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DIALING

143

Of Universal Dials,

I. The Universal Dial, invented by Pardie, fig. IS?, consists ofthree principal parts; the first whereof is called the horizontalplane (A,) because in practice it must be parallel to the horizon.In this plane is lived an upright pin, which enters into the edge ofthe second part BD, called the meridional plane; which is madeof two pieces, the lowest whereof (B) is called the quadrant, be-cause it contains a quarter of a circle, divided into 90 degrees; andit is only into this pari, near B, that (he pin enters. The otherpiece is a semicircle (D) adjusted to the quadrant, and turning init by a groove, for raising and depressing the diameter (KF) of thesemicircle, which diameter is called the axis of the instrument.The third piece is a circle (G,) divided on both sides into 24 equalparts, which are the hours. 'Phis circle is put upon the meridionalplane so, that the axis (KF) may be perpendicular to the circle,and the point C he the common centre ot the circle, semicircle,and quadrant. The straight edge of the semicircle is chamferedon both sides to a sharp edge, which passes through the centre ofthe circle. On one side of the chamfered part, the first six monthsof the year art' laid down, according to the sun’s declination fortheir respective days, and on the other side the last six months.And against the days on which the sun enters the signs, there arestraight lines draw n upon the semicircle, with the characters of thesigns marked upon them. There is a black line drawn along themiddle of die upright edge of the quadrant, over w Inch hangs athread (II,) with its plummet (I,) for levelling the instrument.From the 23d Sept to the 21st March, the upper surface of thecircle must touch both the centre C of the semicircle, and the lineof <y> and ; and from the 21st March to the 23d Sept, thelower surface of the circle must touch that centre and line. Tofind 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 /, until the plumb-linehangs over the back line upon the edge of the quadrant, and pa-rallel to the said edge; move the semicircle in the quadrant, untilthe line of and =s» (where the circle touches) comes to the lati-tude of your place in the quadrant; then turn the whole meri-dional plane BD, with its circle G, upon the horizontal plane A,until the edge of the shadow of the circle falls precisely on the dayof the month in the semicircle; and then the meridional plane willbe due Ni and S. the axis EF will be parallel to the axis of theworld, and w ill cast a shadow upon the true time of the day amongUie hours of the circle. \Vh.n the instrument is thus rectified, thequadrant and semicircle are in the plane of die meridian, and thecircle is then in the plane of the equinoctial. Therefore, as thesun is above the equinoctial in summer (in northern latitudes,) andbelow it in w inter ; the axis of the semicircle will cast a shadow onthe hour of the day, on the upper surface of the circle, from the'1st March till the 23d of Sept. ; and from the 23d of Sept, to the'1st March, the hour of the day will he determined by the shadowof the semicircle upon the lower surface of the circle. In the for-mer 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 thelatter case, on the upper part. The method of laving down themonths and signs upon the semicircle is as follows: Draw the rightline ACB, fig. 13, equal to the diameter of the semicircle ADB,and cross it in the middle at right angles with the line ECD, equalin length to ADB; then EC will he the radius of the circle EGG, :whu'h is the same as that of the semicircle. Upon E, as a centre, jdpseribe’tho circle FCG, on which set off the arcs C/i and Cf, each iequal to 23 7 7 j degrees, and divide them accordingly into that num-ber for the sun’s declination. Then laying the edge of a ruler oyerthe centre E, and also over the sun’s declination for every fifthday of each month (as in the card dial,) mark the points on the di-ameter AB of the semicircle from u to g, which are cut In the'viler ; and there place the d lys of the months accordingly , answer-ing to the sun’s declinations.'T'his done, setting one fool of the com-passes in C, and extending the other to a or g, describe the semi-circle abed efg; which divide into six equal parts, and throughthe points of cli\isiou draw right lines parallel to CI), for the be-ginning of the signs (of which one-half are on one side of the semi-circle and the other half on the other,) and set thecharacters of thesigns to their proper lines, as in the figure.

