296 H. S. WILLIAMS PERSISTENCE OF FLUCTUATING VARIATIONS 



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1. Size of shells — values of index L 304 



Uniformity in average size 804 



Length of shell increases on passing upward 304 



Size alone not significant of evolution 304 



2. Size of muscular scar — values of index R- — (2(1) 305 



Phylogenic increase in size of muscular scar 305 



Fluctuating value of index R- for three type species of the 



Hamilton 305 



Comparison between ontogenic fluctuation and phylogenic modi- 

 fication 306 



3. Shape of shell— values of index R^ 306 



Amount of ontogenic fluctuation great 307 



Phylogenic modification slight 308 



Phylogenic modification in same direction as ontogenic growth... 308 



Are the fluctuating characters specific or varietal ? 308 



Are the Hamilton "species" natural or artificial groups? 309 



Mean of the fluctuations 310 



Conclusions 310 



Introduction 



The following paper is the result of investigations which were begun 

 several years ago, under the inspiration of Huxley's prophecy that paleon- 

 tology, when properly interrogated, would reveal to ns the true laws of 

 evolution. I have at last succeeded in getting together a long series of 

 samples of a single race inhabiting successively the same region; have 

 subjected them to minute measurement, and by reducing their morpho- 

 logic characters to mathematical terms have enabled them to speak for 

 themselves regarding at least one of the essential laws of evolution, the 

 law of fluctuating variation. 



Inadequacy of vague descriptive Terms 



One of the greatest difficulties met with in making such an investiga- 

 tion is the practice of using extremely vague and elastic terms in describ- 

 ing the specific characters of fossil organisms. Generic characters are in 

 many cases made more definite by the fact that the diagnostic characters 

 are either present or absent or the repeated parts are found in definite 

 numbers ; but in distinguishing species the use of such terms as short, 

 long, broad, thick, deep, high, oval, ovate, oblong, etcetera, which are very 

 commonly applied to both the gross morphology and the description of 

 each distinguishable part of a fossil, stand directly in the way of all 



