison thereof with the observed effects.

In general, the high-potential phenomena possible in electric circuits are the same three classes of phenomena that can occur in any medium, as a body of water, which is the seat of energy. 1. Steady electrostatic stress, that is, a gradual rise of potential of the total circuit against ground, until a discharge occurs somewhere; just as in a body of water, as a river, the pressure, that is, the water level, may gradually rise until it breaks through the embankment.

2. Impulses, or traveling waves, similar to the ocean waves rolling over the surface of the water.

3. Standing waves, or oscillations or surges, similar to the oscillation of a tuning fork or a violin string.

A more extended discussion on the three forms of electric disturbances, and their causes, I have given in a recent paper before the American Institute of Electrical Engineers.*

Steady electrostatic stress obviously can occur only where the circuit is very well insulated from the ground, but not in a grounded circuit, or a leaky circuit, as low-voltage circuits usually are, and such static stresses can be eliminated by a permanent leak, that is, a high resistance connection between the circuit and the ground.

As sources of impulses or traveling waves only two characteristic phenomena may be considered here: the lightning flash, or induction by the clouds, as external, and the arcing ground as internal cause.

Assuming a thunder cloud to pass over the line. The ground below the cloud then assumes an electrostatic charge, corresponding to the opposite charge of the cloud. The transmission line, as part of the ground, also assumes a static charge higher than that of the ground, since it projects above it. Any equalization of the potential distribution in the cloud by a lightning flash, as discussed in the preceding, requires a change

*American Institute of Electrical Engineers Transactions, March, 1907: Lightning Phenomena in Electric Circuits.

in the electrostatic charge of the line, corresponding to the changed potential difference between ground and cloud above the ground, and the static charge thus set free on the line rushes as impulse or wave along the line. The wave shape of such impulses induced by cloud discharges is in general not a smooth sine-wave, but may be very irregular. During the equalization of the cloud potential by the lightning flash, the potential difference against ground, of the part of the cloud above the electric circuit, may vary in almost any conceivable manner, thus giving rise to very different wave shapes of the impulses. Thus some impulses may rise very rapidly, with extremely steep wave front, and slowly die down. Others may rise slowly, then suddenly fall and reverse, or a series of oscillations may occur in the impulse, and so forth. If the lightning flash is parallel with the line, simultaneous impulses of different directions may be produced, corresponding to the different directions of the potential gradient in the different parts of lightning flash, and these waves, of different directions, intensity and wave-length, traveling over each other, then produce a very complex system of phenomena. Thus, for instance, by the interference of two impulses of nearly equal wave-length, moving in opposite directions, a high-voltage point may be produced, traveling slowly along the line, and visible to the eye as luminous streak.

The frequencies of these impulses are those corresponding to the frequencies of cloud discharge, that is, of the magnitude of hundreds of thousands of cycles per second. With the velocity of light, 188,000 miles per second, they travel along the line until they gradually fade out by the dissipation of their energy, or are reflected at an open end of the line, or at the entrance to the station are broken up by partial reflection in reactances, and interference between the reflected waves, the incoming waves and the waves passing over the reactances, and so give rise to systems of standing waves or oscillations, as an ocean wave rolling on to a sloping beach breaks up into surf.

Where a traveling wave is reflected, the combination of the reflected wave and the incoming wave produces a standing wave or oscillation; that is, a wave in which the voltage maxima and the zero points or nodes have fixed positions on the line.

By superposition of the wave maxima of incoming and

reflected wave, the standing wave rises to a maximum double that of the traveling wave. Where different oscillations or standing waves superimpose upon each other, their maxima subtract at some places and add at others, and so again double the voltage; that is, a traveling wave or impulse, breaking up into systems of oscillations at a station, doubles and quadruples the potential, so that a traveling wave of moderate potential may cause dangerous voltages when breaking up into oscillations, just as in the ocean surf the waves rise to far greater heights than in the rolling ocean wave before it reaches the beach.

If we consider that the impulses traveling along the line are not sine-waves, but of very irregular shape, that is, can be considered as consisting of a fundamental of some hundred thousand cycles, and numerous higher harmonics of still greater frequency, and each of the components when breaking at the station gives rise to a set of oscillations at every interference point, that is, at every reactance, the complexity of the phenomenon can be imagined.

Since the equalization of cloud potential usually occurs by a series of successive discharges in short intervals, a small fraction of a second, and each discharge gives rise to an impulse in the line, and so a system of oscillations at the station, whatever protective device is used, must restore itself instantly after a discharge, so as to receive the next following discharge. Any device depending on mechanical motion to restore itself after a discharge to operative position, thus fails to protect when a series of discharges follow each other in very rapid succession, as discussed above.

Traveling waves very similar in character to those due to induction from the clouds, but frequently of far greater volume, sometimes occur in an electric circuit from internal causes, as arcing grounds, or spark discharges.

Let, for instance, in an insulated underground cable system a spark occur between one of the conductors and the grounded cable armor, through a weak spot in the insulation, as a faulty joint or a cable bell. Normally a potential difference exists between the cable conductor and the ground, equal to the Y potential of the system, and so an electrostatic charge on the conductor corresponding thereto. A spark passing between conductor and ground connects it to ground, and the charge of