The Geometry of the Epeira's Web 



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 obliquely at 

 angles of equal value. 



. By this characteristic we recognize the 

 'logarithmic spiral.' Geometricians give this 

 name to the curve which intersects obliquely, 

 at angles of unvarying \-alue, all the straight 

 lines or 'radii vectores' radiating from a 

 centre called the 'pole.' The Epeira's con- 

 struction, therefore, is a series of chords join- 

 ing the intersections of a logarithmic spiral 

 with a scries 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 

 diange this polygonal line into a curve. 



To suggest an explanation why this spiral 

 has so greatly exercised the meditations of 

 science, let us confine ourselves for the present 

 to a few statements of which the reader will 

 find the proof in any treatise on hi^er 

 geometry. 



The logarithmic spiral describes an endless 



385 



