WHY ISTHE PERIODIC T ABLE ASKEW?

It has been suggested that the new arrangenent of the
periodic table proposed in D ewey B. Larson’s N othing But
Motion entails some fundamental shortcomings in_ its
representation of the relationships among the dements.’ T he
following remarks are intended to clarify the issue with the
aid of some historical considerations.

Larson describes the main innovation of his table in the
following terms:

In the light of the new information now available, it
can be seen that M endeleeff based his arrangement on
the relations existing in the 8-element rotational
groups... and forced the elements of the larger groups
into conformity with this 8-element pattern. The
modern revisers have made a partial correction by set-
ting up their tables on the basis of the 18-element ro-
tational groups... But these tables still retain part of
the original distortion, as they force members of the
32-element groups into the 18-element pattern. To
construct a complete and accurate table, it is only
necessary to carry the revision procedure one step
farther, and set up the table on the basis of... the 32-
element groups.’

At the time that he wrote these words in 1979, Larson
seems not to have been aware of the periodic table proposed

'D. Maurice Gilroy, “The Old and the N ew Periodic T ables,” Reciprocity
Vol. XIII, No. 3 (Winter 1985).

* Nothing But M otion, North Pacific Publishers, Portland, Oregon, 1979,
pp. 135-138.

Jan Sammer Why is the Period Table Askew?

by the Swedish physicist Johannes Robert Rydberg in 1914.
Rydberg was then at the pinnacle of his fame, having two
major discoveries to his credit— in 1890 he had established
the existence of the fundamental frequency that now goes by
his name, and in 1897 he had recognized the significance of
atomic numbers, as distinct from atomic weights, in
determining the true sequence of the denents. In his paper
of 1914,’ Rydberg tried to go a step farther, and integrate
this knowledge in devising a new periodic table that would
overcome the evident inadequacies of the original one
proposed by M endedeeff in 1869. Rydberg formulated a
simple arithmetical rule, which he called the rule of
“quadratic groups,” based on the formula 2n?—an
expression that will be familiar to a student of the Reciprocal
System, since it appears on page 129 of N othing But M otion,
where it is derived from the fundamental postulates.
Rydberg calculated as follows: 2 x 12, 2 x 22, 2 x 32 and 2 x
4z. H ence, he postulated two periods of 2, two of 8, two of
18 and two of 32 elements. Howeve, in trying to
accommodate the first two periods of two eenents,
Rydberg was led to assume that there had to be two un-
discovered elements between hydrogen and helium.

Once scientists were able to prove that no such denents
existed, Rydberg’s rule of “quadratic groups” and his 32-
member periods fell into disrepute. In light of the Reciprocal
System, however, we can fill in the two missing “elenents”
whose non-existence derailed R ydberg’s theory— they are the
Subatomic particles known as the neutrino (a particle with
one unit of negative onedimensonal displacenent, like

> Phil. Mag. [6] 28, 144.

Jan Sammer Why is the Period Table Askew?

hydrogen) and the massless neutron (a particle with zero
one-dimensional displacement, like the noble gas series that
begins with helium). Rydberg was right in his mathematical
formula, and right in his deduction that the periodic table
would start with two 2-denent periods. What he did not
realize is that the first of these periods was not made up of
elements, but rather of subatomic particles.

Rydberg’s table was not rejected in its entirely, however,
and some of its features survive in the currently-accepted
one. The separation of the lanthanide and actinide rare earth
series from the main body of the table is a remnant of his
dual 32-menber periods. T his separation also constitutes the
major difference between the currently-acceoted periodic
table and that proposed by Larson. In the currently-accepted
table two 15-element groups, the lanthanides (57-71) and
actinides (89-103) occupy but a single space each. |.e, the
element lanthanum, number 57, and the 14 dements that
follow it, together occupy position 57 in the table only
with elenent 72 does the progression resume. Similarly
actinium, number 89, and the 14 dements that follow it,
together occupy position 89 in the table only with element
104 does the progression resume. In other words, dement
72 occupies the place where dement 58 would be expected
to appear, were it not for the anomalous properties of the
lanthanides, and denent 104 occupies the place whee
element 90 would be expected to appear, were it not for the
anomalous propeties of the actinides. |n Larson's table the
lanthanides and actinides enjoy no special position; instead
two different 1 S-elament groups are given a special place—
europium (63) to iridium (77), and americum (95) to what
we might tem “eka-iridium,” or elenent 109. We could

