30 RELATIONSHIPS OF THE COCCACE.^E 



stain by Gram, and show a second set of group reactions 

 to immune sera. The principle which differentiates 

 these specific types is the same as that involved in the 

 distinction of the liquefying and non-liquefying cocci; 

 but the difference in this case is so marked as not to 

 require statistical demonstration. 



The essential viewpoint which our biometrical study 

 of the cocci has developed may be briefly restated as 

 follows. 



Bacteria show, in many groups at least, great varia- 

 tions. A comparative study of a considerable number 

 of strains shows that certain characters, or combinations 

 of characters, occur with special numerical frequency. 

 These frequency types represent the centers about 

 which related organisms are varying. Each type center 

 which is distinguished from other type centers by the 

 exhibition of a definitely measurable character may be 

 given the rank of a species. Genera may be constituted 

 for nearly related groups of species which exhibit charac- 

 ters in common. Such species and genera represent 

 real, natural groups of bacteria, which owe their 

 similarity either to community of descent (phylogenetic 

 species) or to similar pressure of environment (onto- 

 genetic species). 



