714 



DIALLING. 



Babylo- 

 nian and 

 Italian 

 dials. 



Fig. 1C. 



tend the thifekness of the stile abed; and in the same 

 manner draw the like thickness of the three other stiles 

 efg h, ikl m and n o p q, all standing outright as from 

 the centre. 



On a as a centre, with any convenient radius a A 

 (which leaves proper strength of stuff when KI is equal 

 to a A) describe the quadrantal arc Ac; and with the 

 same radius, on b as a centre, describe the quadrantal 

 arc d B. All the quadrantal arcs in the Figure are to be 

 described with the same radius, and in the same man- 

 ner, on their centres ef, i h, and n o, and each quadrant 

 is to be divided into six equal parts, for as many hours 

 as in the Figure, each of which may be subdivided into 

 four for the half hours and quarters. At equal dis- 

 tances from each corner, draw the right lines I P and 

 Kp, L q and M q, N r and Or, P s and Q s, to form the 

 four angular hollows I p K, L q M, N r 0, and P s Q, 

 making the distances between the tips of the hollows, 

 as IK, LM, NO and PQ, each equal to the radius of the 

 quadrants, and leaving room within the angular points 

 p, q, r, and s, for the equinoctial circle in the middle. 



To divide the insides of these angles properly for the 

 hour spaces thereon ; on K and I as centres, with KI as 

 a radius, describe the arcs K t, It, meeting in t. Di- 

 vide each arc into four equal parts, and from their cen- 

 tres, through the points of division, draw the right 

 lines I 3, I 4, I 5, I 6', I 7, and K 2, K 1, K 12, K 1 1 ; 

 and they will meet the sides Kp, and I p, where the 

 hours thereon must be placed, and these hour spaces 

 in the arcs must be subdivided into half hours and quar- 

 ters. 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 qua- 

 drants and in 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 the four gnomons 

 are to stand ; and lay down the hours on their insides, 

 as in Fig. 49, and then set in their four gnomons, 

 which must be as broad as the dial is thick ; and this 

 breadth and thickness must be large enough to keep 

 the shadows of the gnomons from ever falling quite out 

 at the sides of the hollows, even when the sun's decli- 

 nation is at the greatest. Lastly, draw the equinoc- 

 tial dial in the middle, all the hours of which are equi- 

 distant from each other, and the dial will be finished. 



Bali/Ionian and Italian Dials. 



92. The hours of these dials are not reckoned from 

 noon, as with us, but on a Babylonian dial they are 

 reckoned from sunrise to sunrise, and on an Italian 

 dial from sunset to sunset. Thus, in Italy, the hour 

 before sunset is the 23d hour of the day ; and the se- 

 cond hour before sunset is the 22d hour, and so on. 

 As the time of sunrise is continually varying, the be- 

 ginning of the day ( and consequently, the time from 

 noon at which any one of the hours shewn by these 

 dials happens) is never the same on two succeeding 

 days ; the hours however are all equal. As both dials 

 must be constructed on the same principles, it will be 

 sufficient if we explain a particular case of one of them. 



The hour is shewn by the shadow of the top of an 

 upright stile, which is commonly the extremity of the 

 axis of a common dial. Let us suppose that Fig. 15. 

 represents a vertical south dial, on which it is propo- 



2 



Descrfp. 

 tiou of 

 Dials. 



sed to trace the Babylonian hours ; FC being the up» 

 right stile, and P the centre of the dial. 



Find the hour next following sunrise, when the sun 

 describes either tropic ; for example, let it be four in '"""~ Y " 

 summer, and eight in winter. Find next the sun's de- 

 clination when he rises at these hours, and trace on the 

 dial the hyperbolic curves mm, nn, which are the paths 

 of the shadow when the sun has those declinations. 

 Trace also the paths of the shadow when the sun de- 

 scribes the tropics : these last are only of use to termi- 

 nate the hour lines when drawn on the dial. 



Observe all the points where the hour lines of the 

 dial cut the south parallel m m, then since the Babylo- 

 nian hours pi-oceed from 1 to 24, and in this parallel 

 the sun rises at 8, therefore write 24 at that point of the 

 parallel, where the 8 o'clock '<ae passes, and write 1 at 

 9, 2 at 10,3 at 11, &c. 



Again, observe all the points where the hour lines 

 of the dial cut the northern parallel n n ; and since here 

 the sun rises at 4, call that 24, at 5 write 1, at 6 write 

 2, at 7 write 3, at 8 write 4, at 9 write 5, at 1 1 write 

 7, at 12 write 8, and so on. 



Next draw straight lines joining those points of m m, 

 n n the paths of the shadow which are marked with the 

 same number, as 22, 33, 44, 55, and these are the Ba- 

 bylonian hour lines ; that is, the shadow of the end of 

 the stile will always be somewhere on the line 11, one 

 'hour after sunrise ; it will be on the line 22, two hours 

 after sunrise, and so on. 



To understand the theory of this construction, we 

 must consider that all the points of the sphere at which 

 the sun is seen at sunrising, at different times of the 

 year, are in the circumference of a great circle ; and 

 therefore its positions at one hour after sunrise, or at 

 two hours after sunrise, &c. must also be in great circles. 

 But with a little consideration it will appear that the 

 extremities of the shadows projected by the gnomon, 

 when the sun is at different points in a great circle, 

 must all lie in a straight line, which will be the com- 

 mon section of that circle, and the plane of the dial; 

 therefore the Babylonian hour lines must be straight 

 lines, and two points in any one of them being known, 

 the line itself is known ; hence the truth of the con- 

 struction is obvious. 



As the hyperbolic lines m m, n n, are only of use in 

 determining the hour lines, they need not appear on 

 the dial. 



Jewish Dial. 



93. The Jewish hours, called the naturals, and also Je ; h 

 the planetary hours, begin at sunrise, and twelve are dial, 

 reckoned until sunset ; hence they are all equal on the 

 same day, but their length varies from day to day. 



To delineate a dial of this kind, the paths of the sha- 

 dow must be traced when the sun is in the tropics, and 

 also in several intermediate points. The times of the 

 day (reckoned according to the usual method) must 

 be found at which the different Jewish hours happen, 

 when the shadow describes each path; and the posi- 

 tion of the shadow in its path must be found at the com- 

 mencement of each Jewish hour. If curve lines be 

 now traced through the same Jewish hour on all the n 

 hyperbolic paths, these curves will be the horn lines of 

 the dial. The time is indicated by the shadow of the 

 top of the stile, exactly as in the Babylonian dial. 



The subject of dialling will be again adverted to, 

 when we come to treat of the gnomonical projection of 

 the sphere. See Projection of the Sphere. (|) 



