Not even this seemingly precise pinpointing, however, would satisfy Colonel J. D. Abell and his associates in the Army Map Service. New methods of navigation, such as Loran, have disclosed gross errors in cartographic data. Particularly inaccurate are the positions of the oceanic islands; some important atolls in the Pacific appear to be as much as half a mile or more off their true positions on the map.

The personnel of Colonel Abell's bureau, in conjunction with the 30th Engineer Group under Colonel William C. Holley, has developed an ingenious method of surveying by astronomical occultations which promises greatly improved accuracy. They have invited amateurs-in or out of military service -to join in their fascinating research program.

"Our trouble," writes John A. O'Keefe, chief of the Research and Analysis Branch of the Army Map Service, "stems from the fact that we don't know straight up! If we had some way of pinpointing our zenith we could draw maps to any desired accuracy." In other words, if accurately known positions on the earth were correlated with one another by locating them with reference to the known positions of stars when they are at the zenith, the correlations would enable the cartographers to draw a good map of the world.

In principle the job is simple. You wait until a selected star of known position is directly overhead and clock it. Accurate timing is necessary because the relationship of the earth's surface to the sky changes continually as the earth rotates. Time signals broadcast from the U. S. Bureau of Standards' station WWV make precise clocking easy.

The usual instrument used for locating the zenith is a transit, which relies on a plumb bob or its counterpart, the bubble level. The source of error resides right here in these two gadgets, according to O'Keefe. Both the plumb bob and the bubble are thrown out of true by local irregularities in the density of the earth's crust which distort the gravitational field. Attempts have been made to correct for local deviations, but "this sort of guesswork gets you nowhere," says Floyd W. Hough, chief of the Service's Geodetic Division. "Even if you could estimate the effect of surface features accurately, you still would need information about conditions underground. Density varies there, too, and generally in the opposite direction."

The Army men decided to fix positions on the earth by timing occultations of stars by the moon as it moves across their positions in the heavens. One method of using the moon as a geodetic instrument is to photograph its position in relation to stars in the background at a given instant; it has been possible in this way to get fixes accurate to a tenth of a second of arc, which means locating positions on the earth with an accuracy within 600 feet. However, considering that this distance is more than twice the width of an aircraft runway, the desirability of still greater accuracy is obvious. The Army Map Service set out to improve on the accuracy of fixes by the moon's occultations.

The best telescopes, such as the 200-inch reflector on Palomar Mountain and the largest refractors, have a theoretical resolving power considerably better than .1 second of arc. But you cannot carry them from place to place on the earth, and furthermore their resolving power has practical limits, imposed by poor seeing conditions, distortion of the optical train by variations of temperature and so on. Above all there is diffraction, the master image-fuzzer, which arises from the wave character of light itself. Because adjacent waves interfere with one another, the light from a distant star does not cast a knife-sharp shadow when it passes the edge of the moon. Waves of starlight grazing the moon's edge interact, diverge and arrive at the earth's surface as a series of dark and light bands bordering the moon's shadow. The first band, the most pronounced, is about 40 feet wide.

The solution hit upon by O'Keefe and his associates was a new way to use a telescope which makes it capable of incredible resolution. They developed a portable rig (which amateurs can build) that plots lunar positions to within .005 second of arc as a matter of everyday field routine-resolution equivalent to that of an 800-inch telescope working under ideal conditions! It can also do a lot of other interesting things, such as measuring directly the diameters of many stars. It can split into double stars images which the big refractors show as single points of light. Some observers believe that it could even explore the atmosphere of a star layer by layer, as though it were dissecting a gaseous onion. Of greatest interest to the Army, the method measures earth distances of thousands of miles with a margin of uncertainty of no more than 150 feet!

The telescope that yields these impressive results has a physical aperture of only 12 inches. The design-a Cassegrain supported in a Springfield mounting-follows plans laid down by the late Russell W. Porter, for many years one of the world's leading amateur telescope makers. Full details of the optical parts and mounting are presented in Amateur Telescope Making-Book Two.

