## Balance And The American Silver Dollar

### Modeling the Concept And the Quantity 374.1229…

The act of weighing something originally involved the use of a “balance”. A *balance* is the simplest of all *scales*. Geometry recognizes the importance of “balance” and has special *forms* and *scales* (as in sizes) which embody “equality”. The now familiar *Roman* *gallon* of **216** cubic inches is one such real-world example when modeled as a cube. This is because a cube with a **6** unit edge-length has *both* its volume and surface area equal: **216** “units”. These two opposing *qualities* (*volume* being expansive and dispersive, *surface* being contractive and tensive) are in harmony, they are equal. Every outward pressing *volume* unit has one *surface* unit containing it. They are balanced, but *only* in this specific size cube.

Similarly a tetrahedron with an edge-length equal to “the square-root of” **216** also has its *volume* and *surface* in balance one-to-one. Each measures **374.1229746**… units, and like the previously discussed cube, *only* *this* *specific* tetrahedron embodies the concept of “balance”. The height of this tetrahedron is twice the edge-length of the cube: **12** units.

Another way of expressing this unique **374.1229746**… quantity is 1 / .00**2672918**… We saw using the example of the cube above that only by *naming* the cube a *Roman* *gallon* were “cubic” and “square” *inches* made the *units* of measure. Similarly, if we call the **374.1229746**… units in this tetra-volume “*grams*”, then this .00**2672918**… quantity represents a 1 / 10,000 part of **26.72918…** grams, * which is the gross weight of the American silver dollar coin*!

**26.729**18**…** grams / *silver* *dollar’s ***26.729**5503…grams = .**99998**6…

This gross *weight* “quantity” (**26.729**18**…** grams) as the *edge-length* of another tetrahedron generates a volume quantity of **225**0.653…grams. This is the weight of pure silver in **100** “fractional dollars” (**22.5** grams/fractional dollar) to .**999**7… fine. The surface area of this tetrahedron is 1,237.496372… a “quantity” which, as a measure of length, can be **12.3749**6372… *inches,* or **33/32** of one *foot*. This is recognized as the edge-length of the square comprising *the fundamental unit of land* which we saw back on page 7 of this chapter.

A *weight* measure of 374.12297… *grains* is also 24.242760… *grams* which can be equally expressed as 1 / .0**41249**427… Again, this is a quantitative equivalent to the *grain* weight of the *silver dollar coin*.

At its inception, each of two most fundamental constructs embodying the first two dimensions of *the* *Unit*, i.e., . . . *the* *line* configured as the six edges of a tetrahedron; and the unit of *area* configured as the surface of a cube, enclose a specific *volume* quantity. The 1^{2} unit of surface, as a cube’s surface, holds within exactly 124.707658…volumes contained by the 1^{1} unit of length when configured as the sum of a tetrahedrons edges. Three of these **1.0 ***surface* *unit* cubes together contain **374.1229746**…of these units of volume, which as was just shown above, can be equally expressed by the quantity 1 / .00**2672918**… and can represent a 1 / 10,000^{th }part of **26.72918…** grams, or equally **412.5** grains. This is the gross weight of *the Silver Dollar*, to .**99998**6… fine.

The following exercise will show just how deeply embedded in geometry are some of the weight measures “chosen” in the 1790’s for *both* the *American silver dollar coin* and again the “new” *metric* *system* in France, in which its new *gram* based-unit is equal to the weight of 15.43235835… *grains*. Just above we saw how three one-surface unit quantities (configured as cubes) together hold a volume equal to **374.1229746… **“units” (of the volume contained by the line of **1.0** unit as the sum of a tetrahedron’s edges). If these three **1.0** unit surfaces are reconfigured into a single two-dimensional square, then the *edge-length* of this square is the *square-root-of-three*, or **(3) ^{1/2}**. How does this relate?

Look at the *first* *two* equations below. Note the “quantities” involved: the *square-root-of-three*, or **(3) ^{1/2}** times

__the exact__; and, what is arguably

*grain/gram*conversion ratio*the weight of the American silver dollar*in

*grams*in the first equation, and

*grains*in the second!

