BIOMETBIC IDEAS AND METHODS 51 



that when you can measure what you are speaking 

 about and express it in numbers, you know some- 

 thing about it, but when you cannot measure it, 

 when you cannot express it in numbers, your 

 knowledge is of a meager and unsatisfactory kind ; 

 it may be the beginning of knowledge, but you 

 have scarcely in your thoughts, advanced to the 

 stage of science, whatever the matter may be." 



Having taken this position, the next thing in 

 order obviously is to develop mathematical 

 methods especially adapted to the treatment of 

 biological data. Such a step is no more to be 

 criticized than is the demand of the experimentalist 

 that he shall have apparatus adapted to his needs, 

 or of the morphologist that he shall have the 

 latest and best type of microscope for his most 

 detailed and important researches. It is the most 

 obvious right of an investigator that he shall 

 have highly developed and adapted technical 

 aids whatever his field of work. In accord with 

 this principle there has been developed (partly by 

 borrowing from pure mathematics and partly 

 de novo) a very efficient and tolerably complete 

 system of special mathematical methods partic- 

 ularly adapted to the analysis of quantitative 

 biological data. 



Unfortunately the more recondite of these 

 methods cannot be understood at all by the 

 general biologist unless a considerable amount of 

 careful and thorough study is given to them. 



