74 PHYSIOLOGICAL EEGULATIONS 



such kind of regulation prevails. Instead, the physiological states 

 of water content turn out to be random according to most criteria 

 of randomness, but confined within the restricted range permitted 

 to them. Two problems therefore arise, to see in how many re- 

 spects the time-series of water contents is random, and to derive 

 parameters by means of which the variability among water con- 

 tents may be compared with the variabilities of other components. 

 Data consist in the mere sequence of body weights (fig. 43) in 

 a dog consuming the same kind and amount of food each day, living 

 under conditions arbitrarily fixed. The important aspect is that 

 measurements are made at equal intervals of time in an individual 

 upon uniform regime. 



(1) There is a marked trend in the series. Hence to analyze 

 the fluctuations as deviations from a mean (C.V. ± 2.09) is of no 

 significance for the study of regulation of water content as such. 



(2) The trend may be found (B = 17.335 kg. + 0.0460t), and 

 the fluctuations may be regarded as deviations from it. The root 

 mean square of this deviation amounts to only ±: 0.62% of Bm- 



(3) More simply, first differences between successive values 

 may be taken, their root mean square obtained, and divided by V2 

 to correct for the fact that each value enters twice in the series. 

 This parameter I designate standard difference, and relative to the 

 mean ordinate, coefiicient of difference (CA). Here CA is ±: 0.67% 

 of Bm. Only on one-third of days is the shift of weight greater 

 than this. 



The latter two parameters, which are in any random series (as 

 here) identical, serve to characterize fluctuations. They do not, 

 however, utilize all the information about temporal sequence. In 

 that lies more grist for the algebraic mill. 



(4) For instance, the frequency of inversions of body weight 

 may be counted. In a random series they occur in 50 per cent of 

 the first differences. Here they occur 73 ± 10.2 per cent of the 

 times, which is not very significantly different. After the ± sign 

 the standard error is shown. 



(5) Frequency of movements toward the line of trend may be 

 counted. Randomly they occur in 75 per cent of the first differ- 

 ences ; here they occur in 64 ± 10.0 per cent. 



(6) Numbers of points succeeding in one direction may be ob- 

 served. Such a succession is termed a run, and when first and last 

 point are both included in each run, it randomly consists of 2.5 



