1230 NEW YORK STATE MUSEUM 



theoretically if not actually has all values from 0° to 360°. In 

 the inserted diagram Noetling chooses to take eight points equi- 

 distant on the circle as expressions of eight groups but it is not 

 to be assumed that these groups have either coequal val ue or are 

 other than links in this circular chain. 



1 a. > Q 9 but < 90°. The axes make an acute angle and 

 growth takes place in a posteroventral direction. These are the 

 Loxogoniacea and are representd by Venus and a large group of 

 sinupalliate Dimyaria. 



2 «=90°. The axes stand at right angles; growth takes place 

 ventral ly, perpendicular to O — A. These are the Orthogoniacea 

 represented by Pectunculus. 



3 a > 90° but < 180°. The angle of the axes is obtuse and 

 growth takes place anteroventrally. These are the Prosogoniaeea 

 represented by Mesodesma and Nucula. It is to be here noted 

 that this expression is just the reverse of that of the Loxogoniacea 

 the two standing in the relation of left and right valves of 

 Venus. Here as well as in groups 4 and 5 the beaks are truly 

 opisthogyre and current characterization of these valves conse- 

 quently erroneous. 



4 a=rl80°. Both axes coincide but growth is forward rather 

 than backward as in 8. No examples are! known. Noetling be- 

 lieves they should be looked for among paleozoic forms. 



5 a > 180° but < 270°. These are the Protoconchae. 

 Growth takes place dorso-orally and the ventral organs and pal- 

 lial line would lie close beneath the umbo. No examples of 

 these were recognized, but it is thought that such forms will be 

 found among the paleozoic species. 



6 a > 270°. These are the Staurogoniacea, mathematically 

 like group 2 but with growth in the opposite direction, i. e. dor- 

 sally instead of ventral ly. No examples are known but these 

 are also to be sought in the paleozoic. 



7 a > 270° but < 360°. The axial angle is again acute, the 

 growth posterodorsal. These are the Opisthogoniacea and em- 

 brace Avicula and the Heteromyaria. 



8a-0° or 360°. That is the axes coincide. These are the 

 Symptogoniacea and are represented by Pecten. Growth is pos- 

 terior. The species are Monomyarian. 



