Fig. LI. : And here Note] That the Declination thus found, is always I. If therefore, The Degrees of Declination do exceed 90 deg. II. If the Degrees of Declination exceed 180; then the Excess CHAP IV. How Hour-Lines may be described upon an Horizontal E I. By the Globe. Levate the Globe to the Latitude of the place for which you would make your Dial, (suppose for London, in the Latitude of 51 deg. 30 min.). Then bring the Vernal Equinoctial Colure (which is the first point of Aries alfo) to the Meridian, and (if you will) the Index of the Hour-Circle to 12. This done, 1. Turn the Globe about Westward, till the Hour-Index points at I a Clock, or rather [till 15 degrees of the Equinoctial come to be just under the Meridian] and there keeping the Globe, look upon the Horizon how many degrees thereof are cut by the Equinoctial Colure; which you shall find to be 11 deg. 30 min. which fet down in a little Table, as you fee here is done; for this 11 deg. 50 min. is the distance that the Hour-lines of 11 and 1 a clock are di stant from the Meridian upon the Dial Plain. d. m. Latitude 51. 30 12 HI 10 2 193 d. 00.00 2. Turn the Globe more Westward, till 30 75 6 3. Turn the Globe still more Westward, till 45 degrees of the Equinoctial come to the Meridian; and then fhall the Equinoctial Colure cut 38 deg. 3 min. of the Horizon counted from the Micridian, which is the distance of 9 and 3 a clock. Do thus with the other hours of 8 and 4, of 7 and 5, and fo shall the Colure cut 90 degrees at 6 a clock, or when 90 degrees - of the Equinoctial comes to the Meridian. And this being done, your Dial is fo far made as the Globe can affist you. i II. The Geometrical Construction of this Dial, in order to the Trigome-trical Calculation. : 1. With 60 Degrees of a Scale of Chords, defcribe a Circle re- Fig.. presenting your Dial-plain, and Horizon of the Place, (viz. Lon- LIL don.) Cross it with 2 Diameters SN, reprefenting the Meridian of the Globe, and Hour-line of XII; and the Line EW, for the Hour-line of VI: then will Z represent the Zewith of the Place, and be the Centre of the Dial. 4 2. The Latitude of the Place being 51 d. 30 m. Set them from Sto a, and from W to b: Then a Ruler laid from W to a, will cross the Meridian SN in P, the Pole of the World: And laid from E to b, it will cross the Meridian N Sin E, the interfecti- on of the Meridian and Equinoctial. And now you have three Points, viz. W, Æ, E; through which you may defcribe the Equinoctial Circle WÆ E, whose Centre will be at c, always in some part of the Line N S, extended, if need be. 3. Divide the Semicirle WNE, into 12 equal parts, at the points, &c. And laying a Ruler to Z, and every of those points, it will cross the Aquinoctial Circle W EE, in the points ***, &c. dividing that Semicircle into 12 unequal parts. 4. A Ruler laid to P, the Pole of the World, and to the seve-ral points * * *, &c. it will cut the Circle of your Plain in the points 1, 2, 3, &c. on the East-fide of N, and 11, 10, 9, &c. on the West-fide of N.. Laftly. If you lay a Ruler to the Centre Z, and the respeEtive points 1, 2, 3, &c. and 11, 10, 9, &c. they shall be the true Hour-lincs belonging to an Horizontal Dial for the Latitude -of 51 de. 30 m. And their respective distances from N will be the.. fame as in the Table they were found to be by the Globe. III.: By Fig. III. By Trigonometrical Calculation. In these Horizontal Dials, there is nothing to be found by Calculation Trigonometrical, but the Hour-distances upon the Plain from the Meridian; for which, This is The Canon for Calculation. As the Sine of 90 de. Is to the Sine of the Latitude PN, 51 de. 30 m. So is the Tangent of 15 d. (the Equinoctial Distance of One hour; of 30 d. for Two hours; of 45 d. for Three hours, &c.) To the Tangent of 11 d. 50 m. for II and 1---- of 24 d. 20 m. for 10 and 2---- for 38 d. 3 min. for 9 and 3, &c. as in the Table, before found by the Globe. So have you all the Hour-lines between 6 in the morning and 6 at night; and for the Hour-lines of 