The following two chapters have been added to the initial publication of *The Geometry of Money* (which represents less than two dozen *handmade* volumes thus far). Both have been included here with this next printing to clarify and expand upon important topics previously discussed in earlier chapters. They were written for readers who may not have read this book so some of the previous illustrations have been repeated for clarity.

**THE SPHERE IN THE CYLINDER**

**Modeling Both, the Measures of Man, and of Nature**

Following is an example of one of the most *fundamental* of all* geometric transformations*: A sphere may be viewed as both *units* of *volume* and *units* of *surface-area*. But for “quanta-sizing” a system of geometric form, *only* one of these *qualities* may be considered “The Unit” at any given time. For example, in the photo above, the sphere in the cylinder can be either **1.0** unit of *surface* (in the form of a sphere) or **1.0** unit of *volume*.

This “Unit” in the form of a sphere may be *distorted*, *fused* with another, or *divided*. If the sphere is (**1.0**) unit of *surface*, and fuses its *volume* with that of another identical sphere’s *volume,* then the result is too much *surface*-area for the new single larger sphere*. Geometry packages this “excess” surface area in the form of a regular tetrahedron. This tetrahedron is depicted a-top the sphere in the above photo and in the diagram below. In *The Geometry of Form* this is the “transitional tetrahedron”, or simply *transit*–*tet*.

Now, if in stead of combining the *volumes* of two of these **1.0** *surface* unit spheres into one, divide the *surface*–*area* of one of these spheres into two new spheres; each one now has a **½ **unit *surface* area. This transformation results in “excess *volume*”, which geometry packages in *two* of these “transitional tetrahedrons”.

Let’s now look at the mathematics describing each of the above two transformations. We started each with “one unit of *surface*–*area* in the form of a sphere”. This sphere’s radius (found by the formula 4πr^{2} = surface area) is 0.282094792… Using this radius, its 0.094031597… *volume* is found by the formula 4πr^{3}/3.

*This new single sphere has only a 1.58740 surface-area. The 0.**4125**989… quantity of excess surface-area becomes the surface of the *transit*–*tetrahedron*.

In the first example, two of these *volumes* were fused into one, resulting in an excess *surface*–*area* of 0.**4125**989… unit. Configured as the *surface* of a regular tetrahedron, its 0488071804… *edge*–*length* was found by a tetrahedron’s surface-area being equal to its [(edge)^{2} X 3^{1/2}]. Now use [(edge)^{3} X (2^{1/2})] / 12 to find *this* transit-tetrahedron’s **0.137**02032… volume.

The second example divides the sphere’s **1.0** unit of surface into two new spheres. Using the formulas above we find that the combined volume of the now two spheres is only 0.066490380… compared to the previous single sphere volume of 0.094031597… There is an excess volume of 0.027541217… unit. In The Geometry of Form, this is packaged not as *one*, but *two* tetrahedrons; each has a volume of **0.01377**0609… unit.

These two slightly different tetrahedrons are *both* constructs from transforming the *same* **1.0** *surface* unit sphere. Certainly they are related in that respect, as well as their function as to *accounting* for the residual quantities created in transformations. Unless fine enough calibrations are applied in measurement, these two *different* “transitional-tetrahedrons” in physical form would be practically indistinguishable from one another; or from the tetrahedron atop the cylinder with the sphere within, depicted in the graphic and photo above.

** The Sphere and Cylinder**

The cylinder in the photo is inseparable from the sphere. This is because *a sphere bores a cylindrical hole through the fabric of “space-time”*. The proportions of the cylinder depicted make it a “Cylinder of Maximum Volume”: given a fixed unit of surface-area, *this proportioned cylinder* captures the most *volume* using the least *surface*–*area*. The diameter of its circular end planes is equal to the “height” of its side, and to the diameter of the sphere within.

The surface-area of the cylinder’s side is *exactly* *equal* to the surface-area of the sphere within. The total surface-area of the cylinder is 3/2 times the sphere’s surface-area. And its volume is 3/2 times the sphere’s volume as well. Since this sphere’s surface is 1.0 square unit, the cylinder’s surface is 1.5 square units.

These are some of the quantities and proportions built into the very structure of transformational geometry along with their appropriate forms. These presented thus far are *purely* *geometric* in that no *name* (inch, foot, yard, meter, etc.) has been assigned to the Unit, nor *substance* assigned to the volume of the forms.

** An Analogous Physical Model**

Compared to a trained physicist, I know *nothing* about physics. But I do know *something* about geometric quantities that are *constants of geometric structure*. Some of these have been shown above.

The physicists have measured the masses of the *proton*, *neutron*, and *electron* and have come up with quantities describing their sizes *relative to one another*. They’ve found that a proton’s mass is 1836.152701 times an electron’s mass; and likewise, that a neutron’s mass is 1838.683662 times the size of an electron. Here the electron has been assigned the role of being the (**1.0**) Unit. Using simple subtraction, it can be determined that the *difference* between a neutron and a proton is 2.530961 “electron masses”.

