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the gnomort the same way as directed above for the horizontal dial,and the whole will be finished.,

To make an erect South Dial, take the ro-latitude of yourplace from the scale of latitudes, and then proceed in all respectsfor the hotir-line as in the horizontal dial; only reversing thehours, as in fig. 4, and making the angle of the stile’s height equalto the co-latitude.

Gf.omethical Method of drawing the Hour Lines upon

Dials.

I. To construct a Horizontal Dial, fig. 7. Describe with.any opening of the compasses, as ZL, the two semicircles LE#rand LQ£, upon the centres Z and z, where the six o’clock linecrosses tlie double meridian-lino, and divide each semicircle into12 equal parts, begiimna'at I. (though strictlv speaking, only thequadrants from L to the six o’clock line need be divided) ; thenconnect the divisions which are equidistant from L, by the parallelline KM, IN, HO, GP, and FQ. Draw YZ for tlie hypothe-nuse ol the stile, making the angle YZ F. equal to the latitude otyour place; and cintiiiue the line YZ to R. Draw the line R rparallel to the six o’clock line, and set oil' the distance a K from/ to Y, the distance b I from Z to X, c II from Z to W, d Gfrom Z to T, and e F from Z to S. Then draw the lines S s, T t,M rc, X .r, and Y y, each pa allel to R r. Set oft’ the di-ftancey Y, from a to 11, and from/to 1 ; the distance X x from b to 10,and from g (o 2; n \V from c to 9, and from h to 3 ; t T from dto 8, and from i to 4; * S from c to 7, and from n. to 5. Thenlaying a ruler to the centre Z, draw the forenoon hour-linesthrough the points 11, 10, 9, 8, 7 ; and laying it to the centre z,draw the afternoon lines through the points I, 2,3, 4, 3: con-tinuing the forenoon lines of VII and ^ III through the centre Z,to the opposite side of the dial, for the like afternoon hours; andthe afternoon lines IV and V through the centre z, to the oppositeside, for the like morning hours. Set the hours to these lines as inthe figure, and then erect the stile or gnomon, and the horizontaldial will be finished.

H. To construct a South Dial, draw the line YZ, making anangle with the meridian ZL, equal to the co-latitude of your place ;and proceed in all respects as in the above horizontal dial for thesame latitude, reversing the hours as in fig. 4, and making the ele-vation of the gnomon equal to the ro-latilude.

III. To construct a North Dial. See fig. 8. If the hour-lines IV and V, as also VII and VIII on the south dial, fig. 4, becontinued beyond the line VI a VI, and the triangle a g h turnedabout the point a, till a h fall on a XH produced, it is evident anorth 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 themorning 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 onthe north dial. The manner of placing the characters lor the otherhours is therefore obvious.

IV. To describe an Last Dial. On the eastern side of theplane of the meridian, draw aline AB, fig. <), parallel to the hori-zon ; draw also aline AK, making with All an angle KAB equalto the complement of the latitude of the place for which the dial ismade. Take a point I) in AK, and on that point for a centredescribe a circle. Through D draw EG perpendicular to AK,thus the circle will be divided into four quadrants; divide two ofthese quadrants into 0 equal parts, as in the figure. Draw- astraight line LEG perpendicular to EC, the diameter of the circle,rind from the centre D, through the several divisions, *draw therigid lines 1) IV, D V, DM, DY1I, I) VIII, D IX, D X,D XI. Through IV, V, VI, VII, Sec. draw lines IV IV, V V,Sec., parallel to EDC. Lastly, in D erect a stile equal to the ra-dius DE, perpendicular to the plane ; or on two little pieces per-pendicularly fixed in EC, and equal to the same DE, fit an iron rodparnlUl to tiC, thus w ill each index at the several hours protect ashadow to the respective hour-lines IV IV, VV, VI VI, &c.The east dial, it is obvious, can only shew the hours till tw elveo’clock.

V. To describe a Vest Dial. Tin* construction is perfectlythe 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 afternoon, and therefore, joined with ancast dial, shews all the hours of the day.

