```                Revising the Planck Unit Values and
Determining the Gravitational Constant

As the alternative numerical expression, symbol use, and unit

labels facilitate greater information density in maps, increased

search and sort capability in digitized literature, and superior

value comparison in tables, Geometrical Dimensional Analysis exposes

a key similarity of values.  With the structuring of definitions and

formulas of fundamental constants into the lattices of logic, the

vector spaces, the factoring pathway maps projected by acceptance of

the International System of Units (S.I.), identities and patterns of

relationship are displayed which correct the estimates of the Planck

units and indicate a specific value for the constant of gravitation.

Proposing that [G] has numerical value 6.6917625079...e-11 , exactly

the same as other quantities with different units, the implication

is that the difficulties in relating gravity to other forces and the

gravitational to other constants has involved an inadequacy in the

definition or use of the quantity calculus.

With the atomic units of mass, length, and frequency as the unit

vectors defining the Corrsin diagrams(006) of GJN017 and GJN018,

both known and unsuspected factoring combinations within the atomic

units become visible, validating the premise that unit systems can

be treated as vector spaces(027) and inviting a similar display of

the Planck units, as in diagram GJN020.  As an overlay of the two

natural unit systems, each of GJN023 and GJN024 is, at any point,

a dimensionless ratio of a Planck unit numerator to an atomic unit

denominator, relating together all of the quantities portrayed in

the two individual unit system maps.  For better understanding of

that metaratio, however, [hB], [c], and [G] as unit vectors form yet

another view of the Planck unit system in GJN016, where it is more

obvious which quantities, lying in the plane created by adopted [hB]

and defined [c], cannot be changed, and which entities, not in that

plane, will be altered with the adjustments required to [PM], [PL],

and [Pf]: just as the product [PL][Pf] must match [v0][aa] as equal

to [c] and both [c][PL][PM] and {[PL]^2}[PM][Pf] must equal [hB],

[PL][PM] must be as equal to [hB]/[c] as is [Me][a0][aa], [PM]/[Pf]

must match both [Me]{[aa]^2}/[2af] and [hB]/[c^2], and [G]{[PM]^2},

[PM]{[PL]^3}{[Pf]^2}, and {[PQ]^2}/[k] must all be as identical to

[hB][c] as are {[Q0]^2}[Ke]/[aa] and [Me][v0^2][a0]/[aa].

While the need for some more consistent set of Planck units thus

becomes obvious, determination of the one correct set, and therefore

of the value of the gravitational constant as the factor combination

{[PL]^3}{[Pf]^2}/[PM], that arises from a very near miss in a value

table as [G] is adjusted to reflect contemporary estimates.

** For Txx.xxxxxxx = 10^xx.xxxxxxx... , current publication(322) has

[G] located in the middle of modern experimental results(023b)(322)

at T-10.1743792 = 6.693e-11 in {Meter^3)/[(Kilogram)(Second^2)], or

(Newton)(Meter^2)/(Kilogram^2), or

(Meter)(Weber^2)/[(Henry)(Kilogram^2)], or

(Meter^3)(Ohm)/[(Henry)(Kilogram)(Second)], or

(Ampere^2)(Weber^2)/[(Kilogram^2)(Newton)], or

(Coulomb)(Meter^3)(Tesla)/[(Kilogram^2)(Second)].

In (Henry)/(Meter) or (Newton)/(Ampere^2), quantity [d]{[aa]^2}

and those which are identical to it all have a numerical value of

6.6917625...e-11 as T-10.1744595 , quite close to T-10.1743792 and

even more centered in that result range.  In fact, that near miss

not only stands out in the values table, it is also true that if [G]

and immutable product [d]{[aa]^2} both have that numerical value of

T-10.1744595 , so that [PM] is T-7.6628219 , [PL] is T-34.7909227 ,

and [Pf] is T+43.2677434 , a number of dimensioned and dimensionless

quantities acquire identical numerical values.  While a uniform map

such as those above will locate numerical values in parallel planes,

the revised Planck unit maps now exhibit important new alignments.