**(3) ^{1/2}(15.43235835…) = 26.729**628…

**and**

** ****(3) ^{1/2}(15.43235835…)^{2} = 412.5**0120…

** (3) ^{1/2}(.037412297…) = .0648000000040…**

Now look at the third equation immediately above. It too is dependent on “the square root of three units”. But most importantly, it literally unites the two * different* measures of the

*weight:*

__same__**412.5**0120… X **.0648000000040 = 26.729**628…

One ten-thousandth part of the *equilibrious-tetrahedron’s* volume is .**037412297**… This equation again shows that the proportions defining the grain/gram quantitative relationship *is built into the system of geometry and was NOT a creation of the French scientists.* One “gram” divided into .0648 unit quantities contains 15.43209876… such quantities. Of course we now call these quantities “grains”.

The following example also demonstrates just how important the *name* is that is assigned to any particular *unit*. This equation makes no mathematical sense *without* the quantities being assigned the names (first) *grains*, and then *grams*:

**[(3) ^{1/2} / 3]10^{4} **

*grains*

**= 374.1166815…**

*grams*

**=**

1 / .00**2672918**…*grams*

** **Another example showing just how deeply rooted in geometry is this quantity **374.12297**… can be seen when modeled in the form of a cube’s *volume* quantity. The *edge-length* of this cube is 7.20562173… which is also the *surface* *area* of **1.0** unit of *volume* when modeled in the form of a tetrahedron.

Certainly, the previous examples firmly establish that this **374.12297**… quantity is an essential part of the very fabric of geometry itself. Now, take a look at its impact on some of the other measures of man.

A few pages back we saw how the *Winchester* *Bushel* and its subdivisions are actually measures built into the structure of geometry. They are very special quantities not just to geometry, but as we also saw, to the volume size packaging of the **412.5** grain units of pure silver and copper. The fact that these *physical* *elements* themselves conform to the geometry of the *gallon* *dry* measure is a signpost that there is some kind of “special-ness” associated with this unit of volume. Some of this becomes apparent when this measure is used with another measure just shown to be special as well. This is the quantity **374.12297**… which, as a measure of *gallons* *dry*, reveals some quite astounding correlations among some other common units of *volume* measurement.

For example, **374.12297**… *gallons* *dry* is 100,565.1908… cubic inches. But this measure of volume is also 58,000.3741… *imperial* *fluid* *ounces*; that’s *exactly*** 58,000 **to a precision of better than .**99999**… fine! (Note: the “zero” separation creates and clearly shows a well defined “discrete” quantity.) This means that, to the same precision, this measure is also **11,600** *imperial* gills; **2900** *imperial* pints; and, **1450** *imperial* quarts. These two supposedly *unrelated* systems (gallon *dry* and gallon *imperial*) become *correlated* or *commensurate* when this special measure embodying *harmony* and *balance* comes into play uniting the two.

“Proof” that the relationships above are NOT coincidence can be found when we look at the *reciprocal* *expression* of this special measure: **1.0 / 374.12297**… which equals .**002672918**… Again, as a *portion* of a *gallon* *dry*, it is at the same time .00**311034**3… the *standard* *American* *gallon* which was England’s *wine* *gallon* for centuries before; .0**2488**14… its *pint* measure; and, .0**12441**3… the *standard American quart*. Now, look at these measured quantities in light of the following:

**31.1034**768… = number of *grams* in **1.0** *troy* *ounce*

**24.88**27814… = gross weight in *grams* of 1^{st} debasing

of the fractional silver dollar (1853-1873)

**12.44**13907… = gross weight in *grams* of 1^{st} debasing

of the fractional ½ silver dollar (1853-1873)

The measure corresponding to **1.0** troy ounce is the same measure gleaned from pure geometry to a precision of .**999998**495 fine! So too do the others correspond to at least .**99999**+ fine.

