three conditions of gas, liquid, and solid in the same vessel. It is the triple point at which three lines meet, namely (1) the steam line, which shows at what temperatures and pressures water is just upon the point of becoming gaseous; (2) the ice line, showing when ice is just about to melt; and (3) the hoar-frost line, which similarly indicates the pressures and temperatures at which ice is capable of passing directly into the state of gaseous vapour.6
Divergent Exceptions.
Closely analogous to singular exceptions are those divergent exceptions, in which a phenomenon manifests itself in unusual magnitude or character, without becoming subject to peculiar laws. Thus in throwing ten coins, it happened in four cases out of 2,048 throws, that all the coins fell with heads uppermost (p. 208); these would usually be regarded as very singular events, and, according to the theory of probabilities, they would be rare; yet they proceed only from an unusual conjunction of accidental events, and from no really exceptional causes. In all classes of natural phenomena we may expect to meet with similar divergencies from the average, sometimes due merely to the principles of probability, sometimes to deeper reasons. Among every large collection of persons, we shall probably find some persons who are remarkably large or remarkably small, giants or dwarfs, whether in bodily or mental conformation. Such cases appear to be not mere lusus naturæ, since they occur with a frequency closely accordant with the law of error or divergence from an average, as shown by Quetelet and Mr. Galton.7 The rise of genius, and the occurrence of extraordinary musical or mathematical faculties, are attributed by Mr. Galton to the same principle of divergence.
When several distinct forces happen to concur together, we may have surprising or alarming results. Great storms, floods, droughts, and other extreme deviations from the average condition of the atmosphere thus arise. They must be expected to happen from time to time, and will yet be very infrequent compared with minor disturbances. They are not anomalous but only extreme events, analogous to extreme runs of luck. There seems, indeed, to be a fallacious impression in the minds of many persons, that the theory of probabilities necessitates uniformity in the happening of events, so that in the same space of time there will always be nearly the same number of railway accidents and murders. Buckle has superficially remarked upon the constancy of such events as ascertained by Quetelet, and some of his readers acquire the false notion that there is a mysterious inexorable law producing uniformity in human affairs. But nothing can be more opposed to the teachings of the theory of probability, which always contemplates the occurrence of unusual runs of luck. That theory shows the great improbability that the number of railway accidents per month should be always equal, or nearly so. The public attention is strongly attracted to any unusual conjunction of events, and there is a fallacious tendency to suppose that such conjunction must be due to a peculiar new cause coming into operation. Unless it can be clearly shown that such unusual conjunctions occur more frequently than they should do according to the theory of probabilities, we should regard them as merely divergent exceptions.
Eclipses and remarkable conjunctions of the heavenly bodies may also be regarded as results of ordinary laws which nevertheless appear to break the regular course of nature, and never fail to excite surprise. Such events vary greatly in frequency. One or other of the satellites of Jupiter is eclipsed almost every day, but the simultaneous eclipse of three satellites can only take place, according to the calculations of Wargentin, after the lapse of 1,317,900 years. The relations of the four satellites are so remarkable, that it is actually impossible, according to the theory of gravity, that they should all suffer eclipse simultaneously. But it may