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. 1 to 7) that each part varies to a considerable extent, _independently_, the materials constantly ready for natural selection to act upon are abundant in quantity and very varied in kind. Almost any combination of variations of distinct parts will be available, where required; and this, as we shall see further on, obviates one of the most weighty objections which have been urged against the efficiency of natural selection in producing new species, genera, and higher groups. [Illustration: FIG. 12.] _Variation in the Mammalia._ Owing to the generally large size of this class of animals, and the comparatively small number of naturalists who study them, large series of specimens are only occasionally examined and compared, and thus the materials for determining the question of their variability in a state of nature are comparatively scanty. The fact that our domestic animals belonging to this group, especially dogs, present extreme varieties not surpassed even by pigeons and poultry among birds, renders it almost certain that an equal amount of variability exists in the wild state; and this is confirmed by the example of a species of squirrel (Sciurus carolinensis), of which sixteen specimens, all males and all taken in Florida, were measured and tabulated by Mr. Allen. The diagram here given shows, that, both the general amount of the variation and the independent variability of the several members of the body, accord completely with the variations so common in the class of birds; while their amount and their independence of each other are even greater than usual. _Variation in the Internal Organs of Animals._