2 INTRODUCTORY <^i,J^^H 



making use of the chemistry, and of the physics, of the age. Littl 

 by httle it draws nearer to our conception of a true science with 

 each branch of physical science which it brings into relation with 

 itself: with every physical law and mathematical theorem which it 

 learns to take into its employ*. Between the physiology of Haller, 

 fine as it was, and that of Liebig, Helmholtz, Ludwig, Claude 

 Bernard, there was all the difference in the worldf. 



As soon as we adventure on the paths of the physicist, we learn 

 to weigh and to measure, to deal with time and space and mass and 

 their related concepts, and to find more and more our knowledge 

 expressed and our needs satisfied through the concept of number, 

 as in the dreams and visions of Plato and Pythagoras ; for modern 

 chemistry would have gladdened the hearts of those great philo- 

 sophic dreamers. Dreams apart, numerical precision is the very 

 soul of science, and its attainment affords the best, perhaps, the 

 only criterion of the truth of theories and the correctness of experi- 

 mentsj:. So said Sir John Herschel, a hundred years ago; and 

 Kant had said that it was Nature herself, and not the mathematician, 

 who brings mathematics into natural philosophy. 



But the zoologist or morphologist has been slow, where the 

 physiologist has long been eager, to invoke the aid of the physical 

 or mathematical sciences; and the reasons for this difference lie 

 deep, and are partly rooted in old tradition and partly in the 

 diverse minds and temperaments of men. To treat the living body 

 as a mechanism was repugnant, and seemed even ludicrous, to 

 Pascal §; and Goethe, lover of nature as he was, ruled mathematics 

 out of place in natural history. Even now the zoologist has scarce 

 begun to dream of defining in mathematical language even the 

 simplest organic forms. When he meets with a simple geometrical 



* "Sine profunda Mechanices Scientia nil veri vos intellecturos, nil boni pro- 

 laturos aliis": Boerhaave, De usu ratiocinii Mechanici in Medicina, 1713. 



t It is well within my own memor how Thomson and Tait, and Klein and 

 Sylvester had to lay stress on the mathematical aspect, and urge the mathematical 

 study, of physical science itself! 



X Dr Johnson says that "to count is a modern practice, the ancient method was 

 to guess"; but Seneca was alive to the difference — "magnum esse solem philosophus 

 probabit, quantus sit mathematicus." 



§ Cf. Pensees, xxix, "II faut dire, en gros, cela se fait par figure et mouvement, 

 car cela est yrai. Mais de dire quels, et composer la machine, cela est ridicule, 

 car cela est inutile, et incertain, et penible." 



