H H CI -I- CI == HC1 HC1; or we may write the whole operation in the fol lowing simple manner : H. + 2HC1 Dalton, assuming that the formula of am monia is NH, and knowing by experiment that the weight of the nitrogen present is 4.67 times as great as the weight of the hydrogen, would conclude that the atomic weight of nitrogen is 4.67; but since experiment shows that when ammonia gas is separated into its constituent elements, two volumes of the ammonia yield one volume of nitrogen and three volumes of hydro gen, Avogadro's law requires us to conclude that the true formula for ammonia is NH,; and hence we must take 3 X 4.67 = 14 as the atomic weight of nitrogen. This example will suffice to show how Avogadro's law obliged chemists to modify the atomic weights that would be ob tained by the methods known to Dalton. Di rect analysis of compounds of an element whose atomic weight is desired will give either that atomic weight itself, or some simple multiple or submultiple of it; but to decide between these several multiples (as for example between 4.67 and 14, in the case cited above), it is necessary to have recourse to Avogadro's law, or to some other equally general principle. Unfortunately Avogadro's law cannot always be applied to the determination of atomic weights, because it frequently happens that no compound of the element under examination can be obtained in the gaseous condition, or that the gaseous com pounds that can be obtained are unsatisfactory, for one reason or another, and not adapted to the determination of the particular multiple that should be selected as the atomic weight of the element. In such cases recourse may be had to the law of Dulong and Petit, or to the "pe riodic law* of Meyer and Mendelieff. In 1819 two distinguished French physicists, MM. Du long and Petit, announced that the specific heats of 13 elements upon which they had made care ful experiments are inversely proportional to the respective atomic weights of those elements. In other words, that the product of the specific heat and the atomic weight (which product is called the "atomic heat") is the same for all of them. This remarkable generalization did not meet with universal and immediate acceptance, be cause it failed in numerous cases unless the atomic weights of the corresponding elements were changed somewhat from the values that had been previously assigned to them from purely chemical considerations. Thus in the cases of bismuth, platinum, silver and cobalt, Dulong and Petit substituted multiples or sub multiples of the atomic weights then in use; and other changes were also made. Moreover, the law could not possibly be exact, because the specific heats of bodies are not constant, hut vary with the temperature, and sometimes to a considerable extent. Subsequent experi menters have paid great attention to Dulong and Petit's law, however, and now that the atomic weights of the more familiar elements have been pretty well determined in one way and another, the law is found to be surprisingly near to the truth, and most of the changes for which they contended, in connection with previ ously accepted atomic weights, have since been made. A list of 10 elements whose specific heats have been well determined are presented in the table, to illustrate the degree of accuracy with which a proposed clement may be ex pected to conform to it. The atomic weights in the table range from 7 to 238, and yet when we multiply each one by the corresponding specific heat, we find that the product (or "atomic heat") remains constant, or nearly so. In some cases (notably for boron, silicon and carbon), a large deviation from the law is observed; but these exceptions cannot be considered in the present place. As an example of the use of Dulong and Petit's law, the case of silver may be cited. Previous to the publication of that
law, the atomic weight of silver had been taken at 215. Dulong and Petit pointed out that if this value were retained, the product of the atomic weight and the specific heat greatly ex ceeded the value 6, to which many of the other elements approximated. They therefore pro posed to halve the then accepted atomic weight of this element, and to make (of course) a corresponding change in the formulas of all compounds of silver. Regnault confirmed their experiments, and repeated their demand that the atomic weight be halved. But Berzelius, then the greatest living authority on such mat ters, refused to consent to the change, on the ground that silver and sodium compounds are isomorphous (see Isomoarn ism), and that the analogy between the formulas of their corre sponding compounds would be destroyed, if the atomic weight of silver were halved, while that of sodium was left unchanged. Regnault then determined the specific heat of metallic sodium, and showed that the atomic weight of that element should also be halved, in order for it to conform to Dulong and Petit's law. Berzelius' objection thus lost its force, and the atomic weights of both silver and sodium were ultimately halved, by universal consent. The "periodic law," already referred to, cannot be adequately treated in this place (see PERIODIC LAW) ; but it may be said that when the known elements are arranged in the order of their atomic weights, it is found that certain attributes recur in a remarkable "periodic" manner, as we pass from one end of the array to the other. This fact is of great assistance in the determination of atomic weights, because any great error in the assignment of the atomic weight of an element would throw that ele ment among others with which it would have relations entirely out of harmony with analo gous relations prevailing in other parts of the array. This "periodic" classification is so powerful and far-reaching that the existence of new and previously unsuspected elements has been predicted by it, and afterward verified (in some cases) by the actual discovery of the elements themselves. The gas "argon" (q.v.) affords an interesting case of the determination of an atomic weight by indirect means. Argon has resisted all attempts to make it combine with other substances, and hence it has been impossible, thus far, to analyze any of its com pounds. Its density was found, by direct ex periment, to be about 20 times as great as that of hydrogen. Now if, as Avogadro's law states, a cubic inch of argon contains just as many molecules as a cubic inch of hydrogen (under the same conditions of temperature and pressure), then it follows that a molecule of argon weighs 20 times as much as a mole cule of hydrogen, or 40 times as much as an atom of hydrogen. To find the weight of an atom of argon we therefore merely have to divide 40 by the number of atoms that there are in its molecule. For an explanation of the method by which the number of atoms in the molecule of such a gas is obtained, we must refer to the article GASES, KINETIC THEORY or; it will suffice,in the present place, to state that it was found that argon is monatomic, its molecule containing but a single atom. There fore the conclusion was, that the atomic weight of argon is about 40. The "periodic law" was not of any great service in this case, because the properties of the new gas proved to be so unlike those of any previously known substance that its proper place in the general scheme could not he even guessed until its atomic weight had been determined. The subsequent discovery of helium and the other inert gases of the same group showed, however, that the atomic weight already assigned to argon is in reasonably good accordance with the periodic law.