110 Mr DAVIES on the Nature of the Hour-Lines 



4. If we take \ = 90 + 90 I = 180 I, the dial will be horizontal. 

 Of this kind, I believe, there is no specimen remaining in any collection. 



5. If x = 270 I, the dial is a north vertical one, such as the BOPEAS 

 of ANDRONICUS, a sketch of which is given in plate xi. vol. i. of 

 STUART, 



6. For the four intermediary dials of ANDRONICUS, we may readily find 

 the values of I and A, which correspond to each of them. For by right- 

 angled spherical triangles we readily obtain 



7. In like manner, by the solution of a right angled spherical triangle, 



imagine the dial plane, after the hectemoria are traced, to be revolved upon its intersec- 

 tion with the horizon through 180, and the gnomon to be a continuation of the radius of 

 the sphere and equal thereto, the extremity of it will be the gnomonic point to the dial 

 as it is now placed. The reasons for this departure from common usage cannot be con- 

 veniently explained here : nor is it of importance that it should be, a bare indication of 

 the fact being sufficient to prevent misapprehension. 



