CHAPTER XI 



THE EQUIANGULAR SPIRAL 



The very numerous examples of spiral conformation which we 

 meet with in our studies of organic form are pecuUarly adapted 

 to mathematical methods of investigation. But ere we begin to 

 study them we must take care to define our terms, and we had 

 better also attempt some rough preliminary classification of the 

 objects with which we shall have to deal. 



In general terms, a Spiral is a curve which, starting from 

 a point of origin, continually diminishes in curvature as it recedes 

 from that point; or, in other words, whose radius of curvature 

 continually increases. This definition is wide enough to include 

 a number of different curves, but on the other hand it excludes 

 at least one which in popular speech we are apt to confuse with 

 a true spiral. This latter curve is the simple screw, or cyhndrical 

 helix, which curve neither starts from a definite origin nor changes 

 its curvature as it proceeds. The "spiral" thickening of a woody 

 plant-cell, the "spiral" thread within an insect's tracheal tube, or 

 the "spiral" twist and twine of a climbing stem are not, mathe- 

 matically speaking, spirals at all, but screws or helices. They belong 

 to a distinct, though not very remote, family of curves. 



Of true organic spirals we have no lack*. We think at once of 

 horns of ruminants, and of still more exquisitely beautiful molluscan 

 shells — in which (as Pliny says) tnagna ludentis Naturae varietas. 

 Closely related spirals may be traced in the florets of a sunflower; 

 a true spiral, though not, by the way, so easy of investigation, is seen 

 in the outhne of a cordiform leaf; and yet again, we can recognise 

 typical though transitory spirals in a lock of hair, in a staple of 

 woolt, in the coil of an elephant's trunk, in the "circling spires" 



* A great number of spiral forms, both organic and artificial, are described 

 and beautifully illustrated in Sir T. A. Cook's Spirals in Nature and Art, 1903, and 

 Curves of Life, 1914. 



t On this interesting case see, e.g. J. E. Duerden, in Science, May 25, 1934. 



