Let us take, for example, the peal which begins when the sound waves reach the ear from the point A. In the first unit of time the sound that reaches the ear is the sound produced along the lines A B and A C; in the second unit, the sound produced along the lines B D and C E; in the third unit, the sound produced along D F and E G. So far the peal has been fairly uniform in its intensity; though there has been a slight falling off in the second and third units of time, as compared with the first. But in the fourth unit there is a considerable falling away of the sound; for the line F K is only about one-third as long as D F and E G taken together; therefore the quantity of sound that reaches the ear in the fourth unit of time is only one-third of that which reaches it in each of the three preceding units; and consequently the sound is only one-third as loud. In the fifth unit, however, the peal must rise to a sudden crash; for the portion of the lightning path inclosed between the fifth and sixth circles is about six times as great as that between the fourth and fifth; therefore the intensity of the sound will be suddenly increased about six-fold. After this sudden crash, the sound as suddenly dies away in the sixth unit of time; it continues feeble as the path of the lightning goes nearly straight away from the observer; it swells again slightly in the ninth unit of time; and then continues without much variation to the end. This is only a single illustration, but it seems quite sufficient to show that the changes of intensity in a peal of thunder must be largely due to the position of the spectator in relation to the several parts of the lightning flash.
Distance of a Flash of Lightning.—I need hardly remind you that, by observing the interval that elapses between the flash of lightning and the peal of thunder that follows it, we may estimate approximately the distance of the nearest point of the discharge. Light travels with such amazing velocity that we may assume, without any sensible error, that we see the flash of lightning at the very moment in which the discharge takes place. But sound, as we have seen, takes a sensible time to travel even short distances; and therefore a measurable interval almost always elapses between the moment in which the flash is seen and the moment in which the peal of thunder first reaches the ear. And the distance through which sound travels in this interval will be the distance of the nearest point through which the discharge has passed. Now, the velocity of sound in air varies slightly with the temperature; but, at the ordinary temperature of our climate, we shall not be far astray if we allow 1,100 feet for every second, or about one mile for every five seconds.
You will observe also that, by repeating this observation, we can determine whether the thundercloud is coming toward us, or going away from us. So long as the interval between each successive flash and the corresponding peal of thunder, continues to get shorter and shorter, the thundercloud is approaching; when the interval begins to increase, the thundercloud is receding from us, and the danger is passed.
The crash of thunder is terrific when the lightning is close at hand; but it is a curious fact, that the sound does not seem to travel as far as the report of an ordinary cannon. We have no authentic record of thunder having been heard at a greater distance than from twelve to fifteen miles, whereas the report of a single cannon has been heard at five times that distance; and the roar of artillery, in battle, at a greater distance still. On the occasion of the Queen’s visit to Cherbourg, in August, 1858, the salute fired in honor of her arrival was heard at Bonchurch, in the Isle of Wight, a distance of sixty miles. It was also heard at Lyme Regis, in Dorsetshire, which is eighty-five miles from Cherbourg, as the crow flies; and we are told that, not only was it audible in its general effect, but the report of individual guns was distinctly recognized. The artillery of Waterloo is said to have been heard at the town of Creil, in France, 115 miles from the field of battle; and the cannonading at the siege of Valenciennes, in 1793, was heard, from day to day, at Deal, on the coast of England, a distance of 120 miles.[15]
So far, I have endeavored to set forth some general ideas on the nature and origin of lightning, and of the thunder that accompanies it. In my next Lecture I propose to give a short account of the destructive effects of lightning, and to consider how these effects may best be averted by means of lightning conductors.
Note to Page 20.
On the High Potential of a Flash of Lightning.
The potential of an electrified sphere is equal to the quantity of electricity with which the sphere is charged, divided by the radius of the sphere. Now the minute cloud particles, which go to make up a drop of rain, may be taken to be very small spheres; and if v represent the potential of each one, q the quantity of electricity with which it is charged, and r the radius of the sphere, we have v = q/r. Suppose 1,000 of these cloud particles to unite into one; the quantity of electricity in the drop, thus formed, will be 1,000q; and the radius, which increases in the ratio of the cube root of the volume, will be 10r. Therefore the potential of the new sphere will be 1000q/10r, or 100q/r; that is to say, it will be 100 times as great as the potential of each of the cloud particles which compose it. When a million of cloud particles are blended into a single drop, the same process will show that the potential has been increased ten thousandfold; and when a drop is produced by the agglomeration of a million of millions of cloud particles, the potential of the drop will be a hundred million times as great as that of the individual particles.[16]