FUNDAMENTAL PROPERTIES OF THE ELEMENTS—RICHARDS. 203 
other two causes, unless the inclusion of foreign substances by pre- 
cipitates may be ranked as an equal vitiating effect. But these are 
merely details. The scope and method of the recent work on this 
subject at Harvard Gn the course of which 30 atomic weights have 
been redetermined) may be seen in their full bearing only in the original 
papers.’ 
That the atomic weights may be connected by precise mathematical 
equations seems highly probable; but, although many interesting 
attempts have been made to solve the problem,? the exact nature of 
such relationships has not yet been discovered. No attempt which 
takes liberties with the more certain of the observed values is worthy 
of much respect. It seems to me that the discovery of the ultimate 
generalization is not likely to occur until many atomic weights have 
been determined with the greatest accuracy. No trouble being too 
great to attain this end, the Harvard work will be continued indefi- 
nitely, and attempts will be made to improve its quality, for the dis- 
covery of an exact mathematical relationship between atomic weights 
would afford us an immeasurably precious insight into the ultimate 
nature of things. 
But weight is only one of the fundamental properties of an element 
Volume is almost, if not quite, as important in its own way, although 
far more variable and confusing. All gases, indeed, approach 
closely to a simple relationship of volumes, defined by the law of 
Gay Lussac and the rule of Avogadro, and well known to you all. 
In the liquid and solid state, however, great irregularities are mani- 
fest, and very little system as regards volume is generally recognized. 
About 12 years ago, the study of such small irregularities as exist 
among gases led me to the suspicion of a possible cause for the 
greater irregularities in liquids and solids. On applying van der 
Waals’s well-known equation to several gases, in some tentative 
and unpublished computations, it seemed clear that the quantity 6 
is not really a constant quantity, but is subject to change under 
the influence of both pressure and temperature. This conclusion 
has also been reached independently by van der Waals himself.‘ 
But if the quantity b (supposed to be dependent upon the space 
1 An important part in these researches has been taken by G. P. Baxter, and many able students also have 
assisted the author in the work. A complete bibliography is givenin Publications Carnegie Institution of 
Washington, 1910, No. 125, p. 91. Most of the papers are reprinted in full in a volume entitled, ‘‘ Experi- 
mentelle Untersuchungen tiber Atomgewichte,” by the author and his collaborators (Hamburg, 1909). 
The Carnegie Institution of Washington has generously subsidized the work in recent years. 
2 See especially Rydberg, Zeitsch. anorg. Chem., 1897, vol. 14, p. 66. 
3 Richards, The Significance of Changing Atomic Volume, Proceedings American Academy, 1901, vol. 
37, p. 1; 1902, vol. 37, p. 300; 1902, vol. 38, p. 293; 1904, vol. 39, p. 581; Zeitsch. physikal. Chem., 1902, vol. 
40, pp. 169, 597; 1903, vol. 42, p. 129; 1904, vol. 49, p. 15. 
4Van der Waals, Zeitsch. physikal. Chem., 1901, vol. 38, p. 257. His earlier publication on this topic 
(Proc. R. Akad. Wetensch. Amsterdam, 1898, vol. 29, p. 138) was unknown to me at that time. See also 
Lewis, Proceedings American Academy, 1899, vol. 35, p. 21. 
