310 H. S. WILLIAMS PERSISTENCE OF FLUCTUATING VARIATIONS 



Ten specimens are above 113, of which 2 are 0. cyclas, 1 is 0. idoneus, 

 5 are 0. penelope, and 2 are 0. vanuxemi. 



It is evident from these statistics that the specimens selected as types 

 of the 5 Hamilton species have no constancy in the value of E^. Distri- 

 bution of the type specimens in the order of value of K^ show this charac- 

 ter to be a constantly fluctuating character for each so-called species, and 

 not one of the species is strictly discontinuous in respect of this character 

 from each of the other sets of types, although selected as types of specific 

 groups ; from which the conclusion is drawn that, so far as this character 

 is concerned, the so-called species are artificial rather than natural groups. 



The mean of the fluctuations. — It is further evident from examination 

 of the statistics that the mean of these fluctuations for the Hamilton is 

 near 109, and the mean does not vary by 4 points either side of 109 for 

 any of the zones in the upper Devonian. 



The total range of fluctuation in a fair set of specimens from any 

 local faunule from one end of the series to the other rarely is less than 

 20 points, and while on passing upward there is a clear tendency to in- 

 crease of the range of this fluctuation and a drop in its mean value, the 

 amount of this phylogenic change is but a fractional portion of the onto- 

 genic fluctuation observed in every sample in which a couple dozen of 

 specimens are in evidence. 



Conclusions 



For the present paper it is unnecessary to go into further details. The 

 examination of the shape of the muscular scar, as expressed by the index 

 E^, shows the same law reported for the other indexes. 



All three indexes, E\ E^, and E^, point to the same conclusions, namely : 



(a) The characters under examination are fluctuating variations in 

 the Hamilton stage. 



(h) Sample sets of specimens taken from the recurrent faunules of the 

 Ithaca, Van Etten, Owego, and Swartwood zones exhibit the same char- 

 acters as fluctuating variations. 



(c) The fluctuations affect all the representatives of the genus without 

 regard to any arrangement of the specimens into artificial specific groups 

 and express themselves in sets of specimens derived from a single faunule 

 or sets of faunules from a single zone. 



(d) There is in the successive zones evidence of a tendency to move 

 in a definite direction on passing from lower to higher geologic horizons, 

 and this phylogenic modification is, in each case, in the same direction 

 as the modification, expressed by individuals in their ontogenic growth. 



