320 THE PRINCIPLES OF SCIENCE. 



have yet been proved to have such axes. It seems likely 

 that the class would constitute only a singular case of the 

 more general triclinic system, in which all three axes are 

 inclined to each other at various angles. Now if the di- 

 clinic form were merely accidental, and not necessitated 

 by any general law of molecular constitution, its actual 

 occurrence would be infinitely improbable, just as it is 

 infinitely improbable that any star should indicate the 

 North Pole with perfect exactness. 



In the curves denoting the relation between the temper- 

 ature and pressure of water there is one very remarkable 

 point entirely single and unique, at which alone water 

 can remain in the three conditions of gas, liquid, and solid 

 in the same vessel. It is the point at which three curves 

 intersect, namely, the steam line showing at what temper- 

 atures and pressures water is just upon the point of be- 

 coming gaseous, and other similar lines which show when 

 ice is just on the point of melting, and when ice is just 

 about to assume the gaseous state directly. 



Divergent Exceptions. 



Closely analogous to singular exceptions are those diver- 

 gent exceptions, in which a phenomenon manifests itself 

 in very unusual magnitude or character, without however 

 in any degree becoming subject to peculiar laws. Thus 

 in throwing ten coins, it happened in four cases out of 

 2048 throws, that all the coins fell with heads uppermost 

 (vol. i. p. 238) ; these would usually be regarded as very 

 singular events, and, according to the theory of proba- 

 bilities, they would be comparatively very 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 



