UNIFORMITIES AND COMPARISONS AMONG COMPONENTS 369 



'38). Anyone can within a few minutes construct a curve (like A, 

 fig. 180) for heart frequencies in man. 



With respect to rates of exchange, the sequences are bound up 

 with those of load. The same five states may be distinguished in 

 the exchange diagram (B and C, fig. 180) whether net rates, total 

 rates, or certain partial rates are measured. In instances in which 

 gains and losses have been measured, one exceeds the other during 

 any transitional state and the converse relation holds during the 

 recovery state. Moreover, since net rate integrated with respect 

 to time equals load, the areas of difference between total gain and 

 total loss are equivalent to maximal load, and very often are equal 

 to one another (M = N). When M does not equal N, it is perti- 

 nent to inquire in what identifiable respects state V differs from 

 state I. 



Further consideration may be given to recovery states. Kates 

 of recovery are rates of decrease of load. Some of the loads stud- 

 ied follow exponential equations of the type AC = ae"*"', as was early 

 shown by Michaelis ('07). Differentiating with respect to time, 

 SC/At = R = -a/i;e-" (§71). 



The load throughout the five states might be analogous to the 

 height of a ball thrown upward. The height attained depends on 

 several distinct factors; the fall (recovery) exhibits accelerations 

 free of the force of the throw. In ballistics the usual trajectory is 

 a parabola ; in physiological tolerance curves it is often two expo- 

 nentials. 



Certainly the relation between load and time is not an invari- 

 able one for diverse components, nor for one component in many 

 species. No augmentation of exchange may be evident for 0.3 hour 

 (water excess in dog), or the load may be proportional to time 

 (ethyl alcohol in dog), or no recovery may be measurable (ampu- 

 tated leg in dog). The last part of recovery may take as long as 

 the individual lives ; the first part may be infinitely slow or fast. 



In practice, recoveries are compared quantitatively either in a 

 uniform fraction of the recovery {^C/a) or within an arbitrary 

 interval of time during the recovery (At). With each set of data 

 it is therefore necessary to designate the value of 1/a or of At that 

 is used. Very often the half -life (tq) of the load {a = 2) is a suit- 

 able means of comparison, and A: = In 0.5/tq. However, when, as 

 is often the case, the entire curve of loads during recovery is known. 



