764 THE EQUIANGULAR SPIRAL [ch. 



growth of the horn, of the shell, and of all other organic forms in 

 which an equiangular spiral can be recognised, that each successive 

 increment of growth is similar, and similarly magnified, and similarly 



Fig. 360*. Logarithmic spiral derived from corresponding points in 

 a system of squares. 



Fig. 361. The same in a system of hexagons. From Naber. 



situated to its predecessor, and is in consequence a gnomon to the entire 

 pre-existing structure. Conversely (3) it follows that in the spiral 



* This diagram was at fault in my first edition (p. 512), as Dr G. T. Bennett shews 

 me. The curve met its chords at equal angles at either end: whereas it ought to 

 meet the further end at a lesser angle than the other, and ought in consequence to 

 intersect the hues of the coordinate framework. The constant angle of this spiral 

 is about 66° 11' (tan a=7r/2 logg2). 



