814 THE EQUIANGULAR SPIRAL [ch. 



ellipse; but an exception to this rule may be found in certain 

 Ammonites, forming the group " Cordati," where (as Blake points out) 

 the curve is very nearly represented by a cardioid, whose equation 

 is r = a (1 + cos 6). 



When the generating curves of successive whorls cut one another, 

 the hne of intersection forms the conspicuous heHco-spiral or 

 loxodromic curve called the suture by conchologists. 



The generating curve may grow slowly or quickly; its growth- 

 factor is very slow in Dentalium or Turritella, very rapid in Nerita, 

 or Pileopsis, or Haliotis or the Limpet. It may contain the axis 

 in its plane, as in Nautilus ; it may be parallel to the axis, as in the 

 majority of Gastropods; or it may be inclined to the axis, as it is in 

 a very marked degree in Haliotis, In fact, in Haliotis the generating 



B 



A 



Fig. 396. A, Lanydlaria perspicua; B, Sigaretus haliotoides. 

 After Woodward. 



curve is so oblique to the axis of the shell that the latter appears 

 to grow by additions to one margin only (cf. Fig. 362), as in the 

 case of the opercula of Turbo and Nerita referred to on p. 775; 

 and this is what Moseley supposed it to do. 



The general appearance of the entire shell is determined (apart 

 from the form of its generating curve) by the magnitude of three 

 angles; and these in turn are determined, as has been sufficiently 

 explained, by the ratios of certain velocities of growth. These 

 angles are (1) the constant angle of the equiangular spiral (a); (2) in 

 turbinate shells, the enveloping angle of the cone, or (taking half 

 that angle) the angle (p) which a tangent to the whorls makes with 

 the axis of the shell; and (3) an angle called the "angle of retarda- 

 tion" (y), which expresses the retardation in growth of the inner 

 as compared with the outer part of each whorl, and therefore 

 measures the extent to which one whorl overlaps, or the extent to 

 which it is separated from, another. 



