Introduction to Animal ]\Iorphology. 283 



discoid, auriculate, lenticular, he. They may be 

 coiled to the left (laotrope), rarely to the right 

 (dexiotrope) ; in the former the mouth is to the right, 

 and the shell is called dextral ; in the latter to the 

 left ; hence the form is called sinistral. This may be 

 normal,* but is often an abnormalty. Coiled shells 

 are spirals of a peculiar modulus, resembling (and in 

 Ammonites identical with) the true logarithmic spiral, 

 usually differing in having a definite point of start- 

 ing, and forming another geometrical species, the 

 concho-spiral.f (In Argonauta, of the next class, the 

 spiral is parabolic, Heis). In some cases the starting 

 point of the spiral is at a certain distance from the 

 centre, and the first whorl runs around a central 

 nucleus with a definite radius (cyclocentric, concho- 

 spiral).^ In discoidal shells the shape is determined 

 by the nature of the centre and the ratio of the pro- 

 gression, as well as the shape of the section of the 

 chamber! (which is constant). In most coiled shells, 



* Clausilia, Busycon. 



t If the width of the first whorl = the parameter of the spiral «, the 



spire in general = h, and the ratio of progression = p ; then in the first 



whorl, h = a; in the second, h = ap ; in the third, h - ap- ; in the w'*, 



a 

 h = ap {^^). The radius (r) of the m"' whorl = r = ip"''^)- There 



may be two valves for p in the inner and outer whorls, when the spire is said 

 to be diplo-spiral. This is the case in many gasteropods. My measure- 

 ments lead me to beheve that some land moUuscs are triplospiral. 



a a 



t The radius would then be r = a + (/"'"^) ; if a = , this be- 



* p - \ ^'^ ' p - 1 



comes logarithmic as r = ap"*. 



§ It was determined by the Rev. Canon Moseley that the geometrical 

 form of this section was constant, so that the spire might be said to be 

 produced by the revolution of a constant geometrical form around an axis, 

 the producing plane being constantly increasing, but retaining its specific 

 form throughout. 



