have misled the human intellect throughout the historical period. Pythagoras imagined a connection between the seven planets and the seven intervals of the monochord. The alchemists were never tired of drawing inferences from the coincidence in numbers of the seven planets and the seven metals, not to speak of the seven days of the week.
A singular circumstance was pointed out concerning the dimensions of the earth, sun, and moon; the sun’s diameter was almost exactly 110 times as great as the earth’s diameter, while in almost exactly the same ratio the mean distance of the earth was greater than the sun’s diameter, and the mean distance of the moon from the earth was greater than the moon’s diameter. The agreement was so close that it might have proved more than casual, but its fortuitous character is now sufficiently shown by the fact, that the coincidence ceases to be remarkable when we adopt the amended dimensions of the planetary system.
A considerable number of the elements have atomic weights, which are apparently exact multiples of that of hydrogen. If this be not a law to be ultimately extended to all the elements, as supposed by Prout, it is a most remarkable coincidence. But, as I have observed, we have no means of absolutely discriminating accidental coincidences from those which imply a deep producing cause. A coincidence must either be very strong in itself, or it must be corroborated by some explanation or connection with other laws of nature. Little attention was ever given to the coincidence concerning the dimensions of the sun, earth, and moon, because it was not very strong in itself, and had no apparent connection with the principles of physical astronomy. Prout’s Law bears more probability because it would bring the constitution of the elements themselves in close connection with the atomic theory, representing them as built up out of a simpler substance.
In historical and social matters, coincidences are frequently pointed out which are due to chance, although there is always a strong popular tendency to regard them as the work of design, or as having some hidden meaning. If to 1794, the number of the year in which Robespierre fell, we add the sum of its digits, the result is 1815, the year in which Napoleon fell; the repetition of the process gives 1830 the year in which Charles the Tenth abdicated. Again, the French Chamber of Deputies, in 1830, consisted of 402 members, of whom 221 formed the party called “La queue de Robespierre,” while the remainder, 181 in number, were named “Les honnêtes gens.” If we give to each letter a numerical value corresponding to its place in the alphabet, it will be found that the sum of the values of the letters in each name exactly indicates the number of the party.
A number of such coincidences, often of a very curious character, might be adduced, and the probability against the occurrence of each is enormously great. They must be attributed to chance, because they cannot be shown to have the slightest connection with the general laws of nature; but persons are often found to be greatly influenced by such coincidences, regarding them as evidence of fatality, that is of a system of causation governing human affairs independently of the ordinary laws of nature. Let it be remembered that there are an infinite number of opportunities in life for some strange coincidence to present itself, so that it is quite to be expected that remarkable conjunctions will sometimes happen.
In all matters of judicial evidence, we must bear in mind the probable occurrence from time to time of unaccountable coincidences. The Roman jurists refused for this reason to invalidate a testamentary deed, the witnesses of which had sealed it with the same seal. For witnesses independently using their own seals might be found to possess identical ones by accident.28 It is well known that circumstantial evidence of apparently overwhelming completeness will sometimes lead to a mistaken judgment, and as absolute certainty is never really attainable, every court must act upon probabilities of a high amount, and in a certain small proportion