274 THE PRINCIPLES OF SCIENCE. 



probably assert with safety that between whatever points 

 of temperature we examined ice, there would be found 

 some indication, doubtless almost infinitesimally small, 

 of the apparently abrupt change which was to occur at a 

 higher temperature. It might also be pointed out that 

 all the most important and apparently simple physical 

 laws, such as those of Boyle and Marriotte, Dalton and 

 Gay-Lussac, &c., are only approximately true, and the 

 divergences from observation are forewarnings of abrupt 

 changes, which would otherwise break the law of con- 

 tinuity. 



Secondly, it must be remembered that mathematical 

 laws of any complexity will probably present singular 

 cases or negative results, which may present the appear- 

 ance of discontinuity, as when the law of refraction sud- 

 denly yields us with perfect abruptness the entirely 

 different phenomenon of total internal reflection. In the 

 undulatory theory there is no real change of law between 

 the phenomenon of refraction and that of reflection. 



Faraday in the earlier part of his career found so many 

 substances possessing more or less magnetic power, that 

 he ventured on a great generalization, and asserted that 

 all bodies shared in the magnetic property of iron. His 

 mistake, as he afterwards himself discovered, consisted in 

 overlooking the fact that though magnetic in a certain 

 sense, some substances might have negative magnetism, 

 and be repelled instead of attracted by the magnet. 

 Between magnetism and diamagnetism there must be a 

 zero near or even at which some substances mav be 



i 



classed, but otherwise magnetic properties appear to be 

 universally present in matter. 



Thirdly, where we might expect to find a uniform 

 mathematical law prevailing, the law may undergo abrupt 

 change at singular points, and actual discontinuity may 

 arise. We may sometimes be in danger of treating under 



