Of THE UHIVP^ ,ty Of ''-UNO* 3 The University of Chicago The Freezing Point Lowerings of Mixtures and in Solutions of Cobaltammines, and Other Salts of Various Types of Ionization The Periodic System and the Properties of the Elements A DISSERTATION SUBMITTED TO THE FACULTY OF THE OGDEN GRADUATE SCHOOL OF SCIENCE IN CANDIDACY FOR THE , DEGREE OF DOCTOR OF PHILOSOPHY (DEPARTMENT OF CHEMISTRY) By Ralph E* Hall (t *s, ry '*3/ A Private Edition Distributed by The University of Chicago Libraries ESCHENBACH PRINTING COMPANY EASTON, PA. 5 v/' 4 ? The Periodic System and the Properties the Elements. The periodic system is the most important generalization of the facts embodied in the science of chemistry, and one of the most glaring errors in chemical pedagogy during the past fifteen years has been the neglect of this system, both in the so-called modern text-books and in the courses of instruction given in some of our universities. This has probably been due, in a large measure, to the unfortunate attempt which has been made by certain chemists to present chemistry without the use of the atomic theory. Recent remarkable discoveries made by physicists have, how- ever,. made it evident that the atomic theory and the periodic system are of supreme importance in both chemistry and physics. The total number of elements in our present ordinary system from helium to uranium, inclusive, is 91, and with hydrogen this makes 92 elements in all. The system from helium to uranium seems to be com- pletely known, though not all of the elements have been discovered, but nothing is known as to whether there are any elements which belong to the ordinary system and fall between hydrogen and helium in atomic [Reprinted from an article by W. D. Harkins and R. E. Hall in the Journal of the American Chemical Society for February, 1916.] 58787 4 weight (possibly with atomic weights 2 and 3). Of the 92 elements, 87 have already been discovered and 5 are still unknown. Of these 5, three belong to the seventh group, two being in group VIIB, and these may be given the provisional names eka-manganese I (atomic weight about 99), and eka manganese II (divi-manganese) (atomic weight about 188). These elements, particularly the second, should have extremely high melt- ing points. In group VIIA eka-iodine should have an atomic weight near 219, and in group I A eka-caesium, for which Baxter made a search, but without success, should have an atomic weight of about 225. An unknown element of the rare earth group may be called eka-neodymium (atomic weight about 146). In addition to these 92 elements of the ordinary system, Nicholson assumes that there is another system of simpler elements such as proto- hydrogen, nebulium, protofluorine (coronium), arconium, and other ele- ments, of atomic weights 0.082, 1.31, 2.1, and 2.9. Of these elements the spectra attributed to nebulium and arconium are found in the nebula and that of the hypothetical protofluorine is found in the corona of the sun. The evidence in favor of this simpler system is not very conclusive, but the existence of these spectra makes it evident either that some other- wise unknown elements exist in the nebulae and the corona of the sun or that the spectra are due to enhanced lines from some of the ordinary elements. 1 If such elements actually exist, they may belong to the ordinary system, or they may belong to another system, possibly with a simpler structure as Nicholson assumes. Nicholson’s atomic weights were obtained from the width of the spectral lines, and also from the differences between the calculated and the observed values of the wave lengths. Both of these methods are very uncertain under the con- ditions of observation, so there is no conclusive evidence for the particu- lar atomic weights which Nicholson gives. 2 It has been found that the number of the element in the periodic table, beginning with hydrogen as 1, helium as 2, lithium as 3, etc.; or what is called the atomic number is more characteristic of an element than its atomic weight. For example lead, with an atomic number of 82, con- sists of Atomic weight. 1. Lead from radium 206.1 2. Ordinary lead 207.20 3. Lead from thorium 208.1 1 Merton, Proc. Roy. Soc., ( A ) 91, 498 (1915), has obtained enhanced lines by a discharge between carbon poles in a vacuum tube, previously filled with hydrogen, which have practically the same wave length, and the same nebulous character as eight of the lines obtained in the spectrum of the Wolf-Rayet stars. 2 For a more complete description and discussion of Nicholson’s work see a paper on “Recent Work on the Structure of the Atom,’’ Harkins and Wilson, J. Am. Chem. Soc., 37, 1396-1421 (1915). Note, Fig. i. — The connections between the main and the sub- groups are shown better in Fig. 2 than in Fig. 1, since in Fig. 1 the connections were modified slightly by the artist to bring out the perspective. Fig. 2. 5 Atomic weight. 4. Radium D 210. 1 5. Thorium B 214. 1 6. Radium B 212. 1 7. Lead from actinium Unknown 8. Lead from actinium B Unknown 9. Product of branch chain, radium series 210. 1 10. Product of branch chain, actinium series Unknown Thus the same element may have very widely different atomic weights, but the atomic number, which presumably gives the number of positive charges on the nucleus of the atom, remains constant, and in the case of lead is 82. A Periodic Table which Gives all of the Elements Plotted According to Their Atomic Weights, and Shows the Correct Relations from the Chemical Standpoint. The periodic system of Mendeleeff classified the elements as well as was possible at the time when it was devised, and practically none of the more recent tables have made any improvement upon the original form, but the discoveries of the last few years make it possible to design a table which expresses the relations existing between the elements much more perfectly. A modern table should meet the following requirements: (1) It should plot the atomic weights so that the isotopes of such an element as lead may be included in it, their atomic weights shown, and so that the alpha and beta decompositions of the radioactive elements may be clearly depicted. (2) It should give no blanks except those corresponding to atomic numbers of elements which remain to be discovered. The Mendeleeff table contains many blanks which can never be filled. (3) It should in a natural way relate the main group elements to the ' elements in the corresponding sub-group. The principal defect of many of the periodic tables is that they have been constructed without any consideration of this important condition. A table which shows no rela- tions between such a main group as the Be, Mg, Ca, Sr, Ba and Ra main group, and the corresponding sub-group, Zn, Cd, Hg, is not at all correct from the chemical standpoint. On the other hand, the form of the table itself should distinguish between the main and the sub-group elements. One of the disadvantages of the Mendeleeff table is that the table by its form makes no such distinction, since it throws the main and sub-groups together. However, the Mendeleeff form is much to be preferred to those given by Staigmiiller, Werner and others, in which these chemical rela- tions are not shown at all. (4) Both the zero and the eighth groups should fit naturally into the system. 6 (5) All of the above relations should be shown by a continuous curve which should connect the elements in the order of their atomic numbers. In the ordinary form of table there is nothing to indicate the relation of one series to the next. (6) As has been shown by Harkins and Wilson, the atomic weights are a linear function of the atomic numbers, and can be represented by the equation W = 2 (n + n') + 1/2 + i/2( — i)” -1 , where n is the atomic number and n' is ZERO for the lighter ELEMENTS. It is therefore better to plot the atomic weights themselves than to plot the logarithms as has been done. 1 A modern table which meets these requirements and also shows other relationships not expressed by the ordinary form of table, may be con- structed as a helix in space, or as a spiral on a plane. The space form is more nearly like the ordinary table, and is therefore to be preferred. A model of this space form, a photograph of which is shown in Fig. 3, has been constructed, and is in use in the work in inorganic chemistry in the University of Chicago. The atomic weights are plotted from the top down, one unit of atomic weight being represented by one centimeter, so the model is about two and one- half meters high. Although the model gives the relations with extreme clearness, it is difficult to photograph it so that all of the details are visible. However, this is remedied in Fig. 1, which gives a drawing of the system. In order that the atomic weights may be plotted directly, the drawing has been made as a vertical projection of the model, but drawn with line per- spective, and the base is given in perspective so that the table may be easily visualized in space. The balls representing the elements are supposed to be strung on vertical rods. All of the elements on one vertical rod belong to one group, 2 have on the whole the same maximum valence, and are represented by the same color. The group numbers are given at the bottom of the rods. On the outer cylinder in Fig. 2, the electro-negative elements are represented by black circles at the back of the cylinder, and electro-positive elements by white circles on the front of the cylinder. The transition elements 1 Stoney, Chem. News, 57, 163 (1888); and Proc. Roy. Soc., 46, 115 (1888). 2 In Figs. 1 and 2 some of the elements are represented by small, and others by larger circles. The small circles are not meant to show any difference in the elements which they represent, but are used whenever there is not room on the diagram for the larger circles. At the bottom of the table many isotopes are represented, and each intersection of the helix with a vertical group rod represents only one element, even where there arc six circles as there are for the isotopes of lead. While the six circles for lead represent only one atomic number, each of the small circles on the rare earth loop represents an atomic number of its own. The three eighth group triads, and the rare earth group resemble each other in that in these four cases the atomic number increases while the group number remains constant. r of the zero and fourth groups are represented by circles which are half black and half white. The inner loop elements are intermediate in their properties. Elements on the back of the inner loop are shown as heavily shaded circles, while those on the front are shaded only slightly. In order to understand the table it may be well to take an imaginary journey down the helix in Fig. 2, beginning at the top. Hydrogen (atomic number and atomic weight = 1) stands by itself, and is followed by the first inert, zero group, and zero valent element helium. Here there comes the extremely sharp break in chemical properties with the change to the strongly positive, univalent element lithium, followed by the somewhat less positive bivalent element, beryllium, and the third group element boron, with a positive valence of three, and a weaker negative valence. At the extreme right of the outer cylinder is carbon, the fourth group transition element, with a positive valence of four, and an equal negative valence, both of approximately equal strength. The first element on the back of the cylinder is more negative than posi- tive, and has a positive valence of five, and a negative valence of three. The negative properties increase until fluorine is reached and then there is a sharp break of properties, with the change from the