Protons and neutrons are collectively known as “nucleons” and are, on the average, about 1837.418182… times the size of an electron. Thus an electron is about 1/1837.418182 the mass of a “nucleon”, which can also be written as .000544242… Therefore, 2.530961… of these quantities is

2.530961… X .000544242… = 0.0**01377**455…

and is seen to be directly related to *The Geometry of Form*’s transit-tetrahedron’s *volume* quantity since it is 1/10^{th} of its 0.**01377**_{06087} volume. From the perspective of *The Geometry of Form*, the transit-tetrahedron is appropriate as model basis since its role in geometry arises when accounting for *surface* and *volume* “differences” in basic geometrical transformations.

Using geometric forms to model this difference in mass between the two nucleons can be done in the following manner: First, divide the transit-tetrahedron’s volume into two separate packages, into what amounts to ½ volume “t-tets”. Each of these two volume quantities is reconfigured into the form of a *star-tetrahedron* (imagine the four faces of a tetrahedron being the base triangles of four other tetrahedrons; the resulting form is the “star-tetrahedron”). Any *one* of its five sub-tetrahedronal chambers has a volume of 0.0**01377**_{06087} and is a model of this mass difference between the two different sized nucleons. Below are three views of the *star-tetrahedron*.

There is something else about physics that I know little about. It’s called the *fine*–*structure* *constant*. Its value is .00**7297**352568…, or inversely 1/**137.03**5999139… For what it is worth to future researchers, it should be noted that **37 **of these quantities together total 0.**27**00020… This is **27**/100 to better than .**99999**… fine. Also worth noting is the relationship between **27** and **37**: i.e. 1/**27** = .0**37**0**37**0**37**… and 1/**37** = .0**27**0**27**0**27**…; and, **37**/**27** = **1.3703**70370…

Again, since I know nothing about physics, I’ll leave it to the trained physicists (and the reader) as to whether the above lines of inquiry have *any* merit. But for now, look again at the photograph at the beginning of this section. If the *surface* of the tetrahedron atop the sphere is the .**4125**98947… “excess surface-area” resulting from *fusing* the volumes of *two* of the spheres (with *surface-area* equal to **1.0** unit) into *one *sphere, then its *volume* is .0**13702**03…

Now, we already know that the *volume* of the sphere within the cylinder is .**0940**31597…; and, that the *volume* of its *cylindrical* *domain* is 1.5 times the sphere’s *volume* making the cylinder .**1410**47396… *cubic* unit. So what we are looking at, with respect to *volume* (in the right-hand side of the photo) is *the* *sum* of the tetrahedron’s *volume* and the cylinder’s *volume*. This *combined* volume is .154749428… cubic unit. The cube (to the left in the photograph) is this *combined volume* reconfigured.

So, what is it about this cube and the forms it represents that’s so important* to your* understanding of history? It is with respect to exposing *the truth *about where the *measures of Man* truly have been derived? Below is some very persuasive evidence.

__Volume of cylinder__ = .__1410473…__ = .__91145____66…__

Combined volumes .1547494… 1.000000…

__A.V. Ounce__ = __437.5grains__ = __. 9114583…__

Troy Ounce 480.0grains 1.000000…

In the photo, the *entire* *cube*, or the combined *tetrahedron*–*cylinder* is the Troy ounce. The *white* portion of the cube, or the *lone* cylinder is the Avoirdupois ounce. The Troy ounce has been in use since *at least* 800 AD; the Avoirdupois ounce since the late 1400’s. These supposedly “arbitrary and subjective” *measures of Man* conform to the immutable and eternal *measures of geometry* to an incredible .**999998**… approach to perfection. Let’s see what other *gems of forensic history* lay buried in the simple geometry thus far presented above.

This quantity, **.154749428**… divided in half is .0**7737**47…, or in thirds is .0**5153**143… And there is .**7734**375 troy oz. pure silver in America’s dollar coin and .**5156**25 troy oz. pure gold in the $10 *eagle* coin. The gross weight of the $10 eagle was **270 **grains; which can also be written as 1/.**00370**37… and, .**00370**58… is (.**154749428**…)^{3}. If .**154749428**… is the edge-length of a cube, the cube’s volume is 1/**270**. And if it is the edge-length of a *cuboctahedron*, then the sum of this form’s edges is **3.713**986… reflecting the **371.25** grains of pure silver in the dollar coin. *All of these monetary measures are better than ***99.9***% identical to the measures of geometry!*

* ***The Meter Measure, the Ton, and the Element Gold**

From what we’ve seen thus far, it’s safe to conclude that for some reason the “quantities” *chosen* to define our systems of *weights* (troy/avoirdupois and gram) and *monetary* *measures* mirror geometry’s choice of “quantities” with respect to spherical transformations. As we’ll see next, these *measures*, and the *geometry* from which they’ve been spawned, can also be found in the very *monetary* *metals* comprising the coins. Again, the reader should refer to the previous photo and diagram.

To start with we must quantify the tetrahedron, the cylinder, and the sphere within. Since we began with the sphere equaling **1.0** *surface*–*unit* in the form of a sphere, all we need to do now is to “name” this unit. Let’s see what happens when this one unit of surface is **1.0** *square “meter”*.