The secret of the instrument's high resolving power is in the way it is used rather than in uniqueness of optical design. The telescope is trained on a selected star lying in the moon's orbit and is guided carefully until the advancing edge of the moon overtakes and begins to cover the star. Depending on the diameter and distance of the star, it may take up to .125 of a second for the moon to cover (occult) it completely. During w this interval the edge of the moon becomes, in effect, part of the telescope-like a pinhole objective with an equivalent focal length of 240,000 miles. As the edge of the moon passes across the star, the intensity of the starlight diminishes, and the differences in intensity at successive instants are measured. It is as if a 240,000-mile-long tube were equipped at the distant end with a series of slit objectives-with the moon covering one slit at a time. The resolving power depends upon the great focal length.

The tiny successive steps in the starlight's decay are detected by a photomultiplier tube and a high-speed recorder. In principle the measurement of terrestrial distances by lunar occultation resembles measuring by the solar eclipse technique. The moon's shadow races over the earth's surface at about 1,800 feet per second. Except for differences in instrumentation and the mathematical reduction of results, the eclipse of the star is essentially the same kind of event as the eclipse of the sun. The insensitivity of the eye prevents star eclipses from making newspaper headlines, but photomultiplier tubes respond to such an eclipse strongly. They also detect the fuzziness caused by diffraction at the edge of the moon's shadow. The most prominent diffraction band, as previously mentioned, is some 40 feet across-the limit to which measurements by occultation are carried. The sharpest drop in starlight registered on typical recordings spans .015 second of time. Since the moon near the meridian has an average apparent speed of about .33 of a second of angular arc per second of time, the recorded interval of .015 of a second corresponds to .005 of a second of arc. This is the instrument's effective resolving power.

Any amateur who owns a Springfield mounting equipped with a high-quality mirror of eight inches aperture or larger can convert for high resolution work at a cost which is modest in proportion to the gain in performance. What he needs is a photomultiplier tube, a power supply, an amplifier and a high-speed recorder.

The photocell costs about $150. The amplifier must be of the direct-current type with a linear response good to at least 200 pulses per second. The recorder should be a double-channel job-one pen for registering time signals and the other for starlight. The Brush Development Company of Cleveland markets a recorder of the recommended type along with a companion amplifier for about $1,000. With a little ingenuity the amateur can contrive adequate counterparts for substantially less. He also needs a filter to cut out the 400- and 600-cycle tone of WWV, so beloved of musicians. These units are available through dealers in radio equipment for about $15.

The eyepiece must be equipped with a cell for the photomultiplier tube and with a pinhole aperture for screening out unwanted moonlight. The pinhole (about .010 of an inch in diameter) is made in a metal mirror assembled in the eyepiece tube at an angle of 45 degrees, as shown in the drawing on the opposite page. A Ramsden eyepiece focuses on the pinhole. In operation the mirror is seen as a bright field with a small black speck, the pinhole, in the center. The star's image appears against the mirror as a brighter speck on the bright field. Thus it is easy to guide the image-into position over the pinhole. When properly centered, some starlight strikes the edge of the pinhole, forming a small brilliant ring surrounding a jet-black speck. The ring aids in subsequent guiding.

Occultation observing has attracted a substantial following among amateurs in recent years. In the U. S. their interest in the work has been stimulated by the Occultation Section of the American Association of Variable Star Observers, whose offices are at 4 Brattle Street, Cambridge 38, Mass. Their world-wide observations, made by eye and timed by chronograph, are forwarded to Flora M. McBain at Greenwich, England. She supervises the mathematical reductions. The results of occultation observations have been used to establish irregularities in the rotation of the earth and to improve the tabulations of the moon's orbit.

