Page images
PDF
EPUB
[subsumed][merged small][merged small][merged small][merged small][merged small][merged small][merged small][subsumed][subsumed][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][subsumed][merged small][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][merged small][graphic][ocr errors][subsumed][merged small][merged small]

figure. If every sixth part of the quadrant be
subdivided into four equal parts, right lines
drawn from the centre through these points of
division, and continued to the line rs, will divide
each hour upon it into quarters.

METHOD OF CONSTRUCTING DIALS BY DIALLING
LINES.

42. This is the easiest of all mechanical me-
thods, and by much the best, when the lines are
truly divided: and not only the half hours and
quarters may be laid down by all of them, but
every fifth minute by most, and every single mi-
nute by those where the line of hours is a foot in
length. Having drawn the double meridian line
a b, c d, fig. 6, on the plane intended for a hori-
zontal dial, and crossed it at right angles by the
six o'clock line fe, as in fig. 3, take the latitude
of the place with the compasses, from the scale of
latitudes, and set that extent from c to e, and
from a to f, on the six o'clock line: then, taking
the whole six hours between the points of the
compasses from the scale of hours, with that ex-
tent set one foot on the point e, and let the other
foot fall where it will upon the meridian line cd,
as at d. Do the same from ƒ to b, and draw the
right lines c d and fb, each of them will be equal
in length to the whole scale of hours. Then,
setting one foot of the compasses in the begin-
ning of the scale at XII, and extending the other
to each hour on the scale, lay off these extents
from a to e for the afternoon hours, and from b
to f for those of the forenoon: this will divide
the lines de and bƒ in the same manner as the
hour scale is divided at 1, 2, 3, 4, and 6; on
which the quarters may also be laid down, if re-
quired. Then, laying a ruler on the point c, draw
the first five hours in the afternoon, from that
point, through the dots at the numeral figures 1,
2, 3, 4, 5, on the line de; and continue the lines
of IV and V through the centre c, to the other
side of the dial, for the like hours of the morn-
ing: which done, lay the ruler on the point a,
and draw the last five hours in the forenoon
through the dots, 5, 4, 3, 2, 1, on the line ƒ b;
continuing the hour lines of VII and VIII through
the centre a to the other side of the dial, for the
like hours of the evening; and set the hours to
Lastly,
their respective lines, as in the figure.
make the gnomon the same way as directed above
for the horizontal dial, and the whole will be

finished.

43. To make an erect south dial, take the colatitude of your place from the scale of latitudes, and then proceed in all respects for the hour line as in the horizontal dial; only reversing the hours as in fig. 4, and making the angle of the stile's height equal to the co-latitude.

GEOMETRICAL METHOD OF DRAWING THE HOUR

LINES.

44. I. To construct a horizontal dial, fig. 1, plate II.-Describe with any opening of the compasses, as Z L, the two semicircles LFk and LQk, upon the cen tres Z and z, where the six o'clock line crosses the double meridian line, and divide each semicircle into twelve equal parts, beginning at L (though strictly speaking, only the quadrants from L to the six o'clock line need be

divided); then connect the divisions which are equi-distant from L, by the parallel lines K M, IN, HO, G P, and FQ. Draw V Z for the hypothenuse of the stile, making the angle V ZE equal to the latitude of the place; and continue the line V Z to R. Draw the line Rr parallel to the six o'clock line, and set off the distance a K from Z to Y, the distance b I from Z to X, c H from Z to W, d G from Z to T, and e F from Zo S. Then draw the lines S s, Tt, W w, Xx, and Y y, each parallel to Rr. Set off the distance y Y, from a to 11, and from ƒ to 1; the distance x X from b to 10, and from g to 2; wW from c to 9, and from h to 3; tT from d to 8, and from i to 4; s S from e to 7, and from n to 5. Then laying a ruler to the centre Z, draw the forenoon hour lines through the points 11, 10, 9, 8, 7; and laying it to the centre z, draw the afternoon lines through the points 1, 2, 3, 4, 5; continuing the forenoon lines of VII and VIII through the centre Z, to the opposite side of the dial, for the like afternoon hours; and the afternoon lines IV and V through the centre z, to the opposite side for 'the like morning hours. Set the hours to these lines as in the figure, and then erect the stile or gnomon, and the dial will be finished.

