Chapter VIII. we considered the limit to which carbon tends in its

compounds, and in a similar manner there is for every element in its compounds a tendency to attain a certain highest limit RX_{_n_}. This view was particularly developed in the middle of the present century by Frankland in studying the metallo-organic compounds, _i.e._ those in which X is wholly or partially a hydrocarbon radicle; for instance, X = CH_{3} or C_{2}H_{5} &c. Thus, for example, antimony, Sb (Chapter XIX.) gives, with chlorine, compounds SbCl_{3} and SbCl_{5} and corresponding oxygen compounds Sb_{2}O_{3} and Sb_{2}O_{5}, whilst under the action of CH_{3}I, C_{2}H_{5}I, or in general EI (where E is a hydrocarbon radicle of the paraffin series), upon antimony or its alloy with sodium there are formed SbE_{3} (for example, Sb(CH_{3})_{3}, boiling at about 81°), which, corresponding to the lower form of combination SbX_{3}, are able to combine further with EI, or Cl_{2}, or O, and to form compounds of the limiting type SbX_{5}; for example, SbE_{4}Cl corresponding to NH_{4}Cl with the substitution of nitrogen by antimony, and of hydrogen by the hydrocarbon radicle. The elements which are most chemically analogous are characterised by the fact of their giving compounds of similar form RX_{_n_}. The halogens which are analogous give both higher and lower compounds. So also do the metals of the alkalis and of the alkaline earths. And we saw that this analogy extends to the composition and properties of the nitrogen and hydrogen compounds of these metals, which is best seen in the salts. Many such groups of analogous elements have long been known. Thus there are analogues of oxygen, nitrogen, and carbon, and we shall meet with many such groups. But an acquaintance with them inevitably leads to the questions, what is the cause of analogy and what is the relation of one group to another? If these questions remain unanswered, it is easy to fall into error in the formation of the groups, because the notions of the degree of analogy will always be relative, and will not present any accuracy or distinctness Thus lithium is analogous in some respects to potassium and in others to magnesium; beryllium is analogous to both aluminium and magnesium. Thallium, as we shall afterwards see and as was observed on its discovery, has much kinship with lead and mercury, but some of its properties appertain to lithium and potassium. Naturally, where it is impossible to make measurements one is reluctantly obliged to limit oneself to approximate comparisons, founded on apparent signs which are not distinct and are wanting in exactitude. But in the elements there is one accurately measurable property, which is subject to no doubt--namely, that property which is expressed in their atomic weights. Its magnitude indicates the relative mass of the atom, or, if we avoid the conception of the atom, its magnitude shows the relation between the masses forming the chemical and independent individuals or elements. And according to the teaching of all exact data about the phenomena of nature, the mass of a substance is that property on which all its remaining properties must be dependent, because they are all determined by similar conditions or by those forces which act in the weight of a substance, and this is directly proportional to its mass. Therefore it is most natural to seek for a dependence between the properties and analogies of the elements on the one hand and their atomic weights on the other.

This is the fundamental idea which leads _to arranging all the elements according to their atomic weights_. A periodic repetition of properties is then immediately observed in the elements. We are already familiar with examples of this:--

F = 19, Cl = 35·5, Br = 80, I = 127, Na = 23, K = 39, Rb = 85, Cs = 133, Mg = 24, Ca = 40, Sr = 87, Ba = 137.