4 and 5 in the morning, and of 7 and 8 at night, draw the same Lines before and after 6, through the Centre, as in the Figure, and they shall be the true Hour-lines: And so is your Dial finished. The Stile must stand upright at 12 of the clock, not inclining on either fide. And in this manner may you describe Hour-lines upon an Horizontal Plain in any Latitude. CHAP. V. How to describe Hour-Lines upon an Erect direct South A Lines to be drawn through the Centre, for that the Sun never Fig. Shines upon them before 6 in the Morning, nor after 6 at Night. The Stile of these Dials must stand upon the Hour-Line of 12, and must point downwards towards the South Pole. As in Figure LIII. LIII. CHAP. VI. To make an Erect Direct North Dial, in the Latitude of HF. North Erect Direct Dial, is the fame with the South, on- Fig. TH the hours about Midnight, as 9, 10, 11, 12, at Night; and I, 2 and 3 in the Morning must be left out, and 4 and 5 in the Morning; and 7 and 8 at Night must be drawn through the Centre: So is your North-Dial also finished, as in Fig. LIV. CHAP. VII. To make an Erect Direct East or West Dial in the Latitude of London, 51 de. 30 m. T I. By the Globe. HE Globe rectified to the Latitude, the Index to 12, the Fig. Quadrant of Altitude in drant of Altitude so about till the graduated edge thereof do behold the direct East or West-points of the Horizon, you shall find that it will lie in the very Plain of the Meridian-Circle, and fo the Pole will have no elevation over it; for turning the Globe about, the Equinoctial Colure will not cut the Quadrant of Altitude in any particular degree, but it will cut all the degrees thereof at the fame time; wherefore the Hour-lines of these Plains will make no Angles at the Pole, and therefore must be parallel one to the other, which the Globe evidently demonstrates, but will not conveniently give the parallel distance of each from other, they being the Zenith: If you turn the Qua- LV. B b b nearer : Fig. nearer or farther off each other according as the Stile is propor- For the Reafons aforesaid, there is no Trigonometrical Calculation required in the making of these Dials; and therefore, I shall proceed to II. The Geometrical Conftruction of these Dials. Let the Plain upon which you would make an East or West Dial, be ABCD. 1. Upon D (or any where towards the lower part of the Line BD, for an East Dial, or of AC for a West) with 60 degrees of your Chord, defcribe an Arch FG, upon which fet the Complement of the Latitude of the place, viz. 38 deg. 30 min. from F to G, and draw the Line DGE for the Equinoctial.. 2. Towards the upper part of this Line, as at P, affume any point, and through it draw the Line 6 P6 perpendicular to the Equinoctial, for the Hour-line of Six. Alfo, towards the lower part of the fame Line, affume another point. as L, and through it draw the Line 11 L 11. perpendicular also to the Equinoctial for the Hour-line of Eleven. 3. With 60 degrees of your Chords, upon the point L, describe a finall Arch of a Circle, as HK, and upon it (always) fet 15 degrees (or one hours distance) from H to K, and draw the Line LKM, cutting the Hour-line of Six in M. 4. Upon Mas a Centre, with 60 degrees of your Chord, de seribe an Arch of a Circle NO, which divide into five equal parts. in the points000. 5. Lay a Ruler upon M, and each of these points o and the Ruler will cut the Equinoctial-line E D in the points ****, through which points, if you draw Right Lines parallel to the Hour-line of 6, they shall be the Hour-lines of 7, 8, 9, and 10 of the Clock, the Hour-lines of 6 and 11 being drawn before. 6. For the Hour-lines of 4 and 5 in the Morning, before 6, they retain the fame distance from 6, as, do the hours of 7 and 8; and thus is your Dial finished... The Stile must stand upon the Hour-line of 6, and be e levated so high as is the length of the Line MP, and may either be a Pin of Wyre, or a Plate of Brass or Iron. The West Dial is the fame with the East, only changing the names of the Hours For: |