There are now numerous instances where significant quantities with

dissimilar units share a line parallel to that which transfixes both

[G] and [d] : a line of multiplication by some power of the factor

[G]/[d] = [c^2][PL]/([PM][d]) = [c^4][k][PL]/[PM][d], which equals

{[aa]^2}(Coulomb^2){Meter^2)/[(Kilogram^2)(Second^2)], or

[PC][PL]/[PM] which is [aa](Coulomb){Meter)/[(Kilogram)(Second)] .

In the comparison table, values in the first column are based on

[G] as T-10.1744595 , and those in the second column derive from the

currently published NIST values(023f).  The "dissimilar" quantities

which share a given numerical value are denoted by differing numbers

of dollar signs and those with units will lie on one of the lines of

coincidence mentioned above.  Notice that the NIST adopted values of

the Planck units produce results which fail to match those values

required by the dimensional analysis, that different combinations of

those NIST values as factors can produce differing numerical results

for the same end product, and that some of the identical numerical

occurrences which exist only for the proposed values of [PL], [PM],

[Pf], and [G] have significant implications:

{[aa]^2} as compared to [G][k][c^2] = [G]/[d] and therefore also

[PL]/[PM] contrasted with {[aa]^2}/{[k][c^4]} = {[aa]^2}[d]/[c^2],

[PM] in contrast to [PQ][c]/[aa] or [Pf] to [PQ][c^3]/{[aa][hB]},

[PL] contrasted with [Me]{[aa]^3}/[PQ][2af] = [PQ][aa][d]/[c],

[PC] in contrast to [c^2]/{[d][aa]} and to [PM][aa]/[PL],

[G]/[k] as compared to {[E0]/[H0]}^2 = {[v0][d]}^2 = {[z0][aa]}^2

= {([He][a0][d])/[hB]}^2 = {[aa]^2}[d]/[k] = 4{[aa]^4}{[RK]}^2 ,

and [Fe]/[Fg] = ([Q0]^2)[Ke]/([G][Me][Mp]) = [aa]{[PM]^2}/{[Me][Mp]}

= {[PQ]^2}[aa][PM][d]/{[Me][Mp][PL]} = ([aa]^2)[PM][a0]/([Mp][PL])

= {[PQ]^2}[aa]/{[G][k][Me][Mp]} = ([aa]^3)[PM][Pf]/([Mp][2af])

in contrast to [c^4][a0][k]/[Mp] or to [PC][a0][aa]/[Mp] .

While it is interesting to compare the alignment factor above to

his magnetic charge and tempting to declare an insufficiency of

bases in the S.I. similar to that proposed by Desloge(102)(103),

this report intentionally declares only "inadequacy".  The issue of

measurements not only includes notable argument for fewer base units

instead of more(030)(056)(235), it possesses all the potential for

misunderstanding and confusion to be inferred from centuries of

controversy and such contentions as distinguishing straight length

from arc length(076), having separate units for lengths in different

frames of reference(169), and proposals that length differs in the

direction of an electron's travel(100) or can change when measured

from a different scale(087).

More physical dimensions in the microcosm(029)(055), gravity

screening investigations(059), Foucault pendulum anomalies during

solar eclipses(323), spacecraft trajectory abnormalities(316), even

claims of antigravity experiments(324) are due consideration as an

understanding of gravity remains elusive.  With visible proof that

the Planck units can be related to the other constants well enough

to correct incompatibilities with them, because the adjusted set

combines as factors to produce a numerical value shared by [G] and

quantities with factors which are significant in defining any system

of units(027)(123)(245)(261)(262), and considering the pattern

alignments by such significant numerical coincidences, the proposal

here is that reconsideration is called for of the mathematical logic

found at the foundation of all of physics.  To that end, this writer

is pursuing and joins others in recommending a general review of the

works by authors such as Birge(223)(262)(263), Bridgman(067)(251),

DeBoer(147), Esnault-Pelterie(235), Hall(082), Karapetoff(232),

Maxwell(090), Page(261), Palacios(124), Petley(077), Sena(245),

Silsbee(066), Tuninsky(148), Varner(123), and Weber(233), as well as

the comments on the subject by Abraham(056) and Jackson(136) and the

more officially sanctioned publications(023)(288)(313).

