38 The Ajiierican Geologist. January, 1903. 
These, the Staiirogoiiiacca, correspond mathematically to 
the Orthogoniacea, but growth takes place in an opposite di- 
rection, i.e. dorsally. No example known, but they are to be 
sought among the paleozoic forms with a rectangular "Scha- 
lenschiefe." 
8) a > 270°, but < 360°; tan« < i, but > o ; H < L. 
Among these, the Opisthogonicca, the Schalenschiefe forms 
an angle in the fourth quadrant. As « = 3R+ "\ the Scha- 
lenschiefe forms again apparently an acute angle, but the 
growth takes place in dorso-anal direction. To this group 
belong the Heteromyaria and Avicula can be considered as its 
type. 
These are the eight cases, which, according to Noetling, 
are possible for the size of the Schalenschiefe. In four of 
these, where "■ =^0°, iR, 2R, 3R the number of possibilities is 
absolutely limited but wdiere a = o + '/^ (acute angle), iR+«i 
(obtuse), 2R+a^ (acute in third quadrant), 3R+ai (acute in 
fourth quadrant), the number of possible sizes is indefinite. "■ 
appears therefore always as an acute angle and the great diffi- 
culty is to determine to which quadrant it belongs. Where the 
pallial sinus can 'be observed no difficulty is found to determine 
whether « lies in the first or second quadrant ; the external 
ligament can also be used for this purpose. The direction of 
growth of the shell will readily decide whether « lies in the 
fourth quadrant. If the shell in question covers none of these 
eases and « is acute it could be logically concluded that it lies 
in the third quadrant. As with paleozoic fossils both the ex- 
ternal ligaments and the pallial sinus often fail of observation, 
this determination will mostly be very difficult and other cri- 
teria are therefore sought for. 
The author has the eight cases under discussion, so ar- 
ranged in a diagram, that they form a closed circle. This 
diagram is here copied. All figures of valves are placed so that 
the dorsal side is above and the oro-anal axis (A-O) lies hori- 
zontal. W represents the axis of growth, the latter having tak- 
en place in the direction of the marker. The central ring of 
angles represents the corresponding Schalenschiefe, the angle 
formed by the axis of growth and the oro-anal axis. The 
torsion of the shells becomes in this diagram directly apparent. 
Mr. Noetling then points out the deep hiatus existing be- 