45. II. To construct a south dial, draw the line V Z, making an angle with the meridian Z L equal to the co-latitude of your place; and proceed in all respects as in the above horizontal dial for the same latitude, reversing the hours as in fig. 4, and making the elevation of the gnomon equal to the co-latitude.

46. III. To construct a north dial. See fig. 2. If the hour lines IV and V, as also VII and VIII on the south dial, fig. 4, plate I. be continued beyond the line VI a VI, and the triangle agh turned about the point a, till a h fall on a XII produced, it is evident a north dial is thereby had. The hour line for VII in the morning on the south dial, when produced, forms the hour line for V in the morning on the north dial: and the hour line for V in the afternoon, on the south dial, forms the hour line for VII in the evening on the north dial. The manner of placing the 'characters for the other hours is therefore obvious.

47. IV. To construct an east dial. On the eastern side of the plane of the meridian, draw a line A B, fig. 3, parallel to the horizon, draw also a line AK, making with AB an angle KAB equal to the complement of the latitude of the place for which the dial is made. Take a point D in AK, and on that point for a centre describe a circle. Through D draw EC perpendicular to A K, thus the circle will be divided into four quadrants; divide two of these quadrants into six equal parts, as in the figure. Draw a straight line F EG perpendicular to EC, the diameter of the circle, and from the centre D through the several divisions, draw the right lines D IV, D V, D VI, D ́VII, D VIII, D IX, DX, D XI. Through IV, V, VI, VII, &c.; draw lines IV, IV, V, V, &c. parallel to EDC. Lastly, in D erect a stile equal to the radius DE, perpendicular to the plane; or on two little pieces perpendicularly fixed in EC, and equal to the same D E, fit an iron rod parallel to

EC, thus will each index at the several hours project a shadow to the respective hour lines IV ÎV, V V, VI VI, &c. The east dial, it is obvious, can only show the hours till twelve o'clock. 48. V. To construct a west dial. The construction is perfectly the same as that of an east dial, only that its situation is inverted, and the hours are written accordingly. A west dial, it is obvious, can only be illuminated after noon, and therefore, joined with an east dial, shows all the hours of the day.

OF UNIVERSAL DIALS.

49. I. The universal dial, invented by Pardie, fig. 4, consists of three principal parts; the first whereof is called the horizontal plane A, because in practice it must be parallel to the horizon. In this plane is fixed an upright pin, which enters into the edge of the second part BD, called the meridional plane; which is made of two pieces, the lowest whereof, B, is called the quadrant, because it contains a quarter of a circle, divided into 90°; and it is only into this part, near B, that the pin enters. The other piece is a semicircle D adjusted to the quadrant, and turning in it by a groove, for raising and depressing the diameter EF of the semicircle, which diameter is called the axis of the instrument. The third piece is a circle, G, divided on both sides into twenty-four equal parts, which are the hours. This circle is put upon the meridional plane, so that the axis EF may be perpendicular to the circle, and the point C be the common centre of the circle, semicircle, and quadrant. The straight edge of the semicircle is chamfered on both sides to a sharp edge, which passes through the centre of the circle. On one side of the chamfered part, the first six months of the year are laid down, according to the sun's declination for their respective days, and on the other side the last six months. And against the days on which the sun enters the signs, there are straight lines drawn upon the semicircle, with the characters of the signs marked upon them. There is a black line drawn along the middle of the upright edge of the quadrant, over which hangs a thread H, with its plummet I, for levelling the instrument. From the 23d of September to the 20th of March, the upper surface of the circle must touch both the centre C of the semicircle, and the line of and; and from the 20th of March to the 23d of September, the lower surface of the circle must touch that centre and

line.

50. To find the time of day by this dial, set it on a level place in sun-shine, and adjust it by the levelling screws k and l, until the plumbline hangs over the black line upon the edge of the quadrant, and parallel to the said edge; move the semicircle in the quadrant, until the line of and (where the circle touches) comes to the latitude of the place in the quadrant: then turn the whole meridional plane BD, with its circle G, upon the horizontal plane A, until the edge of the shadow of the circle falls on the day of the month in the semicircle; and then the meridional plane will be due north and south; the axis EF will be parallel to the axis

of the world, and will cast a shadow upon the true time of the day among the hours of the circle.

