488 Hackh — Modification of the Periodic Table. 



Er 



Tm' 



Tm" 



Yb 



Lu 



Ta 



W 



75 



Os 



Ir 



Pt 



lx-\- 14 



15 



16 



















8x4- 6 



7 



8 



9 



10 



11 



12 



13 



14 



15 



16 



9x + 







1 



2 



3 



4 



5 



6 



7 



8 



Au 



Hg 



Tl 



Pb 

















9x+ 9 



10 



12 



12 

















10^-1- 1 



2 



3 



4 

















This indicates that e. g. the atom of gold is an equilibrium 

 of the system 9x + 9 = 10.r + 1 etc. It is outside the 

 scope of this paper to treat the constitution of the atoms, 

 and the above was mentioned in order to bring out the 

 length of the different periods, together with the impos- 

 sibility of the existence of another rare gas between Xe 

 and Nt. 



The next task is then to arrange these results in the 

 best possible way. There are numerous modifications of 

 the periodic table, a proof that the table is not perfect. 

 One of the main objections to the periodic table is the 

 placing of the main and sub groups together in one col- 

 umn; another, far more serious objection is that no 

 indication is made of the different length of the periods. 

 Table III will meet these objections, besides having 

 other advantages. This table was derived from a 

 curve 27 by the simple method of using the upper part of a 

 spiral in its relation to the lower part like an image and 

 its mirrored semblance. 



The ideal way of representing the periodic system is 

 naturally a curve, which may take the form of a spiral 

 drawn on a plane, or a helix constructed in space, as has 

 been pointed out by Harkins. 2S In the literature we find 

 many such spirals, compare e. g. those of Revnolds, 2iJ 

 Spring, 30 Huth, 31 Crookes, 32 Houghton, 33 Stoney, 34 Erd- 

 mann, 35 Tocher, 36 Emerson, 37 Ravlei^h, 38 Scheringa, 30 

 Hack, 40 Hackh, 41 Rydberg, 42 Soddy> 3 Bilecki, 44 Loring, 45 

 Kunz 46 and others. But the more extensive use of those 

 spirals is encumbered by the technical difficulties of 

 reproducing them, and for this reason a table derived 

 from a spiral and embodying its advantages is practical 

 and useful. The table presented in this paper preserves 

 not only those relationships among the elements which 

 are expressed by the customary table of the periodic 

 system, but illustrates also a number of new correlations 

 among the elements. 



