I now turn to the consideration of the second factor of the theory of selection--heredity. This also, according to Von Hartmann is not a mechanical principle. Darwin himself has now become convinced how great is the probability against the hereditary retention of modifications which, whether feebly or strongly pronounced, appear _only in single individuals_, _i.e._ of those so-called “fortuitous” variations which are not the expression of a directive developmental principle. “But as among the numberless possible directions of an indefinite variability, useful modifications can only occur in single cases, Darwin has by this supplementary admission himself retracted an inadmissible assumption of his theory of selection,” and so forth. A “regular, designed tendency to variation, acting from within and contemporaneously affecting a large number of individuals,” must therefore be assumed “in order to insure the by itself improbable inheritance.” But even from the unbounded variability laid down by the author, it by no means follows that useful variations can only occur in single individuals. In the whole category of _quantitative_ variations the reverse is always the case. Is it the lengthening of some part that is concerned; so would a large number of individuals always possess the useful variation, since we are not dealing with an _absolute_ enlargement, but only with the fact that the part concerned is longer than in other individuals.[292] But if _qualitative_ variations come into consideration, it may be asked whether Darwin’s “supplementary admission” does not go too far. Such calculations as those quoted by Darwin from the article in the _North British Review_ of March 1867 are extremely deceptive, since we have no means of measuring the amount of protection afforded by a useful variation, and we can therefore hardly compute with any certainty, in how great a percentage of individuals a change must contemporaneously occur in order to have a chance of becoming transferred to the following generation. If our blue rock-pigeon could exist in a polar climate, and if we had the power of introducing it gradually, but not suddenly, into these regions in a wild state, who can doubt that it would assume the white colour of all polar animals? Nevertheless, among wild rock-pigeons white varieties do not occur more frequently than among swallows, crows, or magpies. Or must the white colour of polar animals, the yellow colour of desert species, and the green colour of leaf-frequenting forms, be always referred to a “regular, designed, fixed tendency to variation acting from within,” and causing a “large number of individuals” to vary in a similar manner?