SUNDIAL. Up to a comparatively recent period the science of constructing sundials, under the came of Gnomonics, was an import ant part of a mathematical course. As long as watches were scarce, and clocks not very common, the dial, which is now only a toy, was in actual use as a timekeeper. Of the mathematical works of the 17th century which are found on book-stalls, none are so common as those on dialling. All that is now necessary is to give some idea of the priesiples on which such instruments arc constructed, as an illustration of a loading fact in astronomy. if a person were to place a staff in the ground, so as to point either vertically or otherwise, and to watch its shadow at the same hour, ou different days at some intervals from each other, marking its direction at each day's observation, he would in all probability find that the direction of the shadow, the hour being always the same, varied from day to day. He might, however, find that the shadow was always in one direction at the same hour, and this might happen in two different ways. First, he might by accident fix the staff in a direction parallel to that of the earth's axis, in which case the direction of the shadow would always be the same at the same hour, at all times of the year, and for every hour. Secondly, having fixed the staff in a position not parallel to the axis of the earth, ho might happen to choose that particular hour, or interval between two hours, at which the shadow of a staff in that one direction always points one way. But if, as is most likely, he were to fix the staff in a direction which is not that of the earth's axis ; and if, as is again most likely, he were to choose any time of observation but one, the shadow would certainly point in different directions at different periods.
A sundial consists of two parts : the style, which is the staff above mentioned, usually supplied to the edge of a plate of metal, always made parallel to the earth's axis, and therefore pointing towards the north ; and the dial, which is another plate of metal, horizontal or not, on which are marked the directions of the shadow for the several hours, their halves and quarters, and sometimes smaller subdivisions. In the accompanying diagram, the style is seen throwing its shadow between the directions marked ix and x, on the western side, and indicating that it is about a quarter past nine in the wonting. But there is one prominent part of the figure which is never seen on a dial, namely, the hour circles, which are represented as all passing through the edge of the style. As the diagram stands, a skeleton globe of hour circles only is made a part of the construction, to assist in the explanation.
Let us suppose the sun to move with an equable motion, so that it shows the same time as the clock. It does not do so in reality, but the consideration of this point belongs to the article TIME. A large sundial is frequently furnished with a table of the correction of sun time, to turn it into clock-time, engraved on its face ; but this is generally soon corroded. Nor is knowledge of the simplest elements
of astronomy so widely diffused as to make such a table of any great use. A person who stations himself in any place of resort which has a sundial, will soon find a lounger who looks in amazement at the makes with the meridian (m), be given. From r, the pole, draw Q r perpendicular to the plane of the dial ; and the line joining r with the centre being the continuation of the style, that joining the centre with difference, perhaps a quarter of an hour, between his watch, which ho knows to be right, and the shadow. The church-clock and the sun, in both of which he implicitly believes, are at variance, and he is hardly able to resist the melancholy conclusion that his watch has gained or lost a quarter of an hour in a ten minutes' walk. Neglecting the cause of this, which is an irregularity of solar time, and has nothing to do with any particular mode of reading the results, let us suppose that it is nine o'clock in the morning, solar time. This means that the sun is in that hour-circle which belongs to three hours before noon, or is 3 x 15 or 45 degrees from the meridian hour-circle towards the east. The meridian hour circle is that which cuts the plate of the dial in the line xtt xtt; and the hour-circle in question (the right-hand one of the two which are not shaded) cuts the dial-plate in ix ix. Now when the sun is in the continuation of any plane, the shadow of that plane is only that of the edge presented to the sun. The upper edge of the style is common to all the hour-circles ; and its shadow is, therefore, for the time, part of that of the hour-circle in which the sun is Hence at nine o'clock before noon the line o ix will be the shadow of the style, o being at the intersection of the edge of the style and the dial plate (marked by a large dot in the figure). In the diagram, the clay has moved on about a quarter of an hour after the time just described, and the shadow has advanced accordingly. There is in it a trifling error of shading (it was taken from De Parcieux's ' Trigonometry,' a work which is very rich in well-drawn solid figures), which will serve to illustrate the subject. The time being between nine and ten o'clock, the sun ought to be looking directly into the crevice between the hour-circles ix and x, in which crevice there ought therefore to be no shadow; but the crevice which is entirely devoid of shadow is that between the hour-circles vm and ix, so that the sun is made to tell one story on the north side, and another on the south, of the figure. The reader will easily set this right, and will see that as far as the whole hours are concerned, the crevices themselves might be made to answer the purpose of a sundial.