TER VII

THE ANALEMMA AND ITS APPLICATIONS

1. In distinction from the subjects first mentioned, we must ourselves
explain the principles which govern the shortening and lengthening of
the day. When the sun is at the equinoxes, that is, passing through
Aries or Libra, he makes the gnomon cast a shadow equal to eight ninths
of its own length, in the latitude of Rome. In Athens, the shadow is
equal to three fourths of the length of the gnomon; at Rhodes to five
sevenths; at Tarentum, to nine elevenths; at Alexandria, to three
fifths; and so at other places it is found that the shadows of
equinoctial gnomons are naturally different from one another.

2. Hence, wherever a sundial is to be constructed, we must take the
equinoctial shadow of the place. If it is found to be, as in Rome, equal
to eight ninths of the gnomon, let a line be drawn on a plane surface,
and in the middle thereof erect a perpendicular, plumb to the line,
which perpendicular is called the gnomon. Then, from the line in the
plane, let the line of the gnomon be divided off by the compasses into
nine parts, and take the point designating the ninth part as a centre,
to be marked by the letter A. Then, opening the compasses from that
centre to the line in the plane at the point B, describe a circle. This
circle is called the meridian.

3. Then, of the nine parts between the plane and the centre on the
gnomon, take eight, and mark them off on the line in the plane to the
point C. This will be the equinoctial shadow of the gnomon. From that
point, marked by C, let a line be drawn through the centre at the point
A, and this will represent a ray of the sun at the equinox. Then,
extending the compasses from the centre to the line in the plane, mark
off the equidistant points E on the left and I on the right, on the two
sides of the circumference, and let a line be drawn through the centre,
dividing the circle into two equal semicircles. This line is called by
mathematicians the horizon.

[Illustration]

4. Then, take a fifteenth part of the entire circumference, and, placing
the centre of the compasses on the circumference at the point where the
equinoctial ray cuts it at the letter F, mark off the points G and H on
the right and left. Then lines must be drawn from these (and the centre)
to the line of the plane at the points T and R, and thus, one will
represent the ray of the sun in winter, and the other the ray in summer.
Opposite E will be the point