The essence of the matter is seen in these groups. The halogens have smaller atomic weights than the alkali metals, and the latter than the metals of the alkaline earths. Therefore, _if all the elements be arranged in the order of their atomic weights, a periodic repetition of properties is obtained_. This is expressed by the _law of periodicity_, _the properties of the elements, as well as the forms and properties of their compounds, are in periodic dependence or (expressing ourselves algebraically) form a periodic function of the atomic weights of the elements_.[8] Table I. of _the periodic system of the elements_, which is placed at the very beginning of this book, is designed to illustrate this law. It is arranged in conformity with the eight types of oxides described in the preceding pages, and those elements which give the oxides, R_{2}O and consequently salts RX, form the 1st group; the elements giving R_{2}O_{2} or RO as their highest grade of oxidation belong to the 2nd group; those giving R_{2}O_{3} as their highest oxides form the 3rd group, and so on; whilst the elements of all the groups which are nearest in their atomic weights are arranged in series from 1 to 12. The even and uneven series of the same groups present the same forms and limits, but differ in their properties, and therefore two contiguous series, one even and the other uneven--for instance, the 4th and 5th--form a period. Hence the elements of the 4th, 6th, 8th, 10th, and 12th, or of the 3rd, 5th, 7th, 9th, and 11th, series form analogues, like the halogens, the alkali metals, &c. The conjunction of two series, one even and one contiguous uneven series, thus forms one large _period_. These periods, beginning with the alkali metals, end with the halogens. The elements of the first two series have the lowest atomic weights, and in consequence of this very circumstance, although they bear the general properties of a group, they still show many peculiar and independent properties.[9] Thus fluorine, as we know, differs in many points from the other halogens, and lithium from the other alkali metals, and so on. These lightest elements may be termed _typical elements_. They include--

H. Li, Be, B, C, N, O, F. Na, Mg....

In the annexed table all the remaining elements are arranged, not in groups and series, but _according to periods_. In order to understand the essence of the matter, it must be remembered that here the atomic weight gradually increases along a given line; for instance, in the line commencing with K = 39 and ending with Br = 80, the intermediate elements have intermediate atomic weights, as is clearly seen in Table III., where the elements stand in the order of their atomic weights.

I. II. III. IV. V. VI. VII. I. II. III. IV. V. VI. VII. { Even Series. } Mg Al Si P S Cl K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Rb Sr Y Zr Nb Mo -- Ru Rh Pd Ag Cd In Sn Sb Te I Cs Ba La Ce Di? -- -- -- -- -- -- -- -- -- -- -- -- -- -- Yb -- Ta W -- Os Ir Pt Au Hg Tl Pb Bi -- -- -- -- -- Th -- U { Uneven Series }

The same degree of analogy that we know to exist between potassium, rubidium, and cæsium; or chlorine, bromine, and iodine; or calcium, strontium, and barium, also exists between the elements of the other vertical columns. Thus, for example, zinc, cadmium, and mercury, which are described in the following chapter, present a very close analogy with magnesium. For a true comprehension of the matter[10] it is very important to see that all the aspects of the distribution of the elements according to their atomic weights essentially express one and the same fundamental _dependence_--_periodic properties_.[11] The following points then must be remarked in it.

[8] The periodic law and the periodic system of the elements appeared in the same form as here given in the first edition of this work, begun in 1868 and finished in 1871. In laying out the accumulated information respecting the elements, I had occasion to reflect on their mutual relations. At the beginning of 1869 I distributed among many chemists a pamphlet entitled 'An Attempted System of the Elements, based on their Atomic Weights and Chemical Analogies,' and at the March meeting of the Russian Chemical Society, 1869, I communicated a paper 'On the Correlation of the Properties and Atomic Weights of the Elements.' The substance of this paper is embraced in the following conclusions: (1) The elements, if arranged according to their atomic weights, exhibit an evident _periodicity_ of properties. (2) Elements which are similar as regards their chemical properties have atomic weights which are either of nearly the same value (platinum, iridium, osmium) or which increase regularly (_e.g._ potassium, rubidium, cæsium). (3) The arrangement of the elements or of groups of elements in the order of their atomic weights corresponds with their so-called _valencies_. (4) The elements, which are the most widely distributed in nature, have _small_ atomic weights, and all the elements of small atomic weight are characterised by sharply defined properties. They are therefore typical elements. (5) The _magnitude_ of the atomic weight determines the character of an element. (6) The discovery of many yet unknown elements may be expected. For instance, elements analogous to aluminium and silicon, whose atomic weights would be between 65 and 75. (7) The atomic weight of an element may sometimes be corrected by aid of a knowledge of those of the adjacent elements. Thus the combining weight of tellurium must lie between 123 and 126, and cannot be 128. (8) Certain characteristic properties of the elements can be foretold from their atomic weights.

