After having completed briefly the description of the dial and the
indices and their motions, I have not without reason delayed in
satisfying the desires of many who wish to learn at least the method by
which, from this mechanism, may be calculated the true times of new and
full moons, and their ecliptics. In order to make these matters clearer,
it is necessary that they be explained here at greater length.
With the indices, then, adjusted astronomically-geographically to the
longitude of any given region, and to the mean time whether past,
present or future, and assuming the clock to be in normal operation (as
at present it has been for a whole year and more), then the moon will be
in conjunction with the sun in the heavens. When the equations on the
mechanism are examined, the sun and moon shall be found to be in the
same degree of longitude, and in the same part of a degree. There will
also be an ecliptic new moon that is in conjunction with a solar
eclipse, or rather with a terrestrial eclipse. This will occur if, at
that time, both apexes of the first index, located below the center of
the clock, are hidden by the two segments of the circle extending from
the center of the mechanism through the lowest index.
And the eclipse will be greater and greater and, consequently, visible
in more regions of the earth, the more deeply the two pointers,
indicating the distance of the sun from its apogee, are hidden in the
center of the segments.
But whether the eclipse takes place in the head or in the tail of the
dragon, or whether it is north or south, is indicated by the small disk
of the sun attached to one of the two pointers hidden by the segments of
the circle. If, at that time, the little disk shall be found in the head
of the dragon inscribed on the plane of the dial, then the sun has been
snatched from the earth and ingloriously entombed, as it were, in the
huge jaw of the dragon. Then, ... the heavens themselves will lend aid
to the woeful pomp of the senseless funeral in full darkness by suddenly
lighting the unhappy lamps of the fixed stars. However, if the little
disk occupies the tail of the dragon on the mechanism, then the sun in
the heavens also, as if freed from the toils of the immense dragon's
tail, will emerge without difficulty.
The center of the eclipse will traverse the hemisphere of the earth
north of the solar path, always nearer to the pole of the ecliptic, in
proportion to the inclination of the disk to the north. On the other
hand, if the little disk inclines to the left semicircle, then the
people south of the solar path will enjoy the spectacle of the total
central eclipse.
But if the little disk remains neutral (inclining neither way) and
remains halfway between the two sections of the circle, then the
greatest solar eclipse will take place at the equator and those who live
near the poles of the ecliptic will not enjoy a trace of that eclipse.
This is because the half of the equatorial diameter enormously
outmeasures even the greatest apparent semidiameters of the sun and of
the moon, even taking as a norm the smallest horizontal parallax of the
moon.
What has been said about the true new moon is to be understood also,
proportionately, about the true full moon. For when, with respect to the
equations of the centers, the moon shall be distant on the mechanism by
a full semicircle from the sun (also in the heavens it will be truly in
opposition to the sun) there will be a true full moon. Likewise, the
moon in the heavens will be in eclipse if, at the time of opposition,
the pointers of the little index (which we mentioned before) situated
below the center of the clock are so far away from the belly of the
dragon that they are forced to lie under the two smaller segments of the
circle which, in all full moons, are always to be moved from the index
of the synodic moon to the region of that little index. As a matter of
fact, the closer the little pointers approach to the middle of the
segments, the more obscured it will be.
You will know, furthermore, that the eclipse of the moon occurs in the
head of the dragon if the disk of the little moon, attached to the other
point of the little index, is raised to the head of the dragon;
conversely, when the little disk of the moon inclines to the tail, the
eclipse is taking place in the tail of the dragon.
And, accordingly, when you observe the little moon of the index inclined
to one or other section of the circle, so also in the heavens, the
eclipse of the moon is only partial and the northern or the southern
part of the moon is illuminated.
The current time will indicate whether the lunar eclipse is visible or
not. As the new moon ecliptic falls during the day, the eclipse will not
be visible, since the earth denies a sight of the moon which is below
the horizon. But, conversely, if there are no clouds, the eclipse will
be visible anywhere, if the luminous bodies are ecliptically in
opposition at night.
Since lunar eclipses appear to all people as being of the same magnitude
and duration, and begin and dissipate at the same absolute moment of
time, I decided to reveal another facet of this spectacle on the right
side of the center of the clock (see chapter III above). There, at the
time of the true ecliptic full moon, as the pointer of the third little
index shows, you can ascertain the hours, etc., of duration, and the
inches of greatest obscuration. The little moon attached to the index is
a model of the actual eclipsed moon.