280 PHYSIOLOGICAL, EEGULATIONS 



tent and time may be divided into infinitesimal gradations ; while 

 paths of exchange and types of displacement are more limited in 

 number and kind, and are usually thought of as qualitatively di- 

 verse. So, (2) to (5a) are at least in part discontinuous variables, 

 while (5b) to (9) are usually quantitative factors. Some belong 

 in both groups. Thus, changes in properties or in age are continu- 

 ous with respect to each component or individual but discontinuous 

 with respect to the many individuals, constituents, and tissues in 

 which they appear. In the numerous cases of this sort, other 

 classifications might be profitably explored. 



Again, some of the variables that can be fixed by an experimenter 

 are often thought of as independent ; those that brook no external 

 selection may be termed dependent. Then (5a) to (6) are usually 

 chosen at the will of the observer, and (7) to (9) follow from the 

 physiological constitution of the organism. Though the distinction 

 is not a biological one, this grouping of variables is useful in that 

 it facilitates quantitative treatment of the coordinated properties. 

 By the methods of nomography, it is simpler to represent on paper 

 any number of dependent variables, provided the number of so- 

 called independent variables is reduced to one or two, than to deal 

 with a greater number of the latter. Accordingly, fixing (2) and 

 (6) so that they do not vary, (5b) and many other quantities can 

 be represented (fig. 131). And in a succession of such nomograms, 

 several selected types of displacement or of conditions for recovery 

 (5a) and ages (9) might be portrayed. In this way an epitome is 

 obtained that describes quantitatively a physiological pattern. 



Having already discussed (section 11) the interrelations of the 

 four variables of the '^ water-time" system, (1) (5b) (6) (7), and 

 treating at least two of the four as dependent variables, I can now 

 show some of the relations among the remaining six sorts of varia- 

 bles. In the list of variables there are many possible subdivisions ; 

 of these some are mutually exclusive, and may be contrasted, while 

 others are duplicate ways of classifying. 



The object in the following section is to indicate general features 

 and contrasts, and not just to represent the numerous transforma- 

 tions of coordinates that could be made. Each sub-heading em- 

 phasizes a single one of the variables named. 



§ 102. Scopes op the classes of variables 

 (1) Rates of ivater exchange (Rw) during recoveries may be 