The entire periodic law is included in these lines. In the series of subsequent papers (1870-72, for example, in the _Transactions_ of the Russian Chemical Society, of the Moscow Meeting of Naturalists, of the St. Petersburg Academy, and Liebig's _Annalen_) on the same subject we only find applications of the same principles, which were afterwards confirmed by the labours of Roscoe, Carnelley, Thorpe, and others in England; of Rammelsberg (cerium and uranium), L. Meyer (the specific volumes of the elements), Zimmermann (uranium), and more especially of C. Winkler (who discovered germanium, and showed its identity with ekasilicon), and others in Germany; of Lecoq de Boisbaudran in France (the discoverer of gallium = ekaaluminium); of Clève (the atomic weights of the cerium metals), Nilson (discoverer of scandium = ekaboron), and Nilson and Pettersson (determination of the vapour density of beryllium chloride) in Sweden; and of Brauner (who investigated cerium, and determined the combining weight of tellurium = 125) in Austria, and Piccini in Italy.

I consider it necessary to state that, in arranging the periodic system of the elements, I made use of the previous researches of Dumas, Gladstone, Pettenkofer, Kremers, and Lenssen on the atomic weights of related elements, but I was not acquainted with the works preceding mine of De Chancourtois (_vis tellurique_, or the spiral of the elements according to their properties and equivalents) in France, and of J. Newlands (Law of Octaves--for instance, H, F, Cl, Co, Br, Pd, I, Pt form the first octave, and O, S, Fe, Se, Rh, Te, Au, Th the last) in England, although certain germs of the periodic law are to be seen in these works. With regard to the work of Prof. Lothar Meyer respecting the periodic law (Notes 12 and 13), it is evident, judging from the method of investigation, and from his statement (Liebig's _Annalen, Supt. Band 7_, 1870, 354), at the very commencement of which he cites my paper of 1869 above mentioned, that he accepted the periodic law in the form which I proposed.

In concluding this historical statement I consider it well to observe that no law of nature, however general, has been established all at once; its recognition is always preceded by many hints; the establishment of a law, however, does not take place when its significance is recognised, but only when it has been confirmed by experiment, which the man of science must consider as the only proof of the correctness of his conjectures and opinions. I therefore, for my part, look upon Roscoe, De Boisbaudran, Nilson, Winkler, Brauner, Carnelley, Thorpe, and others who verified the adaptability of the periodic law to chemical facts, as the true founders of the periodic law, the further development of which still awaits fresh workers.

[9] This resembles the fact, well known to those having an acquaintance with organic chemistry, that in a series of homologues (Chapter VIII.) the first members, in which there is the least carbon, although showing the general properties of the homologous series, still present certain distinct peculiarities.

