112 Dr. J. H. Vincent on a Numerical 



lithium as the third heaviest atom, it is taken as the fifth in 

 the augmented list, germanium as the sixth instead of the 

 fourth, and so on up to samarium. For hydrogen N = l, and 

 for helium N = 3. The formula is of such a type as to give 

 the atomic weight of hydrogen, correctly ; the calculated 

 weight of helium is only "15 of a unit wrong, which, however, 

 is a percentage error of 3*8. The most prohable value for 

 helium is 3*78. 



These two gaps near the beginning of the augmented list 

 have no chemical evidence in their favour. There is no 

 room in the periodic table for an element between helium and 

 lithium, and any theory based on the. . periodic law which 

 would predict any elements between hydrogen and helium 

 would predict several and not merely one. 



It is necessary to assume thirteen other gaps in order to 

 complete the augmented list. The table gives the positions 

 and also the atomic weights which they would have on this 

 theory. 



The periodic table leaves five gaps between samarium and 

 gadolinium. This table also shows that if there are not five 

 missing elements then there are two. In the latter case 

 elements analogous to rhodium, ruthenium, and palladium 

 would not be represented. The augmented list agrees with 

 this second view. The periodic law would lead us to expect ;i 

 maximum of seven elements between gadolinium and terbium. 

 The augmented list indicates that five only are to be expected, 

 Their exact positions in the periodic table cannot be predicted 

 until the positions occupied by terbium, erbium, and thulium 

 are known. An element is predicted by the periodic law 

 between ytterbium and tantalum, and between tungsten and 

 osmium. These an; also predicted by the augmented list, 

 which agrees also in predicting only one element in each of 

 these positions. An unbroken line of elements occurs from 

 osmium to bismuth in both the periodic table and in the 

 augmented list. Between bismuth and thorium both leave 

 six elements to be discovered, while the last gap between 

 thorium and uranium occurs in both the periodic table and 

 the augmented list. 



The results given in the table are shown graphically in 

 Plates I. and II., in which + indicates the atomic weight given 

 by the formula and • shows the actual atomic weight. The 

 sign ^ marks the most probable atomic weight of a predicted 

 element. 



PL I. is drawn on ordinary squared paper, and is thus suited 

 to show the differences between the computed and the expe- 

 rimentally found numbers. 



