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equal to the latitude of the place for which the the intersection a, as a centre, describe the quadial is made.
drant ke with any convenient radius or opening 26. If the pole of the globe be elevated to the of the compasses ; then setting one foot in the co-latitude of the given place, and any meridian intersection b, as a centre, with the same radius be brought to the north point of the horizon, the describe the quadrant fh, and divide each quarest of the meridians will cut the horizon in the drant into ninety equal parts or degrees, as in the respective distances of all the hours from XII, for figure. a direct south dial, the gnomon of which must 29. As the hour lines are less distant from each form an angle with the plane of the dial equal to other about noon than in any other part of the the co-latitude of the place; and the hours on dial, it is best to have the centres of these quathis dial must be placed in a direction contrary drants at a little distance from the centre of to that in which they stand on the horizontal the dial plane, on the side opposite to XII, in dial.
order to enlarge the hour distances thereabouts, 27. But if the globe have more than twenty- under the same angles on the plane. Thus the four meridian semicircles upon it, we must take centre of the plane is at C, but the centres of the the following method for making horizontal and quadrants are at a and b. Lay a ruler over the soith dials:-Elevate the pole to the latitude of point b, and (keeping it there for the centre of all the place, and turn the globe until any particular the afternoon hours in the quadrant fh), draw the meridian (suppose the first) comes to the north hour line of I through 11° 30' in the quadrant; point of the horizon, and the opposite meridian the hour line of Is through 24° 30°; of III will cut the horizon in the south. Then set the through 38° 5'; IV through 53° 30'; and V through hour index to the uppermost XII on its eircle, 71° 4': and, because the sun rises about four in and turn the globe westward until 15° of the the morning on the longest days, at London, conequator pass under the brazen meridian, and the tinue the hour lines of IV and V in the afternoon hour index will be at I, for the sun moves 15° through the centre b to the opposite side of the every hour), and the first meridian will cut the dial. horizon in the number of degrees from the north 30. the other quadrant is now to he divided, point that I is distant from XII. Turn on until but it is very obvious that the same minute proother 15o of the equator pass under the bra- cess need not be gone through in doing so, as the zen meridian, and the hour index will then be divisions already laid down may be readily transat II, and the first meridian will cut the horizon ferred to the quadrant ek; as the labor of dividin the number of degrees that II is distant from ing both may be much shortened by working XII: and so, by making 150 of the equator pass from a scale, having a line of chords upon it, as under the brazen meridian for every hour, the will be shown presently. first meridian of the globe will cut the horizon 31. If a plate similar to this triangle be made in the distances of all the hours from XII to VI, as thick as the distance between the lines ac and which is just 90°; and then the distances of Xi, bd, and set upright between them, touching at a X, IX, VIII, VII, and VI, in the forenoon will and b, its hypothenuse a g will be parallel to be the same from XII, as the distance of I, II, the axis of the world, when the dial is truly III, IV, V, and VI, in the afternoon : and these set; and will cast a shadow on the hour of the hour lines continued through the centre, will give day. the opposite hour lines on the other half of the 32. To make an erect direct south dial, fig.
4, elevate the pole to the co-latitude of the place, 28. To make a horizontal dial for the latitude and proceed in all respects as above for the hoof London, which is 51° 30° north, elevate the rizontal dial, and from VI in the morning to VI north pole of the globe 51° 30' above the north in the afternoon; only the hours must be reversed, point of the horizon; and then turn the globe, as in the figure; and the hypothenuse a g, of the until the first meridian (which, on the British gnomon a gh, must make an angle with the terrestrial globe, is that of London), cuts the dial-plane equal to the co-latitude of the place. north point of the horizon, and set the hour in- As the sun can shine no longer on this dial than dex to XII at noon.
Then turning the globe from six in the morning until six in the evening, Westward until the index points successively there is no occasion for having any more than to I, II, III, IV, V, and VI, in the afternoon, or twelve hours upon it. until 15°, 30°, 45°, 60°, 75°, and 90° of the 33. To make a direct dial, declining from the equator pass under the brazen meridian, the first south towards the east or west, elevate the pole meridian of the globe will cut the horizon in the to the latitude of the place, and screw the quafollowing numbers of degrees from the north drant of altitude to the zenith. Then, if the dial towards the east, viz. 113, 241, 381, 53), 7115, decline towards the E. (which we shall suppose it and 90; which are the respective distances of does), count in the horizon the degrees of declithe above hours from XII upon the plane of the nation, from the E. point towards the N. and horizon. To transfer these, and the rest of the bring the lower end of the quadrant to that dehours
, to a horizontal plane, draw the parallel gree of declination at which the reckoning ends. right lines a c, and db, fig. 3, upon that plane, Then bring any particular meridiau of the globe as far from each other as is equal to the intended (suppose the first) directly under the graduated thickness of the gnomon or stile of the dial, and edge of the upper part of the brazen meridian, the space included between them will be the me and set the hour to XII at noon. Then, keeping ridian or twelve o'clock line on the dial. Cross the quadrant of altitude at the degree of declithis meridian at right angles with the six o'clock nation in the horizon, turn the globe eastward fine, kh, and setting one foot of the compasses in on its axis, and observe the degrees cut by the