This makes all of the other quantities *collapse* into *metric* measures. (Yes, for readers who have not read my book, *The Geometry of Money*, the *metric system* existed eternally in geometry long *before* the French *claimed* they “invented” it in the late 1790’s.) So the “size” of the forms has been established giving them a *real* *world*, or *human* scale. But the “substance” of their volumes still remains unnamed, without which there is no “weight”. *Pure* *gold* seems to be *that one substance* commensurate to both the *metric* *system* of measurement and the base unit of *both* *ounces*, the “grain”. Have a look and decide for yourself.

*One cubic meter of gold* weighs 19,300 *kilograms*. Since the surface of the sphere is **1.0** *square* *meter*, its volume is 0.094031… *cubic meter*. This sphere’s *cylindrical* *domain* is 1.5 times the sphere’s volume and surface-area. To start, how much does the golden sphere within the cylinder weigh?

(0.094031…)(19,300 kilograms) = 1,814.8098…kilograms

Since there is 1000 *grams* in a *kilogram* the golden sphere weighs 1,814,809.8…*grams*. Given that there is 15.43235835… *grains* in one gram makes its weight in *grains* 28,006,795.5… Again, given 7000 *grains* in one *pound* makes the golden sphere within the cylinder . . .

28,006,795.5…grains / 7000 grains/pound = **4,000**.9707…pounds

Made out of *pure gold*, with exactly **1.0** *square meter* of *surface*, this *sphere* weighs **4000** pounds, which is **2.0 “**tons”. This means that the entire *cylinder* of gold, with its **1.5** *square* *meters* of surface, weighs **3.0** tons (**6001**.456… pounds). Both of these measures (**2.0** and **3.0** “tons”) are *exact* measures to an accuracy of better than **99.9**757%. Keep in mind that the *pure* gold and silver metals in American coinage are *by design and legislation* only necessary to be **99.9**000% *pure*.

It seems that with respect to *weight* the *ton* is the Unit (which subdivides into *pounds*, *ounces*, and *grains*); whereas the *meter* is the Unit with respect to *size*. Further confirmation of this conclusion will be clearly seen in the next example.

Look at the diagram back on page five. On the right side is the *transit*–*tetrahedron* atop the cross-section of one hemisphere of the sphere equal to **1.0** surface *unit* (to which *unit* has been assigned the name **1.0** *square* *meter*). The circle equal to the height of the tetrahedron is the cross-section of the sphere having its surface equal to ½ *square meter*. What is the weight of the gold comprising this sphere?

Knowing its surface area we find its volume using the formulas from our previous calculations. It is .03324519… cubic meter. With gold weighing 19,300 kilograms/cubic meter this sphere weighs 641.6321… kilograms. This is **9,90**1,897.542… grains, which *quantity *is **9,90**0,000 grains to a .**999**8… degree of fine-ness. Readers of *The Geometry of Money* know that a quantity of **990** *special* *cubets* (described in a later section) equals a weight of **412.5** grains, which is the gross weight of the *silver* dollar coin.

The previously described division resulted in *two* of these spheres with a ½ *meter surface*. These *together* weigh **4125****7**.9064…*troy* *ounces*. This is **√2.0** tons . . . i.e., 1,414.5567… pounds! This again shows the “ton” as the preferred *named* unit of *weight*, and the *meter* of *length*, *area*, and *volume*, __when gold is the named substance.__

**The Star-tetrahedron and the Monetary Metals**

This next example references the previously introduced geometric form, the *star*–*tetrahedron*. Its relative physical dimensions (in this case) relate directly to the *quantity* defining the volume of the sphere within the cylinder. But in this example, this *quantity* is *not* a *volume-unit* but an increment of *length*. Here is how this works.

As we have seen, geometry clearly shows us that **1.0 ***surface-unit* in the form of a *sphere* has a volume defined by a .**0940**31… quantity. But one must look more closely to see that **1.0 ***surface-unit* in the form of a *circle* has a *radius* measuring *six times* .**0940**31…, or, .5641895… This is how one “normally” would describe this measure. The *diameter* of the .**0940**31 (volume) sphere is *also* this measure. *Many* of geometry’s quantitative structural units work in this fashion.

Now a *line* .**0940**31… unit long, as the side of a *square*, delineates an *area* equal to .008841941… *square* unit. This (.**0940**31…)^{2} quantity, as the *surface* *area* of a *star*–*tetrahedron*, once again reveals in its structuring the two formative quantities defining the *silver dollar coin*. We see the *gross* *weight* of the coin (in *grains*) in its .0**4125**0847… edge-length; and the weight of its *pure* *silver* content in the *two-times *.**37125**761… sum of its edges.

I think it is relevant to mention here that because *gold* weighs 19,300 kilograms/cu. meter, if modeled as cube and subdivided into eight sub-unit cubes, then each of these eight cubes will have a weight of **2.0** (*metric*) *tons* **+** **412.5 **kilograms. Each sub-cube has a surface area equal to the cylinder’s 1.5 square meters.

