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measuring out fixed and invariable periods of time; or, for dividing the natural fixed periods of time, derived from the motions of the heavenly bodies, into smaller equal periods.

If we wish to measure off equal distances along a line we have several ways of doing so—provided we assume the homogeneity of space and the measured distances remain with us and can at any time be compared. Or, if we wish to compare two linear distances already laid down, we may do so either by the superposition of the one on the other, or by the successive superpositions of some common measuring unit to them, as when we apply a divided scale to measure them. In fact, except where very great accuracy is required, the comparison of fixed distances is not a matter of great difficulty, and if the distances be not too great a very good judgment of their relative values may be made by the use of the eye alone. For the distances to be compared are both present to the vision at the same time, and a trained eye can judge them fairly well by visual comparison.

But the case is totally different when we come to deal with periods or intervals of time. We do our work and make our observations in the present only. The moment that has gone has gone forever, and has no existence outside the memory. And we have no ready means of comparing it with the moment that may be present. Superposition, or anything related to it, is here out of the question. And we possess no powers or faculties which enable us to form any reliable judgment upon the relative lengths of time intervals. The fact is that our sense of the passage of time depends too much upon our mental states and nerve conditions to be of any scientific value in the determination of time periods. To one person a day may seem to be much longer than to another, and for the tired slumberer who sleeps without dreaming, time is for the while practically obliterated. And it is a trite saying, although true, that a human life is measured not so much by the number of years over which it extends as by the amount of physical and mental action that has been crowded into it.

Hence the necessity, in measuring out time-periods, of having a machine like the clock, which is devoid of nerves, and of mental states, and of all things depending thereon or affected thereby. But as we cannot directly compare the present hour with the one that has past, how can we know that even a superior clock makes its indicated hours equal in length? The question is scarcely an intelligent one until after we get some definition as to what we mean by equal lengths when applied to time intervals.

There is no doubt that most people have, in their minds, a vague idea as to what these terms mean, but vague ideas cannot take the place or serve the purpose of rigid definitions; and our definition in this case must come from experience backed by reason and judgment. Relying upon the fundamental principles of physics we believe that a ball posited in space, uninflu

a enced by any forces within or without, and rotating upon a fixed axis, will rotate with absolute uniformity for all time. That is to say that each rotation will measure out exactly the same interval of time, and that the nth part of a rotation will occupy the nth part of that interval. And whether we can say that we know this to be true, or not, we are compelled by the necessities of the case to take this, or something equivalent to it, as our definition of what is to be understood by equal time intervals.

Now the earth satisfies the conditions of our rotating ball fairly well, and although it is not wholly uninfluenced in its rotation, yet these influences are so very small that their effects are sensible only after very many years. And thus the earth's axial rotation offers us not only one of the best examples of a uniform time-measure to be found in the universe, it offers to us also the most available one for our purpose. So, our definition of equal time-intervals must be drawn from the motions of the heavenly bodies in general, and from the earth's axial rotation in particular. And, as will be shown hereafter, when this test is applied we are prepared to say that, allowing for the imperfections of mechanical contrivances, in general, a good modern clock measures out time with practical uniformity.

The history of mechanical inventions for measuring time is a very long one, going back even to the days of the ancient Babylonians. And it is also interesting and instructive, showing, as it does, how the human mind discovers one obstacle after another in the way of its progress, and then how it casts about it to discover means for their removal.

Even the history of the geared machine, commonly known as a clock, extends backwards for nearly 600 years; and although the finest clocks built to-day are not complex machines, not as complex as the common type-writing machine or dozens of others, yet, on account of the higher principles entering into it and the great accuracy of movement required of it, the clock has absorbed the inventive genius of nearly six centuries in rising from the crude form which characterized it in the days of DeWyck to the almost perfect machine that it is to-day.

The simplest and most natural way of noting the passage of time and therefore of getting the “time of day”, appears to be by observing the sun and estimating how much of its daily course it has accomplished. With the astronomer supplied with proper instruments and tables, it is not a very difficult matter to determine the sun's altitude above the horizon at any particular moment and then to calculate the corresponding time. But, as the work introduces Spherical Trigonometry it will not be dealt with here.

However, without any such help a person accustomed to it may inake a very fair estimate of the time of day by noting the position, in its daily course, at which the sun has arrived.

When the sun is in the south, or practically at its highest point in its daily course, it is solar noon; and the mariner makes use of this fact, by watching the ascending sun through his sextant until it reaches its highest point in the heavens, in order to find noon-time and thus to get an idea of his place upon the ocean.

On land, in the absence of a clock or for the purpose of regulating a clock, people often fix their noons by a “noon mark”, which is a mark giving the position of the advancing edge of the shadow of some upright past, as the door-post, at the moment of solar noon. As far as solar noon is concerned, this method is quite sufficient and remains correct throughout the year. But, on account of the irregular motion of the sun, and consequently of its shadow, no good clock can be so regulated as to keep pace with solar noons without applying a correction. This will be considered more fully in another place and connection.

Cases, however, are not unknown in which people have boasted of the superior time-keeping properties of their clocks or watches because of their general coincidence with the noon mark.

One might think that he could extend the usefulness of this method by marking the positions of the edge of the shadow at the different hours, as one o'clock, two o'clock, etc. But with an upright post to cast the shadow, such marks would be good only when the sun had the same declination as when they were made, that is at only two special seasons in the year.

To make such a method good and effective for all seasons in the year it is necessary that the edge of the post, or whatever may cast the shadow, shall be parallel to the earth's axis. And this brings us to the construction of the sun-dial.

Haydn, in his dictionary of dates, tells us the sun-dial was invented by Anaximander the Greek in 550 B.C. But in Second Kings we are told that “Isaiah the prophet cried unto the Lord, and he brought the shadow ten degrees backwards, by which it had gone down in the dial of Ahaz.” And the date given for this is about 712 B.C. So that there is some mistake in Haydn's information. But there is evidence that the sun-dial was in use by the ancient Babylonians, and therefore long before the time of Ahaz. In fact it is difficult to see how an intelligent people who had ever observed the motion of a shadow—that of a building, or a tree, or a hill, or a high mountain—from morning until evening, or even for a few hours, could fail to invent the sun-dial.

The sun-dial is either of vertical or of horizontal construction, the latter being not only the most common but also the most useful, and this one we shall try to briefly describe. The essential parts are a horizontal base properly graduated with hours and minutes, and an upright piece with one edge parallel to the earth's axis, which casts its shadow on the base.

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In the illustration, ABCD is the horizontal base, which, on account of being exposed to the weather, should be made of stone or metal; and in setting the instrument in place the base should be carefully leveled. On this base the lines of graduation, as S-II, S-III, S-VIII, etc., are drawn to indicate the position of the edge of the shadow at these respective hours. As these lines do not make equal angles with one another they can be laid down only from a geometrical construction, or from a table formed for the purpose. For the convenience of any one who may wish to construct a horizontal dial we give here a table of the angles which the lines make with the principal line SN, as well as a top view of the base.


SPT is the style or gnomon, which is best made of a thin sheet of brass or aluminum. The edge SP must be parallel to

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