Dec. 26, 1889] 



NATURE 



187 



characteristic, 36, of silicon deduced from an equivalent pro- 

 posed by M. Regnault, and which is very remarkable, from its 

 coincidence with the characteristic of ammonium. 



" By the discussion, which has shown me the advisability of 

 accepting various results hitherto looked on as scarcely recon- 

 cilable, I have been led to conceive the possibility of reproduc- 

 ing the se7-ics of natural numbers in the series formed by the 

 numerical characteristics of the real or supposed simple bodies 

 supplemented by the characteristics of the compound radicles 

 formed from gazolytic ^ elements, such as cyanogen, the ammo- 

 niums, &c., and doubtless also by the compound radicles formed 

 from metallic elements, of which the alloys offer us an example. 

 In this natural series, the bodies which are really simple, or at 

 least irreducible by the ordinary means at our disposal, would 

 be represented by the prime numbers. It will be at once seen 

 that there are in my table at least twelve bodies, which, 

 like sodium (23), have characteristics which are prime numbers. 

 This is what led me to perceive this law, which, I believe, is 

 destined, when established, to form one of the bases for the 

 discovery of the law of molecular attraction. The predomin- 

 ance of the law of divisibility by 4 in the series of my table, 

 a predominance which is also to be found in the elements of the 

 theory of numbers, has confirmed me in the idea — an idea in 

 itself really simple — that there is a perfect agreement between 

 bodies, the elements of the material order, and numbers, the 

 elements of the abstract order of things {elements de la variety 

 matirielle, de la variete abstraite). This goal once caught sight 

 of, it will seem natural that I should have recourse to the theory 

 of numbers to help me attain it. It will seem not less natural 

 that I should also have recourse to higher geometry ; for the 

 series of relations it offers cannot fail to afford resources which 

 may enable one to establish connections between the different 

 numerical characteristics. 



" My helicoidal system in this way leads me on towards abstract 

 views of an extremely general nature ; and on the other hand it 

 should, it seems to me, find an application in the natural"^ 

 sciences, as a method of classification throughout their whole 

 domain, from the series of simple bodies which forms the proto- 

 type, to the opposite extreme of our natural divisions ; in it 

 will be found, I believe, the means of bringing into connection 

 simultaneously, and by all their characters, the different terms 

 of those parallel series, orders, families, genera, species, and 

 races, in each natural kingdom, of which men of science have in 

 vain tried to show the affiliation. In geology, as is evident, the 

 application is implicit. 



"Whatever may be the import of these considerations, and to 

 return to the principal object of the present memoir, I think 

 that the efficacy of the helicoidal system will be admitted as a 

 means towards hastening the advent of the time when chemical 

 phenomena shall be amenable to mathematical investigations. 



" My table, by the distribution of bodies in simple or coupled 

 series, by its indication of the existence of conjugate groups, &c., 

 traces a plan for diverse categories of syntheses and analyses 

 already executed or to be executed ; it draws up very definite 

 programmes for the execution of several researches which are 

 exciting attention. Will not my f-eries, for instance, essentially 

 chromatic as they are, be a guide in researches on the spectrum ? 

 Will not the relations of the different rays of the spectrum prove 

 to be derived directly from the law of numerical characteristics, 

 or vice vcrsd ? This idea, which occurred to me before we were 

 taught the identification of the lines in the spectrum, and the 

 admirable applications of this discovery, seems to me now even 

 more than probable. Finally, looking upon it only as a concise 

 representation of known facts, and reducing it to the points 

 which offer no matter for discussion, the geometrical table of 

 numerical characteristics affords a rapid method for teaching a 

 large number of notions in physics, chemistry, mineralogy, and 

 geology. I hope, therefore, that my natural classification of the 

 simple bodies and radicles being capable of rendering manifold 

 services, will need, like every object in habitual use, a name of 

 easy application ; hence, on account of its graphic representation 

 and its origin, I give it the significant name oitelluHc helix." 



It will be well to point out immediately that M. de Chan- 

 courtois's system assigns to the numerical characteristics of the 

 elements a general formula of the form (« -f l6«'), where «' is 

 necessarily an integer ; '^ and his table thus brings out the fact 



' Metalloid. 



^ The term includes physical science. 



3 u is always represented in the author's table as integral, but he expressly 

 states that he looks on this as by no means necessary. '"The construction of 

 the telluric helix rests on the use of proportional numbers derived from 



5S 



that the differences between the atomic weights oi allied bodies 

 approximate in many cases to multiples of i6.* 



Thus we get the parallel series of which our author speaks — 

 Li Na K 



7 ... 7 -I- 16 = 23 ... 7 + 2 . 16 = 39 

 Rb 

 7 -1-5 . 16 = 87.2 



S Se 



16 + 16 = 32 ... 16 -f 4 . 16 = 80 ... 16 -f 7 . 16 = 128.^ 



As we glance at the first two turns of de Chancourtois's helix, 

 we ask ourselves if the discovery of Newlands and^Mendeleeff 

 does not lie before us. 



O 

 16 



Mn 



7 + 3-16 



Te 



But the discovery of the "octaves" or "periods" cannot be 

 ascribed to our author, although it seems almost impossible that 

 chemists should not have perceived their existence on looking at 

 his table. 



experiment. It would remain valid with fractional numbers, and often the 

 hel.coidal alignments would be even more easily applicable to these than to 

 integers" (Coiitptes rendus, vol. liv. p. 842). 



' This fact, now familiar, has again been noticed by your correspondent, 

 Mr. A. M. Stapley, in the issue of November 21, 1889. 



* The atomic weight of rubidium should be 85. ^A'e may notice that the 

 author gives as probable also Cs = 135 = 7 f 8 . 16, which is thus placed on 

 the same generating line. 



3 Certainly too high a value; according to Brauner, the exact atomic 

 weight of tellurium remains to be determined. 



