But it is also mechanically and chemically broken down; that is, the molecules dissociated and recombined after the discharge in all possible combinations. That is, we get ozone and get nitric acid, and a lightning flash produced by a thousand million volts may so be followed by a deluge of nitric acid. This, fortunately, is not the case.

An estimate of the voltage and the current in a lightning flash would not yet give the energy if the duration of the discharge were not also known. We can, however, get an approximate estimate of the magnitude of the energy of the lightning flash indirectly, from photometric considerations, and eliminate the consideration of the duration of the flash by the integrating feature of the human eye for impressions of very short duration. An impression on the human eye persists for some time, about o.1 second, and any phenomenon of shorter duration than O.1 second thus appears to last o.1 second. Hence the effect on the eye by a lightning flash would be about the same whether the flash lasted 0.1 second or were of 100 times greater intensity, but lasting a hundred times shorter time. This means that the eye would see a lightning flash about in the same manner as if its light, and so probably its energy, were spread uniformly over o.1 second.

The illumination given by a brilliant lightning flash is about of the same magnitude as good artificial illumination, perhaps one foot-candle, since at night time in a well-lighted room the light of a lightning flash is still quite appreciable. Estimating roughly one watt per candle-foot, a lightning flash illuminating a space of two miles square, or 108 square feet, with one footcandle would consume 108 watts. As this is the illumination as averaged by the human eye over o.1 second, the energy is 107 watt-seconds, or 10,000 kilowatt-seconds. The energy of a large lightning flash, estimated from its light, would thus be of the magnitude of 10,000 kilowatt-seconds. This value, while considerable when expressed in electric quantities, is by no means so very great. Reduced to heat measure, it only equals the latent heat of evaporation or condensation of about nine pounds of

water.

As seen, an estimate of the voltage of the lightning flash from length and disruptive potential gradient of the air, does not give reasonable values, that is, the lightning flash can not be

a single discharge as that of a Leyden jar. An estimate of the voltage may therefore be attempted in a different manner.

Lightning flashes usually occur within thunder clouds, and only rarely from cloud to cloud or from cloud to ground. They therefore seem to be due to equalization of potential differences within the cloud rather than to discharges between oppositely charged bodies. Lightning occurs mainly when rapid condensation of moisture takes place in the air, and the electric phenomena seem to be the more intense, the greater the rapidity of condensation, or rain formation. Thus the atmospheric electric disturbances seem to be connected with the condensation of water vapor to clouds and rain.

There exists normally a potential gradient in the air. That is, a potential difference exists between the air at different elevations, reaching sometimes several hundred volts per foot, so that we can estimate as a fair average a natural potential gradient in the air, in vertical direction, of about 100 volts per foot. A point 100 feet above ground may show a potential difference of about 10,000 volts against ground. Usually the higher strata of the air are positive against the lower. The cause of this potential gradient, whether terrestrial or cosmic, is of no interest to us here, but merely its existence.

It is of interest to investigate what effect must be expected, from our well-known physical laws, from the condensation of moisture, and agglomeration of the moisture particles to raindrops, in an atmosphere having such a potential gradient.

Assuming water vapor in a higher stratum of the atmosphere to condense to moisture particles. These moisture particles have the potential of the air in which they float, that is, have a considerable potential difference, perhaps hundreds of thousands of volts, against ground, and so contain an electric charge against ground. These moisture particles conglomerate with each , other to larger moisture particles and ultimately to rain-drops. By the collection of n3 particles into one, the diameter of the particle has thus increased n fold. Its capacity has also increased n fold (the capacity of a sphere being proportional to the diameter). The particle contains, however, the accumulated charges of n smaller particles, and n3 times the charge, with n times the capacity, gives n2 times the potential. It follows herefrom that with the conglomeration of the water particles their

potential must increase rapidly, proportional to the square of their diameter. The conglomeration of moisture particles in the clouds is, however, very uneven, due to the uneven distribution of moisture, as is plainly seen by looking at any cloud, dense or dark parts representing considerable condensation and so considerable moisture contents, alternate with light parts, in which little or no condensation occurs. As a result thereof, starting with a uniform potential in the stratum of the air where condensation begins, differences of potential distribution of necessity result from the differences in the condensation of water vapor to moisture and the accumulation of the moisture particles to larger ones; that is, the denser portions of the cloud are at a higher potential than the lighter portions. Thus, starting with uniform potential, and so zero potential gradient in the air at the moment of the beginning of condensation, potential differences and thus potential gradients appear.

