IN a footnote in his “Principles of Chemistry,”* D. Mendeleeff under the methods with which he was then acquainted of expressing the periodic relations of the elements, summarizes: “By a curve drawn through points obtained in the following manner: The elements are arranged along the horizontal axis as abcissae at distances from zero proportional to their atomic weights, while the values for all the elements of some specific property—for example, the specific volumes or the melting points, are expressed by the ordinates. This method, although graphic, has the theoretical disadvantage that it does not in any way indicate the existence of a limited and definite number of elements in each period. There is nothing, for instance, in this method of expressing the law of periodicity, to show that between magnesium and aluminium there can be no other element with an atomic weight of, say, 25, atomic volume 13, and in general having properties intermediate between those of these two elements. The actual periodic law does not correspond with a continuous change of properties, with a continuous variation of atomic weight— in a word, it does not express an uninterrupted function—and as the law is purely chemical, starting from the conception of atoms and molecules which combine in multiple proportions, with intervals (not continuously) it above all depends on there being but few types of compounds, which are arithmetically simple, repeat themselves, and offer no uninterrupted transitions, so that each period can only contain a definite number of members.” If the atomic volumes of the elements are thus plotted against their atomic weights, and a line drawn connecting the points so obtained, the curve result's, that was first constructed by Lothar Meyer and known by his name. In chemical text books, attention is directed to the periodic character of the curve and its relation to the periodic table, the loops corresponding to the short and the long periods; the transitional elements of periods III, IV, and VI being found at the minima of the large hollows; separating the even series (situated on the descending portion of the curve) from the odd series which lie on the ascending slope; elements of the different groups occupying the same relative positions upon the- different portions of the curve; and the five alkali metals, Li, Na, K, Rb and Cs, being found upon the maxima of the curve, the heavier electro-positive elements (such as Cu, Ag and Au) reappearing at the minima. Relations between a number of other physical properties and atomic volumes have been pointed out. These include refraction of light, specific heat, power to conduct heat and electricity, magnetic properties and fusibility, the last being the most interesting and the most closely allied. In the curve shown here, where several allotropic modifications of an element are known to exist, the atomic volume has been taken of that form which is the most stable and the most characteristic, and crystalline rather than amorphous. In the case of carbon, for instance, graphite (at. vol. 5) has been chosen in preference to diamond (at. vol. 3.4); and also in order that this element should lie in the same relative position on the curve as Ge, Sn and Pb. The density taken for gaseous elements refers to the liquid state, data regarding the solid being unfortunately meager. Leaving out of consideration, for the present, the first two (typical) elements of the groups, it will be noticed that a straight line can be drawn which will pass very nearly through the points K, Rb and Cs. The same holds true for Ca, Sr and Ba. Taking Group O, a line can be drawn which will pass exactly through A, Kr and Xe, and another also through CI, Br, and I.f Continuing, lines can be similarly ruled through Yt, La; As, Sb, Bi; Ti, Zr, Ce, Th; Ge, Sn, Pb; Ga, In, (Er), Tl; Zn, Cd, Hg; V, Nb, (Pr), Ta; Cr, Mo, (Nd), W, U; Cu, Ag, Au; Ni, Pd, Pt; Co, Rh, (Gd), Ir; and Pe, Ru, Os, in the order given, the variation from the mean becoming less as the more eiectro-positive elements are reapproached. Those elements in parenthesis, however, exhibit a marked variation, to which reference will be made later. The mean line for Se and Te is the mean also for O and S, thus apparently including the typical elements in one instance. It will be observed, too, that the line through Mn and Sm runs diagonally across the lower lines which may be designated for convenience as the metallic majority. * Science, vol. ii., part 3, p. 19, note 10. f The remarkable equality of the atomic volumes of the halogens (F excepted) is mentioned by Mendele'eff. Returning, now, to the typical elements, the line through Li and Na intersects the” K Rb Cs line a little more than half way between K and Rb. The Be Mg line meets the Ca Sr Ba line proportionately nearer Ca; and the line of B and Al crosses the Yt La line just behind the interseation of the latter with the curve at a point whose ordinate is 44.5. The atomic weight of Scandium, the element preceding Yt, is 44.1. Also, the C Si line intersects the Ti Zr Ce Th line in front of Ti. Selecting the limiting atomic volumes of C and Na, possible densities of solid N, O and P can be calculated from the assumption that the atomic volume of each of these elementary gases is roughly proportional to its atomic weight, the respective specific gravities resulting being 1.44, 1.38, and 1.15. By the employment of a similar method, the atomic volumes of liquid He and Ne are found to be about 5.1 and 17.2, respectively. Type line He Ne can now be drawn, the negative slope of N P corrected, line H P fixed with greater accuracy, and the true slant of O S determined. The precession of the type lines along corespond-ing group lines can be traced completely; and it will be found that the lines of the typical elements show a tendency to revolve clockwise in the order of their groups, from