On Architecture

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

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 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 0, and those centres marked; then, through

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.

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 pro\s ta\ i(stopou/mena Parmenio; the pro\s pa=n kli=ma, 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. Preeminent 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

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.