[10] Besides arranging the elements (_a_) in a successive order according to their atomic weights, with indication of their analogies by showing some of the properties--for instance, their power of giving one or another form of combination--both of the _elements_ and of their compounds (as is done in Table III. and in the table on p. 36), (_b_) according to periods (as in Table I. at the commencement of volume I. after the preface), and (_c_) according to groups and series or small periods (as in the same tables), I am acquainted with the following methods of expressing the periodic relations of the elements: (1) By a curve drawn through points obtained in the following manner: The elements are arranged along the horizontal axis as abscissæ at distances from zero proportional to their atomic weights, whilst the values for all the elements of some 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. For this reason there can be no other elements between magnesium, which gives the chloride MgCl_{2}, and aluminium, which forms AlX_{3}; there is a break in the continuity, according to the law of multiple proportions. The periodic law ought not, therefore, to be expressed by geometrical figures in which continuity is always understood. Owing to these considerations I never have and never will express the periodic relations of the elements by any geometrical figures. (2) _By a plane spiral._ Radii are traced from a centre, proportional to the atomic weights; analogous elements lie along one radius, and the points of intersection are arranged in a spiral. This method, adopted by De Chancourtois, Baumgauer, E. Huth, and others, has many of the imperfections of the preceding, although it removes the indefiniteness as to the number of elements in a period. It is merely an attempt to reduce the complex relations to a simple graphic representation, since the equation to the spiral and the number of radii are not dependent upon anything. (3) _By the lines of atomicity_, either parallel, as in Reynolds's and the Rev. S. Haughton's method, or as in Crookes's method, arranged to the right and left of an axis, along which the magnitudes of the atomic weights are counted, and the position of the elements marked off, on the one side the members of the even series (paramagnetic, like oxygen, potassium, iron), and on the other side the members of the uneven series (diamagnetic, like sulphur, chlorine, zinc, and mercury). On joining up these points a periodic curve is obtained, compared by Crookes to the oscillations of a pendulum, and, according to Haughton, representing a cubical curve. This method would be very graphic did it not require, for instance, that sulphur should be considered as bivalent and manganese as univalent, although neither of these elements gives stable derivatives of these natures, and although the one is taken on the basis of the lowest possible compound SX_{2}, and the other of the highest, because manganese can be referred to the univalent elements only by the analogy of KMnO_{4} to KClO_{4}. Furthermore, Reynolds and Crookes place hydrogen, iron, nickel, cobalt, and others outside the axis of atomicity, and consider uranium as bivalent without the least foundation. (4) Rantsheff endeavoured to classify the elements in their periodic relations by a system dependent on solid geometry. He communicated this mode of expression to the Russian Chemical Society, but his communication, which is apparently not void of interest, has not yet appeared in print. (5) _By algebraic formulæ_: for example, E. J. Mills (1886) endeavours to express all the atomic weights by the logarithmic function A = 15(_n_ - 0·9375_t_), in which the variables _n_ and _t_ are whole numbers. For instance, for oxygen _n_ = 2, _t_ = 1; hence A = 15·94; for antimony _n_ = 9, _t_ = 0; whence A = 120, and so on. _n_ varies from 1 to 16 and _t_ from 0 to 59. The analogues are hardly distinguishable by this method: thus for chlorine the magnitudes of _n_ and _t_ are 3 and 7; for bromine 6 and 6; for iodine 9 and 9; for potassium 3 and 14; for rubidium 6 and 18; for cæsium 9 and 20; but a certain regularity seems to be shown. (6) A more natural method of expressing the dependence of the properties of elements on their atomic weights is obtained by _trigonometrical functions_, because this dependence is periodic like the functions of trigonometrical lines, and therefore Ridberg in Sweden (Lund, 1885) and F. Flavitzky in Russia (Kazan, 1887) have adopted a similar method of expression, which must be considered as worthy of being worked out, although it does not express the absence of intermediate elements--for instance, between magnesium and aluminium, which is essentially the most important part of the matter. (7) The investigations of B. N. Tchitchérin (1888, _Journal of the Russian Physical and Chemical Society_) form the first effort in the latter direction. He carefully studied the alkali metals, and discovered the following simple relation between their atomic volumes: they can all be expressed by A(2 - 0·0428A_n_), where A is the atomic weight and _n_ = 1 for lithium and sodium, 4/8 for potassium, 3/8 for rubidium, and 2/8 for cæsium. If _n_ always = 1, then the volume of the atom would become zero at A = 46-2/3, and would reach its maximum when A = 23-1/3, and the density increases with the growth of A. In order to explain the variation of _n_, and the relation of the atomic weights of the alkali metals to those of the other elements, as also the atomicity itself, Tchitchérin supposes all atoms to be built up of a primary matter; he considers the relation of the central to the peripheric mass, and, guided by mechanical principles, deduces many of the properties of the atoms from the reaction of the internal and peripheric parts of each atom. This endeavour offers many interesting points, but it admits the hypothesis of the building up of all the elements from one primary matter, and at the present time such an hypothesis has not the least support either in theory or in fact. Besides which the starting-point of the theory is the specific gravity of the metals at a definite temperature (it is not known how the above relation would appear at other temperatures), and the specific gravity varies even under mechanical influences. L. Hugo (1884) endeavoured to represent the atomic weights of Li, Na, K, Rb, and Cs by geometrical figures--for instance, Li = 7 represents a central atom = 1 and six atoms on the six terminals of an octahedron; Na, is obtained by applying two such atoms on each edge of an octahedron, and so on. It is evident that such methods can add nothing new to our data respecting the atomic weights of analogous elements.

