308 H. S. WILLIAMS PERSISTENCE OF FLUCTUATING VARIATIONS 



type figures, amounts to 103.5-121 := 18 per cent — that is, the extreme 

 difference expressed by the type figures of the five species of the Hamilton 

 is only 1 per cent greater than the average difference for each lot of the 

 35 lots of measured specimens. 



Seventeen of the 35 sample lots collected in the field show a greater 

 amount of difference in this character (index E^) than the total amount 

 of difference between the extreme examples of the type specimens of all 

 the species of this genus described from the Hamilton for the New York 

 area. 



The difference between the mean values of index K^ for the Hamilton 

 type figures is only (107.7-113.9 =) 6.2, and 22 of the 35 samples show 

 a wider fluctuation than 6.2. 



Nevertheless, the greatest amount of difference between the average 

 values of E^ for the several zones, taken by zones, is (105.6-111.9=) 

 6.3, and both extreme average values taken by zones are less by almost 

 exactly 2 per cent than the actual extremes expressed by all the typical 

 Hamilton species. 



Phylogenic modification slight. — The statistics show a slight decrease 

 in value of index E^ on passing upward from the Hamilton to the upper 

 Chemung zone, which fact is in harmony with the general ph3dogenic 

 movement for the whole evolutional history of the race, as shown by com- 

 paring two Silurian species with two characteristic Carboniferous species : 



Value of Index R'. Average. 



Orthis circulus of the Clinton 117 . 3) 116 6 



Orthis hybrida of the Niagara 116.0) 



0. pecosi Marcou, Coal Measures 86. 2| Rf\ fi 



0. penniana Derby, Coal Measures 87 . 5 ) 



showing a decrease of about 30 per cent on passing from the Silurian to 

 the close of the Carboniferous (Pennsylvanian). 



Phylogenic modification in same direction as ontogenic growth. — This 

 phylogenic decrease in the value of index E^ is also in harmony with the 

 ontogenic law shown by comparing the young with the adult stage of a 

 single specimen. The young forms are always broader than the adult, 

 which would be expressed by higher percentage in the value of E^ for 

 young than for adult stages of growth. 



Are the fluctuating characters specific or varietal? — In order to test 

 the question whether these fluctuations in E^ are truly varietal or may 

 result from mixing several distinct species, the following facts have a 

 bearing, namely: 



