∴ True zenith distance of sun’s centre = 87° 50′ + 17′ + 14′ = 88° 21′. _Declination_:-- Having obtained the zenith distance, and the azimuth, the latitude being known, the N.P.D. (North Polar Distance) of the sun may be found by the following equations:-- (1) tan θ = tan _z_. cos A, where θ is the subsidiary angle which must be determined for the purpose of computation, _z_ is the true zenith distance, and A is the distance from the _North_ point. cos _z_. cos (c - θ)[134] (2) cos Δ = -------------------------, cos θ where Δ is the N.P.D. of the celestial object, and _c_ is the colatitude (90° - lat.) of the place of observation. In the example taken this gives us-- (1) tan θ = tan 88° 21′. cos 66° 38′ θ = 85° 50′ 45″ cos 88° 21′. cos (39° 52′ - 85° 50′ 45″) (2) cos Δ = ---------------------------------------- cos 85° 50′ 45″ Δ = 73° 57′ 50″ Declination, δ, = (90° - Δ) = 16° 2′ 10″ N. Reference to the Nautical Almanac shows that this is the sun’s declination on May 5 and August 9. We may therefore conclude that the Long-stone was erected to mark the May sunrise, as seen from the Tregeseal Circle. Had we been dealing with a star, instead of the sun, the only modification necessary in the process of calculating the declination would have been to omit the semi-diameter correction of 14′. Having obtained a declination, we must refer to the curves given on pp. 115-6 in order to see if there is any star which fits it, and to find the date. Take, for example, the case of the apex of Carn Kenidjack, as seen from the Tregeseal circle-- Az. = N. 12° 8′ E.; hill = 4° 0.′ lat. = 50° 8′. This gives us a declination of 42° 33′ N., and a reference to the stellar-declination curves (p. 115-6) shows that Arcturus had that declination in 2330 B.C. From the table given on p. 117, we see that at that epoch Arcturus acted as warning-star for the August sun. In cases where the elevation of the horizon is 30′, or in preliminary examinations, where it may be assumed as 30′, the refraction exactly counterbalances the hill, and therefore the true zenith distance at the moment of star-rise is 90°. Hence the N.P.D. of the star may be found from the following simple equation-- (3) cos Δ = cos A cos λ where Δ and A have the same significance as before and λ is the _latitude_ of the place of observation. [133] _Demonstrations and Practical Work in Astronomical Physics at the Royal College of Science, South Kensington._ Wyman and Sons, 1_s._ [134] cos (c - θ) = cos -(c - θ). INDEX A. =Abydos=, clock star at, 297. =Africa=, sacred stones and trees, 235. =Aldebaran=, _see_ Tauri α. “=Allée couverte=,” 41, 317. “=All Hallows=,” 187; Irish and Welsh equivalents, 195. “=All Souls=,” change of date, 186. =Alsia well=, 227. =Altar stone=, Stonehenge, 81; Aberdeen type, 36. =Amen-Rā=, 2; temple of, 55, 297.