** The CODATA 2006 adjustment of the fundamental constants
specifically states that both the Fixler et al results and the
Bernoldi et al results play no significant part in the officially
adopted value for Newtonian gravitational constant [G],
(Rev Mod Phys, Vol 80, No 2, Apr-Jun 2008, table XXVII and fig 2),
but dimensional analysis still requires a set of Planck mass, Planck
length, and Planck time values that correctly combine into all the
quantities and there still exists a repeating, all-pervasive pattern
of numerical coincidences among fundamental constants if [G] has the
same numerical value as the product of the magnetic constant and the
square of the fine structure constant.

COMPARISON TABLE

Mappings           Complete values table        Symbol key
=================================++=================================
\$ = DIFFERENT DIMENSIONS, \$\$ = STILL DIFFERENT DIMENSIONS, etc.
* as divider: value will vary with adjustment of value of [G]
| as divider: value will NOT vary with adjustment of value of [G]

WITH EACH VALUE AS A POWER OF TEN:     G=T-10.1744595  NIST Jul2010
=================================++=================================
[G]                                        -10.1744595 * -10.1755956
{[PL]^3}{[Pf]^2}/[PM]                      -10.1744594 * -10.1755968
{[PL]^2}[Pf][c]/[PM]                       -10.1744594 * -10.1755965
[c^2][PL]/[PM]                             -10.1744594 * -10.1755962
[c^2]{[PL]^2}/{[a0][Me][aa]}               -10.1744593 * -10.1755958
([Q0]^2)/([4Pi][aa][k]([PM]^2))            -10.1744593 * -10.1755966
{[PQ]^2}/([k]{[PM]^2})                     -10.1744595 * -10.1755962
{([2af][Me]/[B0][PM])^2}/{[4Pi][aa][k]}    -10.1744595 * -10.1755966
in k2rmM2trNwtn = kgrmM3trs2nd = Cuulk2rmM3trscndTsla
= A2prk2rmnwtnW2br = Fradk2rmMetrV2tt = hnrykgrmM3trOhmmscnd
\$ [d]{[aa]^2} = [k]{[v0][d]}^2             -10.1744595 | -10.1744595
\$ [k]{[He][a0][d]/[hB]}^2                  -10.1744595 | -10.1744595
\$ 4[k]{[aa]^4}{[RK]}^2                     -10.1744597 | -10.1744595
\$ [k]{[z0]^2}{[aa]}^2 = [k]{[E0]/[H0]}^2   -10.1744595 | -10.1744595
\$ {4([aa]^2)}/({[Jf]^2}[c^2][Me][a0][Pi])  -10.1744595 | -10.1744595
\$ [d]{[E0]^2}/{[c^2][B0]^2}                -10.1744595 | -10.1744595
\$ {[Q0]^2}{[d]^2}/{[4Pi][Me][a0]}          -10.1744593 | -10.1744595
\$\$ ({[aa]^2}[PL]/[k][PM])^.5               -10.1744595 * -10.1750278
\$\$ [aa][PQ]/{[c][k][PM]}                   -10.1744595 * -10.1750280
in f12dk12mMetr = kgrmWebr = CuulfradkgrmScnd

[PM]                                       - 7.6628219 * - 7.6622533
{[hB][c]/[G]}^.5                           - 7.6628219 * - 7.6622538
{[aa]^2}[Me][Pf]/[2af]                     - 7.6628219 * - 7.6622540
[Me][a0][aa]/[PL]                          - 7.6628220 * - 7.6622537
{[PQ]^2}[z0]/{[c][PL]}                     - 7.6628220 * - 7.6622537
([Q0]^2)[d]/{[4Pi][aa][PL]}                - 7.6628218 * - 7.6622537
in Kgrm = C2ulm2trOhmmScnd = CuulScndTsla = C2ulfradm2trS2nd
