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the moon had deviated exceedingly from that orbit in which it has always moved; or the position of the earth's axis had suddenly changed; or the atmospherical refraction had been increased to an extent that was never known. Any of all these events must have affected such a vast number of others, that, as no such thing was perceived, an incredible body of evidence is brought to ascertain the continuance of the moon in her regular course. The barrier that generalization and the explanation of causes thus raises against credulity and superstition, the way in which it multiplies the evidence of experience, is highly deserving of attention, and is likely to have a great influence on the future fortunes of the human race.
Against the uniformity, therefore, of such laws, it is impossible for testimony to prevail. But with those laws that are imperfectly known, and that admit of many exceptions, the violations are not so improbable, but that testimony may be sufficient to establish them. In our own time it has happened, that the testimony produced in support of a set of extraordinary facts, has been confirmed by a scrupulous examination into the natural history of the facts themselves. When the stones which were said to have fallen from the heavens came to be chemically analyzed, they were found to have the same characters, and to consist of the same ingredients, nearly in the same proportions. Now, let
us suppose two such instances:-the first person gives the stones into the hands of a naturalist, and their characters are ascertained; the second does so likewise, and the stones have the same character. Now, if this character were one which, like that of sandstone, or of limestone, belongs to a numerous class, the chance of the agreement might be considerable, because the chance that the second observer should fall on a stone exactly of the same species with the first, would be as the number of the stones existing of that species, divided by the whole number of stones, of all different species existing on the face of the earth. This, with regard to sandstone or limestone, might be a large fraction; and the coincidence of the two testimonies in a falsehood might not be extremely improbable. But if the species is a very rare one, the probability of the coincidence becomes extremely small. Suppose, for example, that it is a species, numerous in a medium degree; and as there are reckoned about 261 species, let us suppose that the individuals of the species to which the meteoric stones belong amount toth part of all the stones on the surface of the earth. The accidental coincidence of the second witness with the first is denoted by ; of a third with the other two, by
by (261)3; and so on.
As there are more than ten
such cases, the chance of deceit or imposture is not
more than (261)9: that is, 1 divided by the 9th power of 261, or by a number so large as to consist of 22 places. This fraction, though extremely small, is vastly greater than the truth. The individuals of this species, instead of making a 261th part of all the stones on the surface of the earth, make, so far as we know, no part of them at all. Here, therefore, we have a testimony confirmed, and rendered quite independent of our previous knowledge of the veracity of the witnesses.
The truth of the descent of these stones on the evidence of testimony alone, would have been long before it gained entire credit; and scepticism with respect to it would have been just and philosophical, In certain states of their information, men may, on good grounds, reject the truth altogether.
The way in which probability is affected by the indefinite multiplication of events, is a remarkable part of this theory. If out of a system of events governed by chance (or by no perceivable law) you take a small number, you will find great irregularity, and nothing that looks like order, or obedience to a general rule. Increase the number of events, or take in a larger extent of the domain over which you suppose chance to preside, you will find the irregularities bear a much less proportion
to the whole; they will in a certain degree compensate for one another; and something like order and regularity will begin to emerge. In proportion as the events are further multiplied, this convergency will become more apparent; and in summing up the total amount, the events will appear adjusted to one another, by rules, from which hardly any deviation can be perceived.
Thus, in considering the subject of life and death; if we take a small extent of country, or few people, a single parish for instance, nothing like a general rule will be discovered. The proportion of the deaths to the numbers alive, or to the numbers born; of those living at any age to those above or below that age,-all this will appear the most different in one year, compared with the next; or in one district compared with another. But subject to your examination the parish registers of a great country, or a populous city, and the facts will appear quite different. You will find the proportion of those that die annually out of a given number of inhabitants fixed with great precision, as well as of those that are born, and that have reached to the different periods of life. In the first case, the irregularities bear a great proportion to the whole in the second, they compensate for one another; and a rule emerges, from which the deviations on opposite sides appear almost equal.
This is true not only of natural events, but of
those that arise from the institutions of society, and the transactions of men with one another.Hence insurance against fire, and the dangers of the sea. Nothing is less subject to calculation, than the fate of a particular ship, or a particular house, though under given circumstances. But let a vast number of ships, in these circumstances, or of houses, be included, and the chance of their perishing, to that of their being preserved, is matter of calculation founded on experience, and reduced to such certainty, that men daily stake their fortunes on the accuracy of the results.
This is true, even where chance might be supposed to predominate the most; and where the causes that produce particular effects, are the most independent of one another.
Laplace observes, that at Paris, in ordinary times, the number of letters returned to the Post Office, the persons to whom they were directed not being found, was nearly the same from one year to another. We have heard the same remark stated of the Dead Letter Office, as it is called, in London.
Such is the consequence of the multiplication of the events least under the control of fixed causes: And the instances just given, are sufficient to illustrate the truth of the general proposition; which Laplace has thus stated :
"The recurrences of events that depend on