strongly nega- tive, univalent element fluorine, through the zero valent transition ele- ment neon, to the strongly positive sodium Thus in order around the outer loop the second series elements are as follows : Group number o 1 2 3 4 5 6 7 Maximum valence o 1 2 3 4 5 6 7 Element He Li Be B C N O F Atomic number 2 3 4 5 6 7 8 9 After these comes neon, which is like helium, sodium which is like lithium, etc., to chlorine, the eighth element of the second period. For the third period the journey is continued, still on the outer loop, with argon, potassium, calcium, scandium, and then begins, with titanium, to turn for the first time into the inner loop. Vanadium, chromium, and man- ganese, which come next, are on the inner loop, and thus belong, not to main but to sub-groups. This is the first appearance in the system of sub- group elements. Just beyond manganese a catastrophe of some sort seems to take place, for here three elements of one kind, and therefore belonging to one group, are deposited. The eighth group in this table takes the place on the inner loop which the rare gases of the atmosphere fill on the outer loop. The eighth group is thus a sub-group of the zero group. After the eighth group elements, which have here appeared for the first time, come copper, zinc, and gallium; and with germanium, a fourth group element, the helix returns to the outer loop. It then passes through arsenic, selenium, and bromine, thus completing the first long period of 8 1 8 elements. Following this there comes a second long period, exactly similar, and also containing 18 elements. The relations which exist may be shown by the following natural classi- fication of the elements. They may be divided into cycles and periods as follows: Table I. Cycle i = 4 2 elements. ist short period He — F = 8 = 2 X 2 2 elements. 2nd short period Ne — Cl = 8 = 2 X 2 2 elements. Cycle 2 = 6 2 elements. 1 st long period A — Br= 18 =2 X3 2 elements. 2nd long period Kr — I = 18 = 2 X3 2 elements. Cycle 3 = 8 2 elements. ist very long period. . . Xe — Eka - I = 32 = 2 X 4 2 elements. 2nd very long period. . . Nt — U The last very long period, and therefore the last cycle, is incomplete. It will be seen, however, that these remarkable relations are perfect in their regularity. These are the relations, too, which exist in the com- pleted system, 1 and are not like many false numerical systems which have been proposed in the past where the supposed relations were due to the counting of blanks which do not correspond to atomic numbers. This peculiar relationship is undoubtedly connected with the variations in structure of these complex elements, but their meaning will not be ap- parent until we know more in regard to atomic structure. The first cycle of two short periods is made up wholly of outer loop or main group elements. Each of the long periods of the second cycle is made up of main and of sub-group elements, and each period contains one eighth group. The only complete very long period is made up of main and of sub-group elements, contains one eighth group, and would be of the same length (18 elements) as the long periods if it were not lengthened to 32 elements by the inclusion of the rare earths. The first long period is introduced into the system by the insertion of iron, cobalt, and nickel, in its center, and these are three elements whose atomic numbers increase by steps of one while their valence remains con- stant. The first very long period is formed in a similar way by the in- sertion of the rare earths, another set of elements whose atomic numbers increase by one while the valence remains constant. In this periodic table the maximum valence for a group of elements may be found by beginning with zero for the zero group and counting 1 If elements of atomic weights two and three are ever discovered then the zero cycle would contain 2 2 elements, and period number one should then be said to begin with lithium. Such extrapolation, however, is an uncertain basis for the prediction of such elements. IhL USRAliY Of ih£ 1 H 1.0078 Periodic System of the Elements by W. D. Harkins and R E. Hall (Arranged according to the Atomic Numbers] / Periods Group O Group A I RiO B Group A II RO B Group A III B R 2 O 3 A Group IV B ROj. RHi Group B V A RiO.lRHi Group B VI A ROj, R Hi Group B VII A R 1 O 7 .RH Group VIII RO« 2 3 4 5 6 7 8 9 i He Li Be B C N O F 4.00 6.94 9. 1 11.0 1 2 . 005 14.01 16.00 19.0 10 11 12 13 14 15 16 17 2 Ne Na Mg A1 Si P S Cl 20.2 23 . 00 24.32 27. 1 28.3 31.04 32.06 35 . 46 18 19 20 21 22 23 24 25 26 27 28 A K Ca Sc Ti V Cr Mn Fe Co Ni 3 39.88 39. 10 40.07 44 1 48 1 51.0 52.0 54.93 55.84 58.97 58 . 68 29 30 31 32 33 34 35 [He, Co, Nil Cu Zn Ga Ge As Se Br 63 .57 65 37 69.9 72.5 74.96 79.2 79.92 36 37 38 39 40 41 42 43 44 45 46 Kr Rb Sr Yt Zr Cb Mo — Ru Rh Pd 4 82.92 85 . 45 87 . 63 88.7 90 6 93 5 96.0 101.7 102.9 106.7 47 48 49 50 51 52 53 [Ru.Rh.Pd] Ag Cd In Sn Sb Te I 107.88 112.40 114.8 118 7 120.2 127.5 126.92 54 55 56 57 La 139.0 58 Xe Cs Ba Ce 130.2 132.81 137.37 59 Pr 140.9 1 40 . 25 60 Nd 61 — 144.3 62 Sa 150.4 63 Eu 152.0 64 Gd 157.3 5 65 Tb 159.2 66 Dy 162.5 67 Ho 163.5 68 Er 167.7 69 Tmj 70 T m 2 168.5 71 Yb 1 73 . 5 73 74 75 76 77 78 72 Lu 175.0 Ta w — Os Ir Pt 181.5 184 0 190.9 193.1 195.2 79 80 81 82 ’ 83 84 85 (Os.Ir.Pt ] Au Hg Tl Pb Bi Po 197.2 200.6 204.0 207 . 20 208 0 210.0 | 86 87 88 89 90 91 92 6 Nt — Ra Ac Th Bv U 222.4 226 0 232.2 234 2 238 2 4 4 3 I I 1 Divisions 1 2 J I I 0 0 9 toward the front for positive valence, and toward the back for negative valence. The negative valence runs along the spirals toward the back as follows: o — i — 2 — 3 — 4 Ne F O N C A Cl S P Si Beginning with helium the relations of the maximum theoretical val- ences run as follows : " Case i. He — F o, i, 2, 3, 4, 5, 6, 7, but does not rise to 8. Drops by 7 to o. Ne — Cl. . . . o, 1, 2, 3, 4, 5, 6, 7, but does not rise to 8. Drops by 7 to o. Case 2. A — Mn. ... o, 1, 2, 3, 4, 5, 6, 7, 8, 8, 8. Drops by 7 to 1. Fe. Co, Ni. Case 1 . Cu — Br Case 2. Kr — Ru, Rh, Pd. In the third increase, the group number and maximum valence of the group rise to 8, three elements are formed, and the drop is again by 7 to 1. Thus in every case when the valence drops back the drop in maximum group valence is 7, either from 7 to o, or from 8 to i. 1 This is another illustration of the fact that the eighth group is a sub-group of the zero group. The valence of the zero group is zero. According to Abegg the contra-valence, seemingly not active in this case, is eight. In Fig. 2 the table is divided into five divisions by four straight lines across the base. These divisions contain the following groups: Division o 1 2 3 4 Groups 0,8 1,7 2,6 3,5 4,4 The two groups of any division are said to be complementary. It will be seen that the sum of the group numbers in any division is equal to 8, as is also the sum of the maximum valences. The algebraic sum of the characteristic valences of two complementary groups is always zero. In any division in which the group numbers are very different , the chemical properties of the elements of the complementary main groups are very differ- ent , but when the group numbers become the same, the chemical properties become very much alike. Thus the greatest difference in group numbers occurs in division 8, where the difference is 8, and in the two groups there is an extreme difference in chemical properties, as there is also in division 1 between Groups 1 and 7. Whenever the two main groups of a division are very different in properties , each of the sub-groups is quite different from 1 It should be noted that while in the change from the seventh to the zero group the valence always drops to zero, in the change from the eighth to the IB group, there is a tendency to drop only part way, that is to a valence of 3 for gold (or silver), or to 2 for copper, though these elements also show the valence of one normal for the group, but by the time Group IIB is reached in zinc, cadmium, and mercury, the valence comes to the normal value, which is 2 for this group. IO its related main group. Thus copper in Group IB is not very closely re- lated to potassium group IA in its properties, and manganese is not very similar to chlorine, but as the group numbers approach each other the main and sub-groups become much alike. Thus scandium is quite sim- ilar to gallium in its properties, and titanium and germanium are very closely allied to silicon. One important relation is that on the outer cylinder the main groups I A, II A, III A, become less positive as the group number increases , while on the inner loop the positive character increases from Group IB to IIB , and at the bottom of the table the increase from IIB to IIIB is considerable. Thus thallium is much more positive than mercury. It has already been noted that in the case of the rare earths also the usual rule is inverted, that is the basic properties decrease as the atomic weight increases. Another important relation between the members of the main and the sub-groups is that when the atomic volume of the elements in the main group is large, the atomic volume of the elements in the corresponding sub-groups is small, and as the atomic volume for the main group de- creases, that for the sub-group increases. Thus, the zero group elements have very high atomic volumes, while those for the corresponding sub- groups (Group VIII) are very low. The same is true of the potassium group (high atomic volume) and the copper group (low atomic volume). On the other hand, the members of Groups IVA and IVB do not differ materially in regard to this property. The difference in chemical proper- ties between main and sub-groups is just that which should result from their differences in atomic volume. From this standpoint it may be con- sidered that the difference in chemical properties between the main and the sub-group elements is the result of the fact that the long periods for the cohesional properties (atomic volume, etc.) are twice the length of the series which condition the valence. In cycle i (short periods i and 2), the valence and the cohesional properties have periods of exactly the same length, so both of the periods represent main groups or outer cylinder elements, but in cycle 2 the valence passes through two periods while the cohesion (Fig. 12) is passing through one, so here sub-group elements appear for the first time. While the cohesion does not fix the valence, it does affect the chemical affinity. The increase in the basic properties of the sub-group elements as the group number increases from IB to IIIB, seems to be related to the occurrence of the secondary mini mum in cohesion (and melting points) which comes in group IIIB. (See Fig. 8.) On the first inner loop the positive character of the metal, as measured by the potential between the ions of the elements in unimolar solutions and the metal itself, decreases from manganese to copper, and then in- creases very rapidly in the one step to zinc, as is shown below in Table IA. 1 1 Table Id. — P ositive Character of the Metals in Solutions with Their Bivalent Ions. Mn = +0.798 volt Fe = +0. 122 volt Co = — 0.0138 volt Ni = — o . 