Such potential differences in the clouds increase with increasing agglomeration of moisture particles to rain-drops, and the potential gradient thus rises. Assuming even as low a potential gradient as 100 volts per foot in the cloud at the beginning of agglomeration of moisture particles. The collection of n such particles to one rain-drop of n times the diameter and son times the capacity, but containing the static charge of n3 particles, gives n2 times the potential, and, since the distances between the particles are now n times as large, the potential gradient has increased n fold. That is, by conglomeration of water particles, the potential gradient rises proportionally to the diameter of the particles. Estimating, then, the average size of moisture particles as 10 inches at the beginning of agglomeration, when the potential gradient in the cloud is about 100 volts per foot, then the breakdown potential of the air, of between 100,000 and 200,000 volts per foot, would be reached when the drops have reached about o.1 to 0.2 inch diameter; that is, the size of rain-drops.

Potential gradients in the cloud thus gradually rise until the disruptive strength of the air is reached, and a discharge passes, .equalizing the voltage at this spot. This, however, causes a greater potential gradient at the end of the discharge, exceeding the breakdown strength of the air, and so causes a second discharge, following over the path of the first, then a third,

and so on until all of the potential differences or inequalities of the potential distribution in the cloud are leveled down by a series of successive discharges. This phenomenon is similar to that of a landslide, setting off another and another landslide. Or it can best be pictured by representing the unequal moisture distribution in the cloud by a relief map built of wet sand, the dense portion of the cloud, and so portions of high potential, being represented by the hills, the light or low-potential portions of the cloud by the valleys of the relief map. As soon as the sand dries, somewhere, where the declivity is very steep that is, the potential gradient very high-a slide occurs. This causes another slide, and so on, until the whole configuration of sand settles down to a flat and smooth shape, the hills are leveled off and the valleys filled.

The existence of such successive discharges, following each other after appreciable intervals of time in the same path, has been shown by the photographs of lightning flashes taken with a rotating camera. In this case, by the motion of the camera, the successive flashes are recorded side by side, and sometimes more than 40 successive discharges have been counted, the whole phenomenon lasting about 0.6 second, that is, quite an appreciable time.

It follows herefrom that lightning flashes in the clouds, of several miles length, occur without any considerable potential difference between the ends of the flash, but result from the disruptive equalization of the unequal potential distribution in the clouds, caused by unequal vapor density and so unequal condensation and conglomeration of moisture particles.

This also explains the relatively small tendency to discharge between cloud and ground across a space in which no condensation takes place and so no unequal potential distribution supplies the power of the discharge: although the distance between cloud and ground is smaller than the distance traversed by a lightning flash in the clouds, and the average potential difference between cloud and ground probably greater than the potential differences in the clouds, a discharge to ground probably occurs in general only where by a heavy downpour of rain a range of high potential is carried bodily part way down to ground. This also may explain why lightning discharges to the ground are usually followed by a heavy downpour of rain.

Estimating, then, as disruptive strength of air under discharge conditions in an ununiform field, and at the reduced air pressure in the clouds, 100,000 volts per foot, the average potential gradient in the path of the lightning discharge through the clouds would be about 50,000 volts per foot. This gradient, however, would not be unidirectional, but the potential would rise from a low, or even negative, value at a light portion of the cloud to a maximum value at a dense portion, then decrease again, that is, give a gradient in opposite direction, to a light portion, and so forth, and the potential gradient would vary from nothing at a maximum-potential point to a maximum equal to the breakdown strength of air at the starting point of the discharge, to zero at a minimum-potential point, and so forth.

To estimate the current that discharges in the lightning flash, the conductivity of air in the path of the discharge and the diameter of the discharge are required, and both are unknown, so that any estimate must be very approximate only. The specifice resistance of gases and vapors decreases with increasing temperature and with decreasing pressure. It is a few ohm-centimetres at atmospheric pressure and at the high temperature of the magnetite or carbon arc, and is also a few ohm-centimetres at the low temperature and low pressure of a high-current Geissler tube discharge. The mercury-arc stream also gives a specific resistance of a few ohms. The temperature of the air in the lightning discharge is probably moderately high, but the pressure not far from atmospheric, so that 100 ohmcentimetres may not be far from the true magnitude of the resistance. Estimating one to two feet as diameter of the discharge path, and 100-ohm centimetres as the specific resistance, and allowing for the inductance, gives, with an average potential gradient of 50,000 volts per foot, a current of about 10,000 amperes.

The heating effect and the magnetic effect of lightning strokes also point to the passage of currents of some thousand amperes.

Assuming, then, the average potential gradient in the lightning flash as 50,000 volts per foot, the current as 10,000 amperes, a lightning flash of two miles length would represent a power of 5 x 10 kilowatts. Estimating the energy of the discharge, as approximated from the photometric consideration, as 10,000