112 THE PHILOSOPHY OF BIOLOGY 



reproduce the curve ? Obviously not, for the equa- 

 tions of the tangents would have the form ax + hy 

 while that of the curve itself would be quite different, 

 containing x as powers of x, or as transcendental 

 functions of x. In this investigation what we succeed 

 in obtaining are the derivatives of the curve, and 

 to reproduce the latter from its elements we have to 

 integrate the derivatives ; that is, another operation 

 differing in kind from our analytical one must be per- 

 formed. Now in this illustration we have doubtless 

 something more than an analogy with our physico- 

 chemical analysis of life. The activities of the organsim 

 do reduce to bio-chemical ones (the elemental straight 

 lines on the curve), and each of these reactions has 

 something in common with life (it is tangent to life, 

 touching it at one point). But if we attempt to 

 reconstitute life from its physico-chemical derivatives 

 we must integrate the latter, and in doing so we over- 

 pass the bounds of physics, just as integrating a mathe- 

 matical function we necessarily introduce the concept 

 of the " infinitely small." 



The physico-chemical reactions into which we 

 dissociate any vital function of the organism have^ 

 then, each of them, something in common with the 

 vital function. But their mere sum is not the function. 

 To reproduce the latter we have to effect a co-ordination 

 and give directions to these reactions. In all physio- 

 logical investigations we proceed a certain length with 

 perfect success ; thus the elements, so to speak, of 

 the function of the secretion of saliva are (i) the blood- 

 pressure, (2) the hydrostatic pressure of the secretion 

 in the lumina of the gland tubules, (3) the diffus- 

 bility of the substances dissolved in the blood and 

 lymph through the walls of these vessels, (4) the 

 osmotic pressure of the same substances, and (5) the 



