240 CHAP. XXVI. THE PHYSIOLOGICAL SCALE 



the resulting changes in photosynthesis ; this would enable 

 us to determine the physiological coefficient for the variation 

 of any particular factor. Having thus determined the co- 

 efficients for temperature, for C0 2 -content, and for light, we 

 have next to find out how the result is modified by simul- 

 taneous change in two of these factors. The object of this 

 line of inquiry is to determine whether the resultant effect 

 induced by changes in two variables can in any way be 

 deduced from the separate effects of each, or whether the 

 combined effect is to be regarded as additive or as something 

 quite different. And finally we have to face the still more 

 difficult problems which arise when more than two different 

 factors undergo independent variation. 



The effects of permutation and combination of various 

 factors must be very numerous ; according to the older 

 methods each experiment would take several months, so 

 that it would be hardly possible to complete the necessary 

 investigations in the course of a lifetime. The method 

 which I have adopted offers so many advantages, both in 

 regard to accuracy and quickness of operation, that the 

 problems which confront us are not so formidable as they 

 at first sight appear to be. 



The Characteristic Curve 



We have first to ascertain the modifying effect of variation 

 of a single factor. It may be said in general that when A and 

 B are so related that any change in B produces a correspond- 

 ing variation in A, then A is said to be a function of B. We 

 may discover the relation between B and A by plotting a 

 curve in which the ordinate represents the induced change, 

 and the abscissa the variation that induces it. For a con- 

 crete example we may take the expansion-curve of the volume 

 of i grm. of water from 4 C. to 20 C. (fig. 56). From the 

 character of the curve we are able to establish the formula 

 by which the volume at any temperature may be found, 



