by side like a long row of park palings between the same limits, their upper outline will be identical.  Moreover, it will run smoothly and not in irregular steps.  The theoretical interpretation of the smoothness of outline is that the individual differences in the objects are caused by different combinations of a large number of minute influences; and as the difference between any two adjacent objects in a long row must depend on the absence in one of them of some single influence, or of only a few such, that were present in the other, the amount of difference will be insensible.  Whenever we find on trial that the outline of the row is not a flowing curve, the presumption is that the objects are not all of the same species, but that part are affected by some large influence from which the others are free; consequently there is a confusion of curves.  This presumption is never found to be belied.

It is unfortunate for the peace of mind of the statistician that the influences by which the magnitudes, etc., of the objects are determined can seldom if ever be roundly classed into large and small, without intermediates.  He is tantalised by the hope of getting hold of sub-groups of sufficient size that shall contain no individuals except those belonging strictly to the same species, and he is almost constantly baffled.  In the end he is obliged to exercise his judgment as to the limit at which he should cease to subdivide.  If he subdivides very frequently, the groups become too small to have statistical value; if less frequently, the groups will be less truly specific.

A species may be defined as a group of objects whose individual differences are wholly due to different combinations of the same set of minute causes, no one of which is so powerful as to be able by itself to make any sensible difference in the result.  A well-known mathematical consequence flows from this, which is also universally observed as a fact, namely, that in all species the number of individuals who differ from the average value, up to any given amount, is much greater than the number who differ more than that amount, and up to the double of it.  In short, if an assorted series be represented by upright lines arranged side by side along a horizontal base at equal distances apart, and of lengths proportionate to the magnitude of the quality in the corresponding objects, then their shape will always resemble that shown in Fig. 1.

The form of the bounding curve resembles that which is called in architectural language an ogive, from “augive,” an old French word for a cup, the figure being not unlike the upper half of a cup lying sideways with its axis horizontal.  In consequence of the multitude of mediocre values, we always find that on either side of the middlemost ordinate Cc, which is the median value and may be accepted as the average, there is a much less rapid change of height than elsewhere.  If the figure were pulled out sideways to make it accord with such physical conceptions as that of a row of men standing side by side, the middle part of the curve would be apparently horizontal.