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Editorial transcription lightly normalized from the cited scan; historical claims below are those of The Flaming Sword and are not independently verified.
EDITOR FLAMING SWORD: - I hear it argued by Copernicans that while pre-Copernican astronomers could and did foretell eclipses approximately, from a study of their cycles in the past, they could not map out the path of totality, as is now done with great accuracy by calculation. It is claimed that modern eclipse predictions are necessarily by calculation, since the path is never twice the same, and that no amount of study of cycles could furnish the slightest data for it. And it is further contended that these calculations being based on the Copernican system, their verification by the event demonstrates the truth of that system.
Could that path of totality be correctly mapped, exclusively from cellular data? - C. B., Salem, O.
The reason that neither the Ptolemaic nor the Copernican astronomers could map out the path of totality until recent times, is because the geography of the earth was not known. In addition to the tables of eclipse cycles, other factors must be considered. An eclipse cycle being of definite length (6,585 days, 7 hours, and 42 minutes), indicates the exact time and duration of eclipses; but the place and path must be computed from the basis of astronomical data, in connection with latitude, longitude, and time. The whole earth must be taken into account; its whole surface must be known and mapped before the belt from which the sun is seen to be totally eclipsed, can be mapped upon it.
Any system of astronomy can be made to embrace all of the observed relations of the sun and moon; and any system developed to the extent of the Copernican system, could be taken as a basis of eclipse calculations with results equally accurate. When a theory is developed sufficiently to incorporate an accounting for all of the movements of the physical heavens, it may express, in terms of its own, all of the eclipse elements; and no matter what the system may be, if it contains a system of orbits, with their angular relations, with observed speed of the orbs determined in terms of degrees of arcs, it may give values to each element in time and space, to fit all of the observed relations; and if fictitious values be taken as a basis of calculations, the results are the same. We contend that the accuracy of eclipse predictions, as per astronomical calculations, is not a proof of the correctness of the Copernican theory; the "proof" would prove too much, for it would prove any other theory developed to the same extent, true as well!
The Copernican system embraces all of the facts of the observed relations of the sun and moon; by observed relations we mean the apparent relations of orbits, eccentricities, nodes, apsides, etc. The surface of the earth is commonly supposed to be convex; it has its latitude and longitude, its poles and equator, its ecliptic and tropics, and consequent different periods of daylight, with the dividing line between day and night cutting the equator at different angles at different times, according as the sun is north or south of the equator. The revolving earth brings noon to each successive meridian; and the moon has an observed revolution in the heavens, covering a specific number of degrees in a given time. In the Koreshan System, the earth is of the same size, with same map and same relations of latitude and longitude. One half of its surface is illumined by the sun; it has its seasons; the obliquity of the ecliptic is in accordance with the observed facts of solar declinations, and the moon's relations, orbit, and lunations are the same as in the Copernican system, so far as celestial latitude and longitude are concerned. The Koreshan System is the antithet of the Copernican; it is the complete inversion of all of the principles in the popular theory; and different periods, cycles, changes, eclipses, transits, and all other astronomical phenomena which may be predicted by Copernicans to take place, by means of calculation from the basis of values in which it expresses all of these elements, are susceptible of being as accurately calculated from the basis of the Koreshan values given to the same facts of observation.
Suppose, for instance, that the ecliptic, the equator, and the lunar orbit were in the same plane. It is evident that a solar and a lunar eclipse would occur respectively at every new moon and full moon. It is easy for the reader to see that whether the earth be considered to be convex or concave, the path would be exactly the same - the middle of the eclipse path would be the equator throughout the time of the eclipse. But the ecliptic, equator, and lunar orbit do not sustain these relations, but different relations. But these different relations are constant; and if both the Copernican and the Koreshan systems use exactly the same facts of observation, the same observed relations, the line of totality of a solar eclipse would be marked out in exactly the same direction on the earth in each.
Both the Copernican and the Koreshan astronomers observe and measure the sun's discular diameter, and express it in terms of minutes of a degree - about 32'; and the moon about the same. Each observes that the moon's orbit sustains an obliquity to the ecliptic of 5° 19' (maximum; 4° 57' minimum); in each system, then, the eclipse limits are the same, for in each system the lunar parallax is the same, and the earth's semidiameter the same, the times the same, and the circles in each system contain exactly 360°. If the moon falls within 9° 30' (its minor eclipse limit) of its node, it will enter the zone of the lunar cut-off. By observation, we determine the angular distance of the moon from the sun, at which the moon will just escape producing a solar eclipse. The breadth of the solar eclipse belt or limit is about 3°; if the moon, when it is new, should come within this belt of 3° (1 1/2° north or south of the sun), an eclipse will occur. These 3° are related to 180° of the earth's surface; and when the moon is within the belt of 3°, when it is new it will cast a shadow somewhere in the circumference of the illumined hemisphere of the earth. Where?
Now, suppose the moon becomes new at noon on June 21, when the sun is on the meridian of Washington; - that is, suppose the middle of totality occurs at that time. The shadow would, at that moment, be projected onto that part of the earth of which the sun is the zenith - just north of Cuba. For any solar eclipse we can determine the path of the moon as related to the sun, and with equal accuracy determine the point of projection for every minute of the eclipse.
In both systems, the revolution of the moon in the heavens from west to east, covers exactly the same number of minutes of a degree per hour; and in both systems the moon has crossed the ecliptic at exactly the same angle. In the Koreshan System, the heavens complete a revolution in the same time that the earth is supposed to turn over in the other system; therefore, the speed of the spot of totality (about 100 miles in diameter) toward the east would be exactly the same in both systems; for we are both considering the facts as they are actually known beforehand, from astronomical data, to occur. The difference is, the one is supposing that the shadow is projected on a convex surface, while the other holds that it is projected in a concave earth. No matter whether the earth be convex or concave, the angle at which the moon crosses the ecliptic during the eclipse will project a shadow in the same direction on the earth's surface; and the calculation of the direction of its path, or the path of any eclipse, after the time is fixed, is a simple problem in spherical trigonometry.
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The Flaming Sword · Vol. 13, No. 25 · · PDF pp. 10-11