152 THE PRINCIPLES OF SCIENCE. 



diamagnetic substances are capable of polarity C = CD, it 

 follows by substitution that all substances are capable of 

 polarity, or A = AD. We may divide the class substance 

 again into the three subclasses, solid, liquid, and gas ; 

 and if we can show that in each of these forms it obeys 

 Carnot's thermodynamic law, it follows that all substances 

 obey that law. Similarly we may show that all verte- 

 brate animals possess red blood, if we can show separately 

 that fish, reptiles, birds, marsupials, and mammals possess 

 red blood, there being, as far as is known, only five 

 principal subclasses of vertebrata. 



Our inductions will often be embarrassed by exceptions, 

 real or apparent. We might affirm that all gems are 

 incombustible were not diamond undoubtedly combustible. 

 Nothing seems more evident than that all the metals are 

 opaque until we examine them in fine films, when gold 

 and silver are found to be transparent. All plants absorb 

 carbonic acid except certain fungi ; all the bodies of the 

 planetary system have a progressive motion from west to 

 east, except the sateUites of Uranus and Neptune. Even 

 some of the profoundest laws of matter are not quite 

 universal ; all solids expand by heat except india-rubber, 

 and possibly a few other substances ; all liquids which 

 have been tested expand by heat except water below 4C 

 and fused bismuth ; all gases have a coefficient of expan- 

 sion increasing with the temperature except hydrogen. 

 In a later chapter I shall consider how such anomalous 

 cases may be regarded and classified ; here we have only 

 to express them in a consistent manner in our nota- 

 tion. 



Let us take the case of the transparency of metals, and 

 assign the terms thus 



A = metal D = iron 



B = gold E, F &c. = copper, lead, &c. 



C = silver X = opaque. 



