Configurations formed by Floating Magnets. 105 



from it. Phosphorus, sulphur, and carbon give instances of 

 allotropy. Thus graphite and the diamond are both carbon ; 

 yet how different are they! One is soft, opaque, black, and 

 with a metallic lustre ; the other is the hardest of bodies, 

 transparent, and resplendent by its refractive action on light. 

 Graphite is a good conductor of electricity, crystallizes in 

 small six-sided tables which belong either to the hexagonal or 

 monoclinic system, and has a specific gravity of 2*2 ; while 

 the diamond is a bad conductor of electricity, crystallizes in 

 the monometric system, and has a specific gravity of 3*5. 

 Whenever an element or a compound takes two different 

 crystal-forms, these different crystals always differ in their 

 density. 



These differences of form and density shown in allotropy 

 and isomerism are well illustrated in the configurations which 

 are formed of the same number of magnets. Take figures 5 a 

 and 5 b. The first is a pentagon ; the second is a square with 

 a magnet in its centre. The forces in these floating magnets 

 and in the superposed magnet remain the same in all the con- 

 figurations; and these have all been printed from needles floated 

 in water whose surface was at a constant perpendicular dis- 

 tance from the pole of the superposed magnet. Thus we see 

 how the same atoms, endowed with forces of the same strength, 

 may take different relative positions, and thus produce very 

 different crystal-forms in the same matter. We may take 5 a 

 for an illustration of the atomic arrangement in the diamond, 

 while 5 b may stand for graphite. But there is always a 

 change of density accompanying the different forms in allo- 

 tropy ; and this fact is also illustrated by configurations 5 a and 

 5b. In bodies formed of the same kind of elementary atoms, 

 as in allotropy, it is evident that their relative densities will bo 

 directly as the number of atoms contained in the unit of 

 volume. As our configurations illustrating allotropy contain 

 the same number of magnets, it follows that the relative densi- 

 ties of these configurations are inversely as their areas. Now 

 the area of 5 a (measured on the original prints) is 818 square 

 millimetres, and the area of 5b is 992 square millimetres; 

 hence the density of 5a is to the density of 5b as 992 is to 

 818. Thus we see how the arrangement of magnets in 5 a 

 may stand for the molecular structure in the diamond, while 

 5 b may stand for that in graphite. 



Numerous instances exist in chemistry of the same elements 

 combined in the same proportions, yet producing bodies crys- 

 tallizing in different forms, and having different densities, 

 colour, transparency, hardness, &c. As examples of this phe- 

 nomenon of isomerism we may cite calcium carbonate, which 



