It
therefore appears evident to us that the thread of our sun dial
carried a knot or bead whose shadow was followed upon the curves. This
shadow showed at every hour of the day the approximate date of the day
of observation. The sun dial therefore served as a calendar. But how
was the position of the bead found? Here we are obliged to enter into
new details. Let us project the figure upon a vertical plane (Fig. 3,
No. 1) and designate by H E the summits of the hyperbolas
corresponding to the winter and summer solstices. If P be the position
of the bead, the angles, P H H?, P E E?, will give the height of the
sun above the horizon at noon, at the two solstices. Between these
angles there should exist an angle of 47 deg., double the obliquity of the
ecliptic, that is to say, the excursion of the sun in declination: now
P E E?-P H H? = E P H = 47 deg..
Let us carry, at H and E, the angles, O H E = H E O = 43 deg. = 90 deg.-47 deg.;
the angle at 0 deg. will be equal to 180-86 = 94 deg.. If we trace the
circumference having O for a center, and passing through E and H, each
point, Q, of such circumference will possess the same property as the
angle, H Q E = 47 deg.. The intersection, P, of the circumference with the
straight line, N, therefore gives the position of the bead.
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