In the year 1818 the "law of isomorphism" was stated by Mitscherlich: "Compounds the atoms of which contain equal numbers of elementary atoms, similarly arranged, have the same crystalline form." As thus stated, the law of isomorphism affirms that if two compounds crystallize in the same form, the atoms of these compounds are built up of the same number of elementary atoms—however different may be the nature of the elements in the compounds—and that these elementary atoms are similarly arranged. This statement was soon found to be too absolute, and was accordingly modified; but to go into the history of the law of isomorphism would lead us too far from the great main path of chemical advance, the course of which we are seeking to trace.

Berzelius at once accepted Mitscherlich's law, as an aid in his researches on atomic weights. The help to be derived from this law may be illustrated thus: let us assume that two compounds have been obtained exhibiting identity of crystalline form; let it be further assumed that the number of elementary atoms in the atom of one of these compounds is known; it follows, by the law of isomorphism, that the number of elementary atoms in the atom of the other is known also. Let the two compounds be sulphate of potash and chromate of potash; let it be assumed that the atom of the first named is known to consist of two atoms of potassium, one atom of sulphur, and four atoms of oxygen; and that the second substance is known to be a compound of the elements potassium, chromium and oxygen; then the atom of the second compound contains, by Mitscherlich's law, two atoms of potassium, one atom of chromium and four atoms of oxygen: hence the relative weight of the atom of chromate of potash can be determined, and hence the relative weight of the atom of chromium can also be determined.

A year after the announcement of Mitscherlich's law, the following generalization was stated to hold good, by two French naturalists, Dulong and Petit:—"The atoms of all solid elements have the same capacity for heat."

If the amount of heat required to raise the temperature of one grain of water through one degree be called one unit of heat, then the capacity for heat of any body other than water is the number of units of heat required to raise the temperature of one grain of that substance through one degree. Each chemical substance, elementary and compound, has its own capacity for heat; but, instead of comparing the capacities for heat of equal weights, Dulong and Petit compared the capacities for heat of weights representing the weights of the atoms of various elements. Thus, equal amounts of heat are required to raise, through the same interval of temperature, fifty-six grains of iron, one hundred and eight grains of silver, and sixty-three and a half grains of copper; but the weights of the atoms of these three elements are in the proportion of 56:108:63-1/2. Dulong and Petit based their generalization on measurements of the capacities for heat of thirteen elements; further research has shown that their statement most probably holds good for all the solid elements. Here then was a most important instrument put into the hands of the chemist.

It is only necessary that the atomic weight of one solid element should be certainly known, and that the amount of heat required to raise through one degree the number of grains of that element expressed by its atomic weight should also be known; then the number which expresses the weight, in grains, of any other solid element which is raised through one degree by the same amount of heat, likewise expresses the relative weight of the atom of that element. Thus, suppose that the atomic weight of silver is known to be 108, and suppose that six units of heat are required to raise the temperature of one hundred and eight grains of this metal through one degree; then suppose it is found by experiment that six units of heat suffice to raise the temperature of two hundred and ten grains of bismuth through one degree, it follows—according to the law of Dulong and Petit—that 210 is the atomic weight of bismuth.

The modified generalization of Gay-Lussac—"Equal volumes of elementary gases contain equal numbers of atoms;" the laws of "isomorphism" and of "atomic heat;" and the two empirical rules stated on p. 163;—these were the guides used by Berzelius in interpreting the analytical results which he and his pupils obtained in that memorable series of researches, whereby the conceptions of Dalton were shown to be applicable to a wide range of chemical phenomena.

The fixity of composition of chemical compounds has now been established; a definite meaning has been given to the term "element;" the conception of "atom" has been gained, but much remains to be done in the way of rendering this conception precise; and fairly good, but not altogether satisfactory methods have been introduced by which the relative weights of the atoms of elements and compounds may be determined. At this time chemists are busy preparing and describing new compounds, and many new elements are also being discovered; the need of classification begins to be felt more and more.

In the days of Berzelius and Davy strenuous efforts were made to obtain some generalizations by the application of which the many known elements and compounds might be divided into groups. It was felt that a classification might be founded on the composition of compounds, or perhaps on the properties of the same compounds. These two general principles served as guides in most of the researches then instituted; answers were sought to these two questions: Of what elements is this compound composed? and, What can this compound do; how does it react towards other bodies?

Lavoisier, as we know, regarded oxygen as the characteristic element of all acids. This term acid implies the possession, by all the substances denoted by it, of some common property; let us shortly trace the history of this word in chemistry.

Vinegar was known to the Greeks and Romans, and the names which they gave this substance tell us that sourness was to them its characteristic property. They knew that vinegar effervesced when brought into contact with chalky earths, and that it was able to dissolve many substances—witness the story of Cleopatra's draught of the pearl dissolved in vinegar. Other substances possessed of these properties—for instance oil of vitriol and spirits of salt—as they became known, were classed along with vinegar; but no attempts were made to clearly define the properties of these bodies till comparatively recent times.