96 Mr DAVIES on the Nature of the Hour-Lines 



It might further be observed, that, in the general construction, the 

 circle BLF has been employed merely to give facility to the verbal descrip- 

 tion of the process, and to prevent the necessity of a separate construction 

 to subserve the purposes of demonstration. In real practice it would, how- 

 ever, evidently be more convenient to keep it apart from the dial itself, as 

 A'B' V was kept in (XII. 3.). The lines then employed upon the dial it- 

 self will be less numerous, and the process less complicated, than at first 

 sight it may seem to be. 



We have thus, by simple modifications of one uniform method of con- 

 struction, shown how the hectemoria may be traced upon any plane what- 

 ever. So far, then, as the plane dial is concerned, the problem proposed by 

 DELAMBRE is fully and completely resolved. Dials, however, have been 

 described upon other surfaces, which have been considered as hectemorial, 

 and it may therefore, in continuance of the same system of investigation, be 

 well to notice one or two of them. 



XIII. 



Cylindrical Hectemoria, in contact with the Equator. 



Mr CADELL has given delineations of the hectemoria upon a cylinder 

 touching the sphere at the equator (Ed. Trans, vni. PL 3. figs. 10 14). 

 As the arc D of the equation (A D L ) is projected into its tangent, this equa- 

 tion is a complete representation of that projection. We may hence con- 

 struct those developed cylindrical hectemoria with great facility. It is, in- 

 deed, as will be shown farther on (see XXX.), only a modification of the 

 harmonic curve. 