\$ [PQ][c]/[aa]                             - 7.6628219 | - 7.6628217
\$ [PC][PL]/[aa]                            - 7.6628218 | - 7.6628218
in CuulMetrscnd = AmprMetr
\$\$ [c^4][PL][k]/{[aa]^2}                   - 7.6628218 * - 7.6633900

[PL]                                       -34.7909227 * -34.7914909
{[hB][G]/[c^3]}^.5                         -34.7909228 * -34.7914908
[hB]/{[PM][c]} = [a0]([Me][aa]/[PM])       -34.7909227 * -34.7914913
[G][PM]/[c^2]                              -34.7909228 * -34.7914903
1/{[z0][Pf][k]}                            -34.7909227 * -34.7914906
\$ [Me]{[aa]^3}/[PQ][2af] = [PQ][aa][d]/[c] -34.7909228 | -34.7909228
\$ [PM][aa]/[PC]                            -34.7909228 | -34.7909224
\$ [PM][aa]/{[PQ][Pf]}                      -34.7909227 | -34.7909221
in amprKgrm = cuulKgrmScnd
\$\$ [c^2][PQ]/{[PM][Pf][aa]}                -34.7909227 * -34.7920592
in CuulkgrmM2trscnd
\$\$\$ [PM][d]{[aa]^2}/[c^2]                  -34.7909228 * -34.7903542
in HnryKgrmm3trS2nd

[Pf]                                       +43.2677434 * +43.2683113
{[hB][G]/[c^5]}^-.5                        +43.2677435 * +43.2683115
[2af][Pp]/([p0][aa])                       +43.2677434 * +43.2683117
[2af][a0]/([PL][aa])                       +43.2677434 * +43.2683116
[2af][PM]/([Me]{[aa]^2})                   +43.2677435 * +43.2683120
[2af][PE]/[He]                             +43.2677434 * +43.2683120
in Hrtz
\$ [PC][c]/{[aa][PM]}                       +43.2677435 | +43.2677431
\$ [PQ][c^3]/{[aa][hB]}                     +43.2677434 | +43.2677435
in AmprkgrmMetrscnd = CuulM3trjuuls4nd
\$\$ [PM][aa]/{[PQ][PL]}                     +43.2677434 * +43.2688802
\$\$ [PQ][d][aa]/{[PL]^2}                    +43.2677433 * +43.2688798
in cuulKgrmmetr = CuulHnrym3tr

{[E0]/[H0]}^2 = {[v0][d]}^2 = {[z0][aa]}^2 + 0.8783918 | + 0.8783918
{([He][a0][d])/[hB]}^2 = {[aa]^2}[d]/[k]   + 0.8783918 | + 0.8783918
4{[aa]^4}{[RK]}^2                          + 0.8783916 | + 0.8783918
\$ [G]/[k]                                  + 0.8783918 * + 0.8772557
\$ [hB][c]/([k]{[PM]^2})                    + 0.8783919 * + 0.8772547
\$ {[PL]^3}{[Pf]^2}/{[PM][k]}               + 0.8783919 * + 0.8772545
\$\$ {[c][G]/[aa]}^2                         + 0.8783918 * + 0.8761196
in k2rmM8trs6nd

[G][c^2][k] = [G]/[d]                      - 4.2736694 * - 4.2748054
[c^4][PL][k]/[PM]                          - 4.2736694 * - 4.2748061
{[PC]^2}{[PL]^2}/{[PM]^2}                  - 4.2736692 * - 4.2748064
in Fradk2rmM3trNwtns2nd = hnrykgrmM4trs2nd = A2prk2rmM2tr
\$ {[aa]^2}                                 - 4.2736694 | - 4.2736693
is dimensionless
\$\$ [d][PC]{[aa]^3}/[c^2]                   - 4.2736694 * - 4.2731011
in amprm2trNwtnS2nd = AmprHnrym3trS2nd

[d] = 1/([c^2][k]) = {[z0]^2}[k]           - 5.9007901 | - 5.9007901
in a2prNwtn = Hnrymetr
\$ [PQ]/([k][c][PM][aa])                    - 5.9007901 * - 5.9013587
\$\$ [G]/{[aa]^2}                            - 5.9007902 * - 5.9019262
in kgrmM3trs2nd

