PERIODICITY IN HUMAN BEINGS AND MICE 805 



physical periodicities, since the former phenomena do not exhibit the 

 strict regularity of the latter. The "regularity" of data on physiologic 

 periodicity is usually only an approximation. Thus arises the knotty 

 problem of how to acquire a quantitative description of bodily 

 periodicity in terms of sample estimates of period and amplitude. The 

 short-range data, which are quite adequate in order to establish the 

 occurrence of a given physiologic rhythm, no longer are satisfactory 

 — more extensive time series are usually required. To long-range data 

 in turn, mathematical methods may be applied, such as the periodo- 

 gram or correlogram analysis — yet such methods have their limita- 

 tions. The dangers associated with the use of various formulas for 

 periodicity analysis must also be recognized, if we are to apply such 

 mathematical methods fruitfully. Let us therefore note, first, what 

 periodograms are not likely to do reliably for periodicity analysis, be- 

 fore we illustrate their uses. 



In the past, periodograms, among other computational procedures, 

 have repeatedly been employed for the detection of periodicity in a 

 given geophysical or other time series. Similar searches for physiologic 

 periodicity, carried out merely by the appHcation of a mathematical 

 method to an arbitrary biologic time series, are not recommended 

 herein as the procedure of choice, since spurious as well as real periods 

 may thus be described, while real ones occasionally may be concealed 

 (Gumbel et al., 1953). Indeed, different "periodicities" may be 

 obtained from the same time series by the use of different formulas. 

 Along these lines of thought, justified criticisms of the periodogram 

 have been made (Cole, 1957). But by references to such examples, 

 the entire field of periodicity analysis must not be discredited. We can 

 use periodograms for the study of physiologic periodicity without 

 searching for some imaginary period (Koehler et ah, 1956). The 

 method can be applied to phenomena for which, under appropriate 

 circumstances of observation, the reality of a given period has em- 

 pirically been noted and for which, in addition, the statistical signifi- 

 cance of the periodicity has independently been ascertained. If, then, 

 the periodogram will yield periods other than those anticipated, the 

 reality of such periods, in turn, can again be checked empirically, in 

 additional studies. By proceeding along such lines, we minimize the 

 dangers of dealing with spurious periodicities, i.e., with artifacts of the 



