Hackh — Modification of the Periodic Table. 499 



the isotopes of lead (PbTh, PbAc, RaD). The connec- 

 tion between the uranium and actinium series is doubtful 

 (U-Uy-Uz-Ac) and indicated by a broken arrow. The 

 other series begin as follows : 



U-Ux'-Ux"(Bv)-LVIo-Ra, etc. 

 Th-MsT'-MsT"-Rafh-ThX. etc. 

 Ac-RaAc-AcX, etc. 



At the bottom of the table are given the number of known 

 isotopes and their atomic weights. The atomic weights 

 of the isotopes of the longest life periods are underlined, 

 while the missing atomic weights of the actinium series 

 are indicated by an arrow. A regularity in the atomic 

 weights is naturally to be expected and clearly seen from 

 a study of the table. 



This table of the radioactive elements can be attached 

 at the bottom of the main table, or as done in Table VIII, 

 these elements may be put in brackets, indicating their 

 isotopes, and also their group-relationship, indicated by 

 horizontal or vertical lines respectively. 



An exhaustive treatise on the periodic system is in 

 preparation, of which this paper is intended to be a 

 preliminary statement. 



Conclusion. 



1. By plotting the elements, as to their atomic num- 

 bers against their relative position in the displacement 

 series, a periodic curve is obtained, in which a similarity 

 among the element groups and periods exists. (Fig. 1.) 



2. A similar periodicity is shown by the polar num- 

 bers of the elements (fig. 2) ; accordingly the elements 

 are divided into two short, two long and one very long- 

 period. 



3. From both curves it can be predicted that no new 

 rare gas can be discovered, because such a new element 

 would demand characteristic properties of about thirteen 

 other elements, and of these thirteen elements none is 

 known, or in other words, no known element between the 

 atomic numbers 63 and 76 exhibits these characteristic 

 properties. Therefore all the elements of the electro- 

 potential ± oo are known. 



