120 PLANT PHYSIOLOGY 



The wanderings of the academic philosophers on the extreme 

 limits of human knowledge, and even beyond them, lead only to 

 transitory results, which in turn may be called into question, while 

 science advances steadily in its development. A celebrated physicist 

 and thinker has said that sound human understanding is a lasting 

 product of nature, while philosophy is a meaningless, ephemeral, arti- 

 ficial product. 1 



Only that philosophy will profit us which has arisen from the true 

 spirit of science, even though it advances in the causal and teleo- 

 logical only by way of description. In the spirit of our descriptive 

 methods let us not, when opportunity offers, withhold from speaking 

 of the purposefulness of organization, or of purposes and goals in the 

 realm of life, as in the adequate observation of a machine. In doing 

 so, we renounce the explanation and exposition of final causes of 

 things and events; this lies beyond the limits of the knowledge of 

 nature and beyond the power of man. 



From mathematics we have greater hope for the furtherance of 

 our science. Small beginnings are already visible, which at first 

 attain only to a primitive expression in arithmetical representa- 

 tion of quantitative experiments. A further advance is to be noticed 

 in representing mathematically simple physical relations, e. g., to 

 express the entrance and exit of gases into and out of the plant as 

 phenomena of effusion or gas transpiration, or the graphic repre- 

 sentation by means of a system of coordinates of the relation of a 

 phenomenon (e. g., heliotropism) to a variable factor (e. g., inten- 

 sity of light). When a simplification of the conception of a morpho- 

 logical relation (e. g., leaf arrangement) or of a state (e. g., rigidity or 

 elasticity of the plant body or the use of light to plants) is possible, 

 we use mathematical expressions to advantage, and similarly for 

 precise illustration of certain principles (e. g., by means of the bio- 

 chronic equation of H. de Vries), etc. 



Yet these are, as we have said, only small beginnings. Mathe- 

 matical calculation plays yet a very minor role in plant physiology 

 because, in the lack of deeper knowledge of the facts, everything 

 seems as if so hidden in a cloud that the congeries of active factors 

 may not yet be brought to a corresponding mathematical form; 

 that the setting up of a mathematical formula or equation of any 

 kind from which, upon the basis of adequate observations, future 

 conditions may be inferred, appears not yet possible. Animal physi- 

 ology has already taken the lead, in that in some questions it uses 

 the differential equation, and so it may be expected that mathe- 

 matical calculation, after the example of physics, will become an 

 important means of advance in our science. 



Almost every problem in plant physiology gives us in the pro- 



1 E. Mach, Die Analyse der Empfindungcn, Dritte Auflage, Jena, 1902, p. 29. 