108 volt Cu = — 0.606 volt Zn = +0.493 volt The Rare Earths. There are some questions concerning the placing of the rare earth ele- ments which are of minor importance, and may be settled by each user of such a table to suit his own convenience. Thus cerium, following the usual custom, has been put in the fourth group. This makes an extra small loop in the table which could be avoided by placing cerium in the third group with the other rare earths. That after passing lanthanum there is a tendency to swing into the fourth group with cerium, and then with praseodymium and neodymium to swing back into the third group, is indicated by the fact that cerium forms an extremely stable dioxide (CeCb); praseodymium forms a dioxide less stable than manganese di- oxide, which is itself not extremely stable; while neodymium is said to form a higher oxide only when mixed with cerium and praseodymium, or perhaps not at all; and samarium forms no higher oxide. On the other hand, the position of the rare earths as a whole is very important. Their valence, the difficulty with which they" are separated from yttrium, and their chemical reactions clearly indicate that they should be related to the third group, but put on a loop of their own. In many periodic tables, for example, even in the otherwise very good table given by Rydberg, 1 thulium is put in the chlorine family, samarium in the eighth group, europium in the silver group, etc. The system presented here shows that such a procedure is altogether unjustified, for there are not enough rare earths to go around the table, since there are four less than the required number , even when the one unknown rare earth is counted. That the number of elements in this, the fifth period, is taken correctly as 32 can be seen from the work of Moseley upon the X-ray spectra of the elements, and is indicated also by the regularity in the numerical relations between the number of elements in the different periods as al- ready pointed out by Table I. If the rare earths are to be distributed around the table, then there should be a considerable variation in their atomic volumes. Although the atomic volumes of very few of the rare earths have been determined, the data are available for the calculation of the molecular volumes of a number of the chlorides and oxides. Thus the molecular volumes of the chlorides are as follows : 1 Hicks, Phil. Mag., [6] 28, 139 (1914). 12 LaCls. CeCl 3 . PrCl 3 . NdCl 3 SmCl 3 GdCla TbCl 3 . DyCl 3 In order to understand the interpretation of these molecular volumes in terms of the atomic volumes of the rare earths, their basic properties must be taken into account. The order of the rare earths in terms of their basic properties is as follows, where the most basic element is given first: Lanthanum, praseodymium, neodymium, cerium 111 , (yttrium), samarium, gadolinium, terbium, holmium, erbium, thulium, and ytter- bium. Thus, exactly the opposite of the usual rule holds, for in this rare earth group the basic properties decrease just in the order in which the atomic weights increase. Cerium is the only element which falls out of the regular order, and it is the element which in the table (Fig. 2) is classified differently from the others. If the rare earth elements were to be distributed around the table, then samarium, europium, and gado- linium would fall in the eighth group, and therefore should have minimum atomic volumes. That these are the elements of the rare earths which do have minimum atomic volumes is indicated by the molecular volumes of the chlorides. The increase in the molecular volume of the chlorides in the case of dysprosium chloride seems to indicate that there is a minor peak in the atomic volumes beyond this point. It would be interesting in this connection to know the molecular volumes of ytterbium and lute- cium trichlorides, or much better of course, the atomic volumes of ytter- bium and lutecium. These facts may be taken to indicate that when in the formation of the elements the 57th element, lanthanum, belonging to the third group, is passed, there is a tendency for the elements to form ac- cording to the usual rule, that is, that the valence shall increase by steps of one and the atomic volume shall vary as usual. From this point on, the tendency for the atomic volumes to hold to the regular system of variation is quite likely partly effective. On the other hand, the valence succeeds only in rising by one to four in the case of cerium, the 58th ele- ment, and then only for a few of its compounds. With praseodymium and neodymium the valence returns toward three, and for samarium and the remainder of the group the highest valence seems to be constant at three. Such relationships as these need not seem peculiar, since the valence is usually supposed to be due to only a few of the electrons in the atom, in this case to three electrons, while the atomic volumes are un- doubtedly conditioned by the other electrons in the atom, external to the nucleus, as well. That the atomic volumes do not wholly follow 13 the ordinary rule is shown by the fact that the atomic volumes of samarium, europium, and gadolinium do not fall nearly so low as the ordinary eighth group elements. The exceptional behavior of the rare earths in regard to their basic properties may be explained in somewhat the same way as the probable atomic volume relations. Just before coming to the rare earths the basic properties decrease rapidly from caesium, to barium, and to lanthanum. This decrease persists through the rare earth loop, which may be called a tertiary loop, but probably the opposing tendency, that is for the ele- ments of any one main group to increase in basic properties, also has an effect, for the rare earths do not decrease in basic properties with any- thing like the rapidity which would be apparent if they were distributed around the table in the order of the other elements . 1 If they were thus distributed, either ytterbium or lutecium should be chemically similar to iodine, and that is not the case. The elements on the outer cylinder in Table I may be said to be on primary loops, the inner loops may be designated as secondary, and the rare earths as a tertiary loop. This tertiary loop connects lanthanum and cerium to tantalum, and could be drawn inside the outer cylinder, but since the valence of the rare earths is three, it has been thought best to show them on the vertical rod which represents this valence, in order to make the figure as simple as possible. Thus, the rare earths belong in a sense to the third group, but bear a some- what peculiar relationship to the other elements of the group. Supposed Imperfections of the Periodic System. A great deal of attention has been given in papers in journals, and in books, to what have been called the imperfections in the periodic system. Among the most emphasized of these has been the fact that when ar- ranged in a periodic table in the order of their properties, a few elements, argon, cobalt, and tellurium, are not in the strict order of their atomic weights. It has now been shown by Moseley that the elements in the periodic system are not plotted according to the order of their atomic weights , but according to the order of their X-ray spectra , or what is called the atomic number. According to a theory developed by Rutherford, the atomic number represents the number of positive charges on the nucleus of the atom. If this is true THE periodic system shows The relation BE- TWEEN THE PROPERTIES OF THE ELEMENTS AND THE NUCLEAR CHARGE OF THE ATOMS. AND THIS IS PRESUMABLY EQUAL TO THE NUMBER OF NEGATIVE Electrons external to the nucleus. It is probably the spacing and arrangement of these external electrons which determines the chemical properties 1 In this decrease of basic properties with increase in atomic weight inside one group the rare earths act in the same way as the elements on the front of the inner loop, and it is quite possible that it is better to state the fact thus than to give the some- what involved explanation expressed above. J c. 14 and those physical properties of the elements which are not functions of the nuclear mass. When considered in this way it is apparent that there remain no imperfections in the system to be explained, for it is not necessary that the mass of the atom shall vary just as the nuclear charge. Neither is it to be supposed that* all of the properties of the atoms should vary according to the same function of this charge. Explanation of Regularities and Irregularities in the Atomic Weight Relations. In a recent series of papers 1 Harkins and Wilson have presented a theory in regard to the formation of complex from simple atoms, which may be used to explain some of the remarkable relations in the atomic weights, such as exist in one of the triads of Dobereiner. At. wt. Difference. Lithium 6.94 Sodium 23.00 Potassium 39. 10 16.06 16 . 10 In addition to the occurrence of the difference 16 in this triad it is found that the atomic weights of six of the eight elements of the third series may be found by adding 16 to the atomic weights of the elements just above them. Between Series 3 and 4, two of the differences are again 16, and five amount to 20. The greatest common divisor of these numbers is 4, and this is assumed to mean that in general the differences in mass between the atoms of any one group in the periodic table are due to differences in the number of helium atoms, of mass 4, which have been used up in their formation. The proof of this system can not be given here, but can be found in the papers to which reference has been made. The explanation of these regularities is made more apparent by Table II. The explanation for the irregularities in the atomic weights may be il- lustrated by citing the case of argon, which has an atomic weight greater than potassium, which comes just after it. This irregularity is due to the tendency for the atoms as they grow larger to take on helium units more rapidly. If argon followed the rule of aggregation as followed in Series 2, its mass would be 36, but the tendency to take on helium atoms more rapidly characterizes Series 4. The elements of the third series are formed from those of the second by the addition of four helium units, but this difference grows to five helium units between Series 3 and 4. , Thus from neon to argon is 5 helium units or 20, and 20 + 20 gives 40, the atomic weight of argon. Only in the cases of potassium and calcium does the increment between the series fall back to that between the sec- 1 J. Am. Chem. Soc., 37, 1367-96 (1915); Phil- Mag., 30, 723-34 (1915)- i5 Table II. — A Periodic System Representing in General the System Accord- ING TO WHICH THE ElEMEMTS HAVE BEEN BUILT Up FROM Hydrogen . and Helium. H detd. = 1 . 0078 . Group. 0 . 1 . 2 . 3. 4. 5. 6 . 7. 8 Series 2. He Li Be B C N O F He He+Hj. 2He+H. 2He+H 3 . 3He. 3He+2H. 4He. 4He+H 3 . Calc . =h 4 7 9 II 12 14 16 19 Detd . . . • 4 6.94 9-i II 12 14 .OI 16 19 Series 3. Ne Na Mg A1 Si P S Cl 5He. 5He+Ha. 6 He. 6 He+H 3 . 7He. 7He+H 3 . 8 He. 8 He+H 3 . Calc . 20 23 24 27 28 31 32 35 Detd . . . . 20 23 24-3 27 .I 28.3 31 .02 32 -07 35-46 Series 4. A K Ca Sc Ti V Cr Mn Fe Co lOHe. 9He+H 3 . lOHe. 1 lHe. 12He. 12He+H 3 . 13He. 13He+H 3 . 1 3He. 14He+H 3 . Calc.... . 40 39 40 00 4" 51 52 55 56 59 Detd . . . . 