9] [Illustration: FIG.

10.] [Illustration: FIG.

11.] In order fully to appreciate the teaching of these diagrams, we must remember, that, whatever kind and amount of variations are exhibited by the few specimens here compared, would be greatly extended and brought into symmetrical form if large numbers--thousands or millions--were subjected to the same process of measurement and registration.

We know, from the general law which governs variations from a mean value, that with increasing numbers the range of variation of each part would increase also, at first rather rapidly and then more slowly; while gaps and irregularities would be gradually filled up, and at length the distribution of the dots would indicate a tolerably regular curve of double curvature like those shown in Fig.11.The great divergence of the dots, when even a few specimens are compared, shows that the curve, with high numbers, would be a flat one like the lower curve in the illustration here given.

This being the case it would follow that a very large proportion of the total number of individuals constituting a species would diverge considerably from its average condition as regards each part or organ; and as we know from the previous diagrams of variation (Figs.