NA TURE 



49 



THURSDAY, NOVEMBER 16, 1905. 



" MATHEMATICS " APPLIED TO CHEMISTRY. 



Researches on the Affinity of the Elements, and on 

 the Causes of the Chemical Similarity or Dis- 

 similarity of Elements and Compounds. By 

 Geoffrey Martin. Pp. xii + 287- (London: J. and 

 A. Churchill, 1905.) Price 16.?. net. 



THE word " mathematics " has been placed in the 

 title of this review in inverted commas, because, 

 although the mathematical formula? employed appear 

 to be formally correct, the application of mathematical 

 formulae to the data collected in Mr. Martin's work 

 appears to the reviewer to be unjustified. To demon- 

 strate this a sketch of Mr. Martin's scheme is 

 necessary. 



Mr. Martin's endeavour is to find for each element, 

 and, if desired, for each compound, a formula which 

 will express its affinity for all other elements and 

 compounds, so that it may be possible, in his own 

 words, " to discover the law regulating- the chemical 

 attraction the elements mutually exert on each 

 other"; and this is achieved, according to him, by 

 " the construction of some geometrical figure which 

 will quantitatively pourtray the chemical properties of 

 the element." 



The plan adopted is to arrange the elements into 

 scries and columns, as in the usual periodic diagram; 

 the group numbers are plotted along a horizontal 

 ordinate OX, and the series numbers along an 

 ordinate at right angles to the former, OY. There 

 are ten points along OX, filled in the second group 

 by the elements Li, Be, B, C, N, O, F, and Ne, and 

 there are eleven points along the ordinate OY, 

 occupied in the first column by the elements H, Li, 

 Na, K, Ca, Rb, Ag, Cs, ?, ?, and Au. This, it will 

 be seen, gives one of the common forms of the 

 periodic table. Next, for any one element, having 

 one definite valency (one, it may be, of several 

 valencies which it may possess), perpendiculars are 

 erected on the point occupied by each of the known 

 elements, expressing by its height the affinity of that 

 element for each of the others. Thus, choosing the 

 element chlorine, and regarding it as monovalent, 

 vertical lines are to be erected, showing by their 

 length that that erected on, say, the point occupied 

 by caesium, expresses a high degree of affinity or 

 attraction ; the vertical on the point occupied by 

 arsenic, for example, viewed as triad, would show 

 by its shorter length that the affinity of chlorine for 

 arsenic is less than it is for caesium ; a repetition of 

 this process for all known elements produces a number 

 of points, 10 x 11, or no in number, if all spaces are 

 considered, or a smaller number, the number of the 

 actually known elements, in actual practice. Mr. 

 Martin imagined a curved surface to be drain, 

 through these points, and proceeds to develop equa- 

 tions which will represent that surface. He shows, 

 so far as the reviewer can see, correctly, that for the 

 complete characteristic equation for the supposed no 

 elements, each of which is supposed capable of exist- 



no. 1 88 1, vol. 73] 



ing in 8 degrees of valency, there are 2.3486 x io 108 

 different possibilities of associating degrees of 

 valency ! However, by a device the author merci- 

 fully lowers this number to 844S, being 64 times 132; 

 [32 represents the number of constants for the 

 characteristic affinity-surface for each element exist- 

 ing with only one of its possible eight valencies 

 exen Ned. 



We have italicised the words "imagined a curved 

 surface to be drawn through these points " because 

 there lies the crux of Mr. Martin's attempt. What 

 reason has he to join his points? Does he imagine 

 that the interspaces are filled by an infinity of elements 

 of all conceivable atomic weights between the known 

 limits 1 and 240? If not, then the whole system is 

 discontinuous, and the characteristic surface is non- 

 existent. 



But we will accept Mr. Martin's method for the 

 moment, and inquire how he imagines affinity to be 

 measured, so as to obtain the lengths of his vertical 

 coordinates. The methods of estimating comparative 

 affinity may be taken as three in number. First, he 

 suggests that while the " energy of combination " 

 should be measured by the heat generated by a re- 

 action starting from the absolute zero, such measure- 

 ments are impracticable, and, faute de mieux, the 

 " heats of formation " at ordinary temperatures must 

 suffice. This method may be better realised by a 

 concrete example. One-third of the heat evolved 

 when boron burns in chlorine amounts to 34.7 calories ; 

 one-quarter of that of the formation of silicon 

 chloride is 39.4 calories. These numbers are approxi- 

 mately equal, hence the affinities of boron and of 

 silicon for chlorine are nearly the same. But this is 

 not always the case ; for instance, as Mr. Martin 

 points out, J(Si,H,)=8.2, whereas s(C,H 4 ) = 5.2; yet 

 " undoubtedly of these two bodies, the H is attracted 

 to the C in CH, with a greater intensity than it is 

 attracted to the Si in SiH 4 ." He therefore guards 

 himself by the statement that "it is only when the 

 heat evolved in the formation of a compound is very 

 great that it can be taken as measuring approximately 

 the attractive forces." There may be a little in this, 

 but the reviewer has read something like it before. 

 Second, an estimate of the relative affinity of the 

 elements in two similar compounds may be derived 

 from a consideration of their temperatures of decom- 

 position. Again, that suggestion is at least a centurv 

 and a half old. Third, temperatures of reaction may 

 l» made a rough measure of affinity. For instance, 

 lead oxide is reduced by hydrogen at a lower tempera- 

 ture than iron oxide, hence the affinity of lead for 

 oxygen is less than that of iron. Estimates of such 

 affinities, and their application to the formation of 

 curved surfaces as described, fill 206 pages of the 

 work. Three appendices treat respectively the 

 causes of the absence of other compounds of elements 

 than those which contain the element at a high or 

 al a low grade of valency; the bearing on the pheno- 

 menon of life of the critical temperature of decom- 

 position of chemical compounds; and lastly, "the 

 possible significance of alcohol drinking," in which 

 the glorious hope is held out to our remote de- 



D 



