The reason is clear. Here are a hundred male land birds compelled by change of environment to take to the water. Ten of them show an infinitesimal rudimentary webbing between the toes of their feet, and that is a first infinitesimal advantage in swimming. Ten hens are of the same kind. _Left to mere chance_ there is no reason why a season’s mating should allocate the web-footed male to the web-footed female. Each one of the ten males has nine chances to one of paring with a non-advantaged mate, and only one chance of mating with a hen similar to himself and possessing, as he does, this infinitesimal advantageous differentiation. On the average you would have only one couple in each hundred handing on in full even that first tiny advantage to their progeny with a corresponding tiny survival-value. In the case of eighteen others it would be halved, and in the case of a hundred and eighty-one, it would be absent. It is so with each generation. Each little infinitesimal advantage can only be _fully_ handed on to a fraction which is the square of the last, and in even _diminished_ form to a fraction smaller in proportion to the flock in the third generation than in the second. Long before you got anything like an even rudimentary webbed foot the tiny advantage would have been absorbed. The advantage, left to chance, sinks into the common stock. There is no getting away from this conclusion by saying, “Oh! we’re not talking of individuals, we’re talking of great masses.” The masses are made up of individuals, and the mathematical argument is exactly the same whether you are dealing with a hundred or ten million. These four _a priori_ arguments against the theory of Natural Selection as the agent of differentiation in species are as conclusive as arithmetic can make them, and there is really no need for any others—though many others have been urged—e.g. the mathematical chances against one special advantageous variation appearing by pure accident at exactly the time it was needed. But, as I have said, apart from these _a priori_ and sufficient arguments, there are conclusive arguments drawn from actual evidence, and all this evidence is in favour of this _Fixed Type_. A fixed type would be an impossibility under Natural Selection: it goes with a Creator and with Design; and certainly it is true of the real world. Natural Selection, if it had been the agent of Evolution, would have prevented the formation of fixed types. In the old materialist days when Natural Selection was triumphing, its supporters used to say, as we have seen, that it acted “until equilibrium was reached by the organism conforming to its environment.” That was typical of their hiding the weakness of their case under vague phrases which, closely analysed, proved self-contradictory.