51. When the instrument is thus rectified, the quadrant and semicircle are in the plane of the meridian, and the circle is then in the plane of the equinoctial. Therefore as the sun is above the equinoctial in summer (in northern latitudes), and below it in winter, the axis of the semicircle will cast a shadow on the hour of the day, on the upper surface of the circle, from the 20th of March till the 23d of September; and from the 23d of September to the 20th of March, the hour of the day will be determined by the shadow of the semicircle upon the lower surface of the circle. In the former case the shadow of the circle falls upon the day of the month, on the lower part of the diameter of the semicircle; and in the latter case on the upper part.

52. The method of laying down the months and signs upon the semicircle is as follows:Draw the right line ACB, fig. 5, equal to the diameter of the semicircle A D B, and cross it in the middle at right angles with the line ECD, equal in length to ADB; then EC will be the radius of the circle FCG, which is the same as that of the semicircle. Upon E, as a centre, describe the circle FCG, on which set off the arcs Ch and Ci, each equal to 234°, and divide them accordingly into that number for the sun's declination. Then laying the edge of a ruler over the centre E, and also over the sun's declination for every fifth day of each month, mark the points on the diameter A B of the semicircle from a to g, which are cut by the ruler; and there place the days of the months accordingly, answering to the sun's declinations. setting one foot of the compasses in C, and extending the other to a or g, describe the semicircle abcdefg; which divide into six equal parts, and through the points of division draw right lines parallel to CD, for the beginning of the signs (of which one half are on one side of the semicircle, and the other half on the other), and set the characters of the signs to their proper lines, as in the figure.

Then

53. II. The universal, or astronomical equinoctial ring-dial is an instrument that serves to find out the hour of the day in any latitude. It consists of two flat rings or circles, usually from four to twelve inches diameter, and of a moderate thickness; the outward ring representing the meridian of the place it is used at, contains two divisions of 90° each, opposite to one another, serving to let a sliding piece and ring (by which the dial is usually suspended) be placed on one side, from the equator to the N. pole, and on the other side to the S., according to the latitude of the place. The inner ring represents the equator, and turns diametrically within the outer, by means of two pivots inserted in each end of the ring at the hours XII. Across the two circles is screwed to the meridian a thin pierced plate or bridge, with a cursor, that slides along the middle of the bridge: this cursor has a small hole for the sun to shine through. The middle of this bridge is conceived as the axis of the world, and its extremities as the poles; on the one side are delineated

the twelve signs of the zodiac, and sometimes opposite the degrees of the sun's declination; and on the other side the days of the month throughout the year. On the other side of the outer ring A are the divisions of 90°, or a quadrant of latitude. It serves, by the placing of a common pin in the hole, to take the sun's altitude, from which the latitude of the place may easily be found.

54. In using this dial, place the line in the middle of the sliding piece, over the degree of latitude of the place. Suppose, for example, 514 for London; put the line which crosses the hole of the cursor C to the day of the month of the degree of the sign. Open the instrument till the two rings be at right angles to each other, and suspend it by the ring, that the axis of the dial represented by the middle of the bridge may be parallel to the axis of the earth, viz. the north pole to the north, and vice versa. Then turn the flat side of the bridge towards the sun, so that his rays passing through the small hole in the cursor may fall exactly in a line drawn through the middle of the concave surface of the inner ring or hour-circle, the bright spot shows the hour of the day in the said concave surface of the dial. The hour XII cannot be shown by this dial, because the outer ring, being then in the plane of the meridian, excludes the sun's rays from the inner; nor can this dial show the hour when the sun is in the equinoctial, because his rays, then falling parallel to the plane of the inner circle or equinoctial, are excluded by it.

55. III. Figs. 6, 7, and 8, a universal dial or a plain cross, as described by Mr. Ferguson. It is moveable on a joint C, for elevating it to any given latitude on the quadrant Co 90, as it stands upon the horizontal board A. The arms of the cross stand at right angles to the middle part; and the top of it, from a to n, is of equal length with either of the arms ne or mk. See fig. 6. The dial is rectified by setting the middle line tu to the latitude of the place on the quadrant, the board A level, and the point N. northward by the needle; thus, the plane of the cross will be parallel to the plane of the equator. Then, from III o'clock in the morning till VI, the upper edge kl of the arm io will cast a shadow on the time of the day on the side of the arm cm; from VI till IX, the lower edge i of the arm io will cast a shadow on the hours on the side oq. From IX in the morning to XII at noon, the edge ab of the top part an will cast a shadow on the hours on the arm nef; from XII to III in the afternoon, the edge cd of the top part will cast a shadow on the hours on the arm klm; from III to VI in the evening, the edge g h will cast a shadow on the hours on the part pu; and from VI to IX, the shadow of the edge ef will show the time on the top part an. The breadth of each part a b, ef, &c., must be so great, as never to let the shadow fall quite without the part or arm on which the hours are marked, when the sun is at his greatest declination from the equator.