39-88 39-1 40.07 44.1 48.1 51 52 54-93 55.84 58.97 Increment from Series 2 to Series 3=4 He. Increment from Series 3 to Series 4=5 He. (For K and Ca = 4 He.) Increment from Series 4 to Series 5=6 He. ond and third series, that is to 4 times 4 or 16. In other words, potas- sium has the atomic weight which it should have according to the rule that the atomic weight increases four units for each increase of two in the atomic number. Argon has a weight four more than this, due to the taking on of one too many helium units, which, however, is what all of the fourth series elements do except potassium and calcium. The Radioactive Elements. The periodic table presented in this paper is admirably adapted to show the relations existing between the radioactive elements as expressed by the rule of Soddy and Fajans. These relations are expressed on the space model (Fig. 3), and better still, on a space model on which the vertical scale is made much greater, for example, four centimeters to one unit of atomic weight. Fig. 4 gives an enlarged view of the bottom part of the table shown in Fig. 3, and shows the elements from tantalum to uranium. In this figure the elements derived from thorium by disintegra- tion are designated by rectangles, and the members of the radium series, by sections of circles. The actinium series has not been included, since the atomic weights are not known, but they can easily be added as soon as the atomic weight of actinium is determined. This series has been in- cluded in Fig. 5 but the scheme is doubtful so far as the actinium series is concerned. Uranium (atomic weight 238.2), the parent of the members of the radium series, belongs to Group VIB on the back of the inner loop. It shoots off an alpha particle (the doubly positively charged nucleus of a helium atom) and changes into uranium Xi (at. wt. 234.2), which belongs to Group IVA. This gives off a beta particle and changes into uranium i6 Fig. 3 - 17 Fig. 4. — Periodic system showing the radioactive elements of the thorium and radium series. i8 £ 5- — Table of the radioactive elements. Note: A new determination of the atomic weight of thorium gives 232.2, so the decimal in the thorium series should be 0.2. The actinium series is not yet fixed with any certainty. 19 i X2 (Group VB) without a change of atomic weight. A second beta change converts uranium X 2 into uranium 2 , isotopic with uranium and with an atomic weight four less. This is converted into ionium by an alpha Table III. — Periods of the Radioactive Elements, with Isotopes Classed Together. At. Name of Atomic No. Isotopes of isotope. weight. Ray. Period. 92 Uranium Uranium 2 234-2 a 2 million years Uranium 238.2 a 5 billion years 91 Uranium X 2 Uranium X 2 234.2 0 1 . 1 5 minutes 90 Thorium Radiothorium 228 . 2 a 2 . 02 years Ionium 230.2 a 200,000 years Thorium 232 . 2 a 18 billion years Uranium Xi 234.2 a 24.6 days Radioactinium . . . a , (3 19.5 days Uranium Y • . . 1 . 5 days 89 Actinium Meso-thorium 2 228 . 2 0 6.2 hours Actinium . . . . ... 88 Radium Thorium X 224.2 a 3 . 64 days Radium 226 . 2 a 1730 years Meso-thorium 1 228 . 2 a 5 . 5 years Actinium X . • . 1 1 . 4 days 87 (Unknown) 86 Niton Thorium emanation 220 a 54 seconds Radium emanation 222 a 3 . 85 days Actinium emanation . . - a 3 . 9 seconds 85 Unknown 84 Polonium Radium F 210 a 136 days Thorium C' 212 a io -11 seconds Radium C' 214 a io“ 6 seconds Thorium A 2l6 a 0.14 second Radium A 2l8 a 3 minutes Actinium A a 0.002 second Actinium C' 81 Thallium Thorium D 208 0 3 . 1 minutes Radium C 2 210 0 1 . 4 minutes Actinium D • • • 0 4.71 minutes Thallium 204 Extremely long 83 Bismuth Radium E 210 0 5 days Thorium C 212 a,0 60 minutes Radium C 214 a,0 19.5 minutes Actinium C • • . a 2.15 minutes Bismuth 208 • . . 82 Lead Lead from Ra 206 • • • Extremely long Lead from Th 208 • • . Extremely long Lead from actinium • • • Radium D 210 0 16.5 years Thorium B 212 0 10.6 hours Radium B 214 0 26.7 minutes Actinium B • . • 0 36.1 minutes Lead from secondary branch of radium series Lead from secondary branch of actinium series Lead from secondary branch of thorium series / \ > 8 \ \ 20 change, and this in turn changes into radium by another alpha transforma- tion. These changes, and the others until the disintegration ends with lead from radium (Pb Ra), can be easily traced by following the lines in the table. In each loss of an alpha particle the atomic weight de- creases by approximately four, and the valence and group number both decrease by two. Each loss of a beta particle increases the valence and group number by one, but causes no change of atomic weight. The half-period of a radioactive element is the time in which one-half of the element would disintegrate. The half-periods of each set of isotopes are given in Table III. The table giving the periods of the radioactive elements shows that the period for any one isotope varies with the atomic weight in some regular way. It is difficult to make any comparison in this sense which includes the members of the actinium series, since their atomic weights are un- known. In the case of the isotopes of thorium, thorium itself has the longest period, and thus decreases in each direction as the atomic weight decreases or increases. The periods of the isotopes of lead decrease as the atomic weight increases, and the same is true of the periods of bis- muth and its isotopes. However, in the case of the isotopes of polonium (Radium F), Thorium C' has the minimum period, and the period in- creases on .each side as the atomic weight either increases or decreases. The Nature of Isotopes. It is now known , 1 as has already been pointed out, that a single ele- ment, with a single atomic number, may consist of several different kinds of atoms, which are alike in that they seem to have the same nuclear charge, and therefore presumably, the same number of external nega- tive electrons. Isotopes seem to be identical chemically, and so far as is known they give identically the same spectrum, but they may or may not differ in certain physical properties, such as the melting points. Thus neon and meta-neon, which differ in atomic weight by tw T o, were separated by diffusion. On the other hand, Soddy finds that lead from thorium and ordinary lead have the same atomic volume, that is, the lead obtained from thorium minerals is denser than ordinary lead in the ratio of the atomic weights. Richards 2 has found that the lead from radium is also different in density from ordinary lead. Such isotopes as these differ in those properties which are functions of the mass of the particle, and they may be called isotopes of the first class. A second kind of iso- topism is that in which there is no difference in mass except that due to a difference in the packing effect. Thus Radium D and the end num- ber of the secondary radium disintegration series, which is as yet un- named, have the same atomic weight except for the very slight difference 1 Le Radium, io, 17 1. 2 J. Am. Chem. Soc., 38 , 221 (1916). 21 in mass due to a difference in the internal energy of the atoms, and this difference is so slight as to be experimentally undetectable, so these may be called isotopes of equal mass. Also, though the atomic weight of actinium has not been determined as yet, enough is known of its disin- tegration series so that it is practically certain that a number of actin- ium derivatives show this form of isotopism with members of the radium series. Thus if we assume that the atomic weight of actinium is 230, then radio-actinium and ionium which are isotopic must both have atomic weights of 230, but the latter has a half-period of 200,000 years, and the former of only 19.5 days, so there is a very great difference in stability. Even if the atomic weight of actinium is different, it will be seen from Fig. 5 that some of the other members of the two series must show this form of isotopism. Isotopes of approximately equal atomic mass are derived from the same ancestral atom, that is from either uranium or thorium, for no thorium disintegration product is known which has the same mass as a uranium disintegration product. In the formation of isotopes of this class, differ- ent amounts of energy seem to be given out, so they must differ in internal energy, and to a greater or lesser extent in stability. It does not seem improbable that this difference may be due to the expulsion in the differ- ent cases of alpha and beta particles which lie in structurally different positions in the nucleus. The Nuclei of Complex Atoms. , According to the above views, and those advanced by Harkins and Wilson in the first four papers of this series, which advanced the theory that the nuclei of complex atoms are built up from hydrogen and helium nuclei according to the system presented in Table II, it may be assumed that the chemical nature of the atom is independent of the number of particles present in the nucleus of the atom, and therefore of the mass of the atom, and is also independent of the structure of the nucleus, so long as the structure does not affect the nuclear charge. The chemical properties of the atom are, according to this view, dependent wholly upon the nuclear charge. When the complex nucleus is built up from only a few hydrogen and helium nuclei, there are not many stable ar- rangements which give a single nuclear charge, but when the nuclei are very complex, the possible number of more or less stable structures should be considerably increased. Therefore it is to be expected, as was found by Harkins and Wilson, that the atomic weights of the lighter elements should follow some regular system with only small deviations, but that these deviations should become much more considerable in the case of the more complex heavier elements. In other words, isotopes should be found much more abundantly among the heavy than among the light elements. The fact that the isotopes of any two different series differ « 22 in atomic weight by about two units, suggests that the difference is caused by the presence of two hydrogen atoms in one set of atoms, and their ab- sence from the other. As examples it may be remembered that neon and meta-neon are supposed to differ in atomic weight by two units, and within the accuracy to which the atomic weight of thorium has been de- termined, there is the same difference between two adjacent isotopes of the thorium and the uranium series. A Plane or Spiral Form of the Periodic Table. The periodic table presented in this paper is a space form, though it is easily represented on a plane as in Fig. 2. The space form may, however, be easily converted into a plane diagram by plotting the atomic weights radially from a point in a plane. This gives the table represented in Fig. 6. While this spiral form of table does not seem to the writers to be so well adapted to general use as the space form, it does show ex- actly the same relations between all of the chemical and physical proper- ties of the elements. 1 This table is different, too, from other spiral tables, for none of the earlier tables have been so constructed as to classify the elements correctly. Thus, for example, the spiral table given in Erd- mann’s chemistry classifies Ne, Ni, Rh, and Ir, in one group, Na, Cu, Ag, Gd, and Au in another, and Li, K, Rb, Cs, leaving out Na, in a third. These are obviously improper classifications. The error in all previous spiral tables has been due to a failure in plotting to distinguish between the long and the short periods. In Fig. 7 the short-period elements occur only above the median line, while the long periods make a contin- uous line both above and below. It is interesting to note that around the long periods the group num- bers run o, iA, 2A, 3A, 4A, 5B, 6B, 7B, 8, iB, 2B, 3B, 4B, 5A, 6A, 7A, o, which is exactly the order in the tables presented in Figs. 2 and 4. Table 7 is the first spiral table to give the chemical relations correctly. The Relation between the New Form of the Periodic Table and the other Modifications. In his book entitled “New Ideas on Inorganic Chemistry,” Werner, 2 in discussing the periodic system, says: “. , . . up to the present the satisfactory grouping of the iron group and the rare earths appears to be almost impossible. Most of these difficulties are not difficulties of principle, i. e., they are not to be referred to the nature of the metal in question, but rather to the particular arrangement adopted to illustrate the periodic occurrence of chemically allied elements. “The principle chosen by Mendeleeff, of bringing analogous elements as near as possible together in order to bring out the less evident similarities which exist between such elements, has been followed by his successors. This process has led to a crowding 1 Except that it does not show so well the relations between what have been called complementary groups. 