compounds. At the present day the investigation of the 'constitution' or 'structure' of chemical compounds is one of the chief problems of the science; more particularly is this the case in organic chemistry, which treats of the compounds of carbon. In the course of the last fifty years these investigations have been brought to such a state of perfection, that it is now usual to dogmatically insert the results of such investigations in text-books as the fixed truth, without giving any exact account of the methods by which such intimate knowledge has been achieved.

It is desirable to know the exact grounds on which our knowledge rests, not only in the interests of those who specially devote themselves to such subjects, but also in the interests of the general history of civilisation and the history of science in particular. These investigations form one of the most striking examples of the power of the mind to penetrate into things which are as a sealed book to our senses alone. The path which the science of chemistry pursued to attain its present position was long, and not entirely free from error. But in looking back we can separate the essential from the non-essential and gain without difficulty a clear idea of the chief features of this development.

The chief difference between our present views and the older conceptions consists in this: formerly it was more or less explicitly assumed that a chemical compound was held together by the total attractive force of the affinities of all the atoms contained in it, but as our knowledge increased it was gradually recognised that, although the total attractive force is not without influence, the real chemical union is between atom and atom and that the atoms are attached to each other like the links in a chain, the continuity ceasing if even a single link of the chain is removed. This kind of combination is termed atomic linking'; the idea involved was not a sudden growth, but was the gradual outcome of previous conceptions.

The necessity of studying the atoms themselves was clearly stated by A. Kekulé in 1857, and by A. S. Couper in 1858. The doctrine of atomic linking is the outcome of the investigation of organic compounds, and at the present day it is

chiefly applied to organic bodies; but many conclusions as to the constitution of inorganic compounds have been deduced by its aid.

The theory of atomic linking first gave a satisfactory explanation of the observation that two or more chemical compounds having the same composition may exhibit widely different properties. This remarkable phenomenon has long been known as 'isomerism,' from loos, same, and μépos, the part. Isomeric bodies are those which contain the same constituents, ἴσα μέρη. We distinguish between metamerism' and 'polymerism'; metamerism embraces those cases in which the constituents are present in exactly the same number and quantity, but are differently arranged: the grouping of the constituents has been altered by a change of position, 'metastasis.' 'Polymerism,' or, better, 'pleomerism,' applies to those compounds in which the relative proportion between the constituents is the same, but the absolute number of atoms contained in the molecular weight of one compound is double or treble the number contained in the other.

There are several methods of investigating atomic linking which mutually support and supplement one another. In many simple cases the atomic linking can be deduced on purely theoretical grounds from the composition and molecular weight of the compound and the chemical valency of its constituents. But this can be done only when a single form of combination is possible, and the composition only permits of one interpretation. When the conditions are not so simple we make use of analysis and synthesis, assuming that those constituents which remain combined together when a compound is decomposed were previously united, and inversely in building up a compound, the parts which were united before remain united after the combination has taken place. This assumption is not always correct. Finally, we have a very important aid to such investigations, in the connection which has been established by innumerable comparisons between the chemical and physical properties of a body and its atomic linking.

§ 45. Theoretical Determination of the Possible Forms of Combination. After the composition and the molecular weight

of a compound have been empirically determined, the next question is to ascertain the manner in which the atoms are linked together. This is a purely mathematical problem and the answer can, when necessary, be calculated by permutations. It is obvious that any indefinite number of atoms cannot unite together to form distinct compounds: for instance, the number of monovalent atoms is limited, as each monovalent atom can only unite with one other atom, and cannot lengthen the chain to any greater extent. Compounds composed entirely of monovalent atoms can only exist in the form represented by type I. (§ 40). Compounds composed of one polyvalent atom and several monovalent atoms exhibit forms exemplified by types II. to VIII. The number of monovalent atoms which can enter into combination corresponds to the valency of the polyvalent atom. If a second or third polyvalent atom is added, then two valencies are required for the linking of each additional polyvalent atom, and are, therefore, not available for union with monovalent atoms. The number of monovalent atoms is increased by a number equal to two less than the valency of the new polyvalent atom. If n1, n1, nz, n, represent the number of mono-, di-, tri- and tetra-valent atoms, then the maximum number of monovalent atoms will be

n1 =2n2+3n3+4n4 +5n5 +6n+7n,+8n ̧

−2(n2+ng+ N 4 + N5 + NË + N7 + n − 1)

=2+1n3+2n + 3n5 + 4n6 + 5n7 +6n ̧

In organic compounds, which usually contain only mono-, di-, tri-, and tetra-valent atoms,

n1 =2+1n ̧+2n4•

The number of divalent atoms has no influence on the number of monovalent atoms. Each trivalent atom increases the number of possible monovalent atoms by one, and each tetravalent atom by two. As no compounds are known in which the number n, of monovalent atoms is greater than is here indicated, this is regarded as a confirmation of the theories of valency and of atomic linking.

If there is only one polyvalent atom in the molecule then

only one constitution is possible, even when the monovalent atoms differ in their nature, because the valencies of one and the same atom must be held to be equivalent (§ 43), and it is, consequently, immaterial which atom is united to a given affinity. The following formulæ admit of only one interpretation:

The question (§ 54) whether the formulæ only admit of one interpretation when all four monovalent elements are different is an open one, but will probably be decided in the negative. When two polyvalent atoms combine, the formula has only one meaning when all the affinities are satisfied by monovalent atoms of the same element. For example:

Three similar polyvalent atoms can unite with one kind of monovalent atom to form saturated compounds, which can only exhibit one form of structure, e.g. propane :

CH,--CH2-CH3.

Again, one structure alone is possible in a compound containing two polyvalent atoms where one of the monovalent atoms differs from the others, e.g.:

HỌC – – CH,C

Ethyl Chloride

H2C--CH2I
Ethyl Iodide

Cl2C - - CHCI2

Pentachlorethane

But this is no longer the case when a second monovalent atom of another element enters the compound. The entrance of the first of these two atoms puts an end to the equality between the two polyvalent atoms, and consequently it is now a matter of importance with which particular polyvalent atom the second monovalent atom unites. Isomeric compounds are now possible, and the number of such compounds theoretically possible are actually known. When there are only two atoms of the new kind present, it does not matter whether

they are alike or dissimilar. Only two forms are possible for the compounds

C,H,Cl, and
H,C--CHCI, and
Ethylidene chloride

H,C--CHCIBr and

Ethylidene chlorobromide

C,H,CIBr

H2CIC -- CH2Cl

Ethylene chloride
H,CIC--CH,Br

Ethylene chlorobromide

But if the number of different monovalent elements increases the number of isomerides will increase. If all six monovalent atoms are different, then there will be ten isomerides, as can be calculated by permutation. If the six monovalent atoms are numbered 1, 2, 3, 4, 5, 6, then we have the following combinations:

or (4+3+2+1)=10 combinations.

In the case of three similar or two dissimilar polyvalent atoms, isomerism occurs as soon as a single atom of a second monovalent element enters the compound:

CNH,C1=CH2Cl -- NH2 or CH, - NHCI

2

Chloromethylamine

2

Methylchloramine

C,H,C1=CH,--CH,-- CH,Cl or CH,--CHCI--CH,

Propylchloride

Isopropylchloride

The number of isomeric compounds increases rapidly as the number of polyvalent atoms and the variety of monovalent elements increase. Three carbon atoms and eight similar monovalent atoms can only be arranged in one manner, but if the eight monovalent atoms are all different,

G