figure. If every sixth part of the quadrant be divided); then connect the divisions which are subdivided into four equal parts, right lines equi-distant from L, by the parallel lines KM, drawn from the centre through these points of IN, HO, G P, and FQ. Draw V Z for the hydivision, and continued to the line rs, will divide pothenuse of the stile, making the angle V ZE each hour upon it into quarters. equal to the latitude of the place; and continue the line V Z to R. Draw the line R r parallel METHOD OF CONSTRUCTING DIALS BY DIALLING to the six o'clock line, and set off the distance Lines. a K from Z to Y, the distance b I from 2 to X, 42. This is the easiest of all mechanical me c H from Z to W, A G froin Z to T, and e F from thods, and by much the best, when the lines are Zo S. Then draw the lines Ss, T t, Ww, Xx, truly divided : and not only the half hours and and Y y, each parallel to Rr. Set off the disquarters may be laid down by all of them, but tance y Y, from a to 11, and from f to 1; the every fifth minute by most, and every single mi- distance x X from b to 10, and from g to 2; WW nute by those where the line of hours is a foot in from c to 9, and from h to 3; t T from d to 8, length. Having drawn the double meridian line and from i to 4; ss from e to 7, and from n to 5. ob, cd, fig. 6, on the plane intended for a hori- Then laying a ruler to the centre 2, draw the zonta: dial, and crossed it at right angles by the forenoon hour lines through the points 11, 10, 9, six o'clock line f e, as in fig. 3, take the latitude 8,7; and laying it to the centre z, draw the afof the place with the compasses, from the scale of ternoon lines through the points 1, 2, 3, 4, 5; latitudes, and set that extent from c to e, and continuing the forenoon lines of VII and VIII from a to f, on the six o'clock line: then, taking through the centre 2, to the opposite side of the the whole six hours between the points of the dial, for the like afternoon hours; and the aftercompasses from the scale of hours, with that ex noon lines IV and V through the centre », to tert set one foot on the point e, and let the other the opposite side for 'the like morning hours. frot fall where it will upon the meridian line cd, Set the hours to these lines as in the figure, and as at d. Do the same from f to b, and draw the then erect the stile or gnomon, and the dial will right lines cd and f b, each of them will be equal be finished. in length to the whole scale of hours. Then, 45. II. To construct a south dial, draw the setting one foot of the compasses in the begin- line V Z, making an angle with the meridian Z L ning of the scale at XII, and extending the other equal to the co-latitude of your place; and proto each hour on the scale, lay off these extents ceed in all respects as in the above horizontal from a to e for the afternoon hours, and from b dial for the same latitude, reversing the hours as to f for those of the forenoon: this will divide in fig. 4, and making the elevation of the gnothe lines de and bf in the same manner as the mon equal to the co-latitude. hour scale is divided at 1, 2, 3, 4, and 6; on 46. III. To construct a north dial. See fig. which the quarters may also be laid down, if re- 2. If the hour lines IV and V, as also VII and quired. Then, laying a ruler on the point c, draw VIII on the south dial, fig. 4, plate I. be conthe first five hours in the afternoon, from that tinued beyond the line VI a VI, and the triangle point, through the dots at the numeral figures i, agh turned about the point a, till ah fall on a 2, 3, 4, 5, on the line de; and continue the lines XII produced, it is evident a north dial is thereby of IV and V through the centre c, to the other had. The hour line for VII in the morning on side of the dial, for the like hours of the morn- the south dial, when produced, forms the hour ing: which done, lay the ruler on the point a, line for V in the morning on the north dial: and and draw the last five hours in the forenoon the hour line for V in the afternoon, on the through the dots, 5, 4, 3, 2, 1, on the line fb; south. dial, forms the hour line for VÍI in the continuing the hour lines of VII and VIII through evening on the north dial. The manner of the centre a to the other side of the dial, for the placing the characters for the other hours is like hours of the evening; and set the hours to therefore obvious. their respective lines, as in the figure. Lastly, 47. IV. To construct an east dial. On the make the gnomon the same way as directed above eastern side of the plane of the meridian, draw a for the horizontal dial, and the whole will be line A B, fig. 3, parallel to the horizon, draw finished. also a line AK, making with AB an anglc 43. To make an erect south dial, take the co- KAB equal to the complement of the latitude latitude of your place from the scale of latitudes, of the place for which the dial is made. Take a and then proceed in all respects for the hour point D in A K, and on that point for a centre line as in the horizontal dial ; only reversing the describe a circle. Through D draw EC perhours as in fig. 4, and making the angle of the pendicular to A K, thus the circle will be divided stile's height equal to the co-latitude. into four quadrants; divide two of these quadGEOMETRICAL METHOD OF Drawing the Hour Draw a straight line F EG perpendicular to EC, rants into six equal parts, as in the figure. Lines. the diameter of the circle, and from the centre 1) 44. I. To construct a horizontal dial, fig. 1, through the several divisions, draw the right plate II.