opposite sides of these.  If the whole assemblage comprised a sufficient number of men, it would be found that a class with a given deviation from the average in one direction would contain about the same number of individuals as the class at the same distance from the average in the opposite direction.  Taking into account the relative numbers in the several classes and the various degrees to which they depart from the average, the mathematician describes the whole phenomenon of variation in human stature by a concise formula which outlines the so-called “curve of error.”  From his study of a thousand men, he can tell how many there would be in the various classes if he had the measurements of ten thousand individuals, and how many there would be in the still more extreme classes of very short and very tall men which might not be represented among one thousand people.

It is not possible to explain why variation should follow this or any other mathematical law without entering into an unduly extensive discussion of the laws of error.  The mathematicians themselves tell us in general terms that the observations they describe so simply by their formulae follow as the result of so-called chance, by which they mean that the combined operation of numerous, diverse, and uncorrelated factors brings about this result, and not, of course, that there is such a thing as an uncaused event or phenomenon.

Whenever any extensive series of like organisms has been studied with reference to the variations of a particular character, the variations group themselves so as to be described by identical or similar curves of error.  It is certainly significant that this is true for such diverse characters, cited at random from the lists of the literature, as the number of ray-flowers of white daisies, the number of ribs of beech leaves, and of the bands upon the capsules of poppies, for the shades of color of human eyes, for the number of spines on the backs of shrimps, and for the number of days that caterpillars feed before they turn into pupae.

To summarize the foregoing facts, we have learned that variation is universal throughout the living world, and that the primary factors causing organic difference—­the counterparts of human ingenuity in the case of dead mechanisms—­are the natural influences of the environment, of organic physiological activity, and of congenital inheritance.  These factors are accorded different values in the evolution of new species, as we may see more clearly at a later juncture, but the essential point here is that they are not unreal, although they may not as yet be described by science in final analytical terms.

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