At the extremity of these lines are marked the signs of the zodiac. At
the top, a pretty banderole, which appears at first sight to form a
part of the _ensemble_ of the curves, completes the design. Such is
this wonderful little instrument, in which everything is arranged in
harmonious lines that delight the eye and easily detract one's
attention from a scientific examination of it. Let us enter upon this
drier part of our subject; we shall still have room to wonder, and let
us take up first the higher question.
[Illustration: FIG. 3.--DIAGRAM EXPLANATORY OF THE MANDOLIN SUN DIAL.]
Let us consider a horizontal plane (Fig. 3, No. 2)--a plane
perpendicular to the meridian, and a right line parallel with the axis
of the world. Let P be a point upon this line. As we have seen, such
point is the summit of a very wide cone described in one day by the
solar rays. At the equinox this cone is converted into a plane, which,
in a vertical plane, intersects the straight line A B. Between the
vernal and autumnal equinoxes the sun is situated above this plane,
and, consequently, the shadow of P describes the lower curves at A B.
During winter, on the contrary, it is the upper curves that are
described. It is easily seen that the curves traced by the shadow of
the point P are hyperbolas whose convexity is turned toward A B.
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