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But it is interesting to speculate whether astronomers will ever be in the position to say, “ We have now determined the solar parallax in seconds of arc to a higher degree of accuracy than that of the measurement of the earth," and to call upon geodesists for better results. I can conceive only one direction in which we may be able to worry the successors in your corps of Everest and Clarke. Is the form of the equator a circle or an ellipse? I believe that there is some slight evidence for ellipticity, and that it has been put as high as one in three thousand. If that is so, it is just barely possible that we may have to introduce into the computation of the parallax factors for different observatories a term depending upon the shape of the equator. But I confess that this prospect is remote, and that for inany years, in all probability, geodesists who achieve accuracies of one in a hundred thousand and even talk of one in a million will be able to take a serene view of the labors of astronomers to arrive at the distance of the sun to one part in ten thousand.



By ALEX LARSEN. (hicago, Ill.

Lightning, with its accompaniment of thunder, has always exerted a fascinating influence on the thinking mind. It is not strange that a people living in an age when the laws of nature were less perfectly understood should have associated this beautiful and aweinspiring natural phenomenon with the powers and attributes of their gods.

The ancient Norsemen recognized in the rumbling of the thunder ihe approach of Thor, their most powerful god, in his heavenly chariot, drawn by his two he goats; and in the lightning flash they saw the path cleaved through the air by the never-failing hammer ** Mjolner,” wielded by the mighty arm of Thor when battling with the enemies of the gods, the hammer always returning to his hand. The myth is beautiful, and it would seem as if its authors had noticed the peculiar flickering of most lightning flashes and associated it with the forward and return movement of the hammer.

The principal object of this paper is to place before its readers certain facts to account for this flickering of lightning flashes.

In the latter part of the summer of 1901, while taking some ordinary pictures of lightning, the idea occurred to the writer while noticing this flickering that if the camera be moved in a circle at right angle to the flash the picture ought to show a widening of the flash, if it was composed of separate parts, and thereby also determine its duration. The attempt to do this was made that year, but without success.

It was repeated again in 1902, and on July 17 several successful exposures were made which clearly showed that most flashes are composed of several discharges following one another at certain intervals in the path made by the first discharge. The writer was unaware at the time that others had experimented in the same line and had published their results.

a The study of lightning flashes herewith presented was aided by a grant from the Hodgkins Fund of the Smithsonian Institution,

The camera was moved by hand, being swung from right to left and back again, each swing lasting about one second and covering an angle of about 60°, which was also the angle of the lens. The apparatus employed was an ordinary magazine plate camera, which for all ordinary purposes is the most convenient on account of the rapidity with which the plates can be changed, this being of great importance, because, as a rule, the time most favorable for obtaining good pictures is very short, seldom listing longer than from ten to fifteen minutes.

Several more pictures were obtained in 1903. The three most interesting ones up to that year are shown in figures 1, 2, and 3. (See plates.) Figure 1 shows a flash obtained on July 17, 1902. The lischarge took place between two clouds. It will be noticed that it is composed of a number of separate discharges (or rushes) and bands; as many as thirty-four can be counted on the negative. As the flash covers about half of the plate, and as the approximate speed of the camera was about one second to cover the plate, or 60°, it follows that the approximate duration of this flash was about half a second. Figure 2 shows a flash obtained on July 11, 1903. This flash is interesting for several reasons. It is composed of fourteen separate discharges, the first one being the brightest, and having side branches pointing downward, proving that the first discharge passed from the cloud to the earth and that the resistance which it had to overcome must have been excessive (the side branches prove that). At a distance of 3 millimeters from the first rush is another discharge following the same path, but without side branches (what appear as such are really branches from the first rush). At a distance of 12.5 milliineters from the last discharge will be seen two rushes 0·5 millimeter apart, and from there for a distance of 10 millimeters are a series of discharges close together, forming a broad band. The dark space which divides this flash is a cloud through which the discharge is passing. Another interesting fact about this flash is that the path of it is spiral.shaped, the motion is from right to left, or opposite to the motion of the hands of a clock, looking downward from the cloud. Figure 3 was obtained October 1, 1903. We have here a flash composed, first, of two bright discharges close together, then there appears to be an interval of about a fourth of a second, which in all probability was filled in with a number of fainter oscillations (the lines running across seem to indicate that), and at the conclusion of the flash are four fairly bright rushes.

