One of the most significant achievements of the last half-century has been the demonstration that these gaseous laws are interdependent. Their further study, and in particular the study of their variation from exact mathematical expression, has led to a conception of the real nature of a gas which not only comprehends and knits together these laws, but affords a rational explanation of them. If the laws of Boyle and Dalton concerning the relations between pressure, temperature, and gaseous volume are, and must be from the very nature of the case, only approximations, it follows that the same is equally true of the laws of Gay Lussac and Avogadro, since these are dependent on the others. The definite experimental proof that gases do not actually combine in the precise ratios demanded by the law of Gay Lussac has been forthcoming only during the last twenty years. It has been found that, instead of oxygen and hydrogen combining in the exact ratio of one volume of oxygen to two volumes of hydrogen to form water, as stated by Gay Lussac, one volume of oxygen combines with, according to Scott, 2.00245 vols.; according to Leduc, 2.0024 vols.; according to Morley, 2.00268 vols. of hydrogen. What is true of the volume-ratios in which oxygen and hydrogen are actually found to combine, under ordinary conditions, is no doubt equally true of analogous instances, such as the union of hydrogen and chlorine to form hydrogen chloride. It follows also that the extent of the variation from the mathematical expression of Gay Lussac’s law must get smaller and smaller as the combining gases approach the condition of the ideal gas—as they do, for example, under very low pressures. The precise degree of departure from Gay Lussac’s law is therefore in a sense accidental, and is dependent upon the conditions under which combination takes place.
The more exact study of the physical phenomena of gases, and in particular the clearer recognition of the causes which determine the extent of their departure from the ideal gaseous laws, have afforded valuable assistance in ascertaining the atomic weights of certain elements independently of chemical considerations. The processes of physical measurement have been so refined within recent years that physical methods of arriving at molecular—and, inferentially, at atomic—weights, in the case of all elements and compounds which can be brought into a condition approaching that of the ideal gas, are to be preferred to the gravimetric methods of analysis or synthesis as affording the most probable values of the true atomic weights of the elements. The work of Lord Rayleigh, Leduc, and of Guye and his pupils on the densities of the gases has furnished us with a series of values for the atomic weights of a number of the elements which, in point of accuracy, are as superior to the values of Stas as the values of Stas were superior to those of his predecessors. Daniel Berthelot pointed out in 1898 that the true molecular weight of a gas can be deduced from its density and its observed variations from Boyle’s law under atmospheric pressure and at very low pressures. Incidentally, the study of gaseous phenomena has served to place the theory of atoms upon a far more stable foundation than it occupied half a century ago. How halting was the adhesion which even some of the most eminent chemists then gave to this theory was well exemplified by the remarkable lecture given before the Chemical Society of London in 1869, in which Williamson—one of the most sturdy champions of Dalton’s doctrine—set forth its true value.