306 II. S. WILLIAMS PERSISTENCE OF FLUCTUATING VARIATIONS 



cent; that Orthis penelope may differ from 46.8 (figure 2g), 56.3 (figure 

 2i) to 61.6 (figure 2h), or 14.8 per cent, and that Ortliis vanuxemi (fig- 

 ures 3m and 3r) may normally differ from 69.2 to 74.8, or 5.6 per cent. 



Comparison between ontogenic fluctuation and phyJogenic modifica- 

 tion. — These statistics show a range in value of this index, for the Hamil- 

 ton types alone, from 46.8 to 83.9, or 37 per cent, which exceeds in both 

 extremes the extreme limit reached by any of the specimens measured in 

 our series; it also exceeds the limit of fluctuation of this character ex- 

 pressed by the average value of E^, as recorded by typical figured speci- 

 mens of characteristic species from the early and latter ends of the life 

 history of the genus. 



To bring out this point more distinctly, we note the difference between 

 the extremes in percentage values. 



The extreme fluctuation in value of index E^ between typical Niagara 

 and typical Carboniferous forms is 14 per cent; for typical figured speci- 

 mens of Hamilton species, 37; for typical specimens of the species 0. 

 leucosia, 14.7; for typical specimens of species 0. penelope, 14.8; for 

 typical specimens of species 0. vanuxemi, 5.6; for measured specimens 

 from a single Hamilton faunule, 24; for measured specimens from the 

 Van Etten zone, 25; for measured specimens from the Owego zone, 16; 

 for measured specimens of the Swartwood zone, 26. 



But the total amount of change in the average value of index E^ from 

 the Hamilton to the Swartwood zone is only 4 per cent. 



It seems evident from these statistics that the difference in value of 

 the character E^ is from 4 to 6 times greater for any set of specimens 

 selected at any particular stage in the history of the genus than the 

 difference in value shown by two samples separated by a period of time 

 represented by the sedimentation of 2,300 feet of sediments in the 

 passage from the Hamilton formation to the top of the typical Chemung. 



This law of the persistence of fluctuating variation is equally well 

 indicated by comparison of the evidence of fluctuations for each separate 

 faunule. 



3. Shape of tlie shell — Values of index R^. — The statistics regarding 

 the shape of the shell are found in the measurements of 275 specimens, 

 representing 35 separate sample faunules, and from 5 distinct strati- 

 graphic zones. The morphologic character involved is one of the most 

 conspicuous as well as important of the characters used in specific 

 diagnosis. 



If the average of the values of the index E^ of all the specimens of 

 each zone is taken, the following results are found : 