2 English edition, Longmans, 1911, p. 4. 23 Fig. 6. — A spiral form of the periodic table. 24 together (Ineinanderschachtelung) of the elements which is harmful to the synoptical character of the periodic system, and this is especially true when we consider only the less important analogies: the result of equal valencies. This compression of the ele- ments into the least possible space is the chief cause of many elements not finding a suitable position in Mendeleeff ’s scheme. This remark is particularly applicable to the eighth group, and to the metals of the rare earths.” However, in finding a remedy for the defects which he discusses, Werner goes to the opposite extreme, and places the elements in such a way that many important analogies become obscured. By placing the elements farther apart on the helix, but close together in space, the new table is able to combine all of the advantages, and to eliminate the disadvantages of such widely different forms. The relation between these different tables is discussed below. If, in Figs, t, 2, or 3, the lines of the helix are cut between the seventh and the zero groups, and between the eighth and the iB groups, the table when spread out on a plane becomes much like that of Mendeleeff, except that there are no blanks except those which correspond to atomic numbers, that the rare earths are arranged differently, and that the drawing would still show the distinction between the main and the sub-groups. How- ever, if all of the connecting lines are taken out, the table becomes es- sentially that of Mendeleeff. If the helix is cut only between the seventh and the zero groups, unrolled, and laid on a plane, it takes on the general form of the Carnelley-Richards table, 1 which is probably the best of all of the plane tables except that of Mendeleeff. If the helix is cut between carbon and nitrogen, between silicon and phosphorus, and between the seventh and the zero groups, and again spread on a plane, it gives the form attributed to Meyer, to Palmer, and to Staigmuller. 2 The essential ad- vantage claimed by Staigmuller is that in his table a line separating the non-metals and the metals may be easily drawn, and that the non-metals fall into one group in the table. The elements which he classifies as non- metals are B, C and Si, N, P (and partially As) ; O, S, Se (and partly Te) ; F, Cl, Br, and I; and also He, Ne, A, Kr, and Xe. If this is an advantage of the Staigmuller table, it is much more an advantage of the new space form here presented, as in our table the non-metals are much more closely grouped, as they lie entirely in one group on the outer cylinder, and all except B, C and Si, lie at the back. Werner’s table, 3 except for the arrangement of the rare earths, may be obtained by cutting the helix so that the elements in each of the following pairs of elements become separated: Li and Be, Na and Mg, Ca and Sc, Sr and Y. It should also be cut between the o and iA groups, and then spread out on a plane. The transformation into the form devised by 1 Chem. News, 78, 193-5 (1898). * Nernst’s “Theoretische Chemie,” Siebente Auflage, p. 184. 3 Ibid., p. 185. 25 Walker 1 is also a simple one, since the spiral needs only to be cut between the seventh and zero groups, and the vertical rods severed between K and Rb, between Ca and Sr, Sc and Y, Si and Ti, P and V, S and Cr, and between Cl and Mn. As has already been seen, the new table may be represented on a plane as a spiral, or in space as a figure 8. The use of a figure 8 space form of table was first suggested by Crookes, 2 but the arrangement of the elements in his table was very different. The use of a figure 8 dia- gram has been advocated by Soddy, 3 who gives the best table previously devised but such a representation obscures both what have been called the complementary relations and the relations between the main and the sub-groups. While in the development of the periodic table in space as presented in this paper, no use was made of any previously devised system except that of Mendeleeff, it will be seen that it is a generalized form, of which the Mendeleeff, Carnelley-Richards, Werner, Staigmiiller, and other modi- fications, are special cases, each of which expresses certain relations well, but others poorly or not at all. The space form eliminates the disadvan- tages of the different plane tables, and at the same time combines their advantages. That at first sight it seems more complex than the Mendel- £eff table is due to the fact that it classifies all of the elements, but it is actually more simple, since it contains no blanks except the five which correspond to atomic numbers. Experience has shown that students who have no previous knowledge of the Mendeleeff table find the space form the more simple, at least when they have the model to use in their study. COHESIONAL PROPERTIES. Atomic Volumes, Melting Points, and Related Properties. In Fig. i the elements of highest atomic volume lie at the left of the outer loop, while the elements of lowest atomic volume lie at its right (carbon, silicon and aluminium) as long as the outer loop persists at the ex- treme right, and when the outer loop disappears at this extremity, the line of lowest atomic volume jumps over to the left end of the inner loop. To show these atomic volume relations somewhat more simply the table has been drawn in the form given in Fig. 7. From the standpoint of the chemical relations this latter table is much less perfect than the former, but it has the one advantage that the elements of high atomic volume are at the left of the table, and those of low atomic volume are at the right, so if this table is hung with its left side as the top, the loops take the general form of 1 Chem. News, 63, 251-3 (1891). 2 Ibid., 78, 25 (1898); Proc. Roy. Soc., 63, 408-11 (1898); and Z. anorg. Chem., 18, 72-6 (1898). 3 Chemistry of the Radioactive Elements,” Part II, p. 11. 26 r - 40 6C 80 100 120 140 160 180 20C 220 240 o H li GROUP/ 0 Fig. 7. — Periodic table modified so as to show the atomic volume relations in a simple way. 2 7 the atomic volume curve . 1 Fig 7 has the great disadvantage that it does not show the relations which exist between the main and the sub-groups. It is formed from the table in Fig. 2 by turning each inner loop on a horizontal axis from front to back at its right ends until it falls outside to the right. The atomic volumes of the elements have been plotted against their atomic numbers in Fig. 8. A comparison of Figs, i, 2, 7 and 8 will show how simply the present form of table expresses the atomic volume relations. The elements of lowest melting point lie at the left of the table (Figs. 1, 2, and 7). The absolute melting points for these elements are: Hydrogen Helium . . Neon. Argon Krypton . Xenon Niton 14° _ O 85° 104 0 1 33° 202 0 The line 2 of highest melting points begins exactly opposite at the right of the outer loop with carbon, melting point about 3900 0 absolute, and silicon, 1693°. These are the elements of lowest atomic volume except for the fact that the atomic volume of aluminium is slightly less than that of silicon. It might seem that the line of maximum melting point would here jump at once to the elements of lowest atomic volume in the next series, that is, to the iron group. Instead of doing this, however, it passes to titanium (m. p. 2060° Abs.), and then still further toward the eighth group, but reaches only to Group VIB, and passes straight down through molyb- denum (2800°), tungsten (3300 °), and uranium. The tendency toward the shift of the maximum melting point from the fourth group to Group VIB is already seen in the elements titanium and vanadium. Thus the difference between the melting points of carbon (4th group) and the adja- cent element in the fifth group, nitrogen, is 3800°. Between silicon and phosphorus the corresponding drop is 1400°. Just below this the drop from titanium (4th group) to vanadium (Group VB) is only 70 °. This enormous decrease in the fall between the fourth and fifth groups, clearly predicts a reversal in the next series, where zirconium (4th group) has a melting point of about 2000 0 absolute. Columbium (niobium, 5th group) melts at 2500 °, and molybdenum (Group VIB) melts at about 2800°. 1 If the loops at right, representing the sub-groups, are untwisted, this table takes on the form advocated by Emerson in his “Helix Chemica,” Am. Chem. J 45, 160-210 ( 1 9 1 1 ), except that the new table classifies the rare earths in a different way. While this is also a useful form of the table, it has not been thought necessary to include a figure showing it, since it is easy to see how Emerson’s table can be modified so as to classify the rare earths correctly. 2 For the lines of maximum melting points, and the lines of primary and secondary minima, see Fig. 9. 28 29 MELTING POINTS Line of Line of Line of Primary Minima—... Secondary Minima— Fig. 9 Table IV. — The Elements Arranged According to Atomic Numbers, with the Atomic Weights, Atomic Volumes, Melting Points, Compressibilities, Cubic Coefficients of Expansion, Magnetic Susceptibilities, Atomic Frequencies, and Values of T™/V Representing Cohesion. 30 > cs »o 00 P* s 5 >0 O 0 p- 0 0 . NO O' 0 0 0 NO 0 O • On 0 O cO «o H M 6 NO NO NO O' • P" P - CO M >0 NO O' >0 d • p* 00 CO M to On O' CO • M NO 00 P* NO • cs CS >0 w M .a g a - a «o 10 00 P - NO 0 CO NO 0 cs P* ON to NO P- NO NO NO p- 0 3 - -w CT >0 d d to On • CS CS cs W P* t''. 00 O NO • p- cs M CS >0 <3 2 X M cs CS to HH 4 ; .P o —1 1 w o 3.-X t/1^ o >0 o O' CS p- 10 O NO M NO O CO «0 CS NO M o ON o ON ON Tf O O NO 00 »o O O M X! — J2 MV 2 u 0 J 3 ao o s^ : o M o On 03 a to to r'N O o| « NO O' 47 cs CO cs NO O' S ^ / * • • ■ • • • lO • • • 0* M 0 O' O 3 • w 10 • M CS M CO >0 1 O ' J 3 rt cs On to 0 to • to NO O O M p - CS to to NO W NO NO to NO 0 • NO NO NO CS f" cs CO O' NO M 00 00 CO 00 P* NO 00 00 • CO O' O' NO 00 CO to CO 0 M CS to A ttiX ie 8 o a 0.0 is cs O a x QJ < $ ON _ On (N >0 if) N 00 CS w tO - NO o ON »o >0 cs CS I 10 O w NO P" P* to to «o f" to cs o t>* T3 p O a 03 0 >0 w CS CS _ 10 NO NO to N O O' o3 30 CS p“ P* M P* O to NO 00 •H t>. cs cs to cs O 00 10 cs On 00 o r* 8« -o *3 O nr *P vL- vo O' NO _ _ _ cs 0 co O' i^^J-Ocsiocsr^i-icsioto O' f' no t)- h 00 O N T 00 no 0 0 d 0 0 ►H cs co cs M M HH d M cs cs cs M cs M M d W cs >0 M CO to cs t>- cs 0 t'- O NO p- O NO cs O' CO CO NO co NO tO M NO On to 0 M >0 M 00 »o NO . cs w H-l HH hH HH cs ►H H -4 M HH HH ►H cs cs "T cs 00 NO 0 0 Tt- O M O O O 0 0 cs p- NO NO 00 O 0 0 ON HH 0 O 0 O 0 O 0 0 to M to O O co ►H O M w 'T NO O' M CS NO O' d cs to 00 M CS NO O' O' d M M cs cs cs cs cs cs co to to to P 0 NO 00 a p • aw CJ p 0 .P bC ’P o3 O C/3 w P V- o X5 Q. w O ^ <1 03 PQ m cs co P- »o 6 g 3 a § *w g -X2 w .2 P 3 POP P5 *p DO *P P m xa ^ o p o c /3 O <3 Pi U c/3 i-i P OJ .2 *E o NO f'* 00 O' O •-> H H H H N N Titanium 48.1 10.7 4.50 3 ... 2063 ... 12.4 9.2 193. 3 . 9 B 8 4 Vanadium 51.0 8.5 5. 987 s ... 1993 ... 15.0 9.5 234. 31 O OOOOOOcO'+t'.VOOO •t'-rt-OOO • N CO o N^^NCOHioiflNiO Tt- O «0*0 10 O' N N O' CO O' O' O' O' O' M O' O N >0 • VO 00 rf O' M ■ N <0 m cO lO'tN O O'lOOOOO vt'H o O' O 'O , ' 4 ‘ CO O O' O'!* O'O'OO 1010 •cOMMi-itO'd-'OOO O cO 10 10 00 lO ^ N ” O' O' OV O' o O O' «o 3 - ON OV O' 00 O « (N O I I F cO CO 0 cO 10 0 Ov OO VO • ^ r-~ • • >0 • 0 O 0 d • 0 d m • • O' m ID cO 3 - <■>-. 