696 



DIALLING. 



Theory. j\ s these have almost the same right ascension, and 

 N *"""Y"™" / differ 40° in their declination, they are very proper for 

 determining the position of the meridian. 



32. In whatever way a meridian is traced on the ho- 

 rizontal plane, it should be quite adjoining to the plane 

 on which the dial is to be delineated ; and it ought to 

 be so placed, that a vertical plane passing along the me- 

 ridian line, may cut the dial at the point where the axis 

 is to be fixed. To take a familiar example, we shall 

 suppose that the dial plane is a vertical wall carefully 

 smoothed and verified with a rule and plumb-line ; and 

 this being understood, it will be easy to suit the ope- 



Pl*te ration to any other plane. 



ccxxvni. Let BC (Fig. 6.) be the meridian line on a horizon- 

 Fig. 6. tal table, and tn, sq, two plumb-lines, which descend on 

 the meridian line from a horizontal rod that has one end 

 fixed in the wall, and the other supported on a stand. 

 If the table admits of being pierced with two holes, the 

 plumb-lines may with advantage pass through them, 

 and the plummets hang suspended in vessels filled with 

 water. They will thus be more steady, and more easily 

 adjusted. The eye is now to be directed towards the 

 wall, so that the visual ray may be in the plane of the 

 plumb-lines ; and then the line AK upon the wall, 

 which, they both appear to cover at once, will mani- 

 festly te the intersection of the plane of the meridian, 

 and the plane of the dial ; and consequently will be 

 the twelve o'clock hour line. A point A is now to be 

 assumed, as the centre of the dial ; and the axis AC 

 must be fixed in the wall in such a position, that it may 

 lie in the plane of the threads tn, sq, and make with 

 a horizontal line AD, an angle equal to the latitude of 

 the place, or with CR, a vertical line, an angle equal 

 to the co-latitude ; and then it will manifestly be pa- 

 rallel to the axis of the World. 



33. The stile may have any shape that admits of its 

 being firmly fastened to the dial ; and before it is fixed, 

 it may be convenient to fasten a piece of wood to the 

 wall, so that it may have a plane surface exactly in the 

 plane of the meridian, as indicated by the plumb-lines, 

 and a line traced on its surface in the position of the 

 axis or edge of the stile ; this board will serve to sup- 

 port the stile in its position, until it be fastened either 

 with its plane in the plane of the meridian, or perpen- 

 dicular to the plane of the dial ; but it will look most 

 Symmetrical in this last position. In whatever way it is 

 fixed, the edge which projects the shadow must be in the 

 plane of the meridian, and parallel to the earth's axis. 



34. When the position of the plane of a dial in re- 

 spect of the earth's axis is known, the determination of 

 the hour lines is a geometrical problem by no means 

 difficult. As at every hour the sun is in one or other 

 of twelve great circles of the sphere, which intersect at 

 the poles of the heavens, and which make equal angles 

 with one another, the general problem to be resolved 

 is evidently this: Let (here be livelve planes, which in- 

 tersect in a straight line, and make equal angles with one 

 another ; and let these planes, indefinitely produced, meet 

 another plane in any position whatever, to determine the 

 lines in which they cut that plane. 



In resolving this problem, it will be convenient to 

 begin with the more simple cases, and to reduce the 

 others as much as possible to them. 



Equinoctial Dial. 



Equinoctial S3. Tliis dial, seen obliquely in its proper position, 



dial. is represented by the upper part of Fig. 3. Its plane 



is parallel to the equator, and is the same as the 



plane of the equinoctial circle in the heavens; E is its Theory. 

 centre, and EF its axis. As the hour circles in the , *"~y~"~ 

 heavens are perpendicular to the equinoctial circle, and Put* 

 divide it into 24 equal parts, the lines in which the plane ccxxvni 

 of the dial cuts their planes, that is, the horn- lines, will Fig. 3. 

 make 24 equal angles round the centre of the dial. 



It appears, then, that to delineate a dial of this kind, 

 nothing more is necessary than to describe a circle on 

 its plane, and to divide its circumference into 24 equal 

 parts ; and having drawn lines from the centre to the 

 points of division, these will be the hour lines against 

 which the characters denoting the hours are to be writ- 

 ten ; if the axis be now fixed perpendicular to the 

 plane, the dial will be constructed. 



In fixing this dial, the axis EF must be in the plane 

 of the mei-idian, and must make with the horizontal me- 

 ridian line, an angle equal to the latitude of the place, 

 and then it will point to the pole of the heavens as it 

 ought. 



36. As the sun is one half of the year on the north 

 side of the equinoctial, and the other half on the south 

 side, it will be proper to trace hour lines on both faces 

 of the dial ; and in north latitudes the horns will be 

 shewn on the upper face of the dial in summer, and on 

 the lower face in winter j but on the equinoctial days, 

 neither face will be illuminated. 



The rays of the sun will always fall very obliquely 

 on this dial in our latitudes, but to remedy this, a rim 

 may be put round it, rising a little above the planes of 

 its faces. The inside of the elevated part of the rim 

 will be strongly illuminated by the sun's rays, and thus 

 the hours will be more distinctly shewn. 



37. A dial of this construction, which admits of be- Fig. 7. 

 ing adjusted to any latitude, is delineated at Fig. 7. In 

 this instrument, ABCD, and CDEF are two quadran- 

 gular pieces, (which may be of ivory, wood, or metal,) 

 connected by means of a hinge at C, D. An equinoctial 

 dial is described on each side of ABCD, or on oneof them, 

 and in the centre I, a style is placed at right angles to 

 the planes of the dials. At G, in the middle of the 

 piece EDCF, a magnetic needle is suspended, and co- 

 vered with a plate of glass. At L, there is a quadrant 

 fixed perpendicular to the plane of this piece, and divi- 

 ded into degrees. It passes through H, an aperture 

 made to receive it in the upper piece. 



When the dial is to be used, it must be placed on a 

 horizontal plane, so that the needle may be in the mag- 

 netic meridian. The upper piece must now be turned 

 round the hinge, so that the planes of the two pieces 

 may make with each other an angle equal to the latitude, 

 as measured by the graduated quadrant. The hour of 

 the day will then be shewn by the axis I, on one or 

 other of the two, faces except on the day of the equinox. 



Horizontal Dial. 



38. A dial traced on a horizontal plane, is called a Horizontal 

 Horizontal dial, This is the most common and most Jia1, 

 useful of any, because it admits of being always illumi- 

 nated when the sun shines. A dial of this kind is re- Pute 

 presented in perspective in Fig. 8. The point C is ccxxvni. 

 the centre, and CK, which is directed to the pole of the ^'S- 8 - 

 heavens, and makes with the plane of the dial an angle 

 equal to the latitude of the place, is the axis. 



To understand its nature and construction, let ABD 

 be an equinoctial dial, whose axis EF is the prolon- 

 gation of the axis of the horizontal dial ; and let the 

 planes of the two dials meet in the line PQ, and sup- 

 pose the plane of the meridian to cut the plane of the 

 2 