II. An Universal Dial on a plain cross, fig. 14, 13, 10, as de-scribed by Mr. Ferguson. It is moveable on a joint C for ele- ,eating it to any given latitude on the quadrant Co 90, as it stands I

j upon the horizontal board A. The arms of the cross stand at right 1j angles to the middle part; and the top of it, from a to n, is of equal| length with cither of the arms n e or m k. See fig. 14. The dialis rectified by setting the middle line t u to the latitude of theplace on the quadrant, the hoard A level, and the point N, norih-, ward by the needle ; tin’?, the plane of the cross will be parallelto the plane of the equator. 'I hen, from 111 o’clock in the morn-ing till V (, the upper edge k l of the ami f a will cast a shallow onthe time ot the day on the side of the arm c tn ; from V I. till IX.,the lower edge i a{ the arm i owill cast a shadow on the hours . atHie side u q. From IX. in the morning to XII. at noon, the edgea b of the top part a n wilt cast a shadow on the horn's on the armn ej ; from XII. to Id. in the aitemoon, the edge c</of the loppart will cast a shadow on the hours on the arm kl m ; from 111.to'V I. in the evening, the edge g b will cast a shadow on thehours on the part p iz; and from VI. till IX. the shadow of flicedge cf will shew the time on the top part a n. The breadth ofeach part a b, cf, &c. must he so great, as never to let the shadowfall quite without the part or arm on which the hours are maiked,when the sun is at his greatest declination from the equator. Todetermine the breadth of the sides of the arms which contain thehours, so as to he in just proportion to their length ; make an an-gle ABC (tig. lfi,) of 23,degrees, which is equal to (he sun’sgreatest declination : and suppose the length of each arm, fromthe side of the long middle part, and also the length of the top partj above the arms, to be equal to B d. Then as (lie edges of the! shadow, from each of the arms, will be parallel to Be, making anangle of 23^ degrees with the side B d of the arm, when the sun’sdeclination is 23°jL' : it is plain, tlrat if the length of the arm be B d,the least breadtli that it can liave, to keep (he edge I? c of the sha-dow B e g d from going off tin: side of the arm d e before it comesto the end of it e d, must he equal to e d or d 15. But to keep theshadow within the quarter divisions of the hours, when it comesnear the end of the arm, the breadth of it should he still grater,so as to lie almost doubled, on account of the distance between thetips of the arms. The hours may be placed on the arms, by lay-ing down the cross a b e d, fig. 1 j, on a sheet of paper: and with’ ablack lead pencil held close to it, drawing its shape and size on thepaper. Then take the length a e in the compasses, and with onefoot in the corner a describe with the other the quadrant ef. Di-vide this arc into six equal parts, and through the points of divisiondraw light lines a g, a h, &c. continuing three of them to thearm cc, which are all that can fall upon it; and they will meet thearm in those points through which the lines that divide the hoursfrom each other, as in tig. 14, are to he drawn right across it. DivideJ each arm for the three hours contained in it, in the same manner ;and set the,bom's to their proper places, on the sides of the arms,as they are marked in fig. 14. Each of the hour-spaces should bedivided into four equal parts, for the half-hours and quarters, inthe quadrant ef\ and right lines should be drawn through thesedivision-marks in the quadrant, to the arms of the cross, in orderto determine the places thereon where the subdivision of the hoursmust be marked. This kind of universal dial is easily made, andhas a pretty uncommon appearance in a garden.

111. T he Universal Mechanical Dial, fig. 17, affords, by its equi-noctial circle, an easy method of describing a dial on any kind ofplane. For example : Suppose a dial is required on an horizontalplane. If the plane be immoveable as A Bill), find a meridian-lineas GF; or if moveable, assume the meridian at plea-ure: then bvmeans of the triangle EKF, svlioseba>e is applied oil the meridian-line, raise the equinoctial dial II till the index (51 becomes parallelto the axis of the earth, (which is so, if the angle EKF be equal tothe elevation of the poU-,1 and the 12 o’clock line on the dial hangover the meridian-line of thi plane or the ba-e of the triangle. Ifthen, in the night, or in a dark place, a lighted candle he suc-cessively applied to the axis G I, sous the shadow of the indexor style GI shall fall upon one hour line after another, thesame shadow w ill mark out the several hour-lines on the planeABC1). Noting the points therefore on the shadow, draw linesthrough them to G ; then an index being fixed on G, according tothe angle IGF, its shadow will point out the several hours by thelight of the sun. If a dial were required on a vertical plane., havingraised the equinoctial Circle as directed, push forward the indexGI till the tip thereof 1 touch the plane. If the plane he inclinedto the horizon, the elevation of llie pole should be found on the

If same;