- Describe with any opening of the com- lines D IV, D V; D VI, D VII, D VIII, D passes, as Z L, the two semicircles LF k and LQk, IX, DX, D XI. Through IV, V, VI, VII, &c.; upon the cen tres Z and 2, where the six o'clock draw lines IV, IV, V, V, &c. parallel to EDC. line crosses the double meridian line, and divide Lastly, in D erect a stile equal to the radius each semicircle into twelve equal parts, begin- DE, perpendicular to the plane; or ɔn two ning at L (though strictly speaking, only the little pieces perpendicularly fixed in EC, and quadrants from L to the six o'clock line need be equal io the same D E, fit an iron rod parallel to . EC, thus will each index at the several hours of the world, and will cast a shadow upon the project a shadow to the respective hour lines IV true time of the day among the hours of the ÎV, V V, VI VI, &c. The east dial, it is obvi- circle. ous, can only show the hours till twelve o'clock. 51. When the instrument is thus rectified, the 48. V. To construct a west dial. The con- quadrant and semicircle are in the plane of the struction is perfectly the same as that of an east meridian, and the circle is then in the plane of dial, only that its situation is inverted, and the the equinoctial. Therefore as the sun is above hours are written accordingly. A west dial, it is the equinoctial in summer (in northern latitudes), obvious, can only be illuminated after noon, and and below it in winter, the axis of the semitherefore, joined with an east dial, shows all the circle will cast a shadow on the hour of the day, hours of the day. on the upper surface of the circle, from the 20th of March till the 23d of September; and from Of UNIVERSAL Dials. the 23d of September to the 20th of March, the 49. I. The universal dial, invented by Pardie, hour of the day will be determined by the shadow fig. 4, consists of three principal parts ; the first of the semicircle upon the lower surface of the whereof is called the horizontal plane A, because circle. In the former case the shadow of the in practice it must be parallel to the horizon. circle falls upon the day of the month, on the In this plane is fixed an upright pin, which lower part of the diameter of the semicircle ; enters into the edge of the second part BD, and in the latter case on the upper part. called the meridional plane; which is made of 52. The method of laying down the months iwo pieces, the lowest whereof, B, is called the and signs upon the semicircle is as follows:quadrant, because it contains a quarter of a Draw the right line ACB, fig. 5, equal to the circle, divided into 90°; and it is only into this diameter of the semicircle ADB, and cross it in part, near B, that the pin enters. The other the middle at right angles with the line ECD, piece is a semicircle D adjusted to the quad- equal in length to ADB; then EC will be the rant, and turning in it by a groove, for raising radius of the circle FCG, which is the same as and depressing the diameter E F of the semi- that of the semicircle. Upon E, as a centre, circle, which diameter is called the axis of the describe the circle FCG, on which set off the instrument. The third piece is a circle, G, arcs Ch and Ci, each equal to 231°, and divide divided on both sides into twenty-four equal them accordingly into that number for the sun's parts, which are the hours. This circle is put declination. Then laying the edge of a ruler upon the meridional plane, so that the axis E F over the centre E, and also over the sun's declimay be perpendicular to the circle, and the nation for every fifth day of each month, mark point C be the common centre of the circle, the points on the diameter A B of the semicircle semicircle, and quadrant. The straight edge of from a to g, which are cut by the ruler; and the semicircle is chamfered on both sides to there place the days of the months accordingly, a sharp edge, which passes through the centre of answering to the sun's declinations. Then the circle. On one side of the chamfered part, setting one foot of the compasses in C, and the first six months of the year are laid down, extending the other to a org, describe the semiaccording to the sun's declination for their res- circle abcdefg; which divide into six equal pective days, and on the other side the last six parts, and through the points of division draw months. And against the days on which the right lines parallel to CD, for the beginning of sun enters the signs, there are straight lines the signs (of which one half are on one side of drawn upon the semicircle, with the