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Aug., 1931] SOLUTION OF ECLIPSE PROBLEMS 237
along this line was very small — only 2/3 of a mile across at its maximum.
It is a very curious circumstance that the size of the moon and its distances from the earth and the sun should be in just such a proportion that the length of the moon's shadow (the umbra) very closely approximates the distance of the moon from the earth, i. e., about 240,000 miles. It varies a few thousand miles in length, so that sometimes the earth is within the umbra and we see a total eclipse, and sometimes it is beyond the umbra (i. e., in the penumbra) and the eclipse is annular. It is still more curious and unique when these distances are so closely the same that the point of the coneshadow just touches the earth's surface for so short a path and with so small a spot.
Computation indicated that if pictures were taken from a height of 12,000 to 15,000 feet above the ground this shadow-spot might be entirely contained in the frames of a motion picture with margin enough for identification of nearby objects.
Geometrically, of course, two points are needed to determine a straight line. Hence, to locate the central line of the path of totality (which for a few hundred miles is nearly straight) we required two well separated sets of positions of the shadow. This meant also that we required four stations, two on the ground and two in the air, two good motion picture cameras, and two powerful aeroplanes.
This is not the place to tell the long story of preparation — the preliminary computations, the study of lighting conditions, the investigating and testing of films, the securing of aeroplanes and cameras, the selection of stations, the building and adjustment of auxiliary instruments, the transportation to the stations and setting up of the instruments, the placing of a large pattern of identification marks over miles of desert floor — two or three months of intensive work.
In solving this problem not only the exact location of the shadow was needed, but the exact time of the spot-location for each separate picture. For this, very fortunately, we were able to use a method that would have been quite impossible during previous eclipses — that is, to use a sound-camera to record time signals on the film itself. Hence we had to provide either for an astronomical determination of time on the spot or for the broadcasting of time signals by an astronomical station, and this required a radio receiver in the aeroplane in addition to the camera.
To make a long story short, we established two regular ground