The Ten Books on Architecture
represent the ray of the sun in winter, and the other the ray in summer.
Opposite E will be the point I, where the line drawn through the centre
at the point A cuts the circumference; opposite G and H will be the
points L and K; and opposite C, F, and A will be the point N.
5. Then, diameters are to be drawn from G to L and from H to K. The
upper will denote the summer and the lower the winter portion. These
diameters are to be divided equally in the middle at the points M and O,
and those centres marked; then, through these marks and the centre A,
draw a line extending to the two sides of the circumference at the
points P and Q. This will be a line perpendicular to the equinoctial
ray, and it is called in mathematical figures the axis. From these same
centres open the compasses to the ends of the diameters, and describe
semicircles, one of which will be for summer and the other for winter.
6. Then, at the points at which the parallel lines cut the line called
the horizon, the letter S is to be on the right and the letter V on the
left, and from the extremity of the semicircle, at the point G, draw a
line parallel to the axis, extending to the left-hand semicircle at the
point H. This parallel line is called the Logotomus. Then, centre the
compasses at the point where the equinoctial ray cuts that line, at the
letter D, and open them to the point where the summer ray cuts the
circumference at the letter H. From the equinoctial centre, with a
radius extending to the summer ray, describe the circumference of the
circle of the months, which is called Menaeus. Thus we shall have the
figure of the analemma.
7. This having been drawn and completed, the scheme of hours is next to
be drawn on the baseplates from the analemma, according to the winter
lines, or those of summer, or the equinoxes, or the months, and thus
many different kinds of dials may be laid down and drawn by this
ingenious method. But the result of all these shapes and designs is in
one respect the same: namely, the days of the equinoxes and of the
winter and summer solstices are always divided into twelve equal parts.
Omitting details, therefore,--not for fear of the trouble, but lest I
should prove tiresome by writing too much,--I will state by whom the
different classes and designs of dials have been invented. For I cannot
invent new kinds myself at this late day, nor do I think that I ought to
display the inventions of others as my own. Hence, I will mention those
that have come down to us, and by whom they were invented.
CHAPTER VIII
SUNDIALS AND WATER CLOCKS
1. The semicircular form, hollowed out of a square block, and cut under
to correspond to the polar altitude, is said to have been invented by
Berosus the Chaldean; the Scaphe or Hemisphere, by Aristarchus of Samos,
as well as the disc on a plane surface; the Arachne, by the astronomer
Eudoxus or, as some say, by Apollonius; the Plinthium or Lacunar, like
the one placed in the Circus Flaminius, by Scopinas of Syracuse; the
[Greek: pros ta historoumena], by Parmenio; the [Greek: pros pan klima],
by Theodosius and Andreas; the Pelecinum, by Patrocles; the Cone, by
Dionysodorus; the Quiver, by Apollonius. The men whose names are written
above, as well as many others, have invented and left us other kinds:
as, for instance, the Conarachne, the Conical Plinthium, and the
Antiborean. Many have also left us written directions for making dials
of these kinds for travellers, which can be hung up. Whoever wishes to
find their baseplates, can easily do so from the books of these writers,
provided only he understands the figure of the analemma.
2. Methods of making water clocks have been investigated by the same
writers, and first of all by Ctesibius the Alexandrian, who also
discovered the natural pressure of the air and pneumatic principles. It
is worth while for students to know how these discoveries came about.
Ctesibius, born at Alexandria, was the son of a barber. Preëminent for
natural ability and great industry, he is said to have amused himself
with ingenious devices. For example, wishing to hang a mirror in his
father's shop in such a way that, on being lowered and raised again, its
weight should be raised by means of a concealed cord, he employed the
following mechanical contrivance.
3. Under the roof-beam he fixed a wooden channel in which he arranged a
block of pulleys. He carried the cord along the channel to the corner,
where he set up some small piping. Into this a leaden ball, attached to
the cord, was made to descend. As the weight fell into the narrow limits
of the pipe, it naturally compressed the enclosed air, and, as its fall
was rapid, it forced the mass of compressed air through the outlet into
the open air, thus producing a distinct sound by the concussion.
4. Hence, Ctesibius, observing that sounds and tones were produced by
the contact between the free air and that which was forced from the
pipe, made use of this principle in the construction of the first water
organs. He also devised methods of raising water, automatic
contrivances, and amusing things of many kinds, including among them the
construction of water clocks. He began by making an orifice in a piece
of gold, or by perforating a gem, because these substances are not worn
by the action of water, and do not collect dirt so as to get stopped up.
5. A regular flow of water through the orifice raises an inverted bowl,
called by mechanicians the "cork" or "drum." To this are attached a rack
and a revolving drum, both fitted with teeth at regular intervals. These
teeth, acting upon one another, induce a measured revolution and
movement. Other racks and other drums, similarly toothed and subject to
the same motion, give rise by their revolution to various kinds of
motions, by which figures are moved, cones revolve, pebbles or eggs
fall, trumpets sound, and other incidental effects take place.
