12 Cumings and Mauck — Variation in the 



Group Illa^ Plications on Dorsal Valve. 

 Xumber of shells used, 451. Eange of variation from 11 to 

 29. Mode at 18 with frequency of 199-55. Yariation corre- 

 lated with that of G-roup III. 



Group IV, Plications in Sinus. 

 IS'nmber of shells used, 1412. Range of variation from 1 to 7. 

 Mode at 3 with frequency of 729-1. Yariation in the direc- 

 tion of the larger number of plications. 



Group V, Plications on Fold. 



[N'umber of shells used, 1116. Range of variation from 2 to 

 8. Mode at 4, with a frequency of 793'8. Yariation precisely 

 correlated with that of Group lY." 



The complete data are charted on page 11. The method of 

 constructing the curves of fig. 1 is the usual one of laying off 

 the classes along the axis of abscissas and the frequencies along 

 corresponding ordinates. 



The lack of correspondence between Grroups III and III«, 

 which should be exactly correlated, is due to the relatively 

 small number of specimens used in Group III<2. It forcibly 

 emphasizes the necessity of using as large series of specimens 

 as possible. 



AH the curves are skewed, ^one of them show more than 

 one mode. They all rise abruptly and fall off less abruptly. 

 This shows a certain correlation of the different variants. 



An attempt was made to determine the relation of the num- 

 ber of plications in the sinus to the number on the entire 

 valve. Hall says : " The prevailing number of lateral plica- 

 tions is seven on each side of the sinus or lobe ; and so long as 

 the mesial plications remain three and four, so long the lateral 

 ones are seven. As soon as there is even an appearance of a 

 departure from this number on the mesial lobe and sinus, and 

 where the rudiment of an additional plait is visible, we then 

 find the lateral plaits to be nine or ten."f 



Our material does not bear out this statement. To test the 

 point it was assumed that there is a precise correlation between 

 number of plications in the sinus and number of plications 

 on the whole valve. The area of the frequency polygon for 

 any given number of plications in the sinus should then be 

 equal to the sum of the areas of the frequency polygons of a 

 definite number of plications on the valve. For example, the 

 frequency polygon of three to four plications in the sinus has 

 an area equal to that of the sum of the areas of the frequency 



* While there is necessarily one more plication on the fold than in the 

 sinus, the fact that many specimens, owing to state of preservation, can be 

 nsed for the determination of one group that are not available for the other, 

 makes the two groups supplement each other. 



t Hall, Pal. N. Y., vol. i, 1847, p. 134. 



