- No. 407. PECTEN IRRADIANS LAMARCK. ^ 86 
7 
often somewhat water-worn and broken by the pounding of the 
surf which rolls in on that unprotected shore ; but no shells 
were rejected unless so worn or broken as to obscure the 
grooves. The shells from Cutchogue were very kindly sent me 
by Mr. Huron Bretsch. Mr. Bretsch writes me that all came 
from Peconic Bay, near Cutchogue, some from a shell heap left 
by fishermen, and some picked up on the shore by himself. He 
says, *I did not pick out the best ones, but took them at 
random." 
Results. — I give in tabular form the observed and per mille 
distribution of frequencies of the different classes of groove 
numbers for the two valves from the three localities. 
RicHT (Lower) VALVE | LEFT (UPPER) VALVE 
; | 
z C. S.H Cutchogue | F. I. & O. I. C.S.H. | Cutchogue | F.I.&O.I. 
o | | 
Obs. | p.m. |Obs.| p.m. | Obs.| P.M. | Obs. | su. | Obs.| rm | Obs. | P.M. 
sii Seren! k | Beis A dile 
13 | I 1.2 | | | 
14 2 1.9 I a2 M. 3 a5 5 32.7 | 95.2 
15 15 14.3 33 117.4 6 120 43 53-2 | 3 248.4 190.5 
16 | 108 | 103.3 | 95 | 338.1 | 15 3oo || 269 | 3330 | 77 | 5032 | 10 | 476.2 
17 | 515 | 492.3 | 127 452.0 | 24 480 || 320 396.0 | 27 176.5 4 190.5 
18 | 308 | 294.5 22 78.3 4 8o || 151 186.9 Da 26. 1 47.6 
19 9o 86.0 4 14.2 2 232.3 2 13.1 
20 7 6.7 | | | 
21 1 1.0 | 
1046 1000.0 | 281 | 1000.0 50 | 1000 | 808 | 1000.0 | 153 | 1000.0 | 21 | 1000.0 
The quantitative study of these seriations gives the following 
constants calculated from the observed and not the per mille 
data. Here z is the number of individual shells counted; M 
is the mode, or the prevailing number of rays; A is the average 
number of rays; c is the standard deviation or index of varia- 
tion; c is the coefficient of variation; F is the critical function 
of Pearson, by which the type of the curve is determined. The 
numbers following the + sign are the probable errors of the 
determinations. For further information concerning this 
analysis of frequency distributions, the reader is referred to 
the works of Duncker in Roux’s Archiv, 1899, or my Statistical 
Methods, New York, 1899. 
