DIALLING. 



Descrip. 

 tion of 

 Dial's. 



als should be considered an inconvenience, it may be 

 avoided, by putting different sets of hour points on the 

 dial, corresponding to different times of the year, just as 

 if the hour points were shifted, so as to suit the style, 

 instead of adapting the style to the position of the hour 

 points. 



Having now explained the general theory of dials, 

 as well as the most common and useful of them, upon 

 strictly geometrical principles, we shall now describe 

 some others ; but the limits of our work will not allow 

 us to enter so minutely into the mathematical investi- 

 gation. 



Portable Dial on a Card. 



Portable 88< This dial is represented in Figs. 4. and 5. Its 



card"" geometrical construction is as follows : 



1. Draw a straight line 12 CA parallel to the top of 

 the card, (Fig. 4.) and draw another line AC 6, bisect- 

 ing the former at right angles. On C as a cen- 

 tre, with any convenient radius, describe a semicircle 

 12, 6, A, and divide it into twelve equal parts at the 

 points 11, 10, 9, 8, &c. 



3. From the points 11, 1 0, 9> 8, &c. draw lines perpen- 

 dicular to the diameter 1 2 A ; and these will be the 

 hour lines. The half hours and quarters may also be 

 drawn, by dividing each arc into four equal parts. 



»4. At 12, the extremity of the diameter, chaw a line 

 12 k, to make with 12CA an angle equal to the lati- 

 tude of the place ; let this line meet the 6 o'clock hour 

 line in h, through which draw a line BAD perpendi- 

 cular to 1 2 1c. 



5. At the point 12, draw lines 1 2 B, 12 D, to make 

 each, with 12£, an angle of 23^ degrees, the sun's great- 

 est declination. These lines determine the length of 

 BD, the scale of the months. 



6. Describe a semicircle on BD as a diameter, divide 

 it into six equal parts at H, I, K, L, M, and draw lines 

 HIi, I/, K.k, L/, M?n, perpendicular to BD. These 

 points are the centres of the arcs of the signs. 



7. On B and D as centres, describe arcs 12 >?, 12 gs, 

 to pass through the point 12, and these will be the tro- 

 pics. Also on h and m as centres, describe arcs to pass 

 through 12, and the one will be the arc of the signs 

 ZZ and f , and the other the arc of the signs n and 

 Q,. And on i and / as centres, describe arcs through 

 12, and the one will be the arc of the signs K and rr\_, 

 and the other the arc of the signs tir and tf . And 

 lastly, describe an arc on k as a centre, to pass through 

 12, and it will be the arc of the signs <y and ret. 



8. On the point 12 as a centre, describe an arc of a 

 circle OPQ, terminating in the lines 12 B, 12D, and 

 divide each half PO, PQ, into 23^ equal parts ; then the 

 arc OPQ is a scale of the sun's declination. 



9- Find from a table the sun's declination for every 

 5th day of the year, and laying a ruler over the point 12 

 :;nd the degree of each day, on the scale OQ, mark 

 the point in which the ruler meets BD ; and against 

 the points of division for the clays of each month write 

 Fig. S. the name of the month, (see Fig. 5.) observing, that 

 the days from 21st March to 23d September must lie on 

 the left hand side of k, the middle of the scale. 



10. Cut a slit through the card along the line BD, 

 and through it put a thread, having a bead sliding along 

 it, and a plummit at one end, which hang along the 

 face of the dial when it is held vertically, and make a 

 knot on the other end of the thread at the back of the 

 dial, so that it may not be drawn through the slit. 



1 1 . Draw a line N v parallel to C A, and at one end 

 of the line cut slits along vx, xy, yz, three sides of a 

 rectangle, through the card, so as to admit of its turning 



711 



about the remaining side vz as a hinge. This rectangle 

 is the gnomon of the dial, and the line VN is the shadow 

 line. The manner of placing the hours conveniently 

 against the hour lines, and forming the scale of months, 

 will easily be understood by inspecting Fig. 5, which 

 shews the dial completely finished. 



89. To rectify the dial, set the thread in the slit right 

 against the day of the month, and stretch it over the 

 angular point where the circles meet at XII, then shift 

 the bead to that point of the thread, and the dia' is rec- 

 tified. 



To find the hour of the day, raise the gnomon, (no 

 matter how much or how little, ) and hold the ed^e of 

 the dial next the gnomon towards the sun, so that the 

 uppermost edge of the shadow of the gnomon may just 

 cover the shadow line ; and the bead then moving free- 

 ly on the face of the dial by the weight of the plummet, 

 will shew the time of the day among the hour lines as 

 it is forenoon or afternoon. 



Note. The dial will evidently indicate the hour, but 

 imperfectly, near noon ; but it does not seem that this 

 evil can be avoided in an altitude dial. 



To find the time of sun rising and setting. Having 

 rectified the dial for the given day, move the thread 

 among the hour lines, until it either covers some one 

 of them, or lies parallel betwixt any two, and then it 

 will cut the time of sun rising among the forenoon hours, 

 and the time of sun setting among the afternoon hours. 



To find the sun's declination, stretch the thread from 

 the day of the month over the angular point at XII. 

 and it will indicate the declination on the graduated 

 arch. 



To find on what days the sun enters the signs. When 

 the bead, as above rectified, moves along any of the 

 curve lines, which have the signs of the zodiac marked 

 upon them, the sun enters those signs on the days 

 pointed out by the thread in the scale of months. 



Montucla, in his Mathematical Recreations, says, that 

 this dial originated from an universal rectilineal dial 

 constructed by Father de Saint-Rigaud, a Jesuit, and 

 professor of mathematics in the college of Lyons. He 

 also observes that it is generally called the Capuchin, 

 because it resembles the head of a Capuchin friar with 

 the cowl inverted. 



Dial on a Cylinder. 



90. This dial is shewn in Fig. 6. It indicates the D j a i on 

 hour of the day, the sun's place in the ecliptic, and his cylinder!* 

 altitude at any time of observation. The dial is con- 

 structed by tracing the lines on paper, and pasting it ccXXX 

 round the surface of the cylinder. The lines may be Fig. 6. * ' 

 drawn by the following rules : 



1. Draw aline A aB (Fig. 7.) parallel to the top Fi ~ 7 . 

 of the paper, and on a as a centre, with any conveni- 



ent radius, describe the quadrantal arc AE, and divide 

 it into 90 equal parts or degrees. 



2. Draw AC perpendicular to AB, touching the qua- 

 drant at A, and from a draw lines through as many 

 degrees of the quadrant as are equal to the sun's alti- 

 tude at noon on the longest day of the year, at the place 

 for which the dial is to serve, (this is always equal to 

 the sum of 23^ degrees, and the complement of the la- 

 titude,) and continue those lines until they meet the 

 tangent AC ; from the points of intersection draw lines 

 across the paper parallel to AB, and they will be the 

 parallels of the sun's altitude in whole degrees, from 

 sunrise to sunset, on all the days of the year. (In the 

 Figure, we have only drawn every fifth degree. These 

 lines must be drawn out to the right line BD, which 