VI.’ To describe a portable Dial. This dial is representedin tig. 10, and may be drawn upon a card and carried in a pocketbook, Draw the occult line A15, fig. 11, parallel to the top ofthe card, and cross it at t ight angles with the six o’clock line EGD ;then upon C, as a centre, with the radius CA, describe the semi-circle A EL, and divide it into I ft equal parts (beginning at A), asA r, As, See. and from these points of division draw the hour-lines r, s, t, v, v, E, zc, and .r, all parallel to the six o’clock lineEC. If each part of the semicircle be subdivided into four equalparts, they will give the half hour-lines and quarters, as in fig. 18.Draw the right line ASDo, making the angle SAB equal to thelatitude of your place. Upon the centre A describe the archRS I’, and set oft upon the arcs SR and ST, each equal to Z3-, 7 Tdegrees for the sun’s greatest declination ; and divide them into 23 T 7 Tequal parts, as in tig. 18. Through the intersection D of the linesEGD and A Do, draw the right line I’DG alright angles to A Do.Lay a ruler to the points A and R, and draw the line ARE through23/j degrees of south declination in thearcSR ; and then laying theruler to the points A andT, draw the line A EG through 23-^ de-grees of north declination in the arc ST: so shall the lines AREand A EG cut the line FDG in the proper lengths for the scale ofmonths. Upon the centre I), with the radius DE, describe thesemicircle EoG ; w hich divide into six equal parts, Em, mn, no,&c. and from these points of division draw the right lines mb, ni,pk, and ol, each parallel to oD. Then setting one foot of thecompasses in the point E, extend the other to A, and describe thearc AZH for the tropic of Vy ; (see fig. 10 and 11,) w ith the sameextent, setting one loot in G, describe the arc AEO for thetropic of s. Next setting i-.ie foot in the point h, and ex-tending the other to A, describe the arc AC l for the begin-nings of the signs zz and f ; and with the same extent, settingone foot in the point l, describe tbe arc AN for the beginnings ofthe signs-n and S\_. Set one foot in the point i, and having ex-tended the other to A, describe the arc AK for the beginnings ofthe signs X andTR; and with the same extent, set one foot in <•,and describe the arc AM for the beginning of the signs S and tig.Then setting one foot in tbe pointD, and extending the other to A,describe the curve A L for the beginnings of <Y’ and — ; and thesigns will be finished. This done, lav a ruler from the point Aover the sun’s declination in the arch RST ; and where the rulercuts the line FDG, make marks : and place the days of the mouthsright against these marks, in the manner shewn by fig. 10. Lastly,draw the shadow-line PQ parallel to the occult line AB ; make thegnomon, and set the hours to their respective lines, as in fig. 10,and the dial will be finished. The lines a d, a b, and b e of thegnomon, must be cut quite through the card ; and as the end a bof the gnomon is raised occasionally above the plane of the dial, itturns upon the uncut line c d as on a hinge. The dotted line ABniu-t he slit quite through the card, and the thread C must be putthrough the slit, and have a knot tied behind, to keep it from beingeasilv draw n out. On the other end of this thread is a small plum-met D, and on the middle ot it a small bead for shew ing the hourof the day. To reetiiv this dial, set the thread in the slit ri<?litagainst the day of the month, and stretch the thread from die dayof the month over the angular point where the curve lines meet atXII.; then shift the head to that point on the thread, and the dialI will be rectified. To find the hour of the day, raise the gnomon,(no matter how much or how little) and hold the edge of the dialnext the gnomon towards the sun, so as the uppermost edge of theshadow of the gnomon may just cover the shadow-line; and thehead then playing treely on the face of the dial, by the weight ofthe plummet, will shew the time of the day among the hour-linesas it is forenoon or afternoon. To find the time of sun rising andsetting, move the thread among the hour-lmes, until it either coverssome one of them, or lies, parallel betwixt any two ; and then itw ill cut the time of sun-rising among the forenoon hours; and ofthe sun-setting among the afternoon hours, for that dav of the yearto which the thread is set in the scale of months. To find the sun’sdeclination, stretch the thread from the (lav of the month over theangular point at XII. and it will cut the sun's decliiuftiou, as it isnorth or south, for that day, in the proper scale. To find on whatdays the sun enters the signs: when the bead, as above reef died,moves along any of tbe curve lines which have the sign- of the zo-diac marked upon them, the sttfi enters tno-c signs on the dayspointed out by the thread in the scale of months.

I. The