There is something else even more remarkable about this **374.12297**… measure of *gallons* *dry*. It is also 1.647968284… *cubic* *meter*. This translates to **1.000** *cubic meter* plus .**647968**284… of one *cubic meter *and may be visualized in the form of two perfect cubes. The larger cube contains *exactly* **1000** *liters*, **10** per edge. The smaller cube contains **648** liters to a precision of .**9999**5… which may be reassemble as individual liters into a perfect cuboid **9** *liters* by **9** *liters* by **8** *liters*.

Now refer back to the photo on page 4. The *cuboid* in the foreground models the most efficient packaging of **648** *cubets*. Any one of the ten cubes in the background models **1000** *cubets*. Without naming the “unit” these **10** *cubes* and **1.0** *cuboid* are size-less and without substance. Nonetheless, they display the same ratio or proportioning as the **1000** *liter* and **648** *liter* measures derived from dividing the **374.12297**… *gallon* *dry* measure. This is

**1000 / 648 = 1.543209877…**

By now the reader should recognize **1.543209877… **as a power of **15.43235835…**, which is once again, the *grain/gram* conversion ratio. These are powers of the *same* quantity to better than .**99998** fine.

(Earlier) the reader was shown that the relationship between the *square-root of three *and the quantity defining the number of *grains* in a *gram* was directly related to the gross weight of *the silver dollar coin* in measures of both *grains* and *grams*. The equations proving this have been restated below.

**(3) ^{1/2}(15.43235835…) = 26.729**628…

** ****and**

** ****(3) ^{1/2}(15.43235835…)^{2} = 412.5**0120…

Below (at left) is a drawing of a rectilinear geometric solid which has been derived from these equations. This “cuboid” is an equivalent manifestation of this data. Its volume is **412.5**0120… cubic units; there is **26.729**628… areal units in each of its four rectangular faces; and the edge-length of its two *square* faces is **15.43235835… **lineal units. As presented (without any “named” unit) it is a *size-less* geometric form void of any substance. Its two lineal components are in a **1.0 / 8.9098762**… ratio and are illustrated in the “cuboid” on the right.

In The Geometry of Form there is a similar ratio: **1.0 / .89089871**… Though they differ by a power of 10, these quantities are the *same* *measure* to .**9999**00216. . . fine. This ratio describes the difference in lineal measures which arise when “the unit”, modeled as any geometric solid, *divides from one-into-two* (forms of the original). But, which *quality* of the solid-form unit is being divided? Is it one-unit of *surface* in the form of the solid; or is it one-unit of *volume*? This ratio **1.0 / .89089871**… illustrates this difference.

A simple way to understand this principle is by using a cube with a **1.0** unit edge-length for the solid geometric form. This cube is one-“unit” of volume. After dividing this volume, each new cube’s volume will be .5 unit. Its edge-length is (.5)^{1/3}, which is **.79370**0526… On the other hand, if this same cube’s *surface* area (of six units) divides *one-into-two* instead of its *volume*, each new cube will have a 3 unit surface area; each face measures .5 square unit. This makes its edge-length (.5)^{1/2}, which is .70710678…

The resulting lineal measures of these two different choices for dividing this cube create the ratios seen below:

**.70710678… / .793700526… = .89089871… / 1.0**

Now, there can be no question that this ratio is not only fundamental to geometry, but as such, must also be a significant *quantity* to other geometrical constructs. For example, **.89089871… **as the *surface* *area* of a cubeoctahedron (a cube with its eight vertices truncated to the mid-points of its edges) results in its *volume* becoming **.0680**749… which is equal to the *volume* of a cube with a **1.0 **unit *surface* *area* (to an accuracy of .**999**5… *fine*). Readers of *The Geometry of Money* may recall that in the chapter titled “The Great Metric Hoax” the cuboctahedron is shown to be the geometric model for the *grain*, and for the **480** *grain* troy ounce as well. So we shouldn’t be too surprised when **.89089871… **as the sum of the cuboctahedron’s edge-lengths results in any single edge measuring .0**3712**0780… unit. Again, this is a *power* of the same **371.25** quantity defining the number of grains of pure silver in the silver dollar coin to better than **.99988**… *fine*.

