390 FERGUSON'S LECTURES. 



place at which the dial would be horizontal, and the 

 place for which it is to serve. And likewise, taking care 

 to draw no lines but what are necessary ; which may be 

 done partly by the rules already given for determining 

 the time that the sun shines on any plane ; and partly 

 from this, that on the tropical days, the hyperbola 

 described by the shadow of the point R, limits the ex- 

 tent of all the hour-lines. 



The most useful however, as well as the simplest of 

 such dials, is that which is described on the two sides of 

 a meridian plane. 



That the Babylonian and Italic hours are truly enough 

 marked by right lines, is easily shewn. Mark the three 

 points on a globe, where the horizon cuts the equinoc- 

 tial, and the two tropics, toward the east or west ; and 

 turn the globe on its axis 15, or 1 hour ; and it is plain, 

 that the three points which were in a great circle (viz. 

 the horizon) will be in a great circle still ; which will be 

 projected geometrically into a straight line. But these 

 three points are universally the sun's places, one hour 

 after sun-set (or one hour before sun-rise) on the equi- 

 noctial and solstitial days. The like is true of all other 

 circles of declination, besides the tropics ; and therefore, 

 the hours on such dials are truly marked by straight 

 lines limited by the projections of the tropics ; and 

 which are rightly drawn, as in the foregoing example. 



Note 1. The same dials may be delineated without 

 the hour-lines CD, C E, CF, &c. by setting off the 

 sun's azimuths on the plane of the dial, from the center 

 S, on either side of the substile C S K, and the corres- 

 ponding co-tangents of altitude from the same center S, 

 for I, IT, III, &c. hours before or after the sun is in the 

 horizon of the place for which the dial is to serve, on 

 the equinoctial and solstitial days. 



2. One of these dials has its name from the hours 

 being reckoned from sun-rising, the beginning of the 