Jan Sammer Why is the Period Table Askew?

term them the “europeanide” and the “americanides’— as in
the case of the lanthanides and actinides, each of these groups
of 15 elanents could be said to occupy a single postion in
the table. In both arrangements, two groups of 15 elenents
are separated from the main body; these groups overlap in
part (9 out of 15 of the elanents in each of the groups are
identical). Larson refers to the situation as follows (Nothing
But M otion, p. 136): “The particular dements that are thus
separated on the basis of the electric disolacenent are not the
same ones that are treated separately in the conventional
tables, but the general effect is much the same.” O ne would
like to concur with this opinion; the fact that exactly two
groups of 15 dements need to be treated separately in both
systems is highly suggestive. A common explanation ought
to be available yet the fact renains that the lanthanide and
actinide series do not coincide with the two groups treated
separately in Larson’s table in terms of Larson's table, the
lanthanide and actinide series begin and end 6 postions too
early. That the lanthanides are not arbitrarily chosen and
cannot be arbitrarily shifted up by 6 postions, is
underscored by the history of the discovery of hafnium,
elenent 72.

In the spring of 1922 Niels Bohr predicted that dement
72, which had not yet been discovered, would not belong to
the rare earth series, as most chemists were then assuming,’
but would be a metal related to elenent 40, or zirconium.
In fact, when the new elenent was found later the same year,
it was identified in zirconium deposits, and closely

“See Helge Kragh, “Anatomy of Priority Conflict: The Case of Element
72,” Centaurus 23 (1980), 275-301.

Jan Sammer Why is the Period Table Askew?

resembled zirconium in its properties—it was named
hafnium after the ancient name for Copenhagen, where the
discovery was predicted and made Bohr, who received his
Nobel Prize that same year, included the notice of the
discovery in his Nobel lecture— it was seen by him and by
Scientists at large as a vindication of his understanding of the
atom. Whether or not this was really so— that is whether
Bohr reached the conclusion that elanent 72 would not bea
rare earth on the basis of his own recondite concepts of
backfilling of the electron shdlls within the atom, or on the
basis of a simple deduction from the structure of the
periodic table as it stood at the time— the close affinity of
zirconium and hafnium clinched the special position of the
lanthanides. By the time Bohr made his deduction, elanent
73, or tantalum was known to be closay related to elanent
41, or niobium. Likewise element 74, or tungsten, was
known to be closely related to elenent 42, or molyodenum.
While the identities of elenents 75 and 43 were not ye
known, further down the table, the affinity of platinum (78)
to palladium (46) was well known, as was that of gold (79)
to diver (47). The question that Bohr successfully answered
could be rephrased as follows:

If element 79 is similar to element 47, and element 78
is similar to element 46, and element 74 is similar to
element 42, and element 73 is similar to element 41,
then what will element 72 be similar to?

Of course Bohr not only answered the question but
posed it as well, which is the more difficult part. If the great
Bohr stooped to such crude numerology in making his
prediction, he did not make it Known, and | will leave this
delicate issue to the judgment of the reader. But we can learn

Jan Sammer Why is the Period Table Askew?

something about Bohr’s methodology from H endrik
Kramers, his closest associate at the time

It is interesting to recollect how many physicists abroad
thought, at the time of the appearance of Bohr’s theory
of the periodic system, that it was extensively
supported by unpublished calculations which dealt in
detail with the structure of the individual atoms,
whereas the truth was, in fact, that Bohr had created
and elaborated with a divine glance a synthesis between
the results of a spectroscopic nature and of a chemical
nature.”

If we recall that Bohr adapted for his own use a version of
the periodic table based on that of J ulius Thomsen, in which
the dements are placed in a sort of genealogical chart, and in
which the link between zirconium (40) and dement 72 is
Clearly indicated, we are left to wonder why a mere mortal
glance would not have sufficed. Be that as it may, in the
volume celebrating the centenary of Bohr’s birth this
prediction is hailed as his crowning achievement, the one
that established his reputation in Germany. To an
unprejudiced eye, Bohr simply made a clever deduction of
the kind M endeleeff had made fifty years earlier when he
forecast the properties of eka-aluminum (gallium) and eka-
boron (scandium). The reason for my insisting on this
point, however, is that Bohr would not have been able to
make his prediction of the nature of hafnium had he been
using Larson’s periodic table. Larson does caution us that his

Quoted in H alge Kragh, “The Theory of the Periodic System,” in Nids
Bohr: A Centenary Volume, ed. by A. P. French & P. J. Kennedy
(H arvard Univ. Press: Cambridge, 1985), p. 60.

