260 



Dr. A. E. Trueman- 



3. The left (attached) valve is thickened. 



4. A sulcus appears on the posterior portion of the loft valve ; 

 this is developed at a late stage in forms like G. obliquaia, but at 

 an earlier stage in more advanced forms such as 0. incurva. 



5. The more advanced shells are generally larger. 



6. The twist of the left valve seen in 0. irregularis becomes con- 

 fined to the apical portion of later species, &-- 



The features characteristic of several species are summarized 

 below, and some of the characters named above ^are illustrated 

 diagrammatically in Fig. 1. The twist of the apical portion of the 

 left valve is shown also in Fig. 2, a,h; ixi G. incurva, shown in c of 

 the same figure, the twist is confined to the apical portion, and is 

 therefore concealed in an adult specimen. 



Fig. 2. — ^Members of the lineage of Gryphau incurva, viewed from the rio-ht, 

 to show the twist of the apical portion of the left valve, (n) Gnjphcea 

 aff. obligaata Sow., specimen sho^vn in Fig. I (c). (b) G. obliquataSow., 

 a topotype, St. Donats, Glam. (c) G. incurva Sow., a toputype, Fretherne, 

 Glos. 



It is possible that the lineage as here defined includes more than 

 one series, differing only in such characters as the size or breadth 

 of the shell, but there does not appear to be any reason for attempting 

 to separate them now. 



The CuavE op the Gryph.^an Shell. 

 It has already been noticed that the curve of the left valve of 

 Gryphoea approximates to a logarithmic spiral.^ In such spirals, 

 it Avill be recalled, the constant angle for the spiral is the angle 

 between a tangent to the spiral at any point and a line passing 

 through that point and the origin (o) of the spiral. Thus in Fig. 3 

 a is the angle of the spiral. 



1 D'Arcy Wentworth Tliompson, On, Gronih and Form, 1917, p. 534. 