[11] Many natural phenomena exhibit a dependence of a periodic character. Thus the phenomena of day and night and of the seasons of the year, and vibrations of all kinds, exhibit variations of a periodic character in dependence on time and space. But in ordinary periodic functions one variable varies continuously, whilst the other increases to a limit, then a period of decrease begins, and having in turn reached its limit a period of increase again begins. It is otherwise in the periodic function of the elements. Here the mass of the elements does not increase continuously, but abruptly, by steps, as from magnesium to aluminium. So also the valency or atomicity leaps directly from 1 to 2 to 3, &c., without intermediate quantities, and in my opinion it is these properties which are the most important, and it is their periodicity which forms the substance of the periodic law. It expresses _the properties of the real elements_, and not of what may be termed their manifestations visually known to us. The external properties of elements and compounds are in periodic dependence on the atomic weight of the elements only because these external properties are themselves the result of the properties of the real elements which unite to form the 'free' elements and the compounds. To explain and express the periodic law is to explain and express the cause of the law of multiple proportions, of the difference of the elements, and the variation of their atomicity, and at the same time to understand what mass and gravitation are. In my opinion this is still premature. But just as without knowing the cause of gravitation it is possible to make use of the law of gravity, so for the aims of chemistry it is possible to take advantage of the laws discovered by chemistry without being able to explain their causes. The above-mentioned peculiarity of the laws of chemistry respecting definite compounds and the atomic weights leads one to think that the time has not yet come for their full explanation, and I do not think that it will come before the explanation of such a primary law of nature as the law of gravity.

It will not be out of place here to turn our attention to the many-sided correlation existing between the undecomposable _elements and the compound carbon radicles_, which has long been remarked (Pettenkofer, Dumas, and others), and reconsidered in recent times by Carnelley (1886), and most originally in Pelopidas's work (1883) on the principles of the periodic system. Pelopidas compares the series containing eight hydrocarbon radicles, C_{_n_}H_{2_n_ + 1}, C_{_n_}H_{2_n_} &c., for instance, C_{6}H_{13}, C_{6}H_{12}, C_{6}H_{11}, C_{6}H_{10}, C_{6}H_{9}, C_{6}H_{8}, C_{6}H_{7}, and C_{6}H_{6}--with the series of the elements arranged in eight groups. The analogy is particularly clear owing to the property of C_{_n_}H_{2_n_+1} to combine with X, thus reaching saturation, and of the following members with X_{2}, X_{3} ... X_{8}, and especially because these are followed by an aromatic radicle--for example, C_{6}H_{5}--in which, as is well known, many of the properties of the saturated radicle C_{6}H_{13} are repeated, and in particular the power of forming a univalent radicle again appears. Pelopidas shows a confirmation of the parallel in the property of the above radicles of giving oxygen compounds corresponding with the groups in the periodic system. Thus the hydrocarbon radicles of the first group--for instance, C_{6}H_{13} or C_{6}H_{5}--give oxides of the form R_{2}O and hydroxides RHO, like the metals of the alkalis; and in the third group they form oxides R_{2}O_{3} and hydrates RO_{2}H. For example, in the series CH_{3} the corresponding compounds of the third group will be the oxide (CH)_{2}O_{3} or C_{2}H_{2}O_{3}--that is, formic anhydride and hydrate, CHO_{2}H, or formic acid. In the sixth group, with a composition of C_{2}, the oxide RO_{3} will be C_{2}O_{3}, and hydrate C_{2}H_{2}O_{4}--that is, also a bibasic acid (oxalic) resembling sulphuric, among the inorganic acids. After applying his views to a number of organic compounds, Pelopidas dwells more particularly on the radicles corresponding with ammonium.

