But now, suppose there are a million or a trillion in each of the two families; and of these the one trillion attain varying but splendid success along every line of endeavour, while the other trillion fail, more or less completely, along the same lines. What, then, shall we say? What, then, must we say? Unhesitatingly, that there must have been a very decided difference of average faculty. While we might admit the measurable possibility that chance and time and circumstance played a conspicuous and even a determining part in the fortunes of the one pair, yet we could by no means admit the like for any great number of pairs; and when the number of pairs becomes enormously great, the possibility in question becomes vanishingly small--too small to be dealt with in any system of our thought. Here is the given effect: success of the one class, failure of the other. What the cause? Is it mainly, at least, an (average) uniform difference of faculty? This cause is simple and intelligible and self-repeating; if it worked in one case, it would work in all cases and explain everything as easily as any one thing. But the other cause, the conspiracy of chance and time and circumstance, is not self-repeating, and however great the likelihood of a single such chance combination, the likelihood of innumerable such repetitions is inexpressibly small--on the same principle that the chance of throwing heads once is one-half, but the chance of throwing them consecutively twice is only one-fourth, and thrice is only one-eighth, and so on. We need not parade here the mathematical formulæ for the reckoning of the so-called inverse probability of each of these two hypotheses. Common sense tells us at once that the difference of faculty is practically certain, the chance-effect or coincidence-effect is practically impossible. Now, such is the case really presented. On the one side, the generations of generations of Caucasians; all have distinguished themselves by high and varied achievements along every line of activity yet opened up to man. On the other hand, the primitives--the backward races of Australia, particularly of Africa; they seem scarcely yet quite conscious. Not one has done anything historical. The failure is complete and universal. That this uniform and immense diversity is a mere accident, the age-long result of a fortuitous concourse of circumstances, or ascriptible to any such trivialities as those enumerated, is almost incalculably improbable, except we expand the term accident to include the laws of gravitation and the conservation of energy. We might as well say that the different behaviours of two bodies of oxygen and hydrogen were to be "explained as a chance," and did not argue any greater mass in the average molecule of the former.