654 THE PRINCIPLES OF SCIENCE. [CHAP. 



In astronomy singular exceptions might occur, and in an 

 approximate manner they do occur. We may point to the 

 rings of Saturn as objects which, though undoubtedly obey- 

 ing the law of gravity, are yet unique, as far as our obser- 

 vation of the universe has gone. They agree, indeed, with 

 the other bodies of the planetary system in the stability of 

 their movements, which never diverge far from the mean 

 position. There seems to be little doubt that these rings 

 are composed of swarms of small meteoric stones ; formerly 

 they were thought to be solid continuous rings, and mathema- 

 ticians proved that if so constituted an entirely exceptional 

 event might have happened under certain circumstances. 

 Had the rings been exactly uniform all round, and with a 

 centre of gravity coinciding for a moment with that of 

 Saturn, a singular case of unstable equilibrium would have 

 arisen, necessarily resulting in the sudden collapse of the 

 rings, and the fall of their debris upon the surface of the 

 planet. Thus in one single case the theory of gravity would 

 give a result wholly unlike anything else known in the 

 mechanism of the heavens. 



It is possible that we might meet with singular exceptions 

 in crystallography. If a crystal of the second or dimetric 

 system, in which the third axis is usually unequal to either 

 of the other two, happened to have the three axes equal, it 

 might be mistaken for a crystal of the cubic system, but 

 would exhibit different faces and dissimilar properties. 

 There is, again, a possible class of diclinic crystals in which 

 two axes are at right angles and the third axis inclined to 

 the other two. This class is chiefly remarkable for its 

 non-existence, since no crystals 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 diclinic form were merely accidental, 

 and not produced by any general law of molecular consti- 

 tution, its actual occurrence would be infinitely improbable, 

 just as it is infinitely improbable that any star should indi- 

 cate the North Pole with perfect exactness. 



In the curves denoting the relation between the tem- 

 perature and pressure of water there is, as shown by 

 Professor J. Thomson, one very remarkable point entirely 

 unique, at which alone water can remain in the three 



