FUNDAMENTAL PROPEETIES 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 (in the course of which 30 atomic weights have 

 been redetermined) may be seen in then* full bearing only in the original 

 papers. 1 



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, 2 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 tins end, the Harvard work will be contmued 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, denned 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. 3 On applying van der 

 Waals's well-known equation to several gases, in some tentative 

 and unpublished computations, it seemed clear that the quantity b 

 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. 4 

 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 given in 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 iiber 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. 



'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. 



* Van der Waals, Zeitsch. physikal. Chem., 1901, vol. 38, p. 257. His earlier publication on this topic 

 (Pfoc. 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. 



