376 



FERGUSON'S LECTURES. 



being set perpendicular to the horizon, the dial will 

 have its true position. 



5. If the plane of the dial had declined by an equal 

 angle toward the east, its description would have differed 

 only in this, tnat the hour-line of XII would have fallen 

 on the other side of the substile C L, and the line H O 

 would have a sub-contrary position to what it has in this 

 figure. 



6. And these two dials, with the upper points of their 

 stiles turned toward the north-pole, will serve for the 

 other two planes parallel to them ; the one declining 

 from the north toward the east, and the other from the 

 north toward the west, by the same quantity of angle. 

 The like holds true of all dials in general, whatever be 

 their declination and obliquity of their planes to the 

 horizon. 



CASE II. 



7. If the plane of the dial not only declines, but also 

 reclines, or inclines. Suppose its 

 declination from fronting the 

 south S be equal to the arc S' D 

 on the horizon : and its reclination 

 be equal to the arc D d of the 

 vertical circle D Z: then it is plain, 

 that if the quadrant of altitude 

 Zd D, on the globe, cuts the point 



D in the horizon, and the reclination is counted upon 

 the quadrant from Dtod; the intersection of the hour- 

 circle PRd, with the equinoctial WQE, will deter- 

 mine It d, the latitude of the place d, whose horizon is 

 parallel to tiie given plane Z h at Z ; and R Q will be 

 the difference in longitude of the planes at d and Z. 



Trigonometrically thus : let a great circle pass 

 through the three points W, d, E ; and in the triangle 

 WDd, right-angled at D, the sides W D and ]) d are 