3 PQ CO cO CO M 10 vO O' cO M CO • 6 vO M V CO cO cO 0 cO O *0 O' 10 O' O CO 0* • Ov VO 0 ►H 3 a t'- r*- >o 00 r>» cO VO CO M • 3" O' HH CO O' ■cJ- M M M M M M M ►H l-l o< A O' VO 00 O' O O'* VO tO tO 't >0 CO VO O' vO 3 " o O' 3 o h r — r — >— < N n vo vo r~ O' vj- N VO OO *-l *-! iO tO »o 3 ~ "tT N CO CO IH M 10 vO 00 3 " O' 10 0 0 t- 0 8 8 ►H to VO 00 tj- N vO M O' CO VO O' 00 8 cO o' o' 61 r>. co 00 O'- r» VO O O' 00 O' VO 10 to O' 10 O' o' O' Tj-iO00 00 to 10 O' M "t io'O'O'O'O'O'O'O a 0 • ^ a o u J2 o a; w ll> a 3 tuo § £ a 3 O' O' *3 JO 1j M 0 >1 o O CJ 8 O' O' to 00 O CO u 3 O »o 8 e o § £ ^ 3 tJ no .3 « "S S 3 3 r3 W5 O ^ O . 1-t O N O V) 3 O a o a < <0 8 8 8 w> £ 6 Liebig’s Ann., 361, 1 (1908). 7 Landolt-Bornstein-Meyerhoffer Tabellen. The values for columbium vary greatly, and there is a need for a new determination of the density of the pure substance. Table IV ( continued ). Compressibility Suscep- Atomic At. At. Cubic coeffs. of M. p. at 20° X 1 0«. tibility frequency Element. wt. vol. Density. expansion 3a X 10 6 . absolute. (Richards.) X 10 7 . X 1 0 12 . T m /V. 32 VO • d VO 0 0 CO HH O d d 0 vo CO oo o Ov o» 00 • O Ov • vo o c- o >o M O vo lO CO d o oo lO CO • CN »o • O vo o cn d cn CO vO CO ►H cO d VO >o •00 cn CO CN CN HH % vO o CN oo cn CO to 01 oo Ov M vO HH Ov CN d oo vO d CO cn cn CO cn HH o M CN CO cn CO CO •CO Ov CO • CO o 0 O 00 d cn cn CN vO • 0 O o • d HH M CM lO i — i — z f? CO 1 cO 1 • HH 1 Ov 1 • o • vo O vo cn o • • • VO • • • CO . . . . vO d* i- d" • • • vo O *-■ • Ov d" o * O HH CN *— t CN CO CO CO CM d d 00 VO CO r^. • r- ►H CM CO O' CN O o r- • iO CM oo CM iO d >o Cv (N cn cn M HH O • O t—t vO y s CO /v. rv. r*-. h* - V. X v y vO IO vo ro Ov CO CO CO CO cO • HH CN 00 CO Ov CM oo HH CH • 1 cO HH CN HH O O' CM M • cO v-t hH HH M iO 00 lo CO IO 00 N fO lO N CO O O CNCNCOvOOvCNvOcOvOiO • Ov i-i CN CN CN o r- - O 00 CO VO cO 00 • vo »o o VO CN o HH o • O CN CO VO cO CN CN CN CN M CN HH >o o CN oo CO 0 CN O' cO 4 o 3 2 5 5 »>. O' o vo OV oo oo oo o 00 O Ov oo d- oo cn H N VO o o o (N d- oo O d ' d t-l r- vo CN CN O cn O' to o CO fO O d* 0 d- d d* O CN f- Ov CN co VO I/O VO vO VO VO *iO > O cn d HI V5 E 3 E S 3 E >i 13 E S .3 3 E i *5 a .2 •5 .2 K3 _cd t-i a> 3 E E .2 V-i O E 3 ‘u ^3 D fl 3 O 3 .2 * c /3 E 3 3 3 xs N-l E .3 13 O HI B to 13 0 HI 3 1 .3 ’H 3 3 a o a 4 -» o X! 13 > 13 cd 13 rd 3 4 J G ; 3 3 a> CD rt c rt 3 rt *u CJ 1 3 V- O aj E c 3 u 3 W Pn Pn m U V-< hH H < H HH o m o Ph w W CO Tt” IO vO 00 ON o HH CN O d- IO VO 00 O O _ CN cO d ■d- ■d* d" d - iO IO iO IO IO IO VO >o »o VO VO VO VO E o 3 13 3 S3 E .2 "33 o t-i a C/1 >1 d »o vo t-* 68 Erbium 167.7 35 - 3 (?) 4 - 77 (?) ••• i 523 (?) ••• 323 33 o • H" 00 Th O O'* • • 01 • # NO 0 • 0 ‘9 CO O' wo CO CO WO • 00 3 - • NO O Cl Cl HH CO CO 01 • • • • • • * ci CO co CO ci HH 3 - ci O NO 00 3 - O O 00 O' CO NO • NO WO d cO HH Cl 01 HH • 0 • . . co • • 33 ba • *-« 0 01 3- CO O 5 9 4 2 0 00 0 • • 00 01 • 0 w 00 HI M Cl M 3- • • NO • 'C CJ > INI M • • • • 04 CO 00 3- VO CO wo 01 * CO NO O' co CO O * O o’ * d d CO 01 01 CO • r*-. rv. <*V. V ✓ X ✓ V — y co O • CO CO 00 NO wo O • CM • CO • CO • 01 O • t'- 01 CO CO O 3 - • 0 • t". • • n-. HH co • O' wo 0 CO 01 wo NO wo • • 01 . O' . o ^ • ^ co CO 01 01 01 HI HI P-| A V d* 3 CO i-i • 0 97 O' 01 01 O 79 CO 0 01 M • 01 HH 01 3 " co O' CO co co HH wo cO O O • • • • NO 01 3 * CO 01 wo 00 CO 00 • I" • • • O • O'. NO O' 01 Cl HH O' co HH HH O' wo HH 00 HH HH Cl 01 01 HH HH HH HH HH HH • • • O' t'* • wo NO HH co 00 Cl Cl Cl • • O • • Cl • . • . O O' • 00 00 O' d 00 HH . • O' • HH . Cl HH HH HH HH HH Cl CO Cl HH wo • wo 0 wo 0 • O' HH Cl Cl NO O .20 0 0 • H- • O • H - Cl Cl 00 • co wo HH • 0 co WO O 3 - f'' 00 d • Cl • NO • Cl 00 NO 00 00 O' O' O' O' O O 0 O HH Cl Cl co CO fO HH HH HH rH HH HH HH HH HH Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl s s 3 3 •H • ^“H ?— H 3 3 3 a 33 H H o\ o NO C- E .2 0) .2 •d 32 1-1 -M *3 01 4 -> 3 -H> 3 3 in ba 3 3 E 1 3 34 3 • H E (/} HH 3 • tH X) • »— 1 .S 3 E *3 3 0 li 01 L . 4 *3 33 T 3 3 0) 3 E in • T-* "2 *o 0 1 3 34 >* ►4 H H w O l-i 1 — 1 E O H h 4 PQ Pw W M Cl CO H" wo NO 00 O' 0 M Cl cO 3 - wo 00 00 00 00 00 00 3 O -m 2 NO 00 E .5 'in . 00 00 00 3 X X 2 o 33 < H O' o 00 O' X s .2 *3 3 ui £ E # 3 ’S 3 Cl O' O' 34 The unknown element eka-manganese 2 may prove to have a higher melting point than tungsten. The drop in melting point between car- bon, atomic number 6, and nitrogen, atomic number 7, is the most re- markable sharp change in the whole system, amounting as it does to more than 3800°. It will be shown later that the relations of the physical properties of carbon to those of the other elements, are remarkable in many other respects. In addition to the line of minimum melting points, which lies in the zero group, there is a line of secondary minima, possibly beginning with aluminium, with a very slight minimum. The next element in the third group below this is scandium, and unfortunately its melting point is not known. Below this in Group IIIA there is a very considerable minimum beginning with gallium (at. no. 31) of absolute melting point 303 °, while just before it zinc (at. no. 30) has a melting point of 692°, and just after it comes germanium (at. no. 32) with a melting point of 1231 0 . Below gallium the minimum continues in the same group, IIIB, with indium (m. p. 480°), and then shifts to the left (Fig. 9) toward the iron group, so that the next minimum comes in Group IIB with mercury. Here it is remarkable that the secondary minimum where mercury melts at 234 0 absolute, is almost as low as the corresponding primary minimum at niton, which melts at 202 °, or only 32 0 lower. It will be seen that the line of maximum melting points at the back of the inner loop, and the line of secondary minima at the front of the inner loop, both move to the left toward the iron group as they move down the table. In Fig. 8 the melting points have been plotted as reciprocals, and these secondary minima may be seen as secondary maxima on the curve. Fig. 8 is similar to a figure given by Richards, 1 but differs in the fact that it is plotted to atomic numbers instead of atomic weights, and also gives data for some of the properties of as many as 72 elements, while Richards’ figure shows only 38. The increase in the number of data changes not only the form of individual curves, but it also changes their relationship to each other. When so many data are plotted, there is a considerable advantage in plotting to atomic numbers instead of atomic weights, since when the atomic weights are plotted, each curve is apt to cross itself whenever the atomic weights are not in the order of the atomic numbers, as is the case with argon. Another point in favor of plotting these physical properties according to the atomic numbers instead of atomic weights, is, as will be shown later, that it is the number of external electrons in the atom, and the number of these runs in the same order as the atomic numbers, which, in all probability, deter- mines the cohesional properties of the elements. Moseley’s work seems to indicate that the atomic number and the nuclear charge, pre- 1 J. Am. Chem. Soc., 37, 1649 (1915). 35 sumably equal to the number of external electrons, are expressed by the same number. The data on compressibility given in Table IV, and plotted in Fig. 8, have been taken from Richards’ work, and the other data were obtained from what seemed to be the most reliable sources, though in many cases there is considerable doubt as to which work is the most trustworthy. A few of the data plotted have been taken from work on liquids, but wher- ever this is done the fact is specified in Table IV. A dotted line in the figure indicates that data are not available for the elements along the line, while an unbroken line shows that no data have been omitted. The four curves representing the reciprocals of absolute melting points, coefficients of expansion, atomic volumes, and compressibilities, have all the same form, though they are not so closely similar as those plotted by Richards. The deviations have been introduced by the addition of more data. The two curves at the top, giving the reciprocals of the melting points and coefficients of expansion, 1 are almost exactly similar where the data are complete. Thus the secondary minima in the melting points have corresponding maxima in the coefficients of expansion for indium and mercury, and a maximum may be predicted for gallium, though no determination has been made for this metal The atomic volume curve does not show any corresponding maxima, and they seem also to be absent from the compressibility curve, though not all of them are known in the latter case. The only minimum melting point which exactly corresponds to a max- imum atomic volume, is that for helium. Below this in the table (Figs, i and 8), the maximum atomic volume shifts one group to the alkalies, while the minimum melting point continues to remain in the zero group. In a very similar way carbon is the only element of minimum atomic vol- ume which has the maximum melting point. In the next series the maxi- mum melting point again comes in the fourth group with silicon, but the minimum atomic volume has shifted one group to aluminium in Group III. In the next period molybdenum has the highest melting point, but the element of lowest atomic volume is either ruthenium or columbium, the latter if the density used is correct, but as to this there seems to be considerable doubt, so the minimum is probably at ruthenium. In the next period osmium has the lowest atomic volume, while tungsten with an atomic number two less, has the highest melting point. To a considerable extent, 2 the rule holds that elements of low charac- teristic valence have low melting points, high atomic volumes, high eo- 1 In the figure this curve seems to have much flatter maxima than the one above it, but this is mostly due to the fact that the maxima, which lie in the helium group, are omitted from this curve on account of the absence of data. 2 This is not a true, but only an apparent relation, as is shown later. 36 efficients of expansion, and high compressibility. On the other hand, to the same extent, elements of high maximum characteristic valence have low atomic volumes, small coefficients of expansion, small com- pressibilities, and high melting points. Blom 1 has calculated a quantity, W, which he finds to have the dimensions of a cohesion. His equation for W is v 2 .A W = constant — n- V /s where v is the frequency calculated from the specific heats, A is the atomic weight, and V is the atomic volume. The curve for log W has the general form of the melting point curve, and the reciprocal of this curve would therefore have the general form of those plotted in Fig. 6. In other words, the four properties plotted in Fig. 6 are closely related to the co- hesion, or it may be considered that the cohesion, or the attraction be- / tween the particles, conditions all of the other four properties. The point at which the parallelism between valence and cohesion meets its worst failure is in the case of the sub-group elements such as copper and zinc, which fall just beyond the eighth group, since the valence of these elements is low and their cohesion high. Therefore a better rule than the above is that in Fig. 2 the elements at the ends of the periods He, Ne, A, Kr, Xe, Nt, are elements of high atomic volume, high coefficients of expansion, high compressibilities, low cohesion, and low melting points, while the elements at the middle of the short and long periods, and around the eighth group near the middle of the very long period, are in general the elements of high cohesion and melting points, and low atomic volumes, compressi- bilities, and coefficients of expansion. There is also, as might be expected, a general relation between the hardness of an element and the properties under discussion. Thus, the very hard elements lie near the middle of the periods while the softest elements lie near the ends of the periods. From the above considerations it seems likely that the apparent connec- tion between maximum characteristic valence and cohesion, which how- ever fails so badly in the case of elements of low valence on the inner loop, is not real, but that the cohesion is conditioned by the spacing of all the electrons of the atom external to the nucleus, and that this spacing is a periodic function varying in the periods corresponding to those given in Fig. 2. On the other hand, the valence varies in SERIES, and only partly according to the periods. Thus the valences 1, 2, 3, 4, 5, 6, 7 depend only on the position in the series; and only the occurrence of the two valences o and 8 depends upon the position in the periods. It seems probable that the atom is a system consisting of a positive nucleus, surrounded by one or more negative electrons which are describing 1 Ann. Physik, [4] 42 , 1397-1416 (1913). 