It must be remembered, that the variations on which Natural Selection must work are in each instance extremely minute, well-nigh infinitesimal. Mr. Darwin was as strongly opposed to the idea of Nature making sudden bounds, as to that of a predetermined course of development. But, he argued, an extra chance of living, however slight, must necessarily tell in the long run, the theory of probabilities giving results as certain as any others in mathematics, and, according to these, we may confidently say that, given sufficient time, the favoured individuals would infallibly distance their competitors. The impressiveness of such an argument depends upon its seemingly mathematical character, which is however wholly fallacious, for the probabilities are all the other way. It is perfectly true that a beneficial variation however slight will confer on its happy possessor a corresponding advantage in the struggle for life, as compared with each _individual_ of the non-favoured herd, but, as to that herd collectively, the chances would, on the contrary, ensure that _some_ of its members should outlive the favoured one. Let us even imagine the advantage of the latter to be very great, great enough to double his chances, so that the odds on his surviving each of his fellows will be two to one. Yet if there be a dozen of them to contend with, the odds will be six to one _against_ his surviving the lot. And what of the actual case of minutest benefits conferred by variation? In order to give them even an equal chance of survival, the numbers of those possessing such advantages must be large in proportion as the advantages themselves are small. Thus, if a variation increases the chance of life by one-thousandth part, so that the odds on its possessor are 1001, against 1000 on each non-possessor, yet unless the number of possessors be to that of non-possessors as 1,000 to 1,001, their collective chances will not even be equal. As it is quite absurd to suppose that casual variations could ever occur in such wholesale fashion, how can it be supposed that, were Natural Selection the only factor operating, minute advantages could be accumulated by variation even in the simplest cases?