ON THE ANTIQUE HOUR-LINES. 75 



whose section contains the hectemorial line, is a kind of undu- 

 lated conical surface ; and the right sections of the surface are 

 two infinite unenclosed bases, one on each side of the vertex 

 of the undulated cone. This section, at right angles to the 

 axis, consists of several bicrural branches, varying in number 

 as the cone belongs to each different hectemorial line. 



Of the Gnomonic Instruments of the Ancients. 



The object of the preceding pages has been, to treat of the 

 curves to which the hectemorial lines belong. As an appen- 

 dix, it may not be improper to enumerate some of the remains 

 of art which contain the antique hour-lines ; for these hour- 

 lines are the intertropical parts of the hectemorial lines. Se- 

 veral examples of these gnomonic instruments exist. 



The first to be mentioned, and the most perfect, are the 

 eight sun-dials on the Tower of Andronicus Cyrrhestes, at A- 

 thens. They appear to have been coeval with the building, 

 and to have formed part of the original design, as may be in- 

 ferred from the care with which they are delineated, and from 

 the greatest part of the surface of the wall being left plane to 

 receive the lines. This tower is mentioned under the denomi- 

 nation of horologium by Varro, who flourished in the 85th 

 year before the Christian era ; it is also spoken of by Vitru- 

 vius. The carefully wrought channels, and cylindrical cavities 

 in the pavement, and the cylindrical chamber at the south side, 

 have led to the conjecture, that, betfdes serving to shew the 

 hour when the sun was shining on it, the tower was formed to 

 contain some machine of the nature of the clepsydra, whereby 

 the hour might be known at all times for the use of the city. 

 Another of the destinations of this tower was to indicate the 



K 2 direction 



