Introduction to A n imal Morphology. 283 



discoid, auriculate, lenticular, c. 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 abnormal ty. 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 a, the 

 spire in general = k, 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 m<*, 



h = ap (*}. The radius (r) of the m" whorl = r = (P m '*)- 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 believe that some land molluscs are triplospiral. 



a n 



r The radius would then be r = a + (P m ~ l ) ; if & = , this l>c- 



/> - I p -\ 



comes logarithmic as r = a/". 



$ It was determined by the Rev. Canon Mosclcy that the gcom 



;on was constant, so that the spire might be said to be 

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

 the producing plane being constantly increasing, but retaining its specific 

 form throughout. 



