DIALLING. 



695 



Theory, the sun to be quite uniform, the shadow will always 

 W '"Y~""*' have the same position at the same hour every day 

 throughout the year. 



25. If the two planes ABCD, abed are illuminat- 

 ed at once by the sun, the rod e EF will project a sha- 

 dow on them both. Let us suppose that at the instants 

 the line EF projects its shadow in the directions of the 

 lines E 12, El, E 2, &c. on the upper plane, the sha- 

 dow of eE falls in the lines e 12, el, e 2, &c. respec- 

 tively on the lower plane ; and let other cotemporane- 

 ous positions of the shadows be found for every hour 

 the sun can shine on the planes ; then, as the shadow 

 will always come to the same position on each plane at 

 the same hour of the day, the hours will be indicated 

 also by the shadow on the plane a b cde. 



26. Each of the planes ABCD, abed is a dial : we 

 have supposed the upper plane to be perpendicular to 

 the axis of the world ; and in this particular position, 

 the shadow will describe equal angles on it in equal 

 times. The plane of the dial may, however, have any 

 position ; but if it is not perpendicular to the earth's 

 axis, the motion of the shadow projected on it will not 

 be uniform, as it is on the plane of the equinoctial. 



27. The rod EF, which projects the shadow, is cal- 

 led the Style ; also sometimes the Axis of the dial. 



The lines E 12, E 1, &c. which indicate the position 

 of the shadow at the different hours, are called Hour 

 Lines. The hour lines are evidently the common sec- 

 tion of the plane of the dial, and a plane passing through 

 its axis and the sun. 



The point in which the axis of a dial meets its plane, 

 which is also the common concourse of the hour lines, 

 is called its Centre. There are other technical terms 

 belonging to this subject, but these we shall explain 

 as we proceed. 



28. The latitude of the place for which «t dial is to 

 be made, is an important element in then- construction. 

 This may be known by good maps, or it may be de- 

 termined by astronomical observations, as is particular- 

 ly explained in our article Astronomv, p. 665. 



How to trace a Meridian Line on any Plane. 



Method of ^9. In constructing a dial, it is always necessary to 

 drawing a determine the line in which the plane of the meridian 

 meridian meets the plane of the dial. If the plane of the dial is not 

 Une. horizontal, it will be convenient, in the first place, to 



trace a meridian line on a horizontal plane near it In 

 our article Astronomy, p. 653, we have explained one 

 wav of doing this, by two equal shadows of a pin per- 

 pendicular to the plane. A meridian may also be found 

 by any three shadows of an upright pin or style. Let 

 Plate OV (Fig. 4. ) be the style which stands at right angles 

 ccxxviii. to the plane in O, and OA, OA', O'A" its shadows at 

 F| g- 4 - three different times of the day. Then, if AV, A'V, 

 A"V be joined, the angles AVO, A'VO, A"VO are the 

 sun's distances from the zenith at the times of noting 

 the positions of the shadows ; and these are known, 

 because in the right angled triangles AOV, A'OV, 

 A"OV, the sides about the right angles at O are known, 

 from which the angles at V may be found. 



Let us now suppose that the sphere is projected 

 stereographically on the horizontal plane AA'A", so 

 that O is the centre of the primitive, the eye being in 

 the nadir, then the lines AO, A'O, A"0 produced will 

 be the projections of azimuth circles ; if the projections 

 of the sun's places, in these circles, at the times of ob- 

 servation, be now found, a circle traced through them 

 will evidently be the projection of the circle of declina- 



tion, which the sun describes in the heavens that day ; Theory 

 and the position of the meridian may now be found, "■ 

 because it will pass through the centre of that circle, 

 and O, the centre of the horizon. Hence we derive the 

 following construction. 



Make three right angled triangles AOV, A'OV, Plate 

 A"OV, (Fig. 5.) which have each VO=VO, in Fig. 4. ccxxvwi 

 the height of the- style; and bisect the angles at V, by ^'g- 5 - 

 the lines Va, Va', Va". Produce the shadows AO, AO', 

 AO", so that Oa, 0«', Oa" of Fig. 5. may be respective- 

 ly equal to Oa, Oa', Oa" of Fig. 4. Describe a circle 

 through the points a, a', a", and from X its centre, 

 draw a line through O ; this will be in the direction of 

 the meridian. For by the principles of the stereogra- 

 phic projection of the sphere, if we take the horizontal 

 plane A, A', A", for the plane of projection ; the lines 

 Oa, Oa', Oa", will be the projections of circles passing- 

 through the zenith and the sun, at the times when the 

 shadows have the positions OA, OA', OA" ; and as by 

 construction, Oa, Oa', Oa" are the tangents of half the 

 zenith distances AVO, A'VO, A"VO, the points a, a', 

 a", are the projected places of the sun ; and the circle 

 a, a', a", is the projection of the parallel it describes in 

 the heavens on the day of observation, and OX, which 

 passes through its centre, is the projection of the meri- 

 dian. See Projection of the Sphere. 



30. We may even find the latitude of the place of ob- 

 servation : For if P, the projection of the pole of the 

 circle, be found, then OP will be the tangent of half the 

 distance of the pole from the zenith, (OV being taken 

 as radius,) that is, the tangent of half the complement 

 of the latitude. 



30. In this construction, no allowance is made for re- 

 fraction, or change of declination. The zenith distan- 

 ces may, however, be corrected for refraction by the 

 proper tables : (See Astronomy, pages 660 and 799.) 

 And if the observation be made on the solstitial days, 

 the error from change of declination Avill hardly be any 

 thing. This method of tracing a meridian line was pro- 

 posed by a very old author on dialling, named Mutio 

 Oddi da Urbino, in a work called Gli Horologi Solari 

 Nelle Superjicie piane. 



31. Another method of tracing a meridian line is, by 

 observing when two stars which have the same right 

 ascension, or whose right ascensions differ by ISO , come 

 into the same vertical plane ; for then they are both on 

 the meridian. The observation may be made by means 

 of a plane surface, kept in a vertical position by its own 

 weight, or by any other suitable contrivance, and which 

 is moveable about a vertical line. The pole star and 

 the first i of the tail of the Great Bear, are applicable to 

 this purpose. In the beginning of 1811, their mean 

 right ascensions were, 



Star i, 191° 25' 3" 



Pole Star, 13 41 41 



177 43 22 



This difference, although not exactly 180°, is yet suf- 

 ficiently near ; because when e is on the meridian, the 

 arc of 2° 16' 38", by which the pole star has advanced 

 in the small circle it describes, subtends an angle of 

 about 4' only. The stars u. of Ophiuchus, and ,3 of the 

 Dragon, are well adapted to the same purpose, the right 

 ascensions and declinations are, 



a. of Ophiuchus, 

 £ of Dragon, ■ 



R. Ascen. 



261° 32' 26" 

 261 32 33 



Declin. 



12° 42' 29N". 

 52 26 47N. 