characters the semicircle, and the other half on the other), of the signs marked upon them. There is a and set the characters of the signs to their proper black line drawn along the middle of the upright lines, as in the figure. edge of the quadrant, over which hangs a thread 53. II. The universal, or astronomical equiH, with its plummet I, for levelling the instru- noctial ring-dial is an instrument that serves to ment. From the 23d of September to the 20th find out the hour of the day in any latitude. It of March, the upper surface of the circle must consists of two flat rings or circles, usually from touch both the centre C of the semicircle, and four to twelve inches diameter, and of a modethe line of p and ; and from the 201h of rate thickness; the outward ring representing March to the 23d of September, the lower sur- the meridian of the place it is used at, contains face of the circle must touch that centre and two divisions of 90° each, opposite to line. another, serving to let a sliding piece and ring 50. To find the time day by this dial, set (by which the dial is usually suspended) be it on a level place in sun-shine, and adjust it by placed on one side, from the equator to the N. the levelling screws k and l, until the plumb- pole, and on the other side to the S., according line hangs over the black line upon the edge of to the latitude of the place. The inner ring the quadrant, and parallel to the said edge; represents the equator, and turns diametrically move the semicircle in the quadrant, until the within the outer, by means of two pivots insertline of p and (where the circle touches) ed in each end of the ring at the hours XII. comes to the latitude of the place in the quad- Across the two circles is screwed to the meridian rant: then turn the whole meridional plane BD, a thin pierced plate or bridge, with a cursor, with its circle G, upon the horizontal plane A, that slides along the middle of the bridge: this until the edge of the shadow of the circle falls cursor has a small hole for the sun to shine on the day of the month in the semicircle; and through. The middle of this bridge is conthe he meridional plane will be due north and ceived as the axis of the world, and its extremisouth; the axis E F will be parallel to the axis ties as the poles; on the one side are delineated one the twelve signs of the zodiac, and sometimes length of each arm, from the side of the long opposite the degrees of the sun's declination; middle part, and also the length of the top part and on the other side the days of the month above the arms, to be equal to B d. Then as the throughout the year. On the other side of the edges of the shadow, from each of the arms, will outer ring A are the divisions of 90°, or a quad- be parallel to Be, making an angle of 23° 30' rant of latitude. It serves, by the placing of a with the side Bd of the arın, when the sun's common pin in the hole, to take the sun's declination is 23° 30'; it is plain, that if the altitude, from which the latitude of the place length of the arm be Bd, the least breadth may easily be found. that it can have, to keep the edge Be of the sha54. In using this dial, place the line in the dow Begd from going off the side of the arm de middle of the sliding piece, over the degree of before it comes to the end of it ed, must be equal latitude of the place. Suppose, for example, to ed or d B. But to keep the shadow within 51ļ for London ; put the line which crosses the the quarter divisions of the hours, when it comes hole of the cursor C to the day of the month of near the end of the arm, the breadth of it should the degree of the sign. Open the instrument be still greater, so as to be almost doubled, on till the two rings be at right angles to each other, account of the distance between the tips of the and suspend it by the ring, that the axis of the arms. dial represented by the middle of the bridge may 57. The hours may be placed on the arms, by be parallel to the axis of the earth, viz. the north laying down the cross abcd, fig. 8, on a sheet of pole to the north, and vice versa. Then turn the paper; and with a black lead pencil held close Hat side of the bridge towards the sun, so that to it drawing its shape and size on the paper. his rays passing through the small hole in the Then take the length ae in the compasses, and cursor may fall exactly in a line drawn through with one foot in the corner u, describe with the the middle of the concave surface of the inner other the quadrant ef. Divide this arc into six ring or hour-circle, the bright spot shows the equal parts, and through the points of division hour of the day in the said concave surface of the draw right lines ag, ah, &c., continuing three of dial. The hour XII cannot be shown by this them to the arm ce, which are all that can fall dial, because the outer ring, being then in the upon it; and they will meet the arm in those plane of the meridian, excludes the sun's rays points through which the lines that divide the from the inner; nor can this dial show the hour hours from