372 FERGUSON'S LECTURES. 



LECT. would be a horizontal plane at that place, whose lati- 

 XI ' tude is 30J degrees south of the equator, and longitude 

 421 degrees west of the meridian of London. 



Which difference of longitude being converted into 

 time, is 2 hours 51 minutes. 



The vertical dial declining westward 36 degrees at 

 London, is therefore to be drawn in all respects as a 

 horizontal dial for south latitude 30i degrees ; save only, 

 that the reckoning of the hours is to anticipate the 

 reckoning on the horizontal dial, by 2 hours 51 minutes : 

 for so much sooner will the sun come to the meridian of 

 London, than to the meridian of any place whose longi- 

 tude is 42| degrees west from London. 



2. But to be more exact than the globe will shew us, 

 we shall use a little trigonometry. 



Let NESWbe the horizon of 

 London, whose zenith is Z, and P 

 the north pole of the sphere ; and 

 let Zh be the position of a vertical 

 plane at Z, declining westward 

 from S (the south) by an angle of 

 36 degrees ; on which plane an 

 erect dial for London at Z is to be 

 described. Make the semidiameter Z D perpendicular 

 to Zh, and it will cut the horizon in D, 36 degrees 

 west of the south S. Then, a plane in the tangent H D, 

 touching the sphere in D, will be parallel to the plane 

 Zh; and the axis of the sphere will be equally inclined 

 to both these planes. 



Let W Q E be the equinoctial, whose elevation above 

 the horizon of Z (London) is 38j degrees ; and P R D 

 be the meridian of the place D, cutting the equinoctial 

 in R. Then, it is evident, that the arc R D is the lati- 

 tude of the place D (where the plane Z h would be hori 

 zontal) and the arc R Q, is the difference of longitude of 

 the planes Zh and D H. 



