In speaking of the effect of the average in thus diminishing the irregularities which present themselves in the details, the attention of the student must be prominently directed to the point, that it is not the _absolute_ but the _relative_ irregularities which thus tend to diminish without limit. This idea will be familiar enough to the mathematician, but to others it may require some reflection in order to grasp it clearly. The absolute divergences and irregularities, so far from diminishing, show a disposition to increase, and this (it may be) without limit, though their relative importance shows a corresponding disposition to diminish without limit. Thus in the case of tossing a penny, if we take a few throws, say ten, it is decidedly unlikely that there should be a difference of six between the numbers of heads and tails; that is, that there should be as many as eight heads and therefore as few as two tails, or _vice versâ_. But take a thousand throws, and it becomes in turn exceedingly likely that there should be as much as, or more than, a difference of six between the respective numbers. On the other hand the _proportion_ of heads to tails in the case of the thousand throws will be very much nearer to unity, in most cases, than when we only took ten. In other words, the longer a game of chance continues the larger are the spells and runs of luck in themselves, but the less their relative proportions to the whole amounts involved. 4. In speaking as above of events or things as to the details of which we know little or nothing, it is not of course implied that our ignorance about them is complete and universal, or, what comes to the same thing, that irregularity may be observed in all their qualities. All that is meant is that there are _some_ qualities or marks in them, the existence of which we are not able to predicate with certainty in the individuals. With regard to all their other qualities there may be the utmost uniformity, and consequently the most complete certainty. The irregularity in the length of human life is notorious, but no one doubts the existence of such organs as a heart and brains in any person whom he happens to meet. And even in the qualities in which the irregularity is observed, there are often, indeed generally, positive limits within which it will be found to be confined. No person, for instance, can calculate what may be the length of any particular life, but we feel perfectly certain that it will not stretch out to 150 years. The irregularity of the individual instances is only shown in certain respects, as e.g. the length of the life, and even in these respects it has its limits. The same remark will apply to most of the other examples with which we shall be concerned. The disorder in fact is not universal and unlimited, it only prevails in certain directions and up to certain points.