Let’s now make this .008841941… quantity a *volume*, and then *name* the “unit” that it is a portion of **1.0** *cubic* *meter*. The *substance* of this *volume* is again pure *gold*. Now let’s do the math: .008841941… X 19,300 kilograms/cubic meter = 170.6494… kilograms. This is 170,649.4… *grams* or equally 2,633,523.724… *grains*. There is 7000 grains in one pound, so 376.2176 pounds is the weight of this .008841941… cubic meter of gold.

Now remember, it is the “ton”-measure of weight that has consistently been the “unit” in all of the previous examples. What is this weight when expressed in *tons*? 376.2176 lbs. / 2000 lbs. = .18810 ton. But on closer inspection we also find this weight to be *twice* .**0940**54… ton. What this means is that

.**0940**31… *cubic* *meter* of gold weighs *twice* **1.0**… *ton*.

(.**0940**31…)^{2 }*cubic* *meter* of gold weighs *twice* .**0940**54… *ton*.

The strength of *geometry’s* influence upon the *meter* measure, the pure element *gold*, and the pound-based *ton*, can even be more clearly expressed when we re-write the above relationship:

(**1/36π**)… *cubic* *meter* of gold weighs *twice* (**1/36π**)^{1/2} … *ton*

In the photo of the sphere in the cylinder, the scale of the forms was established when the *sphere’s* surface area was set to equal **1.0** square *meter*, exposing the *ton* as the preferred weight measure when *gold* was the named substance. These relationships are again confirmed when the same **1.0** square *meter* is assigned as the surface area of a tetrahedron made of pure gold. Let’s follow the math.

The *surface* *area* of a tetrahedron is equal to its edge^{2} X √3. Since this surface area is **1.0** square *meter *its edge length equals (1.0 / √3)^{1/2} which is .7598356… meter. Using the edge to find the volume gives us .05170027… cubic meter. To find how much this gold weighs multiply .05170027… cu. meter by 19,300 kilogram/cu. meter: 997.8152… kilograms. At 2.20462… lbs./kilo, it weighs 2199.8059… *pounds*; which is **1.1** *ton* to better than .**9999**11… fine.

The *volume* contained by **1.0** *square* unit in the form of a tetrahedron, by *whatever* name, is .05170027… “unit”. __It is directly related to____ the Coinage Act of 1792__ since the weights specified for the coins are powers of

*this*

*quantity*:

(.05170027…)^{2} = .00**26729**18…

[3(.05170027)]^{2} = .0**24056**26…

6(.05170027…)^{2} = .0**16037**50…

*****

**26.729**55… *grams* equals the silver dollar’s **412.5 ***grain* gross weight; and, **24.056**59… *grams* its **371.25** *grains* of pure silver. And .05170027…, as the edge length of a cube, makes the cube’s *surface* *area* equal to .0**16037**508… unit, and **16.037**73… *grams* is the **247.5** *grain* pure gold content of the $10 *eagle* coin. These coinage weights are **99.998**…% in conformance with their geometric *ideals*.

Once again, we have clear evidence showing that *the quantities structuring geometry were those quantities “chosen” for quantifying the measures of man. *

* ***Why 3.0 Tons is Special**

What makes “**3.0** tons” so special? In light of the above discoveries the following will reveal at least some of the reasons. Previously, it was shown that the relationship between the *cylinder’s* volume and the combined volume of the *cylinder* *and* *tetrahedron* was the same ratio as that between the *avoirdupois* *ounce* and *troy* *ounce*. This relationship is a .**999998**… approach to being perfect! We also saw that gold was naturally commensurate to the *ton* when the *surface* of the sphere was **1.0** square *meter*.

The *ton* is a *pound* and *grain* based measure. And the *troy* *ounce* and *avoirdupois* *ounce* are the first “grain-based” units after the *grain* itself. History says they were arbitrarily arrived at by what *felt* “right” to one or more persons. They don’t seem to be related, especially when a *pound* *troy* is only .822857… a *pound* *avoirdupois*. And despite both being *grain*–*based*, **1.0** *ton* is an even number of *A.V.* *ounces *(32,000) and is an awkward (29,166.666…) number of *troy ounces*. Again, **2.0** tons is an even number of *A.V. ounces *(64,000) and an irreducible number of *troy ounces *(58,333,333…).But **3.0** *tons* is *special* to *both* systems of accounting:

** ****3.0 tons = 96,000 ****A.V. oz.s, or 87,500 ****Troy**** oz.s**

The gallon is a unit of *volume*. The modern gallon of 231 cubic inches was introduced into England at about the same time as the “new” *avoirdupois* ounce. Using this *gallon* unit of measurement, **3.0** *tons* of pure gold equals 37.25 *gallons*, or 149 *quarts*, or 298 *pints* *to an accuracy of better than* **99.99**3%.

The *bushel* measurement is likewise a unit of *volume*. It is 2150.42 cubic inches and subdivides into *pecks*, *gallons* *dry*, *dry* *quarts* and *pints*. Using this gallon dry system, **3.0** *tons* of pure gold equals 4 *bushels*, or 16 *pecks*, 32 *gallons*, 128 *quarts*, or 256 *pints* *dry*. These measures are accurate to better than **99.9**5%

Gold likes the *imperial* *gallon* as a unit of measure almost as much as the *modern* *gallon* and *gallon* *dry*: 31 *imperial* *gallons* equals **3.0** *tons* of pure gold. So does 124 *quarts*, or 248 *pints*. These measures have a better than **99.9**3% correspondence.

