there has been developed (partly by borrowing from mathematics and partly de novo) a very efficient and tolerably complete system of special mathematical methods particularly adapted to the analysis of quantitative biological data. Unfortunately the more recondite of these methods can not be understood at all by the general biologist unless a considerable amount of careful and thorough study is given to them. Even the simpler of current biometric methods are uot fully understood by the majority of biologists, nor can they be except through special study of their mathematical origin and development. But is there any reason why the biologist should expect to have intuitive comprehension of these methods? No one would expect to apply successfully the complicated and delicate surgical technique of Pawlow or Carrel to the solution of biological problems without careful preliminary study and practice of these methods, continued till they were really « mastered ». The case is not different with any other higher development of scientific technique.
Because of the lack of a full comprehension of the meaning and significance of the mathematico-statistical methods used in biometry, these methods have been subjected to a great deal of unreasonable and futile criticism. It is argued that these methods are in large part worthless because they are « too refined ». Biological data are held to be of so coarse and inaccurate a character as to make any but the roughest kind of treatment of them of no significance. Such a view misses entirely the purpose and meaning of the biometrical calculus. It is just because biological data necessarily are often rough that we need refined mathematical methods in their treatment in order to test and check the conclusions to be drawn from them, and in order to show their true trend and significance. An example will help to make the point here clear. Mortality statistics are usually available only in units of years of life. This is a rough unit. For actuarial purposes it is desirable to know, for example, the probable duration of life much more accurately than in terms of years. It is possible to get this information, accurate to a very high degree, by the application of appropriate mathematical treatment to the rough yearly data. In this connection, too, is to be considered the frequently made statement that no statistical constant can be more accurate than the
