344 THE PHILOSOPHY OF BIOLOGY 



We can make arbitrary values of the pressure, but 

 whenever we do this the corresponding values of the 

 volume are fixed. We say, then, that the volume is a 

 function of the pressure. In general, when we choose 

 one value of an independent variable, or argument, 

 there can be only one, or a small number, of values of 

 the dependent variable, or function. If there are two 

 or more values of the function for one value of the 

 argument each of these is necessarily determined by 

 the value which we choose to assign to the argument. 

 There is a strict functionality between the two series 

 of variables. In the experiment we have chosen this 

 functionality is expressed by the equation pv=k(/+ai), 

 where p is the pressure, v the volume, k and a constants, 

 and t is the temperature at which the experiment is 

 carried out. In a number of experiments like that 

 which we have mentioned, k, a, and t are the same 

 throughout, and this is why we call them constants. 

 We give p any value we like, and then v can be calculated 

 from the equation. 



RATE OF VARIATION 



If we know the equation pv=k{/+ at) , we can find how 

 much the volume changes when the pressure changes, 

 that is, the rate of variation of v with respect to p. 

 But even if we don't know that this equation applies, 

 we can still find the rate of variation from our experi- 

 ments. We see from the graph that, when the pressure 

 increases from pi to p^, the volume decreases from v, to 

 V2, but that if the pressure is again increased to p^, that 

 is, by a similar amount to the increase of pressure from 

 pi to pi, the volume decreases from v^ to V3. Now we 

 find, by measurements made on the graph, that the 

 decrease v^ to v^ is greater than the decrease r, to v^, 



