CHOOSING PHYSIOLOGICAL VAKIABLES 425 



for all were measured simultaneously or virtually so. With six 

 variables 15 bi-correlations are established, and with n variables 

 (n^ — n)/2 correlations taken two at a time. But if, as is em- 

 pirically done in "random" physiology, the procedure had been 

 AocB, C°cD, EocF, etc., then with six variables only 3 correlations 

 are established. The same number of data then yield only 3/15 

 as many relations taken two at a time, or in general l/{n — 1) as 

 many. 



(2) Among more than two variables at a time, all quantities 

 measured either actually or virtually simultaneously are inter- 

 related. But methods of representing them had to be selected; 

 those used are contour charts (fig, 19), tables (table 24), and 

 parallel alignment charts (fig. 131). Other techniques of partial 

 correlation and multiple correlation might be applied (Fisher, 

 '38). Further procedures as devised will aid in the comprehension 

 and evaluation of large numbers of coexisting quantities ; need for 

 them grew during the inquiry. 



(3) Very often A oc B, and A' oc C are studied, under the impres- 

 sion that A and A' are the same, perhaps because they have the 

 same name. Thus, both A and A' may represent dehydration of 

 dog, or excitation of nerve, or osmotic pressure of plasma. But as 

 already seen, there are many unidentical dehydrations, or nerve 

 trunks, or osmotic pressures. So it was necessary to define care- 

 fully and provisionally. 



Sometimes the data are averages of statistical groups that later 

 or in the light of other relations require splitting into new cate- 

 gories. At times a rough value obtained under unrecorded condi- 

 tions or by crude methods is useful ; later new refinements are indi- 

 cated, or non-uniformities of conditions are recognized. Sup- 

 posedly homogeneous material turns out to be heterogeneous. One 

 of the tasks was to define diverse types of water load ; there proved 

 to be scores of them (chapter III). To differentiate amphibia 

 from mammals, a few data on water exchanges will suffice ; but to 

 distinguish rabbits from dogs with respect to water equilibrations, 

 numerous factors may be necessary. So, continual revision and 

 refinement of data proceeds as occasion arises. 



(4) Among the measurements of particular variables, some are 

 on diverse species, others at diverse temperatures, others by diverse 

 paths. From them are found (a) what relations persist among the 

 data, what uniformities exist. From them (b) the diversities are 



