SUMMER Rising N-E or Rising N-E or SOLSTICE. Setting N-W. Setting N-W. ° ′ ° ′ Sun’s centre; uncorrected 39 16 50 40 {sea horizon 37 1 49 20 Sun’s upper limb; corrected{hill ¹⁄₂° high 38 34 50 16 for semi-diameter and { „ 1° „ 40 8 51 12 refraction { „ 1¹⁄₂° „ 41 30 52 4 WINTER Rising S-E or Rising S-E or SOLSTICE. Setting S-W. Setting S-W. ° ′ ° ′ Sun’s centre; uncorrected 39 16 50 40 {sea horizon 41 24 52 0 Sun’s upper limb; corrected{hill ¹⁄₂° high 39 54 51 4 for semi-diameter and { „ 1° „ 38 23 50 8 refraction { „ 1¹⁄₂° „ 36 54 49 14 The first important thing we learn from the table is that although at both solstices the azimuths of the rising and setting of the sun’s centre are the same, these azimuths of the upper limb at the summer and winter solstices differ in a high northern latitude by some 5°. The difference arises, of course, from the fact that the limb is some 16′ from the sun’s centre, so that considering the sun’s centre as a star with fixed declination, at rising the limb appears before the centre, and at setting it lags behind it. [Illustration: FIG. 37.--The Azimuths of the Sunrise (upper limb) at the Summer Solstice. The values given in the table have been plotted, and the effect of the height of hills on the azimuth is shown. The range of latitude given enables the diagram to be used in connection with the solstitial alignments at Carnak, Le Ménac, and other monuments in Brittany. ~Vertical axis from bottom: LAT. 47-59.~ ~Horizontal axis from left: AZIMUTHS 37-56.~ ~Curves from left: SEA HORIZON, HILLS ¹⁄₂°, 1°, 1¹⁄₂°~] It will also be seen that at sunrise hills increase the azimuth from N., and refraction reduces it; while at setting, hills reduce the azimuth from S. and refraction increases it. This diagram and table should fully explain the variation of azimuth at sunrise caused by the fact that from our present point of view we do not deal with the sun as a star. To make the foregoing applicable for monuments in all latitudes between Brittany and the Orkneys, I give still another diagram, Fig. 37, also prepared for me by Mr. Rolston which will enable any archæologist to determine approximately, _for the present time_, the azimuth of sunrise at the summer solstice, without waiting for the 21st of June in any year actually to observe it.