ON THE ANTIQUE HOUR-LINES. 15 
whose section contains the hectemorial line, isa 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 
eurves to which the hectemorial lines belong. As an appen- 
dix, it may not be improper to enumetate 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- 
i i Saag 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 Virru- 
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, béfides 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: 
