235

Os Dialing.

Draw, for the like hours aster sun-rising, when the iim is ia thetropic of Capricorn V? V, the like commoa lines CD, CE, CF, &c.and at these hours the fhadow of the point R will be found in thoselines refpectively. Find the fun’s altitudes above the plane of the dialat these hours, and with their co-tangents Sd, Se, Sf, &c. to radiusS R, describe ares intersecting the hour-lines in the points d, e, f &c.fo fhall the right lines i d, 2 e, 3s, &c. be the lines of I, II, III, &c.hours aster sun-rising.

The construction is the fame in every other case, due regard beinghad to the differenee of longitude of the place at which the dial wouldbe horizontal, and the place for which it is to serve. And likewise,taking care to draw no lines but what are necesiary; which may bedone partly by the rules already given for determining the time that thefun stsines on any plane and partly from this, that on the tropical days,the hyperbola deseribed by the fhadow of the point R, limits the ex-tern of ali the hour-lines.

The most useful however, as well as the simplest of such dials, isthat which is deseribed on the two sides of a Meridian plane.

That the Babylonian and Italic hours are truly enough marked byright lines, is easily fhewn. Mark the three points on a globe, wherethe horizon cuts the equinoctial, and the two tropies, toward the east,or west; and turn the globe on its axis 15 0 , or 1 hour; and it is plain,that the three points which were in a great circle (viz. the horizon) willbe in a great circle stili; which will be projected geometrically into astraight line. But these three points are universally the sun’s places, onehour aster sun-set (or one hour before fun rise) on the equinoctial andsolstitial days. The like is true of ali other circles of declination, be-sides the tropies; and therefore, the hours on such dials are truly markedby straight lines limited by the projections of the tropies; and whichare rightly drawn, as in the foregoing example.

Note 1. The fame dials may be delineated without the hour-linesCD, CE, CF, &c. by sctting off the sun’s azimuths on the plane ofthe dial, from the center S, on either side of the fubstile CSK, and thecorrefponding co-tangents of altitude from the fame center S, for I, II,III, &c. hours before or aster the fun is in the horizon of the place forwhich the dial is to serve, on the equinoctial and solstitial days.

2. One of these dials has its name from the hours being reckonedfrom sun-rising, the beginning of the Babylonian day. But we are notthence to imagine that the equal hours, which it sliews, were those inwhich the astronomers of that country marked their observations.These, we know with certainty, were unequal, like the Jewiß>, as

H h 2 being