This next example involves a *special* unit of weight. It is simple to imagine. Start with a cube as the “Unit”. Its volume is comprised of an un-named *substance*, and thus the cube has *weight*; but it too is left un-named for the moment. Now assemble **27** of these cubes into one large cube with three per edge. Finally, divide this now single cube into **1000** *cubets*. We can now “name” the weight. To do this we go back to the original cube, the first one of the twenty-seven. Any name will do, but the choice for this one is “gram”. The **27** together as one cube weigh **27** grams. When divided into **1000** cubets each resulting little cube weighs **27** milligrams. Our entire system of weight measures is based on this **27** milligram *cubet*. I call it “The Chosen One”, and lay out the proof for *it* being this weight-measure base unit in great detail in *The Geometry of Money*. The picture below is from the book and illustrates what we just described above.

Now that we have the “proper” base-unit, we are ready to continue exploring this very special **3.0** *ton* measure. First we calculated this weight in grams knowing that there is 6000 pounds in 3.0 tons, 7000 grains/pound, and 15.43235… grains/gram. This equals 2,721,554.221… grams. Divide this by .027 (27 milligram) and we discover how many of these cubets are in 3.0 tons. The answer is 100,798,304.5.

This is **100,800,000 **cubets to an accuracy of better than **99.998**. . .%. When its *relevant* “factors” are distilled, they are found to be **480** X **480** X **437.5**. Now we can apply these quantities to *the* *white* *portion* of the cube on the left side of the photo at the start of this chapter. Its base is **480** cubets by **480** cubets. And its height is **437.5** cubets. Obviously, here again is confirmation of the “natural affinity” between the two *grain*-based measures called “ounces” and, not only the *ton* measure, but the *gram*–*based* system of weight itself. And already we’ve seen that this white portion of the cube, reformed into the cylinder, embraces a sphere within having a *surface-area* equal to **1.0** *square* *meter*.

Using this **27** *milligram* system makes the weight of the tetrahedron atop the sphere and cylinder equal to 9,792,000 *cubets*. This translates to 264,384 *grams* or 4,080,068.63… *grains*. But the relevant unit quanta-sizing this tetrahedron’s weight (in gold) is the *troy* *ounce*. This is because it weighs **8500**.1429… *troy* ounces. This is **8500** *exact* to a better than .**9999**8… correlation. When this weight is added to the **87,500** troy ounces comprising the 3.0 tons of the cylinder below the tetrahedron, or below the red portion of the cube, the total is **96,000** troy ounces.

Now when we look at the photo we know that the white portion of the cube, or the white cylinder, is **96,000 ***avoirdupois* ounces; and the entire cube, or the cylinder *and* tetrahedron is **96,000 ***troy* ounces.

After examining this *system* of the sphere within the cylinder, it’s obvious that there are “*ideal* geometric quantities” or “perfect” units to which the *actual* *substantive* geometric forms only ever so closely *approach*. We can distill these *ideals* by examining the *weights* of the sphere and cylinder, as we already know that their *size* has been defined from the sphere’s surface being a perfect **1.0** *square* *meter*.

When the actual weights are *grain*-based units the golden sphere weighs 28,006,795.5… *grains*; and, the entire cylinder of gold weighs 42,010,193.3… *grains*. These are the “actual” quantities. The “ideal” quantities to which they have been patterned are respectively **28,000,000 **and **42,000,000.** The sphere’s equatorial plane is tangent to the inside surface of the cylinder and isolates the two spaces exterior of the sphere’s surface. Each of these spaces contain **7,000,000** *grains* of *pure* gold. These, together with the sphere’s four times **7,000,000 ***grains*, comprise the cylinder’s (idealized) **42,000,000** *grain *total.

The conformance to this *ideal* modeling is once again to an accuracy of better than **99.9**757%.

**Some of the Structural Properties of**

**The Fundamental Unit **

*And Their Relationship to the Measures of Man*

*And Their Relationship to the Measures of Man*

In *The Geometry of Form* the “fundamental unit” is a *line* **1.0** *unit* long. But unlike in Euclidian geometry, this line is configured three-dimensionally as the six edges of a tetrahedron. *The Geometry of Form* also recognizes that polyhedrons (in general, and of every size) have unique equivalent forms constructed from the spheres defining each of their individual vertex’s volumetric domains. In this sense, the tetrahedron’s four vertices become synonymous with the center points of four spheres.

Since *this* tetrahedron’s six edges total **1.0** *unit* in length, each edge measures .1666… unit making the radius of its *formative* *spheres* equal to .08333…, or 1/**12**^{th} unit. Keep in mind that what we are seeing is that *these* *specific* quantities and ratios are literally built into, or inherent to this *fundamental unit of length*, regardless of what “name” humanity assigns to that unit; and so too are each of these quantities that arise from the following calculations.