With respect to this remarkable parallelism, it must above all be observed that in the elements the atomic weight increases in passing to contiguous members of a higher valency, whilst here it decreases, which should indicate that the periodic variability of elements and compounds is subject to some higher law whose nature, and still more whose cause, cannot at present be determined. It is probably based on the fundamental principles of the internal mechanics of the atoms and molecules, and as the periodic law has only been generally recognised for a few years it is not surprising that any further progress towards its explanation can only be looked for in the development of facts touching on this subject.

1. The composition of the higher oxygen compounds is determined by the groups: the first group gives R_{2}O, the second R_{2}O_{2} or RO, the third R_{2}O_{3}, &c. There are eight types of oxides and therefore eight groups. Two groups give a period, and the same type of oxide is met with twice in a period. For example, in the period beginning with potassium, oxides of the composition RO are formed by calcium and zinc, and of the composition RO_{3} by molybdenum and tellurium. The oxides of the even series, of the same type, have stronger basic properties than the oxides of the uneven series, and the latter as a rule are endowed with an acid character. Therefore the elements which exclusively give bases, like the alkali metals, will be found at the commencement of the period, whilst such purely acid elements as the halogens will be at the end of the period. The interval will be occupied by intermediate elements, whose character and properties we shall afterwards describe. It must be observed that the acid character is chiefly proper to the elements with small atomic weights in the uneven series, whilst the basic character is exhibited by the heavier elements in the even series. Hence elements which give acids chiefly predominate among the lightest (typical) elements, especially in the last groups; whilst the heaviest elements, even in the last groups (for instance, thallium, uranium) have a basic character. Thus the basic and acid characters of the higher oxides are determined (_a_) by the type of oxide, (_b_) by the even or uneven series, and (_c_) by the atomic weight.[11 bis] The groups are indicated by Roman numerals from I. to VIII.

2. _The hydrogen compounds_ being volatile or gaseous substances which are prone to reaction--such as HCl, H_{2}O, H_{3}N, and H_{4}C[12]--are only formed by the elements of the uneven series and higher groups giving oxides of the forms R_{2}O_{_n_}, RO_{3}, R_{2}O_{5}, and RO_{2}.

3. If an element gives a hydrogen compound, RX_{_m_}, it forms an _organo-metallic compound_ of the same composition, where X = C_{_n_}H_{2_n_ + 1}; that is, X is the radicle of a saturated hydrocarbon. The elements of the uneven series, which are incapable of giving hydrogen compounds, and give oxides of the forms RX, RX_{2}, R_{X}3, also give organo-metallic compounds of this form proper to the higher oxides. Thus zinc forms the oxide ZnO, salts ZnX_{2} and zinc ethyl Zn(C_{2}H_{5})_{2}. The elements of the even series do not seem to form organo-metallic compounds at all; at least all efforts for their preparation have as yet been fruitless--for instance, in the case of titanium, zirconium, or iron.