[c] = [v0]/[aa] = [E0]/{[aa][d][H0]}       + 8.4768207 | + 8.4768207
[aa][H0]/{[k][E0]} = [z0]/[d]              + 8.4768207 | + 8.4768207
[PL][Pf]                                   + 8.4768207 | + 8.4768204
[hB]/{[PL][PM]}                            + 8.4768207 | + 8.4768203
in Metrscnd = metrtslaVltt = AmprfradMetrvltt = hnryMetrOhmm
\$ [PM][aa]/[PQ]                            + 8.4768207 * + 8.4773893
in cuulKgrm
\$\$ [PM]{[aa]^2}/({[PL]^4}{[Pf^3}[k])       + 8.4768206 * + 8.4779583
\$\$ {[aa]^2}/{[G][c][k]}                    + 8.4768207 * + 8.4779568

[Me][c^2]                                  -13.0868697 | -13.0868697
([Q0]^2)[Ke]/({[aa]^2}[a0])                -13.0868695 | -13.0868697
[Fe][a0]/{[aa]^2} = [He]/{[aa]^2}          -13.0868696 | -13.0868697
{[E0]^2}{[a0]^3][4Pi][k]/{[aa]^2}          -13.0868697 | -13.0868697
{[B0]^2}{[a0]^3}[4Pi]/[d]                  -13.0868697 | -13.0868697
{[H0]^2}{[a0]^3][4Pi][d]                   -13.0868697 | -13.0868697
[hB][c]/{[a0][aa]}                         -13.0868696 | -13.0868697
{[PQ]^2}/{[a0][aa][k]}                     -13.0868697 | -13.0868697
[PE][PL]/([a0][aa])                        -13.0868696 | -13.0868693
{[PM]^2}[G]/{[aa][a0]}                     -13.0868697 | -13.0868686
[FBH]([PL]^2)/([aa][a0])                   -13.0868696 | -13.0868697
[PM]{[PL]^3}{[Pf]^2}/([aa][a0])            -13.0868696 | -13.0868699
\$ {[PM]^1.5]{[PL]^.5}/([a0]{[k]^.5})       -13.0868697 * -13.0863009
in f12dK15mm12r = KgrmmetrScndVltt = KgrmMetrTsla
\$\$ {[PM]^2}[aa]/({[Pf]^2}{[PL]^2}[a0][k])  -13.0868697 * -13.0857320

[PL]/{[PM][d]}                             -21.2273107 * -21.2284475
[G][k] = [G][Me][a0]({[Jf][Pi]}^2)/[4Pi]   -21.2273108 * -21.2284468
{[PQ]^2}/{[PM]^2}                          -21.2273108 * -21.2284479
in hnrykgrmM2tr = FradkgrmM2trs2nd = M4trs4ndv2tt = C2ulk2rm
\$ {[aa]^2}/[c^2] = {[aa]^2}[d][k]          -21.2273108 | -21.2273108
\$\$ [aa]({[k][PL]}^.5)/{[PM]^.5}            -21.2273108 * -21.2278791
in F12dk12m = CuulkgrmmetrScnd

[c^2]/{[d][aa]}                            +24.9912662 | +24.9912662
in hnryM3trs2nd = A2prkgrmMetr
\$ [PC] = {[k]([PL]^3)[PM]([Pf]^4)}^.5      +24.9912662 * +24.9918344
\$ {1/[PL]}{[hB][c]/[d]}^.5                 +24.9912662 * +24.9918344
\$ [PQ][Pf]                                 +24.9912661 * +24.9918341
\$ [PM][Pf]{[G][k]}^.5                      +24.9912661 * +24.9918346
\$ ([G]{[PM]^2}/([d]{[PL]^2}))^.5           +24.9912661 * +24.9918349
in Ampr = Cuulscnd = F12dK12mMetrs2nd = h12yK12mMetrscnd
\$\$ [PM][aa]/[PL]                           +24.9912661 * +24.9924030
\$\$ [c^2][aa]/[G]                           +24.9912661 * +24.9924023
in Kgrmmetr

[G]([PM]^2)                                -25.5001033 | -25.5001022
[PM][PL][c^2]                              -25.5001032 | -25.5001028
{[PL]^3}{[Pf]^2}[PM]                       -25.5001032 | -25.5001034
{[PL]^2}{[PC]^2}[d]                        -25.5001031 | -25.5001031
{[PQ]^2}/[k]                               -25.5001033 | -25.5001032