First calculate the *volume* of this sphere: 4πr^{3 }/ 3 = the volume of a sphere. The volume of the *fundamental unit of length’s *structural sphere is .002424068… cubic unit. But this quantity can be *equally* expressed as:

**1.****0** / **412.5**296124…

exposing the American silver dollar’s *gross weight quantity* of **412.5 (***grains*), and the other units of measure exposed in *The Geometry of Money* that are based on this exact same quantity, to be at* the very start of geometry’s three-dimensional system of accounting*. More will be said about this *quantity* with respect to the many measurement systems of which it is an essential quantitative ingredient and to its many “names” within those systems.

But for now, let’s compare this primal structural sphere’s volume with that of the *fundamental unit’s* tetrahedronal volume of:

**1.0 / 1832.82**00776…

Both of these ratios are describing the volumetric “size” of their respective geometric forms. And both are referencing, or scaled to, (first of all) this system’s *Base Unit* of volume (**1.0**)^{3}. This is most easily modeled by a cube with a (**1.0**)^{1} unit edge-length. It is *this* cube that will hold precisely **1832.82**00776… volumes equal to the *fundamental unit’s* tetrahedronal volume; or just as precisely, **412.5**296124… volumes equal to the volume of any one of its *formative spheres*.

Thus far in the few paragraphs above, three distinct geometric forms have been introduced. They are (in order of volume-size starting with the smallest) a tetrahedron (**1.0 / 1832.82**00776…), a sphere (**1.0** / **412.5**296124…), and a cube (**1.0**). But there are two more forms inseparable from this geometry *implied* in the above ratios, which are far larger than the first three. They are another tetrahedron with a volume equal to **412.5**296124… units, each one equal to the cube’s volume of (**1.0**); and it’s *formative sphere *with a volume equal to **1832.82**00776… times this same cubical volume unit. This is because in geometry, with respect to “form”,* every regular polyhedron has a “reciprocal” opposite-formed counterpart with identical quantitative units*.

It’s important to keep in mind that *these* are *the* “quantities” that literally structure three-dimensional geometry at its inception. And so too must we regard the sequential geometric structures *encountered in calculations* associated with investigating any single form. For example, the *radius* of the formative spheres of the tetrahedron with a volume equal to **412.5**296124… units is one-half of this tetrahedron’s 15.1835663… edge-length, which is 7.59178318… But if this same radius be expressed as (**437.5**53729…)^{1/3}, or the “cube root” of **437.5**53729… , we can clearly see that *man’s* **437.5 ***grain*–*based* weight measure known as the *avoirdupois* *ounce*, which is our common marketplace ounce, is also mirroring what is truly a “natural” geometric quantity. And the tetrahedron’s 15.1835663… unit edge-length can also be re-written as (**3500**.42983…)^{1/3} units, or the “cube root” of **3500**.42983… units, which as **3500** *grains* would be the **½** *pound* measure in this same *avoirdupois *system.

Another example of this can be seen in the form of a regular tetrahedron. As demonstrated in *The Geometry of Money*, the *edge-length-sum* of a cube with a **437.5** *unit* volume (**1.0** ounce *avoirdupois*) is the same as a tetrahedron with a **412.5 ***unit* volume.

This shows that the quantitative structure of “man’s” *avoirdupois* system of weight measures is actually borrowed, or “stolen” from some of the earliest manifestations of geometry’s own natural system of quantification. It also shows us that America’s monetary measures (**412.5**; and below, **371.25 **and **2475**) to be geometrically inseparable from the *avoirdupois* measures. This next example confirms this unequivocally.

Transform the cubical **3500**.42983… *volume* unit quantity described above into a tetrahedron. A cube having its edge-lengths-sum exactly equal to this tetrahedron’s (the edge-lengths-sum of both forms equal the *same* length line) will have a volume equal to 8(**3712.7**665…) and is one of the quantitative sources for America’s preference for **371.25 **grains of *pure* silver for its *dollar* coin.

And if we were to now take the **412.5**296124… unit volume tetrahedron’s *formative* *sphere* and divide this sphere’s **1832.82**00776… unit volume into two spheres, and then the two into four spherical volumes, and so on infinitely, all the while reforming them back into a single closest packed unit, the volume will grow from the original’s volume until a limit is reached. In *The Geometry of Form* this limit is known as a sphere’s “Maximum Volume Potential”. It is a property of every sphere. This sphere’s MVP is **2475.**17766… and is the source of another of America’s *monetary* measures in that the 1792 Coinage Act called for precisely **247.5 ***grains* of pure gold to be contained in its $**10** *eagle* coin.

Now look at the following pairs of measures:

**3712.5 **/ **3712.7**665… = **.9999**282…

**412.5 **/ **412.5**296124… = **.9999**282…

**2475 **/** 2475.**17766…** = .9999**282…

On the left in red are America’s monetary measures for her gold and silver coinage. To the right in red are the most primal formative measures distilled directly from *The Geometry of Form’s* fundamental unit of length. As the strings of “**9**s” clearly demonstrate, America’s (behind the scenes) monetary architects managed to create a system enshrining this timeless geometry to a degree of perfection *beyond the ten-thousandths number place*! And many hundreds of years *earlier* in England, when King Richard IV declared **437.5** grains to be the new ounce of the realm, and that 16 of those ounces containing **7000** grains (2 X **3500**) would be the new pound, it was this same geometry back then being enshrined into this secretly coalescing *global* system of weights and measures.

