the earth's axis, so that SN marks the south and north line on the earth, and the angle PST must be equal to the latitude of the place where the dial is intended to be used. The table is calculated for the latitude 45°, that being about the mean latitude for Ontario.

Table for graduating a horizontal dial. Lat. 45°.

The hours counting from noon must be set off both ways from the lines SN. Thus the angle NS-XI is the same as NS-I, but in the opposite direction; NS-I: 15 is the same as NS-X:45, NS-II: 45 is the same as NS-IX: 15, etc.

Sun-dials were commonly in use for astronomical as well as for domestic purposes as late as the time of the Danish astronomer, Tycho Brahe, who was born in 1546 and died in 1601, and who used them in connection with his observations.

With the improvements in clocks and watches and the increase in their numbers, the sun-dial has almost fallen into disuse except for sentimental or ornamental purposes. And it must be admitted by all, except the most matter-of-fact people, that a lawn or a garden, with shrubs and flowers and bordered walks, is much improved in esthetic appearance by the presence of a dial at the centre of some of its open spaces. Of late years improvements have been made in the form of the dial so as to adapt it to any latitude, while at the same time making its graduation lines equidistant, and therefore easier to read accurately. For the purposes of hunters, prospectors, explorers, etc., dials are made to be carried in the pocket, and set up as required. But it must not be forgotten, in the face of all this, that sun-dials, noon marks and all such contrivances depending on the motion of a shadow in sunlight, indicate solar time only,

and that on account of the non-uniformity of the sun's motion, this is not the time kept by clocks and watches, and that to set or regulate a clock by a sun-dial or noon mark, a certain correction, known as the equation of time, has to be applied from day to day. These things will be considered more fully hereafter.

The dial is manifestly useless in cloudy weather and between sunset and sunrise, although a story is told of a man who went out at night with his lamp to read the time upon his sun-dial.

Now, as a great portion of astronomical work has always been done at night, the old astronomers, who preceded modern timepieces, had to invent something to supplement the dialsomething that would record the passing hours when nothing but the stars appear overhead. This brings us to the consideration of the clepsydra, or, as it is more commonly called, the water-clock. A modern example, or rather illustration, of the clepsydra in its simpler form, is the sand glass, called also an hour glass, and an egg boiler, depending upon the use to which it is put. But, although the sand glass and the clepsydra act apparently in somewhat the same way, the principles underlying their operation are quite different, inasmuch as sand and water in flowing through an orifice do not behave in the same way or follow the same law. If a small stream of sand, escaping from a fixed orifice, falls upon a horizontal table the sand. will build up a cone with a definite angle, but water will not do so. And similarly, if a flat bottomed box be filled with fine. sand and a small hole be made in the centre of the bottom, the sand will not all escape, but will so run out as to form an inverted conical space surrounded by sand, and this conical space will have the same definite angle as before. On the other hand, the water would escape until not a drop was left, except what clung to the inner surface of the box by a sort of capillary attraction.

The simplest and earliest form of the clepsydra, especially among the Romans, consisted of an earthenware globular vessel pierced with a few small holes at the bottom. Out of these holes the water gradually escaped or, stole away, and hence the name from kleptein to steal and hudor water. The instrument was used to limit the length of the speeches in the courts of

justice, the speaker being allowed to continue in the courts of amount of water had escaped. Hence the Latin terms-aquam dare, to give water, that is to allow more time; and aquam perdere, to waste time, or speak to no effect.

For the purpose of measuring off equal portions of time for astronomical or domestic purposes, the instrument had to have some practical method of

measuring the amount of water escaping and of connecting this amount with the passing time.

AB is a cylindrical vessel having a small opening at P, and suspended by two chords, or by other means. S is a light scale attached to a float F which floats upon the water at W, and rises or falls with the water in the cylinder. The vessel is filled with water until the scale has its zero point at C. Then as the water escapes at P the float, with its attached scale, gradually descends, the whole descent being indicated at C, and read off from

ल

F

W

A

the scale. The tube f is for filling. Now, water escaping in this way, without any renewal, does not discharge equal amounts in equal times, so that the scale S, if intended to mark equal intervals of time, cannot be graduated into equal parts, but must have the space from 0 to 1 greater than from 1 to 2, and this again greater than from 2 to 3, and so on according to a certain law.

Knowing this law it is an easy matter to properly graduate the scale theoretically; or, without knowing it it would be an easy matter to graduate the scale practically by means of the sun-dial on some bright sunny day, and then the instrument could be employed on dark days or at night.

If the water in the cylinder were kept constantly at the same height, the amount of water discharged at the orifice would be proportional to the time, and the introduction of this principal introduces a very great improvement into the accu

racy of the working of the instrument. The one given in outline in the accompanying figure illustrates these improvements.

T is a source of water supply which keeps the reservoir R continually full, the surplus flowing out at V. The water escapes at P and falls into a small cylinder, so as to avoid disturbing the surface of that in the larger cylinder, the cylinders being connected at the bottom. A cord passing over the pulley F is connected with the float F, and a small weight at ƒ, to keep the cord stretched. The hand, in moving over the graduated dial indicates the amount of water escaped and therefore the length of time which has passed, since the instrument was set going. At Q is an orifice which can be opened to empty the tank in order to set the index at zero.

One difficulty about time-keeping with the Greeks and Romans and some other ancient people was that they did not look upon the whole 24 hours as a day and divide it accordingly, as we do. They counted their day from sunrise to sunset, and their night from sunset to sunrise, and they divided each of these into 12 hours, so that the lengths of their hours, instead of being constant, were singularly variable. The daylight

hours were long in summer and short in winter, and the hours of darkness the very reverse.

That the non-scientific character of the Romans should be contented with such an arrangement is not very much to be wondered at, but that the astute mind of the Greek should be satisfied with it is somewhat remarkable. And yet we are told that the great Plato invented a very complicated clepsydra designed to accommodate itself to these varying hours. It is a pity that we have not a complete description of it.

Some modern people who are well supplied with clocks and watches may wonder at the apparent stupidity of these men of long ago, and may think that if, with their ability, they had lived in those days, they could have done better. But could they? These men mistake knowledge for ability, while the two things are quite distinct. There are to-day not many nobler minds than those of Plato and Aristotle and Archimedes and dozens of other distinguished Greeks, if any, and yet these employed the sun-dial and the clepsydra and separated sharply the day from the night. The clepsydra was the best timemeasure that they possessed, their chronometer so to speak, and they tried hard to perfect its performance. At its best it would be inferior to a common modern clock, yet when carefully constructed and graduated it was no mean instrument, and was in use by Tycho Brahe and other astronomers. Had these pioneers hit upon the modern method of taking light and darkness together as constituting the day, they would have had a day of very nearly uniform length, and would have made matters very much simpler for themselves.

But the traditions of older nations, and especially of Egypt, were against such a view, and who is not influenced to some extent by tradition and traditional usages. Our theological ideas are largely traditional. One belief in a universal creation in six days, by a deity who wearied, and rested on the seventh, our tendency to believe in the sacredness of the numbers three and seven,-our week and our Sabbath and our Easter and many of our holidays are founded upon traditions, many of which are decidedly unscientific. And many people, even in this educated and enlightened present, cannot free themselves from the seductions of the fortune teller and astrologer, or escape from that traditional influence which the