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IN studying atomic weight relations, or the classification of the elements by atomic weight, it is interesting to note that two or three types of irregularity, common to one element or a series of elements, so balance or cancel each other as to leave a mean interpretation representing a normal or regular condition, or, on the other hand, the "irregularity" itself becomes regular by some symmetrical peculiarity. This principle may be tentatively illustrated by the following treatment: Referring to "Studies in Valency," p. 23, a periodic arrangement of all the elements is shown, which lends itself to certain uniform sub-divisions or arrangements of members which are fairly regular when interpreted in a certain manner, as will be seen from the following specification. There appears to be a constant ratio between the number of elements comprising certain branches and the preceding number of non-branch places into which elements fit, not counting those of the chemically inactive class and nitrogen. This reckoning is from branches of like type. The ratios may be expressed by placing the numbers representing the respective branch elements as denominators thus :—21/3 = 14/2 = 14/2 =VII. * While this argument, as it stands, is opposed to the view that elements will ultimately be discovered which will take up places preceding ruthenium and osmium, that is to say, one before each, the observation in the main is true, since there is no reason to suppose that these relations are exact or precise to within, say, one unit or one element. There are, however, other relations which throw consider From H to Ce (inclusive) = 52 (a). From Pr to Lu (inclusive) = 13 (b). 52/13 = IV.. which is the Group No. of b, just as VII. is the Group No. of the other branches, these branch Group Nos. being one unit in excess of the proper classification value, a stepping-back principle being involved (see "Studies in Valency"). Similarly, from Ta to Pb (inclusive)=9. The mean valency of the chemically active radioelements (2+3+4+5+6)/5=4. The ratio should have the same characteristic as those above and differ from this figure by one unit, but since the process of element formation in this case is probably one of devolution rather than evolution (see CHEMICAL NEWS, cix., 241), not only may the ratio be reversed, but the group number may coincide with the mean valency value, so that x/9= IV. There appear to be 32 radio-elements proper, not counting the radio-gases. When including the end products which must form part of the branch system and be equal to four normal elements (Ac-end, Ac-end 1, Ra-end Ra-end-1, Th-end-, Th-end; sum = 4) the figure is increased to 36; therefore, 36/9 = IV. Lead (a) is taken as an element of evolution when considered separate from the isotopic end-products of radioactive origin more or less mixed with it, or forming the entire composition (= 6); these may be designated thus-Pba; Pbb ; Pba+b The table given on page 23 of "Studies in Valency" calls for 64 chemically active elements in the last (7th) division, including two branches, which may be evaluated thus-1 Uri, 2 UrX1, 3 UrY, 4 UrXg, 5 Ur2, 6 Io, 7 Acı?, 8 Ac2 (actinium), 9 RadAc, 10 Ra, 11 ACX, 12 RaA, 13 ACA, 14 RaB, 15 AcB, 16 RaC1, 17 ACC, 17 AcCa. 18 Ac-end, 19 AcD, 20 Ac-end, 20 RaC2, 21 Ra-end, 22 RaC, 23 RaD, 24 RaE, 25 RaF, 26 Ra-end, 27 Tb, 28 MsThi, 29 MsTh2, 30 RadTh, 31 ThX, 32 ThA. 33 ThB, 34 ThC, 34 ThC2, 35 Th-end, 35 ThD, 36 Th-end, 37 Mendeleeff's prediction, 38 Bi (by evolution?), 39 Pb (by evolution, and those following), 40 T1. 41 Hg, 42 Au, 43 Pt, 44 Ir, 45 Os, 46 W, 47 Ta, 48 Lu, 49 Ny (Yb), 50 Thulium 1, 51 Thulium 2?, 52 Er, 53 Ho, 54 Dy, 55 Tb, 56 Gd, 57 Eu, 58 Sa, 59 Nd, 60 Pr, 61 Ce, 62 La, 63 Ba, 64 Cs. The numbers are attached to the radio elements in a manner merely convenient for counting; moreover, the order might be reversed. It will be seen that the emanations are, in a sense, interperiodic (see CHEMICAL NEWS, 1911, ciii., 71). and when the associates part company (see CHEMICAL NEWS, cix., 241) in a homogeneous manner the separate products or those considered as such-are, consequently, pure half-elements relative to the others, at least they may be so regarded for purposes of counting. Referring again to the same table, it is further to be observed that the number of stable elements in the vertical columns containing the branches and including the branchmembers themselves is equal to the number of preceding non-branch members (reckoned in the same manner) by a regular difference of 2. Here, however, a very curious condition in respect to tellurium has to be postulated, which satisfies certain other requirements, most notably the one demanding 32 elements or members in the set (6th division) terminated by tellurium. This regularity calls for 19 elements in Group VII. of the right hand half of the table, as if tellurium were 7'5 and Te17 127'5). Ter.... Tey (in which case Ter The following arrangement will make this clear :L...... I. II. III. IV. V. VI. VII. 6+5+5 2 = 18 5+5 R........ I. II. III. IV. V. 3 +3 +3 +3 +3 2 = 12 VI. VII. + 2 2 = 19 In this case the non-branch elements, nitrogen, potassium, and one supposed element immediately following bismuth (Mendeleeff), are reckoned as occupying their respective chemical places in the table. An alternative apportionment of the numbers is given below, in which the hypothetical element following bismuth is assigned to Group VII., somewhat after the manner of tellurium (see table), the constant to be added being in this case 3 instead of 2, whilst nitrogen and potassium remain in their nonchemical places as shown in the table, the disposition of the numbers being : L...... I. II. III. IV. V. VI. VII. 3-18 3 = 12 From the above it might be supposed that some balanced proportion exists between the right- and left-hand branchbut excluding the three chemically inactive radio gases. members, when taking into account the radio-elements, Indeed, this appears to be the case since VII. L VII. R IV. L IV. R 7 is to 17 as 13 is to 32 The proportion, though not exact, includes the " 17 little telluriums" (of course a fanciful conception, but not unlike the well-known idea of ten heliums forming argon), and implies that the radio-elements collectively form a one-branch system from lead, lead itself being a more or less composite element. There are exactly 32 distinctive radio-elements, omitting the chemically inactive radiogases, and four probably indistinguishable end-products which would be the equivalent of lead, and counting in one undiscovered member preceding actinium (see CHEMICAL NEWS, cix., 241). Dr. H. G. J. Moseley (Phil. Mag., xxvii., 703), in recent work on the X-ray spectra of the elements, shows clearly the lacunæ for undiscovered elements, one preceding ruthenium and one preceding osmium, and confirms the inference that may be drawn from this study, that practically all the elements are known with these possible exceptions, and one in the rare-earth group between neodymium and samarium; there are also thulium I. and thulium II. which may be taken as established, or at least the X-ray spectra require also an additional element to thulium to render the progressive steps of the series of lines regular. extension of his series of lines beyond gold, but there is Dr. Moseley has not as yet published an every reason to believe that, between aluminium and gold, |