37 orbits at a high speed. It is not improbable that the force which keeps two atoms apart is due to the repulsion of the negative electrons of one atom for those of the other. The compression of a solid would bring these atoms closer together and the closer approach of the external electrons would rapidly increase the repulsion. The principal decrease in volume, is, in all probability, most largely due to the decrease in dis- tance between the atoms. When such large pressures as those used by Bridgeman are used, it would seem likely that there may be a considera- ble decrease in the size of the atoms themselves. That the atoms are compressible would seem almost certain, but the possibility exists that the atoms may be very much less compressible than the spaces around them. The Dimensions of Atoms. It is of interest in this connection to compare what are often called atomic diameters, but which are more properly considered as the distances between the centers of two atoms in a gas during a collision, as determined from the kinetic theory, and the distances between the centers of the same atoms in their positions of equilibrium in the solid or liquid state. Such a comparison is given in Table V. Table; V. — Atomic Diameters or Monatomic Gases (Distance between Atomic Centers during Collision) as Determined from the Kinetic Theory, and the Distances between the Centers of the Atoms in Liquids or Solids. Number of Atomic diameter external X 10 8 cm. in gases Distance X 10 8 cm. between cen- Substance. electrons. at 0° C. = D. ters of atoms in solids or liquids. T m/V. 3.38 ( — 258° adsorbed in charcoal) He 2 1.7 3-94 ( — 271. 5 0 ) 0.085 Ne 10 2.1 3.17 (calc.) ' 1.04 A 18 2.5 3.56 (Liq., —189°) 3.0 Xe 54 3.2 3.94 (Liq., — 102 0 ) 3.6 Molecular Diameters of Diatomic Gases. H 2 2.1 3.12 ( — 252 °) N 2 2.8 3-56 ( — 252 .5°, solid) 0 2 2.6 3-33 ( — 252 .5°, solid) At first sight it might seem that the data on the distance between the centers of the atoms in gases during collisions could be explained on the basis that the lighter atoms approach each other more closely because they have the greater velocities, but that this is not true can be seen when it is remembered that the heavier atoms have the greater momentum, so the closer approach of the lighter atoms of the helium group is due to the fact that either (i) the atoms are smaller, or (2) that the fields of force around them are less intense on account of the fact that they have a smaller number of electrons external to the nucleus (as well as a higher nuclear charge). Probably each of these factors plays a part. Thus if the number of external electrons is equal to the 38 nuclear charge, and we use the hypothesis that the nuclear charge is equal to the atomic number, then it might reasonably be expected that the 54 external electrons of xenon would both occupy more space, and create a more intense field of force than the 2 external electrons of helium. If the number of external electrons is indicated by N, then atVs 1N Xe TVfVs iNJ He = 3» so that if the distances between the centers of like atoms during collision were proportional to the cube root of the number of external electrons, then since this distance D is 1.7 for helium it would be 5.1 for xenon, while the calculated value is less than this, or 3.2. However, the momen- tum of the xenon atom is 5.7 that of the helium atom, so that the higher momentum would cause the atoms to approach closer than a distance of 5.1, but it is doubtful if even a momentum 5.7 times as great would be able to reduce D to 3.2. In Table VA, values are given for different roots of N, the momentum, and the calculated values of D from Table V. Table; VA . Relative Atom. momentum. D X 10 8 cm. 1 &iN l / 6 . feN / <. &3NV3. N. He 1.0 1.7 1.7 1.7 1.7 2 Ne 2.2 2.1 2.3 2.5 2.9 10 A '. 3.15 2.5 2.6 2.9 3.5 18 x e 5-7 3-2 3-3 3-9 5-i 54 The table shows that the distance of approach D varies quite closely as the fifth root of the number of external electrons N. If all of the atoms at o° had the same momentum this might be thought to be the law which conditions their approach, but since the momentum increases rapidly with the mass of the atom, it is probable that D would vary more nearly as the fourth or third root if the momenta were the same. That D is found to vary as the fifth root of N, when the momentum is involved in addition to the number of external electrons N, is probably due to the fact that the momentum is a function of the atomic weight, which is a function of the atomic number, or N, in this case the number of charges 1 The values of D are taken from Landolt-Bornstein-Meyerhoffer Tabellen and are calculated from the equation D = ^ ° P ° , where n is the number of mole- \ V 2 7 TW [JL cules per cc. at o° and 760 mm. Hg = 2.705 X io 19 cm. -3 , and ju is the viscosity of the gas, with the application of Sutherland’s correction for cohesional force {Phil. Mag., I 7 > 320 (1904)), and Jean’s correction for the persistence of velocities. The constants involved in this calculation are not very well known, and may vary for different kinds of atoms, but are probably the same for atoms of the same kind, such as those of the helium group. In a table prepared by the General Electric Company the values of D are given as follows: He = 1.905, A = 2.876, and these numbers are in the same ratio as those given by Landolt-Bomstcin. On account of the uncertainty in the constants, it has not been thought worth while to recalculate the numbers, since the relative values would not be affected. 39 on the nucleus. In other words the various factors involved are functions of the same variable. If the heavier helium group atoms are larger it may seem surprising that in the liquid state the distance between the atomic centers is practi- cally the same, but this is due to the fact, as is shown by the last column in Table V, that the cohesion increases very rapidly with the atomic number. At present little is known as to the actual dimensions of atoms, and it seems probable that their dimensions are smaller, rather than larger than those usually cited. It is somewhat difficult to know what is meant by the atomic diameter, since in a simple atom, such as hydrogen, it might be expected that the diameters would be very different in the different directions. In the calculation the number of gram molecules per gram molecular weight was taken as 6.062 X io 23 . According to the table the centers ^ of the atoms in liquids or solids are much farther apart than the distance between the centers in gases at the time of their closest approach during collision. Even in their collisions it is improbable that the exterior elec- trons come very closely in contact in comparison with their dimensions. The data in Table V are in accord with the usual assumption that a large part of the space in liquids and solids is outside the boundaries of the atoms, though the interatomic spaces are certainly regions in which the electro-static and electro-magnetic forces are intense. Atomic Frequencies. The properties of the elements which have been considered thus far are properties of the atoms in bulk, undoubtedly conditioned however, by the structure of the single atoms. An endeavor has been made to find some property which is more characteristic of the atoms themselves. This at- tempt has met with success in the discovery that the atoms of solid sub- stances have characteristic atomic frequencies. While in the simple theory the atomic frequency may be considered as independent of the nature of the substance, this is not altogether true, since, for example, there is found to be a difference in the values obtained for diamond and graphite. On the other hand, it is remarkable, as has been pointed out by Nernst, that the frequencies of sodium atoms in metallic sodium and in sodium chloride, though not exactly, are approximately the same, so as a first approximation the atomic frequencies may be considered as a property of the atom. The characteristic equation for the frequency is the formula for the sim- ple pendulum where A is the atomic weight, and D is the directional force. The fre- quencies for the different atoms are given in Table II, and in Fig. 10. 40 Atomic Number 10 20 30 40 50 60 70 80 90 fOO 4i However, in the figure the reciprocals of the frequencies have been plotted instead of the values themselves, since the change makes the curve com- parable with those representing the atomic volumes, compressibilities, coefficients of expansion, and reciprocals of the melting points, as plotted in Fig. 8. The different equations which may be used for the calculation of v have been discussed by Blom, 1 who has compared them and finds that no one is exclusively better than the others. The equations are given below, where the symbols have the following meanings: T w = absolute melting point. d = density. V = atomic weight. K = compressibility. a = linear coefficient of expansion. C p and C v — atomic heats. 1. Einstein’s equation. 2 yVs D = const. — . K V = 3.3 X io 7 .A- 1/, .(i- ,/ *.K- ,/! . 2. Lindemann’s equation, 3 derived from the hypothesis that at the melting point the orbits of the atoms become just large enough so that the atoms come into direct contact, and that on account of the consequent energy exchange between the atoms, they are no longer able to hold to their positions relative to the space lattice, but begin to slide past each other. T D = const. — T7-. V 2/ 3 v = 31 X io 12 . \l ^ 2/ . \ A.V /a 3. Alterthum, 4 from dimensional considerations, found the following: 1 D = const. aV 2 /s v = 4.2 X 10 11 V AaV 2 /* 4. Benedicks 5 considered D as proportional to the internal pressure of the solid as determined by van der Waal’s equation. D = const. -5-:. 2>aV 1 Ann. Physik, 42, 1397-1416. 2 Ibid., 34, 170 (1911); 35, 679 (1911). 3 Inaug. diss., Berlin, 1911; Physik. Z., 11, 609-12 (1910). 4 Verh. deutsch. physik. Ges., 15, 68 (1913). 6 Benedicks, Ann. Physik, 42, 154 (1913). 5. Griineisen’s 1 equation: D = const. C„ v = 2 '9 X IO “ V 3 (gr-ca 1 -)- 6. Debye’s well known equation is ? = 7.4 x io 7 .A‘ ,/, .14 <42 Do not give comparable com- Ca, Sr, Ba pounds at room temperatures. For any one series investigated, Ephraim 1 finds that the product of the cube root of the atomic volume (V 1/s ) by the cube root of the tempera- ture of decomposition (T D 1/3 ) is practically a constant. In the case of the substituted ammonia compounds, the stability of the ammine seems to depend also upon the molecular volume of the organic base. The nature of the anion influences the stability. The elements which form complex ammonia compounds belong, mostly, in the inner loop of the periodic table (Figs. 1 and 2) and are sub-group elements. On the whole, the elements at the left of the inner loop form the greatest number of these compounds. That the stability increases as the atomic volume of the metal decreases, is apparent from Table III, though there are some minor exceptions to the rule. Thus cadmium, with an atomic volume of 13. 