This scheme of classification, somewhat modified by considerations of valency, and occasionally corrected by more accurate information concerning true analogies (as when vanadium was transferred by Roscoe to the nitrogen group), was in general use for practically a quarter of a century—in fact, until it was superseded by the gradual adoption of Mendeléeff’s arrangement based on periodicity. There can, however, be little doubt that this attempt by Graham at a natural classification paved the way along which Newlands and eventually Mendeléeff were led to devise our present rational system of grouping the chemical elements. The numerical relationships existing among the equivalents and atomic weights of the elements of certain of these groups, pointed out by Dumas, Pettenkofer, Odling, Gladstone, and others, gave rise to much speculation. The values of the gradational differences, of course, depended upon whether equivalents or atomic weights were employed; but the immediate point is that, whichever basis was adopted, definite numerical relations were to be perceived. Thus, in the case of the group of the halogens, it was pointed out that the individual members are connected together as follows: Fluorine. Chlorine. Bromine. Iodine. 19 35.5 80 127 a a + d a + 2d + d´ 2a + 2d + 2d´ where a = 19; d = 16.5; d´ = 28. Thus, too, in the case of the nitrogen group: Nitrogen. Phosphorus. Arsenic. Antimony. Bismuth. 14 31 75 119 207 a a + d a + d + d´ a + d + 2d´ a + d + 4d´ where a = 14; d = 17; d´ = 44. * * * * * On the basis of these and similar numerical relationships it was surmised that, just as the successive members of a group of homologous organic radicals are formed by increments of CH2, so the substances in the several groups of the elements may be produced by successive additions of some form of matter common to them all. This has its counterpart, somewhat modified, in the modern hypothesis of the disintegration of the elements. Dumas conceived the elements in any particular group to be built up by successive accretions of particular forms of matter; Rutherford and Soddy suppose them to be derived by the successive elimination of matter from some unstable parent substance. Since 1850 the existence of at least twenty-two new elements may be said to have been established. Of course, many more than this number have been announced, more or less tentatively; but subsequent investigation has either not confirmed their existence, or has definitely disproved it. The names, symbols, and atomic weights of the twenty-two, arranged in alphabetical order, are as follows: