On the Interpretation of Frequency Curves in Biology

§ i. If one measures the same characteristic of a great number of individuals of one species (or of a great number of equal organs of one individual), one generally will find different values. If all values occurred equally often life would be impossible: rats as big as elephants and men as small as fleas would exist. And if the size of all the characteristics was distributed at random all individuals would have a different form. Happily there seems always to exist a certain system in the results of our measurements. Individuals showing a certain average of the measured characteristic are most frequent, while individuals with a deviating value occur the rarer the greater the deviation from this is. In order to compare two different characteristics of one species, or the same characteristic of two different species, it is necessary to measure a great number of individuals, for if one has measured only one individual for each characteristic (or for each species) it would be impossible to deduce a general law from the results. Perhaps one would find just the reverse in repeating the experiment. To get a good survey of the results it is desirable to plot them in a frequency curve, this means that one plots the results of the measurements against the number of individuals in which that result is found. To make the argumentation less abstract we will limit ourselves to the discussion of the frequency curves of the length of plants, and we will suppose that this length is only the result of a growthprocess. This means that we suppose that the differences in the initial-length are small compared with the differences in the final length. In macroscopic methods of measuring this will generally hold, in microscopic often not. The length of a cell for instance will not only depend on its growth but also on its length directly after the division of Its mother cell. Almost all frequency curves of gradually changing objects, however, originate in a manner comparable to a growth-process.