1, seems to form a more stable hexammino- sulfate than zinc, with an atomic volume of 9.2. However, the ammino- 1 Ber., 45, 1323 (1912); Z. physik. Chem., 81, 513, 539 (1913); 83, 196 (1913)- 5i chlorides of these elements follow the usual rule. The values of T m /V for the elements which represent the cohesion, seem to be in as close a rela- tion to the dissociation temperatures of the chlorides as the atomic volumes. Valence and Electroaffinity. The important subject of the relation between the periodic system and electroaffinity has been so thoroughly treated in the classic papers of Abegg and Bodlander , 1 and Abegg , 2 that it need not be considered here. It may be pointed out that while in general, in any one group, the positive character of the elements increases as they go down the rod on which they lie in the table, this rule is reversed for those elements which are at the left (iron group) and on the front of the inner loop and for the rare earths. Thus copper, silver and gold are progressively more negative, and the same is true of iron, ruthenium, and osmium, and also of zinc, cadmium, and mercury. Other Properties of the Elements. According to Cary Lea , 3 the maxima for color in the ions formed by the elements are in the three-eighth groups and in the rare earth group, with a final maximum at uranium. This is interesting in so far as it is true, in that this relationship is similar to that found for the maxima of suscepti- bility, for in both cases the maxima occur in the groups where the valence remains constant as the atomic number rises. Other properties of the elements, beside those discussed in this paper, which vary in a more or less regular way with their position in the periodic system, are given in the following list, which, however, is not complete : Electrical conductivity 4 Conductivity for heat Boiling points 5 Heats of chemical combination 6 , 7 Electrode potentials 7 Changes of volume on fusion 8 Solubility 9 Latent heat of fusion 10 1 L. Abegg, “Die Valenz und das periodische System Versuch einer Theorie der Molekularverbindungen,” Z. anorg. Chem., 39, 330-80 (1904). 2 Abegg and Bodlander, Ibid., 20, 453-99. 3 Chem. News, 73, 203, 260-2 (1896); Z. anorg. Chem., 9, 312-28 (1895); Am. J. Sci., [3] 49, 357 (1895). 4 Sander, Elektrochem. Z., 6, 133. 6 Carnelley, Numerous papers in Trans. Chem. Soc., Proc. Roy. Soc. and Phil. Mag., from 1876 on. 6 Laurie, Phil. Mag., [5] 15, 42 (1883); Richards, Trans. Chem. Soc., 99, 1201 (1911); Carnelley, Phil. Mag., [5] 18, 1-22 (1884). 7 Abegg, Z. anorg. Chem., 39, 330-80 (1904). 8 Topler, Wied. Ann., 53, 343 (1894). 9 Abegg and Bodlander, Am. Chem. J., 28, 220-8 (1902); Locke, Ibid., 20, 581-92 (1898); 26, 166-85, 332-45 (1901); 27, 455-81 (1902). 10 Rudorf, “Das Periodische Gesetz,” pp. 143-9. 52 Ionic mobilities 1 Refractive indices 2 Ultraviolet vibration frequencies 5 Spectra 3 Mechanical properties 4 Summary. 1 . In this paper a periodic table has been presented, which shows graph- ically the relations between the main and the sub-groups of elements. The main defect of the periodic tables which have been designed formerly, is that they do not show these relations correctly. 2. The table arranges the elements in the exact order of their atomic numbers, and gives no blanks for unknown elements which do not corre- spond to atomic numbers as determined by Moseley’s work on the X-ray spectroscopy of the elements. 3. It also plots the elements according to their atomic weights, so the isotopic forms of an element may be shown graphically on the table, and the alpha and beta decompositions of the radioactive elements may also be plainly depicted. 4. Both the zero and the eighth groups fit naturally into the system. 5. The table may be best represented as a helix in space, but may be shown as a spiral in a plane. The space form is represented by its vertical projection on a plane, but drawn with line perspective so that it may easily be visualized. 6. Beginning at the zero group, the maximum positive valence of a group is found by counting toward the front and toward the right, Li = 1 , Be = 2, etc., and negative valence by counting toward the back, Fe = — 1, O = — 2, N = — 3, etc. 7. The elements in the table divide themselves into cycles, Cycle o Cycle 1 = 4 2 elements Cycle 2 = 6 2 elements Cycle 3 = 8 2 elements but the latter part of the third cycle is missing. The cycles are each divided into two periods. The periods are as follows: Period Oi Period O2 Period 1 = 2 X 2 2 2 = 2 X 2 2 3 = 2 X 3 2 4 = 2 X 3 2 5 = 2 X 4 2 6 = 2 X 4 2 1 Bredig, Z. physik. Chem., 13, 289 (1894). 2 Ibid., 149-57; Bishop, Am. Chem. J., 35, 84 (1906). 3 Ibid., 157-171; Baly, “Spectroscopy.” 4 Ibid., 187-96. 6 Byk, Ann. Physik, [4] 42, 1417- 53 (1913)- 53 These relations are undoubtedly a numerical expression of a function connected in some way with the system according to which the nuclei of the elements have been built up. 8. Whenever the valence drops, in passing along the continuous line connecting the elements in the order of their atomic numbers, it always drops by seven, either from seven to zero, or from eight to one. In the latter case there is evidenced a certain sluggishness in the drop, so that it is not entirely complete, so that copper, silver and gold, the members of which should have the maximum valence one, often exhibits a higher valency, such as two for copper and three for gold. 9. The table arranges the groups into 5 divisions, numbered o, 1, 2, 3, 4. These divisions comprise the following groups: Division 01234 Groups 0.8 1.7 2.6 3.5 4.4 The two groups of one division are said to be complementary. The sum of the group numbers of two complementary groups is always 8, as is also the sum of the maximum valences. The algebraic sum of their charac- teristic valences is, on the other hand, always zero. Thus the characteris- tic valence for Group 1 is +1, and for Group 7 is — 1. The characteristic valence of the eighth group needs to be defined in this sense, and must be taken as — o, which accords with Abegg’s valence system. 10. Another very important relationship given graphically in this table, and not at all by any other which the writers have found, is that between the main and the sub-groups in any one division. Whenever the group numbers in any one division differ considerably, as is the case in divisions o and 1, then the elements in the sub-groups are quite different chemically from the members of the main group, although they are in general alike in valence. As the group numbers in the division approach each other in magnitude, the elements of the sub-group become chemically much like those of the main group. This is true of groups 4A and B, where the group numbers are the same, and the two groups are practically indistin- guishable in their general chemical nature. 11 . On the outer cylinder the main Groups 1 , 2 , 3 become less positive as the group number increases, while the corresponding sub-groups be- come more positive. 12. Whenever the atomic volume of a main-group element is large, that of the corresponding sub-group element is small, and as the atomic volume of the main group element decreases, that of the sub-group in- creases, until the values become about the same in Groups 4A and 4B. 13. The rare earths are put in the third group, since their valence is three, and since if they are distributed around the table there are not enough known and undiscovered elements together to go around. Cerium may be classified either with the third or the fourth group. A discussion 54 of this minor question is given. The elements of the rare earth group (not including yttrium or cerium) decrease in basic properties as the atomic weight increases, which is exactly the opposite of the general rule. As has been explained in the paper, in the rare earths the atomic number, and therefore the nuclear charge, keeps on increasing, while the valence remains constant. On the other hand, it seems probable that the atomic volume tends to keep on as it usually does, but this tendency is masked partly by another influence which tends to keep the atomic volume con- stant. The rare earths lie on the front of the table, where the elements in general become less basic as the atomic number increases, so they, in this case, as they probably do with atomic volumes, effect a compromise be- tween this tendency and that which seeks to cause the elements in a single group to become more basic with increase in atomic weight. The resultant effect is that they become less basic as the atomic number increases, but not with anything like the rapidity which would be shown if they were to go around the table in the usual manner. In this sense the rare earth group forms a loop of its own, but a loop of practically constant valence. 14. The periodic table shows the relation between the properties of the elements and the nuclear charge, and this is presumably equal to the number of external electrons. It is probably the spacing and arrange- ment of these electrons which determines the chemical and most of the physical properties of the elements. 15. In Table II it maybe seen that the spiral forms a series of lines which in any part of the table lie very nearly parallel. This is a graphical expression of the well-known fact that the atomic weights increase in a very regular way in any one group, and at about the same rate in all of the groups. This regularity may be explained on the basis of the theory of Harkins and Wilson, that the nuclei of the elements are built up from hydrogen and helium nuclei, according to a regular system, according to which the differences in mass in any one group are generally due wholly to differences in the number of helium nuclei present, at least in the case of the lighter elements. 16. In Fig. 4 and 5 the relations of the radioactive elements to the periodic table have been given. The nature of isotopes is discussed. 17. A number of figures and tables have been given to illustrate the re- lationship between the cohesional properties of the elements and the periodic system. The following properties have been plotted graphically: Melting points, with lines of maxima and primary and secondary minima, atomic volumes, density, cubic coefficients of expansion, compressibility, susceptibility, atomic frequency, elastic properties, cohesion and hardness. For the discussion of the relations between these properties the body of the paper should be consulted. 55 1 8. A theory as to the factors conditioning variations of cohesion is given. 19. The ordinary theory, that the atoms in solids do not occupy all of the space is supported. Several problems related to the periodic system are now under in- vestigation in this laboratory. One of these is the endeavor to prove whether or not the exceptional atomic weight of chlorine is due to its existence in two isotopic forms. This is a very important problem in its bearing on the theory of complex atoms, whatever may be the facts. Work is also being done upon the melting point of lead derived from rad- ium. A third problem is the attempt to prove whether ordinary lead is or is not a mixture of isotopes. The writers wish to thank Mr. W. A. Roberts for aid in the construc- tion of the model of the periodic system. The next paper in this series will be on “The Evolution of the Elements and the Stability of Complex Atoms." 3 0112 072896894