Jan Sammer Why is the Period Table Askew?

table is meant merely as a convenient way of presenting the
information about the magnetic and electric displacenents;
yet one must wonder why we need to forego useful chenical
information in the process.

| should caution, before proceeding, that the chemical
information is not unequivocally in favor of the currently—
accepted arrangement. For instance, the table currently in use
does not contain any hint of the evident chemical similarity
of thorium (element 90) and zirconium (elenent 40), while
Larson's proposed table puts those two dements in the same
group. Even more striking is the rdationship of
molybdenum (element 42) and uranium (element 92), two
elenents that are brought together in the same group in
Larson’s table but are completely unrelated in the one
currently in use. H owever, as was pointed out by Gilroy,
molybdenum has a remarkable similarity to tungsten
(dement 74), a relationship that is lost in Larson’s
arrangenent, but exists in the current one. It would sean,
then, that no single table can adequately reoresent all of the
rdationships among the elements. This being so, our goal
ought to be the more modest one of constructing a table
based on the correct double periods of 2, 8, 18 and 32
elements, while taking into account the most salient
observed physical properties of the elanents, most especially
the anomalous postion of the lanthanide and actinide series.

Before making an attempt at constructing such a table let
us consider another difference between the old and new
periodic tables— the position of boron (5) and aluminum
(13). In the table as it is acceoted currently, boron and
aluminum are part of a group that continues with gallium
(31). In Larson’s table boron and aluminum are part of a

Jan Sammer Why is the Period Table Askew?

group that continues with scandium (21). As with the lan-
thanides and actinides, the present arrangement is preferable
from the point of view of physical properties— of all the
elements, gallium is most similar to aluminum. In fact,
M endeleeff’s prediction of the properties of dement 31,
which he temed “ekaaluminum,” proved uncannily
accurate when gallium was discovered a few years later, and
this prediction was instrumental in gaining acceptance of
M endedleeff’s table Here is another instance in which
Larson's table sacrifices useful chenical information in favor
of symmetry. But not even here is the situation
unequivocally in favor of the currently-acceoted arrange
ment: A lesser set of chemical properties does link boron and
aluminum to scandium and yttrium, as in Larson’s
arrangement, a fact that has been recognized for many
decades. N ot only did M endeleeff’s “eka-boron” turn out to
be scandium, but in the abovementioned “genealogical”
chart devised by Julius Thomsen, boron and aluminum
could be made to precede either scandium, as in Larson’s
table, or gallium, as in the one currently accepted. In 1923
the British chemist Gilbert Newton Lewis proposed a
periodic table in which boron and aluminum precede scan-
dium and yttrium.° But the two arrangenents are mutually
exclusive: Larson’s table does not account for the close re
lationship of aluminum and gallium, while the standard
table neglects the common features of aluminum and
scandium.

° Gilbert N ewton Lewis, Valence and the Structure of Atoms and M olecules
(TheChemical Catalog Company, 1923), p. 28.

Jan Sammer Why is the Period Table Askew?

To sum up, there are two major differences between the
currently-accepted table and the one proposed by Larson,
which give rise to all the rest: (1) the two 15-member groups
of eleanents that must be separated from the rest do not
coincide (though they partly overlap); (2) boron and
aluminum are in different and mutually exclusive groups.
Could there be a common solution to the two anomalies?
One circumstance that points to a solution is that in
Larson’s table boron and aluminum are part of the same
group as lanthanum and actinium. The two anomalies could
be explained if it could be shown that there is a strong bias
toward the electronegative type rotation on the electric axis,
such that postive onedimensonal rotational disolacenent
does not exceed two units. Thus boron (5) instead of having
the configuration 2-1-3, would instead have the
electronegative configuration 2-2-(5). Similarly, aluminum
(13), instead of having the configuration 2-2-3 would be
configured as 3-2-(5). In this fashion the lanthanides would
begin with 4-4-(29) and end with 4-4-(15), while the
actinides would begin with 5-4-(29) and end with 5-4-(15).
In both cases thee is what we might term “excess
electronegativity,” caused by the postulated inability to
maintain electroposttive rotation greater than 2 on the
electric axis. Once electronegativity enters the normal range,
the observed propetties of the aements change accordingly,
and the special rare-earth series is ended.