4. The atomic weights of elements belonging to contiguous periods differ approximately by 45; for example, K<Rb, Cr<Mo, Br<I. But the elements of the typical series show much smaller differences. Thus the difference between the atomic weights of Li, Na, and K, between Ca, Mg, and Be, between Si and C, between S and O, and between Cl and F, is 16. As a rule, there is a greater difference between the atomic weights of two elements of one group and belonging to two neighbouring series (Ti-Si = V-P = Cr-S = Mn-Cl = Nb-As, &c. = 20); and this difference attains a maximum with the heaviest elements (for example, Th-Pb = 26, Bi-Ta = 26, Ba-Cd = 25, &c.). Furthermore, the difference between the atomic weights of the elements of even and uneven series also increases. In fact, the differences between Na and K, Mg and Ca, Si and Ti, are less abrupt than those between Pb and Th, Ta and Bi, Cd and Ba, &c. Thus even in the magnitude of the differences of the atomic weights of analogous elements there is observable a certain connection with the gradation of their properties.[12 bis]

5. According to the periodic system every element occupies a certain position, determined by the group (indicated in Roman numerals) and series (Arabic numerals) in which it occurs. These indicate the atomic weight, the analogues, properties, and type of the higher oxide, and of the hydrogen and other compounds--in a word, all the chief quantitative and qualitative features of an element, although there yet remain a whole series of further details and peculiarities whose cause should perhaps be looked for in small differences of the atomic weights. If in a certain group there occur elements, R_{1}, R_{2}, R_{3}, and if in that series which contains one of these elements, for instance R_{2}, an element Q_{2} precedes it and an element T_{2} succeeds it, then the properties of R_{2} are determined by the properties of R_{1}, R_{3}, Q_{2}, and T_{2}. Thus, for instance, the atomic weight of R_{2} = 1/4(R_{1} + R_{3} + Q_{2} + T_{2}). For example, selenium occurs in the same group as sulphur, S = 32, and tellurium, Te = 125, and, in the 7th series As = 75 stands before it and Br = 80 after it. Hence the atomic weight of selenium should be 1/4(32 + 125 + 75 + 80) = 78, which is near to the truth. Other properties of selenium may also be determined in this manner. For example, arsenic forms H_{3}As, bromine gives HBr, and it is evident that selenium, which stands between them, should form H_{2}Se, with properties intermediate between those of H_{3}As and HBr. Even the physical properties of selenium and its compounds, not to speak of their composition, being determined by the group in which it occurs, may be foreseen with a close approach to reality from the properties of sulphur, tellurium, arsenic, and bromine. _In this manner it is possible to foretell the properties of still unknown elements._ For instance in the position IV, 5--that is, in the IVth group and 5th series--an element is still wanting. These unknown elements may be named after the preceding known element of the same group by adding to the first syllable the prefix _eka_-, which means _one_ in Sanskrit. The element IV, 5, follows after IV, 3, and this latter position being occupied by silicon, we call the unknown element ekasilicon and its symbol Es. The following are the properties which this element should have on the basis of the known properties of silicon, tin, zinc, and arsenic. Its atomic weight is nearly 72, higher oxide EsO_{2}, lower oxide EsO, compounds of the general form EsX_{4}, and chemically unstable lower compounds of the form EsX_{2}. Es gives volatile organo-metallic compounds--for instance, Es(CH_{3})_{4}, Es(CH_{3})_{3}Cl, and Es(C_{2}H_{5})_{4}, which boil at about 160°, &c.; also a volatile and liquid chloride, EsCl_{4}, boiling at about 90° and of specific gravity about 1·9. EsO_{2} will be the anhydride of a feeble colloidal acid, metallic Es will be rather easily obtainable from the oxides and from K_{2}EsF_{6} by reduction, EsS_{2} will resemble SnS_{2} and SiS_{2}, and will probably be soluble in ammonium sulphide; the specific gravity of Es will be about 5·5, EsO_{2} will have a density of about 4·7, &c. Such a prediction of the properties of ekasilicon was made by me in 1871, on the basis of the properties of the elements analogous to it: IV, 3, = Si, IV, 7 = Sn, and also II, 5 = Zn and V, 5 = As. And now that this element has been discovered by C. Winkler, of Freiberg, it has been found that its actual properties entirely correspond with those which were foretold.[13] In this we see a most important confirmation of the truth of the periodic law. This element is now called germanium, Ge (_see_ Chapter XVIII.). It is not the only one that has been predicted by the periodic law.[14] We shall see in describing the elements of the third group that properties were foretold of an element ekaaluminium, III, 5, El = 68, and were afterwards verified when the metal termed 'gallium' was discovered by De Boisbaudran. So also the properties of scandium corresponded with those predicted for ekaboron, according to Nilson.[15]