56. Tc determine the breadth of the sides of the arms which contain the hours, so as to be in just proportion to their length; make an angle ABC, fig. 7, of 23° 30', which is equal to the sun's greatest declination: and suppose the

length of each arm, from the side of the long middle part, and also the length of the top part above the arms, to be equal to Bd. Then as the edges of the shadow, from each of the arms, will be parallel to Be, making an angle of 23° 30′ with the side Bd of the arm, when the sun's declination is 23° 30′; it is plain, that if the length of the arm be Bd, the least breadth that it can have, to keep the edge Be of the shadow Begd from going off the side of the arm de before it comes to the end of it ed, must be equal to ed or d B. But to keep the shadow within the quarter divisions of the hours, when it comes near the end of the arm, the breadth of it should be still greater, so as to be almost doubled, on account of the distance between the tips of the arms.

57. The hours may be placed on the arms, by laying down the cross a b c d, fig. 8, on a sheet of paper; and with a black lead pencil held close to it drawing its shape and size on the paper. Then take the length ae in the compasses, and with one foot in the corner a, describe with the other the quadrant ef. Divide this arc into six equal parts, and through the points of division draw right lines ag, ah, &c., continuing three of them to the arm ce, which are all that can fall upon it; and they will meet the arm in those points through which the lines that divide the hours from each other are to be drawn right across it. Divide each arm for the three hour contained in it, in the same manner; and set the hours to their proper places, on the sides of the arms, as they are marked in fig. 6. Each of the hour spaces should be divided into four equal parts, for the half hours and quarters, to the quadrant ef; and right lines should be drawn through these division-marks in the quadrant, to the arms of the cross, in order to determine the places thereon where the subdivision of the hours must be marked. This kind of universal dial is easily made, and has a pretty uncommon appearance in a garden.

58. IV. The universal mechanical dial, fig. 9, affords, by its equinoctial circle, an easy method of describing a dial on any kind of plane. For example: suppose a dial is required on a horizontal plane. If the plane be immoveable, as ABCD, find a meridian line as GF; or, if moveable, assume the meridian at pleasure: then by means of the triangle EKF, whose base is applied on the meridian line, raise the equinoctial dial H till the index GI becomes parallel to the axis of the earth (which is so, if the angle KEF be equal to the elevation of the pole), and the XII o'clock line on the dial hang over the meridian line of the plane or the base of the triangle. If then, in the night, or in a dark place, a lighted candle be successively applied to the axis GI, so as the shadow of the index or style GI fall upon one hour line after another, the same shadow will mark out the several hour lines on the plane ABCD. Noting points, therefore, on the shadow, draw lines through them to G; then an index being fixed on G, according to the angle IGF, its shadow will point out the several hours by the light of the sun. a dial were required on a vertical plane, having raised the equinoctial circle as directed, push

If

forward the index GI till the tip thereof, I, touch the plane. If the plane be inclined to the horizon, the elevation of the pole should be found on the same; and the angle of the triangle KEF should be made equal thereto.

59. V. Fig. 1, plate III., represents a universal dial, which shows the hour of the day by a terrestrial globe, and by the shadows of several gnomons, at the same time; together with all the places of the earth which are then enlightened by the sun; and those to which the sun is then rising, or on the meridian or setting. This dial is made of a thick square piece of wood, or hollow metal. The sides are cut into semicircular hollows, in which the hours are placed; the stile of each hollow coming out from the bottom thereof as far as the ends of the hollows project. The coiners are cut out into angles, in the insides of which the hours are also marked; and the edge of the end of each side of the angle serves as a stile for casting a shadow on the hours marked on the other side. In the middle of the uppermost side, or plane, there is an equinoctial dial; in the centre of which an upright wire is fixed, for casting a shadow on the hours of that dial, and supporting a small terrestrial globe on the top.

