794 THE EQUIANGULAR SPIRAL [ch. 



(which is indeed asymptotic) makfes this of Httle use as a method of 

 determining the constant angle. It is, however, a beautiful property 

 of the curve, and all the more interesting that Clerk Maxwell dis- 

 covered it when he was a boy*. 



(2) The following method is useful and easy when we have a 

 portion of a single whorl, such as to shew both its inner and its 

 outer edge. A broken whorl of an Ammonite, a curved shell such 

 as Dentalium, or a horn of similar form to the latter, will fall under 



this head. We have merely to draw a tangent, 

 GEH, to the outer whorl at any point E; then 

 draw to the inner whorl a tangent parallel to GEH, 

 touching the curve in some point F. The straight 

 hne joining the points of contact, EF, must 

 evidently pass through the pole : and^ accordingly, 

 the angle GEF is the angle required. In shells 

 which bear longitudinal striae or other ornaments, 

 any pair of these will suffice for our purpose, 

 instead of thfe actual boundaries of the whorl. 

 But it is obvious that this method will be apt to 

 fail us when the angle a is very small; and 

 when, consequently, the points E and F are very 

 remote. 



(3) In shells (or horns) shewing rings or other transverse 

 ornamentation, we may take it that these ornaments are set at 



Fig. 381. 



Fig. 382. An Ammonite, to 

 shew corrugated surface- 

 pattern. 



* Clerk Maxwell, On the theory of rolling curves. Trans. B.S.E. xvi, pp. 519- 

 540, 1849; Sci. Papers, i, pp. 4-29. 