first meridian in the quadrant of altitude (counted urant to the opposite degree in the horizon, from the zenith), as the hour circle comes to XI, namely, as far from the W. towards the Ņ. and X, IX, &c., in the forenoon, or as 15, 30, 45, &c. then proceed in all respects as above. degrees of the equator pass under the brazen 38. Thus when our declining dial is finished, meridian at these hours respectively; and the de we have four dials, viz. 1. A north dial declining grees then cut in the quadrant by the first meri- eastward by the same number of degrees ; 2. A dian, are the respective distances of the forenoon north dial declining the same number west ; 3. hours from XII on the plane of the dial. A south dial, declining east; and, 4. A south
34. Then, for the afternoon hours, turn the dial declining west; only placing the proper quadrant of altitude round the zenith until it number of hours, and the stile or gnomon recomes to the degree in the horizon opposite to spectively, upon each plane. For, in the S. W. that where it was placed before ; namely, as far plane, the substilar line falls among the aftemoon from the W. point of the horizon towards the S. hours; and in the S. E. of the same declination, as it was set at first from the E. point towards the among the forenoon hours, at equal distances N.; and turn the globe westward on its axis, un from XII. And so all the morning hours on the til the first meridian comes to the brazen meri- W. decliner, will be like the afternoon hours on dian again, and the hour index to XII; then, the E. decliner; and the S. W. decliner, the N. E. continue to turn the globe westward, and as the decliner, by only extending the hour lines, stile index points to the afternoon hours, 1, II, III, and substile, quite through the centre: the axis &c., or as 15°, 30°, 45°, &c., of the equator of the stile (or edge that casts the shadow on the pass under the brazen meridian, the first meri- hour of the day), being in all dials whatever, dian will cut the quadrant of altitude in the re- parallel to the axis of the world, and consespective number of degrees from the zenith that quently pointing towards the north pole of the each of these hours is from XII on the dial. And heaven in north latitudes, and towards the south when the first meridian goes off the quadrant at pole, in south latitudes. the horizon in the forenoon, the hour index shows the time when the sun will come upon this dia. ,
METHOD OF CONSTRUCTING DIALLING LINES. and when it goes off the quadrant in the afternoon, 39. Describe, with any opening of the comthe index will point to the time when the sun goes passes, as E A, fig. 5, according to the intended off the dial. Having thus found all the hour dis- length of the scale, the circle ADC B, and cross tances from XII, lay them down upon the dial it at right angles by the diameters C E A and D E plane, either by dividing a semicircle into two B;divide the quadraut A B first into 9 equal parts, quadrants of 90° each (beginning at the hour and then each part into 10; so shall the quadrant line of XII), or by the line of chords, as above be divided into 90 equal parts or degrees. Draw directed.
the right line A F B for the chord of this quadrant; 35. In all declining dials, the line on which and, setting one foot of the compasses in the point che stile or gnomon stands (commonly called the A, extend the other to the several divisions of the substile line) makes an angle with the twelve quadrant, and transfer these divisions to the line o'clock line, and falls among the forenoon hour A F B by the arcs 10, 20, 30, &c., and this will lines, if the dial declines towards the E; and be a line of chords, divided into 90 unequal among the afternoon hour lines, when the dial parts. declines towards the W. that is, to the left hand 40. Divide the quadrant CD into 90 equal from the twelve o'clock line in the former case, parts, and from each point of division draw right and to the right hand from it in the latter. lines, as i, k, l, &c., to the line C E; alt perpendi
36. To find the distance of the substile from cular to that line, and parallel to D'E, which the twelve o'clock line, if the dial declines from will divide E C into a line of sines ; and although the S. towards the E.count the degrees of the de- these are seldom put among the dialling lines on clination in the horizon from the E. point toward a scale, yet they assist in drawing the line of lathe N. and bring the lower end of the quadrant titudes. For if a ruler be laid upon the point of altitude to that degree of declination where D, and over each division in the line of sines, it the reckoning ends; then, turn the globe until will divide the quadrant C B into 90 unequal the first meridian cuts the horizon in the like num parts, as Ba Bb, &c., shown by the right lines 12 a, ber of degrees, counted from the S. point toward 20 b, 30c, &c., drawn along the edge of the ruler. the E. and the quadrant and the first meridian If the right line B C be drawn, subtending this will then cross one another at right angles; and the quadrant and the nearest distances, Ba, B6, Bc, number of degrees of the quadrant, which are in- &c., be taken in the compasses from B, and set tercepted between the meridian and the zenith, is upon this line in the same manner as directed for equal to the distance of the substile line from the the line of chords, it will make a line of latitudes twelve o'clock line; and the number of degrees of BC, equal in length to the line of chords A B, the first meridian, which are intercepted between and an equal number of divisions, but very unethe quadrant and the N. pole, is equal to the qual as to their lengths. elevation of the stile above the plane of the dial. 41. Draw the right line D G A, subtending the
37. If the dial declines westward from the S., quadrant DA; and parallel to it, draw the right count that declination from the E. point of the line rs, touching the quadrant D B at the numehorizon towards the S. and bring the quadrant of ral figure 3. Divide this quadrant into six altitude to the degree in the horizon at which the equal parts, as 1, 2, 3, &c., and through these reckoning ends ; both for finding the forenoon points of division draw right lines from the centre hours, and distance of the substile from the meri- Eto the liners, which will divide it at the points dian: and for the afternoon hours, bring the qua- where the six hours are to be placed, ad in the