xxix.] EXCEPTIONAL PHENOMENA. 655 



conditions of gas, liquid, and solid in the same vessel It is 

 the triple point at which three lines meet, namely (i) 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. 1 



Divergent Exceptions. 



Closely analogous to singular exceptions are those diver- 

 gent 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 natures, 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. 2 The rise of genius, and the occurrence of 

 extraordinary musical or mathematical faculties, are attri- 

 buted 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. 



1 Max-well's Theory of Heat, (1871), p. 175. 



2 Galton, on the Height and Weight of Boys. Journal of the 

 Anthropological Institute, 1875, p. 174. 



