36 The American Geologist. 
January, 1903. 
Under "hight" one understands conventionally the greatest 
vertical distance between points of the dorsal and ventral mar- 
gins. Noetling shows, first, that the length of this line, thus 
defined, depends largely upon the curvature and the thick- 
ness of the shell, which are accidental, indefinite elements. 
To eliminate these and because this ''hight" is not com- 
parable in Dimyaria and Heteromyaria, the author defines as the 
"true hight" the distance between the ventral margin and the 
ventral edge of the hinge-plate, measured upon a line, which 
is perpendicular to the oro-anal axis and passes through the 
mouth. 
For the mathematical expression of the torsion of the shell 
it has been found necessary to define a third element of the 
shell which is considered as of the greatest significance. For 
example, in the shell of Cypricardia, there is a ridge from 
umbo to ventro-posterior margin, the umbonal ridge (see dia- 
gram i), which marks the direction of greatest longitudinal 
growth of the valve. This line is termed the "Crescenz-linie" 
(growth-axis). Its horizontal projection forms an angle with 
the oro-anal axis, which is termed the "Schalenschiefe" (ob- 
liquity or slant of shell). 
It can now be shown that the expression — = >'■ (an angle 
of obliquity) allows the mathematical determination of the 
Schalenschiefe. The possible values of >j- between 0° and 
360° give an infinite number of stages of torsion which the 
author chooses to place in 8 groups. In the determination of 
these groups it is to be remembered that not the shell, but the 
animal within the shell determines the terms applied to the 
parts of the shell, and that the oro-anal axis lies in the hori- 
zontal line, as it does during the life time of the animal. 
The groups are : 
i) a =: 0° (or 360°), that is, both axes (growth-axis 
and length or oro-anal axis) coincide. In this case the growth 
must take place in the direction of the oro-anal axis, and in 
a posterior direction. These are the Symptogoniacea and as 
classical example for the group is cited Pecten, where growth 
takes place in an anal direction. The hight = o. 
2) « > 0°, but < 90°, tan '/ > 0° but < i. The ax- 
is of growth and the oro-anal axis form an acute angle and 
growth takes place in postero-ventral direction. The hight is 
