CYCLOGRAM ANALYSIS 



21 



Logarithmic plots (fig. 9) have been little used in our studies so far as the 

 original data are concerned. In logarithmic curves, the logarithm of each 

 term is substituted for the term itself or the data are plotted on paper whose 

 ordinates are divided into logarithmic spacing. The general effect is to les- 

 sen the relative importance of high values and increase that of low values. 



Although not found convenient for use up to the present time, the log- 

 arithmic proposal introduces a general problem whose solution is not herein 

 forthcoming. In expressing the thickness of rings, an absent ring receives 

 the value 0, but such a value in a curve is by ratio indefinitely farther away 

 from the mean (considered as unity) than, for example, 2.00 is, but as drawn 

 in the common curve of rain or tree growth it is an equal distance. Are 

 data such as annual values of rainfall and tree growth best handled in terms 



mm 



2.0 



i.o 



10.5 



10.0 



9.5 



9.0 



8.5 



1820 30 



90 



1900 



10 



20 



40 50 60 70 80 



Logarithms of same +10. 

 Fig. 9 — Logarithmic plot (below) compared with non-logarithmic plot (above). 



30 



of addition and subtraction or by ratios? Should they be regarded as quanti- 

 ties above a base or departures from a mean? When correlation coefficients 

 are taken, the data are merely regarded as departures from a mean and the 

 position of a real basic zero line need not be known. But rainfall and tree- 

 ring values do not cling around a mean in any such manner as micrometer 

 measures of a planet's diameter, for example. 



It is to judge this latter type of observation that normal distribution and 

 probable error were invented. We can evaluate some curves by determining 

 the "distribution" of their values; that is, the frequency of occurrence of 

 each separate value whether considered as a departure from the mean or as 

 an amount above a base. In normal distribution (see fig. 10a) there are 

 many values close to the mean. This is the case in measuring a definite 

 quantity like a planet's diameter. Rainfall data usually give a "skew" 