([Q0]^2)/{[4Pi][k][aa]}                    -25.5001031 | -25.5001032
[hB][c]                                    -25.5001032 | -25.5001032
in KgrmM3trs2nd = C2ulfradMetr = A2prhnryMetr = JuulMetr
\$ [PQ][d][c][aa][PM]                       -25.5001033 * -25.4995346
in CuulHnryKgrmscnd
\$\$ [PC]{[PL]^2}[c^2]/[aa]                  -25.5001031 * -25.5006713
in AmprM4trs2nd

[G]/[c^2] = [G][d][k]                      -27.1281009 * -27.1292370
[c^2]/[FBH]                                -27.1281008 * -27.1292372
[PL]/[PM]                                  -27.1281008 * -27.1292376
[Me][a0][aa]/{[PM^2]}                      -27.1281009 * -27.1292380
{[Q0]^2}[d]/([4Pi]{[PM]^2}[aa])            -27.1281008 * -27.1292380
in kgrmMetr = k2rmmetrNwtnS2nd = C2ulHnryk2rmmetr
\$ [aa]/[PC]                                -27.1281009 * -27.1286691
\$ [PQ][d][aa]/{[PM][c]}                    -27.1281009 * -27.1286695
in ampr = CuulHnrykgrmm2trScnd
\$\$ [k]{[d]^2}{[aa]^2} = [d]{[aa]/[c]}^2    -27.1281008 | -27.1281009

[PM][Pf]                                   +35.6049215 * +35.6060580
[c^3]/[G]                                  +35.6049216 * +35.6060577
[hB]/{[PL]^2}                              +35.6049215 * +35.6060579
[FBH][d]/[z0]                              +35.6049215 * +35.6060579
in Kgrmscnd = K2rmMetrnwtns3nd = Juulm2trScnd = HnrymetrNwtnohmm
\$ [PC][c]/[aa]                             +35.6049216 * +35.6054898
in AmprMetrscnd
\$\$ [aa]{[PM]^1.5}{[d]^.5}/{[PL]^1.5})      +35.6049215 * +35.6066267
in KgrmmetrScndTsla

{[PQ]^2}                                   -36.5529546 | -36.5529545
[k][c^2][PL][PM]                           -36.5529545 | -36.5529541
[k][PM]{[PL]^3}{[Pf]^2}                    -36.5529545 | -36.5529547
[[Q0]^2}/{[4Pi][aa]}                       -36.5529544 | -36.5529545
[Me][a0][aa]/[d]                           -36.5529546 | -36.5529545
[hB][c][k]                                 -36.5529545 | -36.5529545
[PL][PM]/[d]                               -36.5529545 | -36.5529541
[G][k]{[PM]^2}                             -36.5529546 | -36.5529534
in C2ul = FradJuul = hnryKgrmM2tr
\$ [PQ][PM][aa]/[c]                         -36.5529546 * -36.5523859
in CuulKgrmmetrScnd
\$\$ ([PM]^2}{[aa]^2}/[c^2]                  -36.5529546 * -36.5518174
in K2rmm2trS2nd

[Fe]/[Fg] = ([Q0]^2)[Ke]/([G][Me][Mp])     +39.3546349 * +39.3557711
{[PQ]^2}[aa]/{[G][k][Me][Mp]}              +39.3546349 * +39.3557711
{[PQ]^2}[aa][PM][d]/{[Me][Mp][PL]}         +39.3546348 * +39.3557717
[aa]{[PM]^2}/{[Me][Mp]}                    +39.3546349 * +39.3557721
([aa]^2)[PM][a0]/([Mp][PL])                +39.3546349 * +39.3557717
([aa]^3)[PM][Pf]/([Mp][2af])               +39.3546348 * +39.3557714
is dimensionless
\$ [PC][a0][aa]/[Mp]                        +39.3546349 * +39.3552032
in AmprkgrmMetr
\$\$ [c^4][a0][k]/[Mp]                       +39.3546349 | +39.3546350
\$\$ {[PC]^2}{[PL]^2}/{[aa][Me][Mp]}         +39.3546351 | +39.3546351
\$\$ {[PQ]^2}[c^2]/{[aa][Me][Mp]}            +39.3546349 | +39.3546350