And if a *power* of this **8.9098762**… quantity becomes **890.98762**… units of the “illuminati’s” **27**mg weight standard, then altogether they weigh 24.0566659. . . grams; or, **371.25**10…grains. And again, referencing the **27** milligram system, 891 cubets assemble together as one *perfectly* *complete* cuboid (9 x 9 x 11).

Another example may be found in the “star-tetrahedron”. This form is comprised of five smaller tetrahedra: one in the center completely surrounded by the four others. The significance of this form to all of geometry cannot be over stated and is explained in my previous book *Some Thoughts on Universe, An Introduction to The Geometry of Form*. The star-tetrahedron is the form of *Unity’s* “potential” * actualized*. If the

*edge-length*of the star-tetrahedron is

**.890898718…**then its surface area is

**4.124**188… and the sum of its edges (or

*edge-length*

*sum*) is

**16.036**17… Again, these are both “monetary measures” directly from the geometry of form:

**4.124**188… / **412.5**(*grains* in silver dollar) **= .**00**9998**032…

and

**16.036**17… / **16.0377**3…(# *grams* of pure gold in *eagle*) = .**9999**03…

The *origin*al form of *Unity’s* __potential__ is called the “decahedron”. In its form as a geometric solid it has ten equilateral triangles. They combine into two five-sided pyramids which are in turn base-bonded into one form with seven vertices. If **.890898718… **is a decahedron’s *surface* *area* then **.45359**03… will be its *edge* measure quantity. This *quantity* is certainly a *power* of **453.59**2370…, or the number of *grams* in one pound *avoirdupois*

**.45359**03… / **453.59**2370… = .000**99999**6…

This same decahedron will have a volume equal to .0**5627**466… which *quantity* is also a *power* of the **270** grain gross weight of the ten dollar *eagle* coin with respect to the *troy* ounce:

.0**5627**466…** X 480** grains **= 27.0**118… grains

Multiples of this special **.890898718… **quantity also show these same “monetary measures” in *gram*-based units to an accuracy of .**9999**+:

18X = **16.036**17… (pure gold content in eagle)

27X = **24.054**26… (pure silver content in dollar)

30X = **26.726**96… (gross weight of dollar coin)

**^^**

What the reader must come to understand is that *this* is “forensic *historical* evidence”. It is based upon an irrefutable level of *mathematical* *certainty* from which is exposed a *magnificent hoax*. This outright “lie” has been perpetrated upon all of humanity by some “others” amongst us who remain hidden from view. This group, *by what ever “name”*, has been uncloaked by their own works . . . something they never imagined would ever happen.

**Simple Mathematics:**

Silver weighs 10,490 *kilograms* per cubic *meter*; this is 10,490,000 grams. The **412.5** *grains* of pure silver is also **26.729**55… *grams*; which is .00000254809… cubic meter:

**26.72955 grams / 10,490,000 grams/m ^{3 } = **

**.00000254809…m**

^{3}There are 39.37007874 inches in a meter. Therefore a cubic meter contains

**(39.37007874”) ^{3} = 61,023.74409… cubic inches**

Since **412.5** *grains* of pure silver as a cube measures .00000**254**809… cubic meter, in cubic “inches” it is:

(.00000**254**809…)**61,023.74409… cubic inches = ****.15549****39921 cubic inch**

The edge-length of **412.5 **grains of pure silver in the form of a *perfect* cube is the “cube root” of .155493… cubic inch, which is .537738591… inch. This means that the edge-length-sum of its 12 edges is 6.452863087… inches. If *this* edge-length-sum becomes the edge of a larger cube (in the same way that the edge-length-sum of **1.0 **cubic *inch* became the edge of a **1.0** cubic *foot* cube) then this larger cube, by man’s own measures, has the name “**1.0** *gallon dry*” and is an eighth part of the 268.8 cubic inch *Winchester Bushel*:

**(6.452863087… inches) ^{3 } = 268.6936184… cubic inches**

** ****and**

** ****268.6936184… cubic inches / 268.8 cubic inches = .9996…**