60. The whole dial stands on a pillar, in the middle of a round horizontal board, in which there is a compass and magnetic needle, for placing the meridian stile towards the S. The pillar has a joint with a quadrant upon it, divided into 90°, for setting it to the latitude of any given place. The equator of the globe is divided into twenty-four equal parts, and the hours are laid down upon it at these parts. The time of the day may be known by these hours, when the sun shines upon the globe.

61. To rectify and use this dial, set it on a level table, or on the sole of a window, where the sun shines, placing the meridian style due S. by means of the needle; which will be, when the needle points as far from the N. fleur-de-lis toward the W. as it declines westward at the place. Then bend the pillar in the joint, till the black line on the pillar comes to the latitude of the place in the quadrant. The machine being thus rectified, the plane of its dial part will be parallel to the equator, the wire or axis that supports the globe will be parallel to the earth's axis, and the N. pole of the globe will point toward the N. pole of the heavens.

62. The same hour will then be shown in several of the hollows, by the ends of the shadows of their respective stiles; the axis of the globe will cast a shadow on the same hour of the day, in the equinoctial dial, in the centre of which is it placed, from the 20th of March to the 23rd of September; and, if the meridian of the place on the globe be set even with the meridian stile, all that part of the globe that the sun shines upon will answer to those places of the real earth which are then enlightened by the sun. The places where the shade is just coming upon the globe, answer to all those places of the earth in which the sun is then setting; as the places where it is going off, and the light coming on, answer to all the places of the earth where the sun is then rising. And lastly, if the hour of VI

be marked on the equator in the meridian of the place (as it is marked on the meridian of London in the figure), the division of the light and shade on the globe will show the time of the day.

63. The northern stile of the dial is hid in the figure by the axis of the globe. The hours in the hollow to which that stile belongs, are also supposed to be hid by the oblique view of the figure: but they are the same as the hours in the front hollow. Those also in the right and left hand semicircular hollows are mostly hid from sight; and so also are all those on the sides next the eye of the four acute angles.

64. The construction of this dial is as follows: on a thick square piece of wood, or metal, draw the lines ac and bd, fig. 2, as far from each other as you intend for the thickness of the stile abcd; and in the same manner, draw the like thickness of the other three stiles, efgh, i klm, and nopq, all standing outright as from the centre. With any convenient opening for the compasses, as a A, so as to leave proper strength when KI is equal to a A, set one foot in a, as a centre, and with the other describe the quadranta! arc Ac. Then, without altering the compasses, set one foot in b as a centre, and with the othe describe the quadrant d B. All the other quadrants in the figure must be described in the same manner, and with the same opening of the compasses, on their centres efik, and no, and each quadrant divided into six equal parts, for as many hours, as in the figure; each of which parts must be subdivided into four, for the half hours and quarters. At equal distances from each corner, draw the right lines Ip and Kp, Lq and Mq, Nr and Or, Ps and Qs: to form the four angular hollows IpK, Lq M, NrO, and PSQ; making the distances between the tips of these hollows, as IK, LM, NO, and PQ, each equal to the radius of the quadrants: and leaving sufficient room within the angular points pqr and s, for the equinoctial in the middle.

65. To divide the inside of these angles for the hour spaces, take the following method:-Set one foot of the compasses in the point I as a centre, and open the other to K; and with that opening describe the arc Kt: then, without altering the compasses, set one foot in K, and with the other describe the arc It. Divide each of these arcs, from I and K to their intersection at t, into four equal parts; and from their centres I and K, through the points of division, draw the right lines 13, 14, 15, 16, 17: and K 2, K 1, K 12, K11; and they will meet the sides Kp and I p of the angle IpK where the hours thereon must be placed. And these hour spaces in the arcs must be subdivided into four equal parts, for the half hours and quarters. Do the like for the other three angles, and draw the dotted lines, and set the hours in the insides where those lines meet them, as in the figure; and the like hour lines will be parallel to each other in all the quadrants and in all the angles. Mark points for all these hours on the upper side: and cut out all the angular hollows, and the quadrantal ones quite through the places where their four gnomons must stand; and lay down the hours on their insides, and set in their gnomons, which must be as broad as the dial is thick, and this

« PreviousContinue »