An equivalent form to the *fundamental unit of length* configured as the sum of a tetrahedron’s edges is this same line (**1.0**) reconfigured as the edge-length-sum of a *cube*. It too comes with its own unique set of eight *formative spheres*. Since a cube has 12 edges, each measures 1/12^{th} unit in length, making the radius of its formative sphere 1/24^{th} unit.

A sphere with a 1/24^{th} unit radius has a volume of .000303009… But this quantity can be equally expressed as 1/**3300**.236…, or just as equally:

[(**1.0** / **412.5**296124…) / **8.0**]

showing once again that this volume is a power of the now familiar **412.5**296124… quantity. It is also showing us that the volumes of the cube’s eight formative spheres *altogether* equal the volume of just *one* of the tetrahedron’s formative spheres.

After the 1873 Coinage Act, the gross weight of the previously debased (in 1853) fractional dollar coins was adjusted slightly upward from *exactly* **384** grains to **385.80895**… This new, rather *awkward*, number of *grains* was now simply **25** *grams *__exact__. This was the “targeted” weight sought after ever since the first coinage act in 1792 *even though America has never officially adopted the metric system to this day*! Nonetheless, it is “the weight” of **25** *grams* (by whatever *name*) that was needed to finally conform to the geometry. Here’s the reason why.

America’s *standard* *coinage* *silver* is an alloy consisting of **9** parts pure silver and **1** part copper. In the **25** grams comprising one dollar in any combination of fractional coins (half-dollars; quarters; and dimes) there is **22.5** *grams* of pure silver. This is .** 7233**91798… of one

*troy ounce*, which is the ounce comprising the

*base-unit*of weight measurement for gold and silver, and for coinage systems throughout the world.

When one calculates the *volume* for the cube with an edge-length-sum equal to geometry’s *fundamental unit of length *(**1.0**) we find it to be (**1/12**)** ^{3}.** This is also

**1/1728**

*exact*, which means that a larger cube equal to

**1.0**unit of

*volume*will hold exactly

**1728**of these cubes. Moreover, these fit perfectly within the larger cube with twelve cubets per edge. This cube’s

*volume*quantity can be expressed many different ways, but as 8(.0000

**7963…) it is clearly a**

__7233__*power*of the quantity of pure silver contained in the coins comprising one

*fractional*dollar. These

*are*the

*same*measures to the

*exact same tolerance*as the

*Illuminati’s*entire clandestine system of weight measures based on the

**27**milligram cubet, where

**2.4**cubets equal one grain.

.0000**7233**7963… / .**7233**91798… = .0000**99998**3179…

In the beginning of my book *The Geometry ofMoney*, I show how **1.0** *troy ounce* of silver (or any substance for that matter) in the form of a perfect *sphere* has the exact same “face value”, i.e. the same *surface area* as a *cube* of silver having a volume of .**723**60125… the volume of the one troy ounce. This cube weighs **22.5**06514… grams.

Look carefully at the image to the left, which appears on page 136 in *The Geometry of Money*. There, these two forms are modeling the *grain* (the cuboid in the foreground) and the *gram* (the ten cubes in back). Both measures are constructed from identical cubets, each weighing 1/10,000^{th} ** gram**. The cuboid representing the

*grain*contains

**648**cubets compared to the 10,000 in the

*gram*assemblage. These forms model the

*actual*measures to better than .

**9999**8318… fine.

Now use these *same* models but change their common *cubet* sub-unit of measure from a 1/10,000^{th} “unit”, or .0001, to .0000**7233**7963… “unit”. As demonstrated above, this is the 1/8^{th} sub-divisional-unit quanta-sizing the unique internal spatial domain of geometry’s *fundamental unit of* *length* when configured into the edges of a cube. Using this scale makes the ten-cube assemblage equal to .**7233**7963… “unit”; and the cuboid in the foreground, with the **648** cubets, equal to .0**46875**000… of the *same* “unit”.

To apply this natural system of geometry to an earthly *human* system of measurements requires that the *unit* be “named”. It seems clear that the *Troy* *Ounce* of **480** *grains*, or **31.1034**7680… *grams* was the chosen *base* *unit*. Have a look.

.**7233**7963… **X 480** *grains* = **347.22**222… *grains*

or

.**7233**7963… X **31.1034**7680… *grams* = **22.499**62152… *grams*

and

.0**46875**000… **X 480** *grains* = **22.5** *grains* (__exact!__)

The amount of pure silver in the fractional dollar coins is **347.22**80629… grains, which is also **22.5** *grams* (exact!):

**347.22**222… **/ 347.22**80629… = .**99998**3179…

and

**22.499**62152… / **22.5** = .**99998**3179…

This shows that *man’s* measures imitate *geometry’s* measures to better than a .**99998 **approach to perfection! Now, the ten cubes in the background represent the *pure silver content* in any combination of coins comprising one *fractional* American dollar. But what then does the cuboid represent, with its 648 sub-unit cubets, shown in the foreground of the image that, in *this* system, equals *exactly* **22.5** *grains*?

