__A. Some simple quotients:__

The simple quotients 7**/**24, 6**/**24,
5**/**24 times 10^{3} approximate
first three numbers of the ES-chain, since total sum of ams R is
nearly 1500 (particularly if we count on Lys and the two Arg uncharged), Note the sum of the series 5 - 4 - 3 - 2 -
1 - 0 = 15.

However, the lower numbers in the ES-chain are
not given through simple quotients.

**Fig 12-1:** * 7,6,
5 parts of 24, decimals ~ ES-numbers:*

* *

Cf. numbers 7, 6, 5 with halved numbers of electrons in orbitals *f, s + d, *and* d*, see below and file 13 about the periodic system.

A division 10-8-6 of the total 24 ams times 1504 in agreement with
number of ams, 10 (2 x 5) in G1 and C1, 8 in A1, 6 in U1, gives
sums that through a displacement of **84** (~ 2/24 = 292 - 208
in the ES-chain) gives the G+C- and U+A-groups, figure 12-2 below..

Applying exponent 2**/**3 to these 10-8-6-parts
of the total, gives abbreviated times 4 the appropriate numbers
of the ES-chain.

**Fig 12-2:** * 10,
8, 6 parts of 24, transformed to ES-numbers:*

**63 x 52** happen to give the whole sum of 24 ams R + B unbound = **3276**.

A note:

Numbers 7**/**24 and 5**/**24 above = 0,292 - 1/3 and 0.208 +2/3.

Orbital numbers with reference to file 13

14 – 2**/**3, **/**24 = 0,5555…

10 + 2**/**3, **/**24 = 0,4444…

__ 8 , __**/**24 = 0,3333…

2 + 2**/**3 , **/**24 = 0,1111...

__B. Survey of different numeral series on x = 5 - 0:__

a)** x**^{1}:** 5 - 4 - 3 - 2 - 1 - 0 read as triplets:**

543 - 432 - 321 - 210

b) **2x**^{2}: **50 - 32 - 18 - 8 - 2 - 0**: the
chain behind the periodic system.

Intervals
in the steps as orbitals in electronic shells.

c) Halved orbital numbers **½(18 - 14 - 10 - 6 - 2)**
as a superposed chain:

**Fig 12-3: ***Halved
orbitals as a superposed chain: *

d) **x**^{3}: 125 - 64 - **27 - 8** - 1 - 0.

e) **x**^{4}: **625 - 256 - 81** - 16
- 1 - 0.

To **The 2x**^{2}-chain