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.