[11 bis] True peroxides (_see_ Note 7), like H_{2}O_{2}, BaO_{2}, S_{2}O_{7} (Chapter XX.), must not be confused with true saline oxides even if the latter contain much oxygen (for instance, N_{2}O_{5}, CrO_{3}, &c.) although one and the other easily oxidise. The difference between them is seen in their fundamental properties: the saline oxides correspond to water, while the peroxides correspond in their reactions and origin to peroxide of hydrogen. This is clearly seen in the difference between Na_{2}O and Na_{2}O_{2} (Chapter XII.). Therefore the peroxides should also have their periodicity. An element R, giving a highest degree of oxidation, R_{2}O_{_n_}, may give both a lower degree of oxidation, R_{2}O_{_n_ - _m_} (where _m_ is evidently less than _n_), and peroxides, R_{2}O_{_n_ + 1}, R_{2}O_{_n_ + 2}, or even more oxygen. This class of oxides, to which attention has only recently been turned (Berthelot, Piccini, &c.), may perhaps on further study give the possibility of generalising the capability of the elements to give unstable complex higher forms of combination, such as double salts, and in my opinion should in the near future be the field of new and important discoveries. And in contemporary chemistry, salts, saline oxides, hydrogen compounds, and other combinations of the elements corresponding to them constitute an important and very complex problem for generalisation, which is satisfied by the periodic law in its present form, to which it has risen from its first state, in which it gave the means of foreseeing (_see_ later on) the existence of unknown elements (Ga, Sc, and Ge), their properties, and many details respecting their compounds. Until those improvements in the periodic system which have been proposed by Prof. Flavitzky (of Kazan) and Prof. Harperath (of Cordoba, in the Argentine Republic), Ugo Alvisi (Italy), and others give similar practical results, I think it unnecessary to discuss them further.

[12] The hydrides generalised by the periodic law are those to which metallo-organic compounds correspond, and they are themselves either volatile or gaseous. The hydrogen compounds like Na_{2}H, BaH, &c. are distinguished by other signs. They resemble alloys. They show (_see_ end of last chapter) a systematic harmony, but they evidently should not be confused with true hydrides, any more than peroxides with saline oxides. Moreover, such hydrides have, like the peroxides, only recently been subjected to research, and have been but little studied. The best known of these compounds are given in the 16th column of Table III., and it will be seen that they already exhibit a periodicity of properties and composition.

[12 bis] The relation between the atomic weights, and especially the difference = 16, was observed in the sixth and seventh decades of this century by Dumas, Pettenkofer, L. Meyer, and others. Thus Lothar Meyer in 1864, following Dumas and others, grouped together the tetravalent elements carbon and silicon; the trivalent elements nitrogen, phosphorus, arsenic, antimony, and bismuth; the bivalent oxygen, sulphur, selenium, and tellurium; the univalent fluorine, chlorine, bromine, and iodine; the univalent metals lithium, sodium, potassium, rubidium, cæsium, and thallium, and the bivalent metals beryllium, magnesium, strontium and barium--observing that in the first the difference is, in general = 16, in the second about = 46, and the last about = 87-90. The first germs of the periodic law are visible in such observations as these. Since its establishment this subject has been most fully worked out by Ridberg (Note 10), who observed a periodicity in the variation of the differences between the atomic weights of two contiguous elements, and its relation to their atomicity. A. Bazaroff (1887) investigated the same subject, taking, not the arithmetical differences of contiguous and analogous elements, but the ratio of their atomic weights; and he also observed that this ratio alternately rises and falls with the rise of the atomic weights. I will here remark that the relation of the eighth group to the others will be considered at the end of this work in