each other are to be drawn right when the sun is in the equinoctial, because his across it. Divide each arm for the three hours rays, then falling parallel to the plane of the inner contained in it, in the same manner; and set the circle or equinoctial, are excluded by it. hours to their proper places, on the sides of the 55. III. Figs. 6,7, and 8, a universal dial or arms, as they are marked in fig. 6. Each of the a plain cross, as described by Mr. Ferguson. It hour spaces should be divided into four equal is moveable on a joint C, for elevating it to any parts, for the half hours and quarters, to the. given latitude on the quadrant Co 90, as it stands quadrant ef; and right lines should be drawn upon the horizontal board A. The arms of the through these division-marks in the quadrant, to cross stand at right angles to the middle part; the arms of the cross, in order to determine the and the top of it , from a to n, is of equal length places thereon where the subdivision of the hours with either of the arms ne or mk. See fig. 6. must be marked. This kind of universal dial is The dial is rectified by setting the middle line easily made, and has a pretty uncommon appeartu to the latitude of the place on the quadrant, ance in a garden. the board A level, and the point N. northward 58. IV. The universal mechanical dial, fig. 9, by the needle; thus, the plane of the cross will affords, by its equinoctial circle, an easy method be parallel to the plane of the equator. Then, of describing a dial on any kind of plane. For from III o'clock in the morning till VI, the upper example: suppose a dial is required on a horiedge kl of the arm io will cast a shadow on the zontal plane. If the plane be immoveable, as time of the day on the side of the arm cm; from ABCÔ, find a meridian line as GF; or, if VI till IX, the lower edge i of the arm io will moveable, assume the meridian at pleasure : then cast a shadow on the hours on the side og. From by means of the triangle EKF, whose base is IX in the morning to XII at noon, the edge ab of applied on the meridian line, raise the equinocthe top part a n will cast a shadow on the hours tial dial H till the index G I becomes parallel to on the arm nef; from XII to III in the after- the axis of the earth (which is so, if the angle noon, the edge cd of the top part will cast a sha- KEF be equal to the elevation of the pole), and dow on the hours on the arm klm; from III to the XII o'clock line on the dial hang over the VI in the evening, the edge gh will cast a sha- meridian line of the plane or the base of the dow on the hours on the part pu; and from VI triangle. If then, in the night, or in a dark to IX, the shadow of the edge ef will show the place, a lighted candle be successively applied to time on the top part an. The breadth of each the axis GI, so as the shadow of the index or part ab, ef, &c., must be so great, as never to style G I fall upon one hour line after another, let the shadow fall quite without the part or arm the same shadow will mark out the several hour on which the hours are marked, when the sun is lines on the plane ABCD. Noting points, at his greatest declination from the equator. therefore, on the shadow, draw lines through 56. Tc determine the breadth of the sides of them to G; then an index being fixed on G, acthe arms which contain the hours, so as to cording to the angle IGF, its shadow will point be in just proportion to their length; make an out the several hours by the light of the sun. If angle A B C, fig. 7, of 23° 30', which is equal to a dial were required on a vertical plane, having the sun's greatest declination: and suppose the raised the equinoctial circle as directed, push the top: forward the index G I till the tip thereof, I, touch be narked on the equator in the meridian of the the plane. If the plane be inclined to the hori- place (as it is marked on the meridian of London zon, the elevation of the pole should be found on in the figure), the division of the light and shade the same; and the angle of the triangle KEF on the globe will show the time of the day. should be made equal thereto. 63. The northern stile of the dial is hid in the 59. V. Fig. 1, plate III., represents a universa! figure hy the axis of the globe. The hours in dial, which shows the hour of the day by a ter- the hollow to which that stile belongs, are also restrial globe, and by the shadows of several supposed to be hid by the oblique view of the gnomons, at the same time; together with all the figure: but they are the same as the hours in the places of the earth which are then enlightened front hollow. Those also in the right and left by the sun; and those to which the sun is then hand semicircular hollows are mostly hid from rising, or on the meridian or setting. This dial sight; and so also are all those on the sides next is made of a thick square piece of wood, or hol- the eye of the four acute angles. low metal. The sides are cut into semicircular 64. The construction of this dial is as follows: hollows, in which the hours are placed; the