Appendix 359 



angles remain constant in the same sector, 

 because the chords are parallel. 



There is more than this : these same angles, 

 the obtuse as well as the acute, do not alter in 

 value, from one sector to another, at any rate 

 so far as the conscientious eye can judge. 

 Taken as a whole, therefore, the rope-latticed 

 edifice consists of a series of cross-bars inter- 

 secting the several radiating lines obhquely at 

 angles of equal value. 



By this characteristic we recognize the ' loga- 

 rithmic spiral.' Geometricians give this name 

 to the curve which intersects obliquely, at 

 angles of unvarying value, all the straight lines 

 or ' radii vectores ' radiating from a centre 

 called the * pole.' The Epeira's construction, 

 therefore, is a series of chords joining the inter- 

 sections of a logarithmic spiral with a series of 

 radii. It would become merged in this spiral 

 if the number of radii were infinite, for this 

 would reduce the length of the rectilinear 

 elements indefinitely and change this polygonal 

 line into a curve. 



To suggest an explanation why this spiral 

 has so greatly exercised the meditations of 



