April 14, 1922] 



SCIENCE 



401 



The Bureau of Standards recently advised 

 me that they did not know of any such puljliea- 

 tion, yet it seems that this would be one of the 

 first requirements for a commercial change, and 

 if it were now provided, might clear the way 

 for the next step. The willingness of certain 

 chemical manufacturers and dealers to furnish 

 goods in metric quantities, does not amount to 

 very much — it is easily done, and has been 

 done automatically since the demand appeared, 

 but a few more practical suggestions with the 

 necessary tools (such as conversion tables as 

 above) would greatly smooth the way in the 

 eyes of the average business man, who is prob- 

 ably accounted the greatest opponent of the 



" ' Henry Paul Busch 



CONCERNING THE ARTICLE "A NEW 

 GRAPHIC ANALYTIC METHOD 



I^f an article entitled, "A New Graphic 

 Analytic Method," in Sciejtce of October 7, 

 1921, Mr. R. von Huhn states a method of de- 

 riving the graph of a special case of a function 

 of a function. Stated in more usual mathe- 

 matical terms : 



Given the curves that represent 

 y =z kx -^ m, 

 z ^ hy -\- n, 

 the curve that represents the resulting equation 



^ = ?x -(- g 

 is drawn. 



Essentially the same method, in a far more 

 general form, and in a more usual mathematical 

 formulation has been given by several mathe- 

 maticians. See the articles by E. H. Moore, 

 "Cross-section paper as a mathematical instru- 

 ment," in The School Review, May, 1906, and 

 hy A. Kempner, "Some hints on plotting 

 graphs in analytic geometry," in The American 

 Mathematical Monthly, Vol. XXIV, pp. 17-21, 

 and, in particular, the more specific article by 

 W. H. Roever, "Graphical constructions for a 

 function of a function and for a function given 

 by a pair of parametric equations," in "The 

 American Mathematical Monthly, Vol. XXIII, 

 pp. 330-333. E. R. Hedrick has suggested the 

 modification of transferring points from one 

 of the two like-named axes to the other by 

 means of a 45° triangle and he has also empha- 



sized the geometric interpretation of the opera- 

 tion as that of finding the projection on the 

 plane xy of the intersection of the two cylin- 

 drical surfaces 



F{x, y) = 0, *{y, .-) = 



This perfectly general problem was well- 

 known to mathematicians and hence the special 

 case treated in the article mentioned above can 

 not be regarded as novel. 



Wll. H. ROEVER 



E. R. Hedrick 

 Washington University 



SPECIAL ARTICLES 



THE PROPERTIES OF ELEMENTS AND SALTS 



AS RELATED TO THE DIMENSIONS 



OF ATOMS AND lONSi 



{An Application of Geometry to the Study of 

 Inorganic Chemistry) 



Recently great interest has been aroused in 

 connection with the determination of the 

 dimensions of atoms and ions by various meth- 

 ods; particularly that of X-ray crystal anal- 

 ysis, — by Bragg, Lande, Hull, Davey, and 

 others. Very recently Fajaus and Grimm, and 

 later Biltz and also Henglein have pointed out 

 that there is a very simple linear relation be- 

 tween the volume of certain series of salts and 

 the atomic volumes of their constituents. Six 

 years ago Professor W. D. Harkins and the 

 writer began work upon what are known as 

 complex chemical compounds, such as am- 

 mines and hydrates, in an attempt to show 

 that a large number of the properties of these 

 compounds, as well as those of simple salts, are 

 very simply related to the sizes of the atoms, 

 atomic groups, and ions, from which the salts 

 are built. This point of view has now been 

 developed in considerable detail by the writer. 

 The simplicity of the relation is apparent when 

 it is realized that for a number of groups in 

 the periodic system of the most common ele- 

 ments, as many as 35 properties of their simple 

 compounds have been found to be related in a 

 linear way to the atomic and ionic volumes of 



1 Prom au address presented at the University 

 of Chicago in December, 1921, and to the Har- 

 vard- Teclniology Chemical Chib in January, 1922. 



