Page:Encyclopædia Britannica, Ninth Edition, v. 7.djvu/174

156 156 DIALLING Madras (13&quot; 4 N. lat.) London (51* 3V N. lat.) 15 9-42! Log. sin. 51 30 9 89354 Log. tan. 15 9-42805 j Log. tan. 15 9-42805 Jx&amp;gt;g. sin. 13 4 9-35427 Log. sin. Log. tan. 3 28 878232 Log. tan. 11 51 9 32159 Edinburgh (55* 67 N. lat) [ Hammerf est (73 40 N. lat.) Log. tan. 15 9 42805 Log. tan. 15 9 42805 Log. sin. 55 57 9 91832 Log. sin. 73 40 9 98211 Log. tan. 12 31 9 34637 ; Log. tan. 14 25 9 41016 Thus the I o clock hour line EB must make an angle on a Madras dial of only 3 28 with the meridian EA, 11 51 on a London dial, 12 31 at Edinburgh, and 14 25 at Hammerfest. In the same way may be found the angles made by the other hour lines. The calculations of these angles must extend throughout one quadrant from noon to vi o clock, but need not be carried further, because all the other hour-lines can at once be deduced from these. In the first place the dial is symmetrically divided by the meridian, and therefore two times equidistant from noon will have their hour lines equidistant from the meridian ; thus the xr o clock line and the I o clock line must make the same angles with it, the xi o clock the came as the II o clock, and so on. And next, the 24 great circles, which were drawn to determine these lines, are in reality only 12 ; for clearly the great circle which gives i o clock after midnight, and that which gives I o clock after noon, are one and the same, and so also for the other hours. Therefore the hour lines between vi in the evening and vi the next morning are the prolongations of the remaining twelve. Let us now remove the imaginary sphere with all its circles, and retain only the style EP and the plane HMA with the lines traced on it, and we shall have the horizontal dial. On the longest day in London the sun rises a little after 4 o clock, and sets a little before 8 o clock ; there is there fore no necessity for extending a London dial beyond those hours. At Edinburgh the limits will be a little longer, while at Hammerfest, which is within the Arctic circle, the whole circuit will be required. Instead of a wire style it is often more convenient to use a metal plate from one quarter to half an inch in thickness. This plate, which is sometimes in the form of a right-angled triangle, must have an acute angle equal to the latitude of the place, and, when properly fixed in a vertical position on the dial, its two faces must coincide with the meridian plane, and the sloping edges formed by the thickness of the plate must point to the pole and form two parallel styles. Since there are two styles, there must be two dials, or rather two half dials, because a little consideration will show that, owing to the thickness of the plate, these styles will only one at a time cast a shadow. Thus the eastern edge will give the shadow for all hours before 6 o clock in the morning. From G o clock until noon the western edge will be used. At noon, it will change again to the eastern edge until 6 o clock in the evening, and finally the western edge for the remaining hours of daylight. The centres of the two dials will be at the points where the styles meet the dial face ; but, in drawing the hour- lines, we must be careful to draw only those lines for which the corresponding style is able to give a shadow as explained above. The dial will thus have the appear ance of a single dial plate, and there will be no confusion (see fig. 3). The line of demarcation between the shadow and the light v/ill be better defined than when a wire style is used ; but the indications by this double dial will always be one minute too fast in the morning and one minute too slow in the afternoon. Thi3 is owing to the magnitude of the sun, whose angular breadth is half a degree. The well- defined shadows are given, not by the centre of the sun, as we should require them, but by the forward limb in the morning and by the backward one in the afternoon ; and the sun takes just about a minute to advance through a space equal to its half-breadth. Dials of this description are frequently met with in the country. Placed on an ornamental pedestal some 4 feet high, they form a pleasing and useful addition to a lawn or to a garden terrace. The dial plate is of metal as well as the vertical piece upon it, and they may be purchased ready for placing on the pedestal, the dial with all the hour-lines traced on it, and the style-plate firmly fastened in its proper position, if not even cast in the same piece with the dial-plate. When placing it on the pedestal care must be taken that the dial be perfectly horizontal and accurately oriented. The levelling will be done with a spirit-level, and the orien tation will be best effected either in the forenoon or in the afternoon, by turning the dial-plate till the time given by the shadow (making the one minute correction mentioned above) agrees with a good watch whose error on solar time is known. It is, however, important to bear in mind that a dial, so built up beforehand, will have the angle at the base equal to the latitude of some selected place, such as London, and the hour-lines will be drawn in directions calculated for the same latitude. Such a dial can therefore not be used near Edinburgh or Glasgow, although it would, without appreciable error, be adapted to any place whose latitude did not differ more than 20 or 30 miles from that of London, and it would be safe to employ it in Essex, Kent, or Wiltshire.. If a series of such dials were constructed, differing by 30 miles in latitude, then an intending purchaser could select one adapted to a place whose latitude was within 15 miles of his own, and the error of time would never exceed a small fraction of a minute. The following table will enable us to check the accuracy of the hour-lines and of the angle of the style, all angles on the dial being readily measured with an ordinary protractor. It extends from 50&quot; lat. to 59^ lat., and therefore includes the whole of Great Britain and Ireland : Lat. XI. A.M. I. P.M. X. A M. II. P.M. IX. A.M. III. P.M. VIII. A.M. IV. P.M. VII. A.M. V. P.M. VI. A.M. VI. F.M 50 11 36 23 51 37 27 53 70 43 90 50 30 11 41 24 1 37 39 53 12 70 51 90 51 11 46 24 10 37 51 53 23 70 59 90 51 30 11 51 24 19 38 3 53 35 71 6 90 52 11 55 24 28 38 14 53 46 71 13 90 52 30 12 24 37 38 25 53 57 71 20 90 53 12 5 24 45 38 37 54 8 71 27 90 53 30 12 9 24 54 38 48 54 19 71 34 90 54 12 14 25 2 38 58 54 29 71 40 90 54 30 12 18 25 10 39 9 54 39 71 47 90 5 12 23 25 19 39 19 54 49 71 53 90 55 30 12 27 25 27 39 30 54 59 71 59 90 56 12 31 25 35 39 40 55 9 72 5 90 56 30 12 36 25 43 39 50 55 18 72 11 90 57 12 40 25 50 39 59 55 27 72 17 90 57 30 12 44 25 58 40 9 55 36 72 22 90 58 12 48 26 5 40 18 55 45 72 28 90 58 30 12 52 26 13 40 27 55 54 72 33 90 59 12 56 26 20 40 36 56 2 72 39 90 59 30 13 26 27 45 45 56 11 72 44 90 Vertical South Dial. Let us take again our imaginary trans parent sphere QZPA (fig. 4), whose axis PEp is parallel to the earth s axis. Let Z be the zenith, and consequently, the great circle QZP the meridian. Through E, the centre of the sphere, draw a vertical plane facing south. This will cut the sphere in the great circle ZMA which, being vertical, will pass through the zenith, and, facing south, will be at right angles to the meridian. Let QMa be the equatorial circle, obtained oy drawing a plane through E at right angles to the axis PEp. The lower portion Ep of the axis will be the style, the vertical line EA in