an angle of about 60 for the H F line to about 30 for that of Os S. The slope of the Argon group would doubtless not be so steep if the density of the solid gases were determined. Likewise the densities of solid chlorine and and bromine should determine a more consistent slant than their line has at present. The fact that I, a solid, is exactly on the line of CI and Br, liquids, can be accounted for by a slight difference in the density of solid and liquid I. The relation implied by the foregoing observations may be stated as follows: Omitting the typical members, the atomic volumes-of elements of the same chemical family constitute a' rectilinear function of their respective atomic weights, the location of each element being determined by the periodic intersection of its series line with the Lothar Meyer curve, Group VIII being read vertically. That is, given the true atomic weight of an element, its approximate specific gravity can be established, and also the position of the element in the periodic table. In the diagram, elements of doubtful position or of unknown atomic volumes, are designated by semicircles, and undiscovered elements by crossed circles. A parenthetical number refers to the- graphical value of an atomic weight, or to a density calculated from the graphical value of an atomic volume. A glance at the curve will show that the loop to the right of Cs is not as deep as might be expected, and that many of the lines never meet this portion of the curve. Again, the elements here belong to the rare earth class and are exceedingly difficult to isolate, both as salts and as elements, the latter being more often described as semi-coherent powders than as true metals. “Elements” of this kind have several times proved mixtures of similar properties and atomic weights. Bearing in mind these facts, it is not strange that this loop should be so irregular and at variance with the others. Granting the definite relation between atomic weights and atomic volumes above given, it is plain that unless the densities of Sm, Pr, Nd and Ce are redetermined and values found which will admit of their atomic volumes being lowered, the elements now tabulated as missing under Ru, Rh, Pd, Ag, Cd, Sn and Sb, will “.never be discovered for the reason that they can not exist, no intersection of this part of the curve being possible with the aforementioned series lines. There is good reason to believe, though, that these missing elements do exist; and further, it can be independently substantiated that the density of Sm is too low. Three members of the Mn series are at present unknown, of atomic weights as indicated by the periodic classification, arithmetically approximate toi 98 TRam- say, Mo+ 2), 185 (W + 1) and 240 (tl + i.D). The Mn Sm line, as it viands, crosses the curve at points whose ordinate's are 94.5, 174.5 and 230. If it harmonized with the metallic majority, these values would he rectified, and the discovery made possible of an element with a higher atomic weight than uranium. An adjustment of the atomic volume of an element downward can he much easier accommodated than a change of atomic weight in either direction, which would usually warp the curve; and it is noteworthy that a corresponding increase in density can be most easily tolerated by the elements whose atomic volumes are most in need of revision and whose metallic characteristics are not well defined; viz., Yt, Pr, Nd. Sm, Er and Gd. A consideration of the change in atomic volume necessitated by the latter is particularly interesting with regard to what, has been said of samarium. Because of its trivalence and other chemical properties, Gd'can not be placed on the line of K, Rb, and Cs as indicated; neither is it conceivable to class it with (he CI, A or Ca group. Eu (152) seems logically placed after Sm (150.4) under Ru, and as Gd has the next highest atomic weight (157.3), it falls under Co and Rh. Putting the remaining rare elements in the order of their atomic weights, Tb (159.2), Ho (162), Dy (162.5), Er (167.4), Tm (168.5), Ny (170±) and Dp (171) fall respectively under Pd, Ag, Cd, Jn, Sn, Sb and Te. Dropping Pr, Ce, Nd and Sm and displacing the curve (dotted) through these elements as well (all shown by circles for clearness), give a loop which appears much more symmetrical than the original one drawn in a full line. The atomic weight, 171, of Dp, fits into the periodic table much better, also, than the present graphical value of 153.5. Since the four elements under I, Xe, Cs and Ba must have atomic •weights ranging from 171 to 172 (Yb), they will probably be found difficult to separate from one another, as is noticeable to a less degree in known elements having nearly the same atomic weight; viz., Co and Ni, Sn and Sb, and Os, Ir and Pt. M is difficuH to conceive the significance, if there iy any, of the convergence of the lines unless a literal interpretation is put upon it as pointing to the ghost of a Prout's hypothesis; but, if so, implying a condensation from something far more subtle than hydrogen. The curve itself is suggestive of an oscillation whose origin might not unreasonably be identical with that of the group lines, and although the type lines are perverse, they tend to point in this direction. Measurements which have been made, locate the origin at + 6, — 237.5. There is undoubtedly a close connection between other properties of the elements and their atomic weights; but except for the melting point, data are incomplete and subject to modifying physical conditions. The relation herein set forth, if true, seems capable of supplementing the usefulness of the periodic law, and of serving to supply desirable quantitative information of the atomic volumes of the elements, both known and undiscovered.
This article was originally published with the title "A Possible Extension of the Periodic Law" in s , , 253-254 (December 2012)