stile on a thick square piece of wood, or metal, draw of each hollow coming out from the bottom the lines ac and bd, fig. 2, as far from each thereof as far as the ends of the hollows project. other as you intend for the thickness of the stile The coiners are cut nut into angles, in the insides abcd; and in the same manner, draw the like of which the hours are also marked; and the thickness of the other three stiles, e f gh, iklm, edge of the end of each side of the angle serves and nopy, all standing outright as from the as a stile for casting a shadow on the bours centre. With any convenient opening for the marked on the other side. In the middle of the compasses, as a A, so as to leave proper strength uppermost side, or plane, there is an equinoctial when KI is equal to a A, set one foot in a, as a dial; in the centre of which an upright wire is centre, and with the other describe the quadranta fixed, for casting a shadow on the hours of that arc Ac. Then, without altering the compasses, dial, and supporting a small terrestrial globe on set one foot in b as a centre, and with the othei describe the quadrant dB. All the other quad60. The whole dial stands on a pillar, in the rants in the figure must be described in the same middle of a round horizontal board, in which manner, and with the same opening of the comthere is a compass and magnetic needle, for passes, on their centres efik, and no, and each placing the meridian stile towards the S. The quadrant divided into six equal parts, for as pillar has a joint with a quadrant upon it, many hours, as in the figure; each of which divided into 300, for setting it to the latitude of parts must be subdivided into four, for the half any given place. The equator of the globe hours and quarters. At equal distances from is divided into twenty-four equal parts, and each corner, draw the right lines Ip and Kp, L9 the hours are laid down upon it at these parts. and M9, Nr and Or, Ps and Qs: to form the The time of the day may be known by these four angular hollows IpK, LqM, Nr0, and hours, when the sun shines upon the globe. PsQ; making the distances between the tips of 61. To rectify and use this dial, set it on a these hollows, as I K, LM, NO, and PQ, each level table, or on the sole of a window, where equal to the radius of the quadrants: and leaving thc sun shines, placing the meridian style due S. sufficient room within the angular points par by means of the needle; which will be, when and s, for the equinoctial in the middle. the needle points as far from the N. fleur-de-lis 65. To divide the inside of these angles for the toward the W. as it declines westward at the hour spaces, take the following method :-Set one place. Then bend the pillar in the joint, till the foot of the compasses in the point I as a centre, black line on the pillar comes to the latitude of and open the other to K; and with that opening the place in the quadrant. The machine being describe the arc Kt: then, without altering the thus rectified, the plane of its dial part will be compasses, set one foot in K, and with the other parallel to the equator, the wire or axis that sup- describe the arc It. Divide each of these ares, ports the globe will he parallel to the earth's from I and K to their intersection at t, into four axis, and the N. pole of the globe will point equal parts; and from their centres I and K, toward the N. pole of the heavens. through the points of division, draw the right 62. The same hour will then be shown in lines I3, I 4, 1 5, 16, 17: and K 2, K 1, K 12, several of the hollows, by the ends of the sha- K 11; and they will meet the sides Kp and I p dows of their respective stiles; the axis of the of the angle I pK where the hours thereon must glube will cast a shadow on the same hour of the be placed. And these hour spaces in the arcs day, in the equinoctial dial, in the centre of must be subdivided into four equal parts, for the which is it placed, from the 20th of March to the half hours and quarters. Do the like for the 23rd of September; and, if the meridian of the other three angles, and draw the dotted lines, place on the globe be set even with the meridian and set the hours in the insides where those lines stile, all that part of the globe that the sun meet them, as in the figure; and the like hour shines upon will answer to those places of the lines will be parallel to each other in all the quadreal earth which are then enlightened by the sun. rants and in all the angles. Mark poir.ts for all The places where the shade is just corning upon these hours on the upper side: and cut out all the globe, answer to all those places of the earth the angular hollows, and the quadrantal ones in which the sun is then setting; as the places quite through the places where their four gnowhere it is going off, and the light coming on, mons must stand; and lay down the hours on all the places of the earth where the their inside and set in their gnomons, which sun is then rising. And lastly, if the hour of VI must be as broad as the dial is thick, and this answer |