A glance at the table attached herewith, in which the
elenents are arranged according to the principles just stated,
allows us to recognize at once the point at which the rare
earth denents begin— one-dimensional space displacanent
in excess of 14 units. H ence, scandium, with displacements

Jan Sammer Why is the Period Table Askew?

of 3-2-(15) and yttrium, with displacenents of 3-3-(15)
belong to the rare earth series; they are, in fact, the only non-
lanthanide and non-actinide rare earth denents. The exact
reason why one-dimensional space displacement in excess of
14 units gives rise to rareearth characteristics is not yet
completely clear; the improbability of such a large number
of units of space displacement accumulating on the electric
axis is evidently the determining factor. W hat renains to be
established is why the dividing line should be at exactly this
point.

T he perceptive reader will notice that so far in this paper |
have turned the usual deductive process on its head and used
inductive reasoning. In other words, up to this point | have
not deduced my conclusions directly from the postulates,
but took them from empirical data, and then searched for
the simplest rules, consistent with the postulates, that would
account for the observed situation. N ow the postulates will
be called upon to accomplish two things—(1) supply a
reason why the probability of onedimensional positive
rotation within the atomic structure becomes negligible
beyond 2 units and (2) provide an explanation of how
electronegativity greater than 14 produces denents with the
special characteristics Known as “rare earth.”

Once the strong bias of the dements toward the dectro-
negative type of rotation is revealed, its cause becomes
almost self-evident. Previous deductions from the postulates
made by Larson have established the ubiquity of uncharged
electrons in the material sector of the universe. U ncharged
electrons are simply rotating units of space, being made up
of a material rotational base, a time structure, with a Single
unit of one-dimensional space displacement. For our present

Jan Sammer Why is the Period Table Askew?

purposes, we might describe them as units of electronegative
one-dimensional rotation. M aterial atoms are continuously
exposed to a massive flux of these rotations— or, more
accurately, atoms are constantly entering and leaving the
space of the uncharged electrons.

In Nothing but Motion (p. 141), Larson makes the
following statement about one-dimensional displacements in
the material sector:

...Electrons are plentiful in the material environment
whereas positrons are extremely rare... We can regard
the positron as essentially a rotating unit of time. As
such it is readily absorbed into the material system of
combinations, the constituents of which are pre
dominantly time structures; that is, rotational motions
with net positive displacement.... The opportunities
for utilizing the negative displacement of the electrons
in these structures, on the contrary, are very limited.

The words! have italicized in the above quotation are the
key to the solution of the material atoms’ observed bias
towards the electronegative type of arrangenent. As Larson
explains, one-dimensional time displacenent is easily
absorbed by the atoms of matter, because both of the
magnetic axes of the double rotating systen have ne
displacenent in time The transfer of positive one
dimensional displacement to the atoms is facilitated by the
fact that the orientation that results in absorption can occur
in any one of three dimensions, whereas in the case of the
negative one dimensional displacement the orientation must
occur along the electric axis if absorption is to take place.
H ence positrons are rare. H owever, as Larson points out, the
material atoms can carry space displacanent along the

11

Jan Sammer Why is the Period Table Askew?

electric (onedimensional) axis of rotation. The
opportunities for utilizing the negative displacement of the
electrons in material atoms may be “very limited,” but they
are not non-existent.

We have seen that the transfer of one-dimensional space
displacenent to the material atom can only take place when
the orientation of the electron in relation to it is along the
electric axis; the opportunities for transfer of the
displacenent are further limited by the circumstance that
while electrons are standing still in the natural reference
systen, the atoms of matter are moving inward in three
dimensions at the full speed of the space— time progression.
The atoms that happen to enter the one-dimensional space
of the electron on ther inward journey do not spend more
than a single unit of time in this combination. It is during
this single unit of time that the space displacement must be
transferred to the three dimensional material structure, if the
transfer is to take place at all. The situation in rdation to
positrons is similar, but not identical. Like the electrons, the
positrons are motionless in the natural system of reference,
and are exposed to a constant flux of material atoms
traveling inward in three dimensions. H owever, the material
atom cannot exist in the time of the positron’s time
displacement, as it does momentarily in the space of the
electron’s space displacement. T he reason is that the physical
universe is one of motion, defined as a reciprocal relation
between space and time The relation of the combination of
one-dimensional and three-dimensional time displacement is
not motion. It is additive, not reciprocal. Thus, once the
three-dimensional time displacement comes into contact
with one-dimensional time disolacenent, and the axes of

