374 



FERGUSON'S LECTURES. 



LECT. height of the equinoctial at Z, so is the co-tangent of 36 

 ,j*- x -^, degrees, the plane's declination, to the co-tangent of the 

 difference of longitudes. Thus, 



To the logarithmic sine of 51 30'"' 9.89354 

 Add the logarithmic tang, of 54 O' m 10.13874 



Their sum radius 10.03228 



is the nearest tangent of 47 8'= W R; which is the co- 

 tangent of 42 52'=jRQ, the difference of longitude 

 sought. Which difference, being reduced to time, is 

 2 hours 51 J minutes. 



3. And thus having found the exact latitude and longi- 

 tude of the place D, to whose horizon the vertical plane 

 at Z is parallel, we shall proceed to the construction of 

 a horizontal dial for the place D, whose latitude is 

 30 14' south ; but anticipating the time at D by 2 hours 

 51 minutes (neglecting the minute in practice) because 

 jD is so far westward in longitude from the meridian of 

 London ; and this will be a true vertical dial at London, 

 declining westward 36 degrees. 



Assume any right line 

 C S L, lu for the substile of 

 the dial, and make the angle 

 K C P equal to the latitude 

 of the place (viz. 30 14) to 

 whose horizon the plane of 

 the dial is parallel ; then 

 C R P will be the axis of 

 the stile, or edge that casts 

 the shadow on the hours of 

 the day, in the dial. This done, draw the contingent 



Note 113. The co-sine of 38 30', or of W D R.Note by the 

 Author. 



Note 114. The co-tangent of 36, or of D W. Idem. 



Note 115. Two parallel lines should be drawn instead of the single 

 line C SL, at the distance of the thickness of the gnomon, from each 

 other. 



