atmospheric conditions. These are particularly valuable to modern science, and they will be discussed more extensively, beginning in §5.

acronychal rising ecliptic/'

(rising at dusk)

heliacal/acronychal setting

\ ecliptic

(last visibility before conjunctii

Figure 3.18. Horizon views of heliacal, cosmical, and acronychal risings and settings. Heliacal or cosmical rising is the occasion when an object is visible for the first time in the dawn sky following (solar) conjunction, and heliacal or achronychal setting is when it is last seen just after sundown. In the context of risings and settings, "cosmical" and "achronychal" refer to phemomena associated with sunrise and sunset, repectively. Drawn by E.F. Milone.

The Big Horn Medicine Wheel in Wyoming (Figures 6.38c-e) may contain terrestrial markers for heliacal risings of several bright stars (Eddy 1974, 1977; Robinson 1980). The azimuths of the stars correspond to declinations at ~1250 a.d., and underlying features of the site suggest even greater antiquity (Fries 1980). Other medicine wheels have had relatively few alignments, suggesting that they were not always constructed with accurate sky measurements in mind, at least in the same way.

A well-known use of the stars through the ages has been for navigation. The requirements for astronomical navigation are implicit in the discussions of spherical astronomy. The latitude can be determined from the altitude of the north celestial pole, and to within about 2°, with the altitude of Polaris, at the present epoch. It can also be determined by the declination of a star passing through the zenith, or which just skims the northern or southern horizon. For the longitude, one needs the instant of transit, or rise or set of a given star, bearing in mind the dimming that accompanies very low altitudes. The local time at sunset is readily obtained by the stars that rise heliacally or acronychally; at any time of night, the local sidereal time is obtained by observing the right ascension of stars that transit the celestial meridian. The difficulty is that to determine the longitude, one needs the time at some other meridian—a meridian whose longitude is known. The best one can do without a chronometer that records the time at that distant meridian is dead reckoning. The direction of travel can be determined, and by estimating the rate of travel, one can compute the distance traveled. There is ample evidence that the Polynesian travelers used just such methods, and their methods are discussed in §11.3.

The type of observations we have described thus far involve systematic study of the Sun, Moon, and the other planets of antiquity. The observational records of ancient Mesopotamia and China also contain references to transient phenomena such as eclipses, comets, novae, meteors, and

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