Page:Encyclopædia Britannica, Ninth Edition, v. 7.djvu/172

154 154 DIALLING can see, however, that the change would necessarily follow the introduction of clocks and other mechanical methods of measuring time ; for, however imperfect these were, the hours they marked would be of the same length in summer and in winter, and the discrepancy between these equal hours and the temporary hours of the sun-dial would soon be too important to be overlooked. Now, we know that a balance clock was put up in the palace of Charles V. of France about the year 1370, and we may reasonably sup pose that the new sun-dials came into general use during the 14th and 15th centuries. Among the earliest of the modern writers on gnomonics must be named Sebastian Munster, a cordelier who pub lished his Horologiographia at Basel in 1531. He gives a number of correct rules, but without demonstrations. Among his inventions was a moon-dial, 1 but this does not admit of much accuracy. During the 17th century dialling was discussed at great length by all writers on astronomy. Clavius devotes a quarto volume of 800 pages entirely to the subject. This was published in 1612, and may be considered to contain all that was known at that time. In the 18th century clocks and watches began to supersede sun-dials, and these have gradually fallen into disuse except as an additional ornament to a garden, or in remote country districts where the old dial on the church tower still serves as an occasional check on the modern clock by its side. The art of constructing dials may now be looked upon as little more than a mathematical recrea tion. General Principles. The diurnal and the annual motions of the earth are the elementary astronomical facts on which dialling is founded. That the earth turns upon its axis uniformly from west to east in 24 hours, and that it is carried round the sun in one year at a nearly uniform rate, is, we know, the correct way of expressing these facts. But the effect will be precisely the same, and it will suit our purpose better, and make our explanations easier, if we adopt the ideas of the ancients, of which our senses furnish apparent confirmation, and assume the earth to be fixed. Then, the sun and stars revolve round the earth s axis uniformly from east to west once a day, the sun lagging a little behind the stars, making its day some 4 minutes longer, so that at the end of the year it finds itself again in the same place, having made a complete revolution of the heavens relatively to the stars from west to east. The fixed axis about which all these bodies revolve daily is a line through the earth s centre ; but the radius of the earth is so small, compared with the enormous distance of the sun, that, if we draw a parallel axis through any point of the earth s surface, we may safely look on that as being the axis of the celestial motions. The error in the case of the sun would not, at its maximum, that is, at 6 A.M. and 6 P.M., exceed half a second of time, and at noon would vanish. An axis so drawn is in the plane of the meridian, and points, as we know, to the pole, its elevation being equal to the latitude of the place. The diurnal motion of the stars is strictly uniform, and so would that of the sun be if the daily retardation of about 4 minutes, spoken of above, were always the same, But this is constantly altering, so that the time, as measured by the sun s motion, and also consequently as measured by a sun-dial, does not move on at a strictly uniform pace. This irregularity, which is slight, would be of little con sequence in the ordinary affairs of life, but clocks and 1 In one of the Courts of Queen s College, Cambridge, there is an elaborate sun-dial dating from the end of the 17th or beginning of the 18th century, and around it a series of numbers whiah make it avail able as a moon-dial when the moon s age is known. watches being mechanical measures of time could not, except by extreme complication, be made to follow this irregularity, even if desirable, which is not the case. The clock is constructed to mark uniform time in such wise that the length of the clock day shall be the average of all the solar days in the year. Four times a year the clock and the sun-dial agree exactly ; but the sun-dial, now going a little slower, now a little faster, will be some times behind, sometimes before the clock the greatest accumulated difference being about 16 minutes for a few days in November, but on the average much less. The four days on which the two agree are April 15, June 15, September 1, and December 24. Clock-time is called mean time, that marked by the sun dial is called apparent time, and the difference between them is the equation of time. It is given in most calendars and almanacs, frequently under the heading &quot; clock slow,&quot; &quot;clock fast.&quot; When the time by the sun-dial is known, the equation of time will at once enable us to obtain the corresponding clock time, or vice versa. Atmospheric refraction introduces another error, by altering the apparent position of the sun ; but the effect is too small to need consideration in the construction of an instrument which, with the best workmanship, does not after all admit of very great accuracy. The general principles of dialling will now be readily understood. The problem before us is the following : A rod, or style, as it is called, being firmly fixed in a direction parallel to the earth s axis, we have to find how and where points or lines of reference must be traced on some fixed surface behind the style, so that when the shadow of the style falls on a certain one of these lines we may know that at that moment it is solar noon, that is, that the plane through the style and through the sun then coincides with the meridian ; again, that when the shadow reaches the next line of reference, it is 1 o clock by solar time, or, which comes to the same thing, that the above plane through the style and through the sun has just turned through the twenty-fourth part of a complete revolution ; and so on for the subsequent hours, the hours before noon being indi cated in a similar manner. The style and the surface on which these lines are traced together constitute the dial. The position of an intended sun-dial having been selected whether on church tower, south front of farm-stead, or garden wall the surface must be prepared, if necessary, to receive the hour-lines. The chief, and in fact the only practical difficulty will be the accurate fixing of the style, for on its accuracy the value of the instrument depends. It must be in the meridian plane, and must make an angle with the horizon equal to the latitude of the place. The latter condition will offer no difficulty, but the exact determination of the meridian plane which passes through the point where the style is fixed to the surface is not so simple. We shall, further on, show how this may be done ; and, in the meantime, we shall assume that we have found the true position, and have firmly fixed the style to the dial and secured it there by cross wires, or by other means. The style itself will be usually a strong metal wire whose thickness may vary with circumstances ; and when we speak of the shadow cast by the style it must always be understood that the middle line of the thin band of shade is meant. The point where the style meets the dial is called the centre of the dial. It is the centre from which all the hour-lines radiate. The position of the xn o clock line is the most important to determine accurately, since all the others are usually made to depend on this one. We cannot trace it correctly