12

Jan Sammer Why is the Period Table Askew?

rotation are congruent in any one of three dimensions, a
combination necessarily takes place Probability
considerations indicate that in most instances the positron’s
time displacenent will be absorbed by one of the two
principal (two-dimensional) axes of rotation; in a relatively
small number of cases the absorption will be along the
electric axis. But whereas the absorption of time displace
ment along the two magnetic axes is paemanent, time dis
placement absorbed along the electric axis is continuously
subject to modification by the prevalent one-dimensional
units of space displacenent (electrons).

The observed stuation— in which one-dimensional time
displacement of the material atoms is limited to two units—
appears to be one of equilibrium, the net result of the
balance of probabilities. While positrons are more readily
absorbed by the material atoms than electrons, the
absorption is sddom along the electric axis. The absorption
of electrons is more difficult, but it is always along the
electric axis.

The effect of this situation is to effectively neutralize all
electropositive onedimensional rotations of the material
atoms greater than two units, so that if the higher dements
are to be formed at all, they must be formed on the “excess
electronegative’ bass. This configuration is rather
improbable to begin with, but the unavailability of the
positive alternative eventually results in the formation of the
higher denents on the electronegative basis, according to the
principles outlined in chapter 26 of Larson’s Badc Propeties
of Matter. The electronegative alternative is aided by the
same preponderance of dectronegative rotations that
discourages the positive configuration— one-dimensional

13

Jan Sammer Why is the Period Table Askew?

space displacement is plentiful in the material environment,
and under the right conditions will be transferred to the
material atoms. Hence the “force” that is skewing the
periodic table to the electronegative side acts both to decrease
the probability of the electropositive configuration and
increase the likelihood of the electronegative one. The only
remaining question is whether the observed limitation of
one-dimensional time displacenent to exactly two units is
simply the result of the balance of probabilities outlined
above, resulting in the establishment of an equilibrium at
this level, or whether some other factor is at work that
makes the two-unit onedimensional time displacenent
configuration in the material atoms unusually stable The
first solution has the advantage of simplicity, but the relative
probabilities need to be worked out mathematically to
determine whether or not an equilibrium at precisely this
level is predicted by the postulates.

In the light of the solution presented above, we are led to
conclude that while the most salient of the properties of the
elements are due to number of units of displacement along
the electric axis, there are other properties that are a function
of total displacement, regardless of how it is constituted. In
the table presented by Larson, which is perfectly symmetrical
along the axis formed by the noble gases, the edectric
displacenents are effectively canceled out; they medy
fortify the structure constructed on the basis of total
displacement alone As a result the table shows only the
relationships due to total displacaenent. The table being
proposed in this paper stresses the effects of dectric
displacenent, which is strongly skewed in favor of the
negative one-dimensional arrangement. Both tables have

Jan Sammer Why is the Period Table Askew?

some features to recommend them, but since the electric
displacement is the major determinant of the properties of
the denents, the new table proposed here is the more useful
one for chemists.

The conclusion that there are two mutually exclusive
criteria for arranging the periodic table—i.e, displacement
along the electric axis and total displacenent may help in
explaining why the rare-earth series of elements should begin
with one-dimensional space displacement of 15 units. We
must visualize the two tables as co-existing in some sense,
since both arrangenents have certain advantages in the way
they represent the observed properties of the deneants. In
nature, as distinct from any table we can devise, each edement
occupies one position by virtue of its electric displacement,
and another postion by virtue of its total disolacenent. On
the basis of total displacenent, however, the elements do
not range beyond 15 postions from the neutral axis (the
noble gas series). Elements are forced into positions that are
beyond this range only with difficulty, due to the rdentless
pressure of the electron flux, which skews the periodic table
away from its ideal, symmetrical arrangement.

15