224

Fig. r.

Of Dlaling.

To find the difference of longitude of the places D and Z, say, asradius is to the co-sine of 38- degrees, the height of the equinoctialat Z, fo is the co-tangent of 36 degrees, the plane’s declination, to theco-tangent of the difference of longi tudes. Thus,

To the logarithmic sine of * 51® 30' 9-^9354

Add the logarithmic tang. of «f* 54 ° °' 10.13874

Their sum — radius ----- 10.03228 is the

nearest tangent of 47° 8 '-WR ; which is the co-tangent of42 0 52'—the difference of longitude sought, Which difference,being reduced to time, is 2 hours 51s minutes.

3. And thus having found the exact latitude and longitude of theplace D, to whose horizon the vertical plane at Z is parallel, we shallproceed to the construction of a horizontal dial for the place D,whose latitude is 30° 14' south ; but anticipating the time at D by2 hours 51 minutes (neglecting the {■ minute in practice) becaufeD is fo far westward in longitude from the meridian of London ;and this will be a true vertical dial at London, declining westward36 degrees.

Assume any right line CSL for the fubstile of the dial, and makethe angle K CP equal to the latitude of the place (viz. 30° 14') towhose horizon the plane of the dial is parallel ; then CRP will bethe axis of the stile, or edge that casts the slzadow on the hours ofthe day, in the dial. This done, draw the contingent line ,cutting the substilar line at right angles in K and from K make KRperpendicular to the axis CRP. Then KG (—KR) being maderadius, that is, equal to the chord of 6o° or tangent of 43° on agood sector, take 42 0 52' (the difference of longitude of the placesZ and D ) from the tangents, and having set it from K to M, drawCM for the hour-line of XII. Take KN equal to the tangent ofan angle less by 15 degrees than KM\ that is, the tangent 27° 52'jand through the point N draw CiVfor the hour-line of 1 . Thetangent of 12° 52 (which is 15 0 less than 27° 52') set off the fameway, will give a point between K and 2 V, through which the hour-line of II is to be drawn. The tangent of 2° 8' (the differencebetween 45° and 42" 52') placed on the other side of CL, will de-termine the point through which the hour-line of III is to be drawn :to which 2° 8', if the tangent of 15 0 be added, it will make 17 0 8'jand this set off from K towards ^ on the line E £>, will give a point

* The co-sinc of 38° 30', ores IVD R. f The co-tangent of 36», or of D IV.

for