Dirk Brouwer of the Yale University Observatory, who has made an exhaustive interpretation of the observations collected during the past century, sees an opportunity in the new photoelectric technique for the group to make an impressive addition to its already substantial scientific contribution. The photoelectric cell betters the response time of the eye (estimated at about .1 second of arc) by 100-fold or more and eliminates human variables. Thus it makes possible far higher accuracy in timing occultations. Moreover, the high-resolution aspect of the technique opens a whole new and relatively unexplored field for original work by amateurs. As Professor Brouwer points out, star occultations, like solar eclipses, can be observed only in certain regions at particular times. A world-wide network of amateur observatories equipped for high resolution work could cover many more star occultations in any year than are accessible to the great telescopes of Southern California.

One serious drawback that prevents utilizing the full potential of the increased accuracy at present is the irregularity of the moon's surface. If these irregularities are not allowed for in the calculations, the resulting position of the moon will frequently be off by several tenths of a second of arc. And if the star happens to be occulted at a point on the moon's limb where a high peak or low valley is located, the result may be off in extreme cases by two seconds of arc. A new study of the irregularities of the moon's surface by C. B. Watts at the United States Naval Observatory in Washington, expected to be completed soon, should make it possible to correct for the deviations with an accuracy matching the sensitivity of the photoelectric technique.

The drawing above shows a pair of typical curves, recording the occultations of a sixth magnitude star and an eighth magnitude one. Note the jaggedness of the fainter star's curve. This is due to "noise," a term borrowed from radio and telephone engineering to describe random fluctuations in the output current of an amplifying device. The output of noise increases when the volume or "gain" control of the amplifier is turned up to compensate for a weak input signal. Noise originating in the photomultiplier (the principal source) can be reduced by chilling the tube with dry ice. The sharp drop in each curve marks the interval of occultation. Its steepness is determined principally by the diffraction pattern. In the case of some big stars, such as Antares, the effect of size can be seen in a flattening of the curve.

When a double-star system is occulted, the curve drops steeply for a time, indicating occultation of the first star, then levels off, and falls steeply again when the companion is occulted. The duration of the flat portion of the curve is the measure of the pair's separation. Some curves of Antares and other large stars show bends and twists which seem to come from bright and dark parts of the star's disk as well as from the stellar atmosphere. The proper interpretation of these records, however, is still considered an open question by some astronomers-another indication of the opportunity the technique presents to an amateur who enjoys original work.

"There is far better than an even chance that we shall stumble onto much that we didn't expect," writes O'Keefe. "We are examining stellar disks with greater resolving power than ever before. We shall certainly find a lot of close, fast binary stars. Perhaps we shall also find stars with extended atmospheres and all that. In occultations of very bright stars we are in a position to detect very faint, close companions. I really do not see how anyone getting into this sport can miss hooking some information of value, and he might catch a really big fish.

Incidentally, if a college man with a background in astronomy faces induction into the armed forces and the idea of occultation work appeals to him, he would be well advised to communicate with the Army Map Service in advance. The bureau is on the lookout for likely candidates.

In many respects photoelectric occultation seems almost too good to be true. Neither poor seeing nor diffraction within the instrument has the slightest effect on the high resolving power of the method, and it is as precise when the moon occults a star low in the sky as overhead. The reasons will be discussed in these pages in a future issue along with other theoretical aspects of the phenomenon, if a significant number of readers express an active interest in the subject.

"The whole thing," writes O'Keefe, "no doubt gives the impression that a rabbit is being produced from a hat. It appears most surprising that such a powerful method for detailed examination of the sky should have gone unexplored for so long. This, of course, we enjoy. Our group did not invent the technique: It was suggested by K. Schwarzschild in Germany and A. E. Whitford in the U. S. It has not been exploited before because people simply could not believe that it works. But if I can get people to disbelieve thoroughly in something which is done before their eyes, then I have at least entertained them-and myself."

Bibliography

ELECTRONICS: EXPERIMENTAL TECHNIQUES. William C. Elmore and Matthew Sands. McGraw-Hill Book Company, Inc., 1949.

AMATEUR TELESCOPE MAKING. Edited by Albert G. Ingalls. Scientific American, Inc., 1952.

AMATEUR TELESCOPE MAKING-ADVANCED. Edited by Albert G. Ingalls. Scientific American, Inc., 1952.

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