PALMER: THE HYPERBOLIC SPIRAL. 169 
Or if we have at hand an instrument of which the constant equals 
360, simply set to OL and strike a spiral arc. Then with a radius 
as long in inches as the number of sides which the polygon is to 
have, strike a circular arc cutting the spiral and join the intersec- 
tion to the center when the required side is determined. 
If instead of a 360 degree instrument an 180 degree one is avail- 
180 
able, set the pole at O” and lay out the angle (==), when the re- 
n 
sult will be the same. Or if desired, O” may be used in any event 
and (=) laid out in the usual way. 
(b) To construct a required polygon on a given length of side, 
AO, Fig. 11. We know that for any polygon of n sides, 
Se Lop=2. 
Pp 
Big ia. 
So it is a simple matter to lay out this angle (=) by use of the 
instrument, just as in the preceding case, by either of the ways 
noticed there. Then, OP known, the circumscribing circle can be 
drawn and the polygon completed. 
GRAPHIC RECTIFICATION OF ARCS. 
By means of the Universal Drawing Curve the graphic rectifi- 
cation of circular arcs is also readily possible. We may have either 