in FradkgrmM4trs4nd = A2prk2rmM2tr = C2ulk2rmM2trs2nd

[PM][PL] = {[PQ]^2}[d]                     -42.4537446 | -42.4537442
[hB]/[c] = [Me][Re]/[aa] = [Me][a0][aa]    -42.4537446 | -42.4537446
[aa][4Pi][k]{[B0]^2}{[a0]^4}               -42.4537446 | -42.4537446
[aa][Ke]{[Me^2}/({[B0]^2}{[a0]^2})         -42.4537447 | -42.4537446
([Q0]^2)[d]/([aa][4Pi])                    -42.4537445 | -42.4537446
[Jf][aa]{[Me]^2}/{4[k][B0]}                -42.4537447 | -42.4537446
4[k][aa]{[w0]^2}/[Pi] = 2[hB][RK][k][aa]   -42.4537447 | -42.4537446
\$ {[PL]^2}[PC]/[aa]                        -42.4537445 * -42.4543127
\$ [c][PL][PQ]/[aa]                         -42.4537446 * -42.4543128
in AmprM2tr
\$\$ [c^4]{[PL]^2}[k]/{[aa]^2}               -42.4537445 * -42.4548810

[G][Me]/([a0]{[v0]^2})                     -42.6185437 * -42.6196798
[G]{[B0]^2}[4Pi][k]/{[2af]^2}              -42.6185437 * -42.6196798
([Me][Fg])/([Fe][Mp]) = [Fge]/[Fe]         -42.6185437 * -42.6196798
([Me]^2)[G][4Pi][k]/([Q0]^2)               -42.6185439 * -42.6196798
{[Me]^2}/([aa]{[PM]^2})                    -42.6185437 * -42.6196809
[Me][c^2]/({[aa]^2}[FBH][a0])              -42.6185436 * -42.6196801
[Me][PL]/([a0][PM]([aa]^2))                -42.6185436 * -42.6196805
[Me][2af]/([PM][Pf]{[aa]^3})               -42.6185436 * -42.6196802
([PL]^2)/{([a0]^2)([aa]^3)}                -42.6185435 * -42.6196801
4[PL][B0][k]/({[aa]^2}[PM][Jf])            -42.6185436 * -42.6196805
[Pf]{[PL]^3}/({[aa]^2}{[a0]^3}[2af])       -42.6185435 * -42.6196804

[FBH] = [hB][c]/{[PL]^2}                   +44.0817422 * +44.0828786
[G]{[PM]^2}/{[PL]^2}                       +44.0817421 * +44.0828797
[PM][PL]{[Pf]^2}                           +44.0817422 * +44.0828784
[PM][C^2]/[PL]                             +44.0817422 * +44.0828790
[c][PM][Pf]                                +44.0817422 * +44.0828787
[c^4]/[G]                                  +44.0817423 * +44.0828784
{[PC^2]}[d]                                +44.0817423 * +44.0828787
{[PQ]^2}/([k]{[PL]^2})                     +44.0817421 * +44.0828786
in Nwtn = KgrmMetrs2nd = A2prHnrymetr = C2ulfradmetr
\$ {[PM]^1.5}[aa]/({[k]^.5}{[PL]^1.5})      +44.0817422 * +44.0834474
in f12dK32mmetr = KgrmTsla
\$\$ [PC][c^2]/[aa]                          +44.0817423 * +44.0823105
in AmprM2trs2nd

[A0]/[PA] = [4Pi]([a0]^2)/{[4Pi]([PL]^2)}  +49.0290476 * +49.0301841
[PM][Pf]/{[Me][2af]}                       +49.0290477 * +49.0301842
[a0][Pf][aa]/([PL][2af])                   +49.0290476 * +49.0301838
[PE][PM]/{[He][Me]}                        +49.0290477 * +49.0301849
{[Pp]^2}/{[p0]^2}                          +49.0290476 * +49.0301843

[PM]/[Pf]                                  -50.9305653 | -50.9305646
[hB]/[c^2] = [Me]{[aa]^2}/[2af]            -50.9305653 | -50.9305653
in KgrmScnd = Juulm2trS3nd
\$ [PL][PQ]/[aa]                            -50.9305653 * -50.9311335
in CuulMetr
\$\$ [c^3]{[PL]^2}[k]/{[aa]^2}               -50.9305652 * -50.9317017