6. The hours are marked in these clocks on a column or a pilaster, and a
figure emerging from the bottom points to them with a rod throughout the
whole day. Their decrease or increase in length with the different days
and months, must be adjusted by inserting or withdrawing wedges. The
shutoffs for regulating the water are constructed as follows. Two cones
are made, one solid and the other hollow, turned on a lathe so that one
will go into the other and fit it perfectly. A rod is used to loosen or
to bring them together, thus causing the water to flow rapidly or slowly
into the vessels. According to these rules, and by this mechanism, water
clocks may be constructed for use in winter.
7. But if it proves that the shortening or lengthening of the day is
not in agreement with the insertion and removal of the wedges, because
the wedges may very often cause errors, the following arrangement will
have to be made. Let the hours be marked off transversely on the column
from the analemma, and let the lines of the months also be marked upon
the column. Then let the column be made to revolve, in such a way that,
as it turns continuously towards the figure and the rod with which the
emerging figure points to the hours, it may make the hours short or long
according to the respective months.
8. There is also another kind of winter dial, called the Anaphoric and
constructed in the following way. The hours, indicated by bronze rods in
accordance with the figure of the analemma, radiate from a centre on the
face. Circles are described upon it, marking the limits of the months.
Behind these rods there is a drum, on which is drawn and painted the
firmament with the circle of the signs. In drawing the figures of the
twelve celestial signs, one is represented larger and the next smaller,
proceeding from the centre. Into the back of the drum, in the middle, a
revolving axis is inserted, and round that axis is wound a flexible
bronze chain, at one end of which hangs the "cork" which is raised by
the water, and at the other a counterpoise of sand, equal in weight to
the "cork."
9. Hence, the sand sinks as the "cork" is raised by the water, and in
sinking turns the axis, and the axis the drum. The revolution of this
drum causes sometimes a larger and sometimes a smaller portion of the
circle of the signs to indicate, during the revolutions, the proper
length of the hours corresponding to their seasons. For in every one of
the signs there are as many holes as the corresponding month has days,
and a boss, which seems to be holding the representation of the sun on a
dial, designates the spaces for the hours. This, as it is carried from
hole to hole, completes the circuit of a full month.
10. Hence, just as the sun during his passage through the constellations
makes the days and hours longer or shorter, so the boss on a dial,
moving from point to point in a direction contrary to that of the
revolution of the drum in the middle, is carried day by day sometimes
over wider and sometimes over narrower spaces, giving a representation
of the hours and days within the limits of each month.
To manage the water so that it may flow regularly, we must proceed as
follows.
11. Inside, behind the face of the dial, place a reservoir, and let the
water run down into it through a pipe, and let it have a hole at the
bottom. Fastened to it is a bronze drum with an opening through which
the water flows into it from the reservoir. Enclosed in this drum there
is a smaller one, the two being perfectly jointed together by tenon and
socket, in such a way that the smaller drum revolves closely but easily
in the larger, like a stopcock.
12. On the lip of the larger drum there are three hundred and sixty-five
points, marked off at equal intervals. The rim of the smaller one has a
tongue fixed on its circumference, with the tip directed towards those
points; and also in this rim is a small opening, through which water
runs into the drum and keeps the works going. The figures of the
celestial signs being on the lip of the larger drum, and this drum being
motionless, let the sign Cancer be drawn at the top, with Capricornus
perpendicular to it at the bottom, Libra at the spectator's right, Aries
at his left, and let the other signs be given places between them as
they are seen in the heavens.
13. Hence, when the sun is in Capricornus, the tongue on the rim touches
every day one of the points in Capricornus on the lip of the larger
drum, and is perpendicular to the strong pressure of the running water.
So the water is quickly driven through the opening in the rim to the
inside of the vessel, which, receiving it and soon becoming full,
shortens and diminishes the length of the days and hours. But when,
owing to the daily revolution of the smaller drum, its tongue reaches
the points in Aquarius, the opening will no longer be perpendicular, and
the water must give up its vigorous flow and run in a slower stream.
Thus, the less the velocity with which the vessel receives the water,
the more the length of the days is increased.
14. Then the opening in the rim passes from point to point in Aquarius
and Pisces, as though going upstairs, and when it reaches the end of the
first eighth of Aries, the fall of the water is of medium strength,
indicating the equinoctial hours. From Aries the opening passes, with
the revolution of the drum, through Taurus and Gemini to the highest
point at the end of the first eighth of Cancer, and when it reaches that
point, the power diminishes, and hence, with the slower flow, its delay
lengthens the days in the sign Cancer, producing the hours of the summer
solstice. From Cancer it begins to decline, and during its return it
passes through Leo and Virgo to the points at the end of the first
eighth of Libra, gradually shortening and diminishing the length of the