DIAL. 



Describe a circle and divide it into four 

 equal parts by the lines AB and C D, in- 

 tersecting in the centre E. Draw the 

 chords A C, C B, B D. Now divide the 

 two segments or quadrants, A D andC B, 

 each into nine equal parts ; either of 

 which contains ten degrees. Placing one 

 leg of your compasses at B for a centre, 

 draw the several arcs from the quadrant 

 subtended by the chord C B, so that they 

 may fall upon that chord, which being 

 numbered according as the several arcs 

 correspond with the division on the qua- 

 drant, will give a line of chords gradu- 

 ally diminishing from B towards C : all 

 the intermediate degrees or the mea- 

 sures of 10 each, thus obtained, may 

 be removed in the same manner from 

 the quadrant, if it be graduated accord- 

 ingly. 



It will be proper to observe, in this 

 place, that the chord of 60 is the radius 

 of a circle whose quadrant is. subtended 

 by 90 of the same scale : hence a line 

 of chords is easily made upon any circle, 

 so that any part of that circle may be cut 

 off at pleasure. This is essential in every 

 branch of mathematics ; but in dialling it 

 is indispensable to be known : the reader 

 will have observed, that in forming the 

 horizontal dial, the hour lines are drawn 

 thrugh particular points, so as to make 

 the required angles. As he may be at 

 a loss how to effect this on many oc- 

 casions, we shall give an example in fig 5, 

 whereby every doubt or difficulty will be 

 removed. 



Let it be required to cut off an angle of 

 forty degrees from the quadrant, which 

 appertains to a circle for which we have 

 not a line of chords in readiness. On the 

 base line A B measure sixty degrees from 

 any line of chords you may have at hand: 

 it may either exceed or be less than your 

 baseline ; we will suppose the former: 

 in this case the base line must be pro- 

 longed to the measurement of 6(J from 

 your scale, which will carry it on to C. 

 With that 60, as a radius, and from A, 

 as a centre, describe the quadrant C D, 

 concentric with the quadrant E B, from 

 which you would cut off 40. Now mea- 

 sure 40 degrees on your line of chords, 

 and, placing one foot of the compasses 

 at C, carry the measurement to F, which 

 will cause the angle F A C to measure 

 40, and the line F A will, atjC, cut off 40 

 degrees from the quadrant E B. For an 

 angle does not vary by prolongation ; 

 therefore, if the exterior quadrant is cut 

 at 40, the interior quadrant, being con- 



centric therewith, must correspond with 

 that division 



We now proceed to the opposite qua- 

 drant, which is not subtended by a chord, 

 but is divided into nine equal parts often 

 degrees each. Draw from the several 

 points of division on the quadrant eight 

 lines, all parallel with E A, and falling on 

 the radius E D ; this gives a line of sines 

 which is of very extensive use in various 

 branches of mathematics. From A draw 

 eight lines, passing through the several 

 points ascertained on the line of sines, 

 to the quadrant B D : these will cut the 

 chord subtending that quadrant, and give 

 thereon a line of latitudes, of equal length 

 with the line of chords, but very differ- 

 ently divided. 



The remaining quadrant C A is to be 

 divided into six equal parts, viz. of 15 

 each : make the chord C F A, and draw 

 its parallel tangent G H. Through the 

 several points of division on the quad- 

 rant, draw lines from the centre E to 

 the line G H, which will then represent 

 a line of hours : one of the extremes will 

 be XII, the other will be VI ; the seve- 

 ral intermediate places of I, II, III, IV, 

 and V, being ascertained by the various 

 lines proceeding from E. 



The 6th figure shews part of a dial, 

 constructed by means of the lines of lati- 

 tudes and of hours. Having set off the 

 parallels for the substile, and drawn the 

 line of VI o'clock, set off the latitude of 

 your place from A towards B ; taking the 

 measurement from the line of latitudes. 

 Then measure the whole extent of your 

 line of hours, and, placing one leg of 

 your compasses at B, let the other fall 

 wherever it may reach on the line C A. 

 Divide the line B C according to the mea- 

 sures on your line of hours; and from A 

 draw line's through the points of division 

 to the hour circle, which will thus be tru- 

 ly intersected at the horal points. We 

 have before stated, that by dividing the 

 quadrant C A, in fig. 4tli, more minutely, 

 that is, by dividing each of the six por- 

 tions into four, the halves and quarters 

 of hours may be shewn. 

 .Having already shewn the modes of con- 

 structing those dials which are in ordina- 

 ry use, we must refer the more curious 

 reader to Ferguson's " Lectures," for a 

 great variety of dials, which could not be 

 introduced into this work without greatly 

 augmenting the volume. He will there 

 find the modes of constructing dials by 

 logarithms, and by trigonometry ; togeth- 

 er with many items relating to the more 

 abstruse parts of our subject. We shall 



