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Of Dialing»

Trigonometrically thus: let a great circle pass through the threepoints W, d, E ; and in the triangle WD d, right-angled at D, thefides W D and Dd are given; and thence the angle DW d is found,and so is the hypotbenuse W d. Again, the difference, or the sum,of DTVd and DJVR , the elevation of the equinoctial above thehorizon of Z, gives the angle d WR ; and the hypothenufe of thetriangle WRd was just now found; whence the sides Rd and WRare fpund, the former being the latitude of the place d, and the latterthe complement of R the difference of longitude fought.

Thus, if the latitude of the place Z be C2 Ö 10'north; the de-clination SD of the plane Zh (which would be horizontal at d)be 36°, and the reclination be 15°, or equal to the arc Dd the fouthlatitude of the place d, that is, the arc R d , will be 15 0 9'; and Rthe difference of longitude, 36° 2'. From thefe data, therefore, let thedial (Fig. 4.) be defcribed, as in the former example.

8. Only it is to be observed, that i.i reclining or inclining dials,the horizontal line will not stand at right angles to the hour-lineof XII, as in erect dials ; but its position may be found as follows.

4 * To the common fubstilar line CKL, on which the dial for theplace d was defcribed, draw the dial Crpm 12 for the place D, whofeDeclination is the fame as that of d (viz. the arc SD-,) and HO yperpendicular to C m, the hour-line of XII on this dial, will be ahorizontal line on the dial CPRM XII. For the declination ofboth dials being the fame, the horizontal line remains parallel toitfelf, while the erect position of one dial is reclined or inclined withrespect to- the position of the other.

Or, the position of the dial may be found by applying it to itsplane, so as to mark the true hour of the day by the fun, as fhewnby another dial; or by a dock, regulated by a true meridian line andequation table.

9. There are several other things requisite in the practice of dialingj, the chief of which I (hall give in the form of arithmetical rules,

simple and eafy to thofe who have learnt the elements of trigonometry.For in practical arts of this kind, arithmetic fhouid be ufed as far as itcan go; and fcales never trusted to, except in the final construction,where they are abfolutely neceffary in laying down the calculatedbour-distances on the plane of the dial. And ahhougb the inimitableartists of this metropolis have no occasi on for such instructions, yetthey may be of forne ufe to students, and to private gentlemen whoamuse themfelves this way.

RULE