GENERAL FEATURES OF WATER EXCHANGES 185 



recovers from water deficit more rapidly than a rat, which in turn 

 has a higher velocity quotient than Phascolosoma, man, and frog 

 (fig. 101). The above description characterizes each recovery 

 according to its velocity, its course over a period of time, and its 

 proportionality to load. To fit a rat with a man's slow recovery 

 of water content would apparently be as incongruous as to fit the 

 rat with a man's arm. For, physiological processes have their con- 

 gruities, however non-material their fixity and invisible their rela- 

 tions to other functions may be. 



The fact that all the tolerance curves represented have similar 

 shapes, allowance being made for the fact that recovery from excess 

 starts after a lag in dog, man, and isolated muscle, suggests that 

 they be expressed by a single equation. An equation that satis- 

 factorily fits very many of the data relating loadi to time (t) is the 

 exponential form AW = ae'^\ a being a coefficient and e the base of 

 natural logarithms. It may be written in the form lnAW = 

 Ina-hi. Values of k therefore express relative slopes of the 

 curves at diverse times. 



The rates of exchange may likewise be compared among species 

 during recoveries of water content (fig. 107). Deriving from the 

 same equation 



h-^/M = -ahe-''' 



Dividing rate by load, the quotient is - k. This k is identical with 

 the velocity quotient, which is computed either by dividing the rate 

 of exchange by the coexisting load, or by the relation 1/At ^k=^ 

 (lnAW-lna)/t obtained by transforming the second equation 

 above. 



The quotients (table 16, 3 and 4) vary in some species with the 

 increment of water content. But for each species and each type 

 of increment there is a mean value and a range of values. Uni- 

 formities become apparent; (!) in many species, values of -k are 

 nearly constant over considerable ranges of negative load or of 

 positive load. (2) Quotients are higher in deficits than in excesses. 

 (3) Quotients tend to be similar, in one species, for both negative 

 loads and positive loads. (4) Quotients are often greatest near 

 zero load; this region of large quotients includes the most usual 

 contents, the most frequent rates of exchange. (5) At great loads 

 the quotients diminish, except in Phascolosoma' s and Bipalium's 

 deficits, whether the chief paths concerned be alimentary tracts or 

 integuments or kidneys. 