In the summer of 1904 copies of some of the photographs were sent to the Smithsonian Institution for examination, and through the suggestions and assistance of the experts of that Institution a new method of moving the camera was devised.

A spring-motor movement (of the kind used to operate revolving stands for exhibiting goods in show windows) was procured and mounted inside a table specially constructed for the purpose, and a stand for supporting the cameras was fitted to the central shaft.

As the speed of the mo was too slow, the fly-vane shaft was reinoved and the vane moved to the next shaft, which was lengthened so as to extend under the table. Thus arranged the fly vane could be made to revolve in a liquid placed in a vessel under the table, thereby preventing much of the vibration and getting a more uniform speed. Figure 4 shows the arrangement of the apparatus. The table top is removed in order to show how the motor movement is placed; the fly vane is seen under the table. The stand is usually revolved at a speed of one revolution in ten seconds, which the writer has found to be the most suitable for ordinary purposes. The reason for employing a motor movement with a uniform speed to move the camera is to ascertain the exact duration of a flash or the intervals between the rushes.

If the angle of the lens and the speed of the camera be known, it is a simple matter of measurement to ascertain the duration of a flash. The formula employed is as follows:

Call the angle of the lens (in degrees)=A°
Time for one rotation of stand (in seconds) =T
Width of plate (in millimeters)=W
Width of flash measured on plate (in millimeters)=N

Then time for flash (in seconds)



The measurements should be taken from the middle of the plate, owing to the distortion of the lens.

A number of photographs have been taken by this method, and about nine out of ten show the multiplicity of a flash. The average number of rushes for each flash is about five or six, and the time varies from an almost instantaneous value up to about half a second for a complete discharge.

The most interesting discharge obtained is shown in figure 5. It was taken September 1, 1905, at 9 p. m. The storm during which this flash was photographed began about 7 p. m., with the wind northeast, which is something very unusual for Chicago. The wind gradually changed to north and northwest. The temperature during the storm was about 24° C., and the barometer varied between 29.89 and 29.92. The flash was obtained when the storm was most severe and while it was raining very hard.

This flash is composed of forty separate discharges, made up of one band, which in all probability is composed of a number of sepa

SM 1905---12

prove that

rate rushes or oscillations very close together and one black discharge. It is this dark discharge which makes this flash interesting, and the photograph shows it running parallel and on both sides of the first bright rush, extending 0.6 millimeter on one side and 0.1 millimeter on the other, the boundary line on the latter side not being very marked. From this black discharge issue several side branches on both sides, a large one spreading out over the other rushes quite prominently. These side branches all pointing downward indicate that the black flash was a downward stroke, and they also tend to

must have had a good deal of resistance to overcome. It must have cleared the way for the first bright discharge, which in all probability proceeded from the ground upward. The difference in width of the bright flash, measured at its lower and upper part, would confirm this opinion, being for the lower part 0.38 millimeter and for the upper part 0.22 millimeter.

An interesting question here presents itself. Have we here two separate discharges with different rates of oscillation traveling the same path? Can such a condition be possible? To the writer's mind the most plausible explanation would be that the two discharges occupied two separate paths, one inside of the other, one discharge forming, so to speak, a tube through which the other passed.

It may also be claimed that the bright flash is probably part of the dark discharge for some reason rendered more luminous. This explanation may be the true one, although it appears as if the bright flash is entirely separate. The measurements of the width of the upper and lower parts of both flashes confirm this opinion, the difference in width of the bright flash being 40 per cent and for the dark discharge only 20 per cent. Authorities vary in their opinions as to the probable cause of these dark flashes. It has been suggested by some that there really are no black discharges, but what appear as such are excessively bright flashes causing a reversal of the image on the plate. This explanation may be the true one if we understand the word “ brightness" to mean increased actinic power of the light. In the black flash represented this chemical effect must have been extremely high, owing to the fact that the smallest hair-like extremities of the side branches are well reproduced on the picture as black, in comparison with the broader and to all appearance more powerful discharges which followed after.

It was at first thought probable that we had to deal with an interference phenomenon, but that idea was discarded. Then it was suggested that the black discharge was probably due to slow oscillations (the width of it would tend to confirm this opinion), and that what appeared as black on the plate would in reality be a dark red discharge on a partially illuminated background. This opinion had to be discarded for the reason that, if such be the case, the side

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