on a similar division of the molecule CH 4 into two equivalent parts, H 2 and CH 2 ; (3) acetylene substitution, or the exchange between CH on the one hand and H 3 on the other; and (4) carbon substitution—that is, the substitution of H 4 by an atom of carbon C, which is founded on the law of substitution just as is the methyl substitution. These four cases of substitution render it possible to understand the principal relations of the hydrocarbons. For instance, the law of even numbers is seen from the fact that in all the cases of substitution mentioned the hydrogen atoms increase or decrease by an even number; but as in CH 4 they are likewise even, it follows that no matter how many substitutions are effected there will always be obtained an even number of hydrogen atoms. When H is replaced by CH 3 there is an increase of CH 2 ; when H 2 is replaced by CH 2 there is no increase of hydrogen; in the acetylene substitution CH replaces H 3 , therefore there is an increase of C and a decrease of H 2 ; in the carbon substitution there is a decrease of H 4 . In a similar way the law of limit may be deduced as a corollary of the law of substitution. For the largest possible quantity of hydrogen is introduced by the methyl substitution, since it leads to the addition of CH 2 ; starting from CH 4 we obtain C 2 H 6 , C 3 H 8 , and in general, C n H 2 n +2 , and these contain the greatest possible amount of hydrogen. Unsaturated hydrocarbons, containing less hydrogen, are evidently only formed when the increase of the new molecule derived from methane proceeds from one of the other forms of substitution. When the methyl substitution alone takes place in methane, CH 4 , it is evident that the saturated hydrocarbon formed is C 2 H 6 or (CH 3 )(CH 3 ). This is called ethane . By means of the methylene substitution alone, ethylene , C 2 H 4 , or (CH 2 )(CH 2 ) may be directly obtained from CH 4 , and by the acetylene substitution C 2 H 2 or (CH)(CH), or acetylene , both the latter being unsaturated hydrocarbons. Thus we have all the possible hydrocarbons with two atoms of carbon in the molecule, C 2 H 6 , ethane, C 2 H 4 , ethylene, and C 2 H 2 , acetylene. But in them, according to the law of substitution, the same forms of substitution may be repeated—that is, the methyl, methylene, acetylene, and even carbon substitutions (because C 2 H 6 will still contain hydrogen when C replaces H 4 ) and therefore further substitutions will serve as a source for the production of a fresh series of saturated and unsaturated hydrocarbons, containing more and more carbon in the molecule and, in the case of the acetylene substitution and carbon substitution, containing less and less hydrogen. Thus by means of the law of substitution we can foresee not only the limit C n H 2 n +2 , but an unlimited number of unsaturated hydrocarbons, C n H 2 n , C n H 2 n -2 ... C n H 2( n-m ) , where m varies from 0 to n -1, and where n increases indefinitely. From these facts not only does the existence of a multitude of polymeric hydrocarbons, differing in molecular weight, become intelligible, but it is also seen that there is a possibility of cases of isomerism with the same molecular weight. This polymerism so common to hydrocarbon compounds is already apparent in the first unsaturated series C n H 2 n , because all the terms of this series C 2 H 4 , C 3 H 6 , C 4 H 8 ... C 30 H 60 ... have one and the same composition CH 2 , but different molecular weights, as has been already explained in Chapter VII. The differences in the vapour density, boiling points, and melting points, of the quantities entering into reactions, and the methods of preparation also so clearly tally with the conception of polymerism, that this example will always be the clearest and most conclusive for the illustration of polymerism and molecular weight. Such a case is also met with among other hydrocarbons. Thus benzene, C 6 H 6 , and cinnamene, C 8 H 8 , correspond with the composition of acetylene or to a compound of the composition CH. The first boils at 81°, the second at 144°; the specific gravity of the first is 0·899; that of the second, 0·925, at 0°—that is, here also the boiling point rises with the increase of molecular weight, and so also, as might be expected, does the density.
Cases of isomerism in the restricted sense of the word—that is, when with an identity of composition and of molecular weight, the properties of the substances are different—are very numerous among the hydrocarbons and their derivatives. Such cases are particularly important for the comprehension of