RESULTS 309 



The set of specimens selected for measurement from the Hamilton 

 zone all belong to the one species Rhipidomella vanuxemi of Hall. (See 

 Cornell University Musemn Catalogue number 9139.) Twenty shells 

 were measured for the statistics. The extremes for index R^ for these 

 20 shells are 103.9 and 125.5, which shows a range of fluctuation of this 

 index of 21.4 per cent for these 20 specimens. These 20 specimens were 

 preserved in the same rock and bear such close resemblance to each other 

 that I think scarcely any paleontologist would question their being one 

 species. They are distributed in number of specimens in the following 

 way by value of the index ~R^ : 



2 specimens have index R^ = 100 to 105 

 4 specimens have index R^ = 105 to 110 

 8 specimens have index R^ = 110 to 115 



3 specimens have index R^ = 115 to 120 

 2 specimens have index R^ = 120 to 125 

 1 specimen has index R^ = 125 to 180 



showing emphatically that no two specimens in this small set of sam- 

 ples are of exactly the same shape; and, while the specimens are more 

 numerous near the average, the difference in E^ is such that at least 10 

 of them are separated hj at least 1 per cent from the next specimen in 

 the series. 



This fact of positive and constant fluctuation is noticeable for all the 

 separate lots, taken either by single faunules or by zones. It is also 

 noticeable when the values of E^ are tabulated for each of the Hamilton 

 species on the basis of the type specimens as figured for each species. 



Are the Hamilton ''species'' natural or artificial groups? — In order to 

 test the question as to whether the described Hamilton species are natural 

 species or only artificial groups, I determined the value of E^ for each of 

 the 37 specimens figured as types of the 5 species described by Hall as 0. 

 cyclas, idoneus, pefielope, leucosia, and vanuxemi. 



I found the range in value of this index for the whole set is 103.5 to 

 121 = 17.5 per cent and the average ahout 109. 



Taking the 7 points (from 106-113), we find 23 of the 37 type speci- 

 mens come within this range and at least half of the types of each species 

 except 0. penelope have the form expressed by this limited range in value 

 of E^, distributed as follows : 



Two are 0. cyclas, 2 are 0. idoneus, 4 are 0. leucosia, 4 are 0. penelope, 

 and 11 are 0. vanuxemi. 



Outside of this mean range are found -4 speciinens below 106, all of 

 which are 0. leucosia. 



XXII— Bull. Geol, Soc, Am., Vol. 21. 1909 