It is the *Eagle*, America’s original ten dollar *gold* coin. The gold in *these* coins is alloyed with copper in a proportion of 11 parts pure gold with 1 part copper. If the assemblage of ten cubes of silver in the background of the image is seen as the pure *silver* content of one *fractional* dollar, then the cuboid in the foreground contains the exact pure *copper* content in one ten dollar gold coin. The *pure gold* *content* of the coin is 11 X **22.5 **grains, or **247.5 **grains; 12 X **22.5 **grains is **270** grains and is the coin’s gross weight. And in the *Illuminati’s* **27**mg system of weight measurement **648** 27mg cubets model the Eagles **270** *grains*.

There is something else very special about this **648** unit *quantity* regardless of what substance it is comprised or what system of measurement in which it is referenced. The gross weight *quantity *of the American silver dollar coin (which was just shown to mimic the internal structuring of the fundamental unit of length) and the mathematical constant **π****,** combine to “create” this special quantity:

**π**** (412.5**296124…**) = 2(648)**

Now what happens if we change the *name* and instead of the *troy ounce* being the reference base-unit (a *weight* modeled by a geometric *volume*) assign the name “inch” (a measure of *length*) to these same geometrically derived quantities? For example,

**648” = 54’ or 18 yds**

** ****648 sq” = 4.5 sq’ **(one-half square yard)

**2(648 sq”) = 1296 sq” **(one square yard)

** **also, remember the equation above but now it is “inch” based

**π”(412.5**296124…**)” = 2(648 sq”) **

Look at the above equations. Notice first of all that **648** square *inches* equals ½ square “yard” *exactly*. Thus a “square yard” is *naturally* subdivided into units of this fundamental geometric quantity. But the equations above also clearly demonstrate that man’s ultimately *arbitrary and subjectively derived* measure known as the “yard” just happens to be *coincidentally* the product of two primal geometric constants when *denominated* in “inches”. Overtly, one square yard is simply 36” X 36”. How can we attribute to “coincidence” the fact that one yard is *exactly* **π**, or **3.1415926**… inches multiplied by **412.5**296124… inches? *Covertly*, meaning “secretly”, is *this* really what a “yard” is equal to “geometrically”? This is just one mathematical/geometrical construct exposing its *true* underlying derivation in geometry.

Since we now know that the square *yard* is a creature of pure geometry so too must be the *acre* measure, which itself is based on whole unit quantities of *yards* or *feet*. There is 43,560 square *feet*, or 4,840 square *yards* in one *acre*. There is also *exactly* 6,272,640 square *inches* in one acre. If these are disassembled into individual square inches, and then placed edge to edge forming a single line, this newly configured *acre* will measure exactly **1.0** *inch* by **99.0** *miles*! Don’t believe it? Do the math, and then realize we’ve all been lied to. *None* of our measures are *arbitrary* and all of them conform to the *same* *clandestine* system of geometry.

Now, let’s see what happens when the “foot” is named this system’s fundamental unit of *length*. Remember! This is still *geometry’s* fundamental “unit”; *we* are just using a different *name* for “unit” and seeing to where it leads us.

We’ve just been looking anew at the *acre* so let’s take up with the *foot* measure where we last left off with the square *inch*. Let’s disassemble the *acre* into its individual 43,560 *foot* squares, and like with the inch measures re-assemble them into a single line. This *acre* now measures **1.0** *foot* by (two units of) **4.125** *miles*.

The equation below is showing one way the *quantity* **648**, as “feet”, relates to the *mile* *measure*. The *equivalent* right side of this equation exposes the *mile* blended with *powers* of America’s afore-mentioned monetary measures of **270** (grains) and **412.5** (grains).

**648 feet = [1.0 mile** (in # feet)

**(2.70)3] / [16(4.125)]**

**The Number of God**

** ** The volume of the *formative* *sphere* associated with the *fundamental* *unit* in its 1^{st} dimension as *a line* (configured into the six edges of a tetrahedron) is 1/**412.5**2961… Now a *quantity* of **412.5**2961…, when multiplied π times, or 3.1415926…, results in a remarkable product: **1296**. This *perfectly* *even* quantity is a surprise, given the two irreconcilable factors from which it is produced:

π (**412.5**2961…) = **1296** exact

And here again is an example of where the value of a “name” becomes all important. If **412.5**2961… is a quantity of “inches”, then **1296**” is also 108 “feet” or 36 “yards”. And if the quantity π is also a number of inches then it becomes **1296** “square” inches which is **1.0** *square yard* or 9.0 square *feet*.

Now a *length* or *area* of π *inches,* or π *square inches,* divided into **412.5**2961… parts (the reciprocal relationship to the above equation) makes each part equal to **.007615435…** *inch *or* square inch*. This measure is, of course, *special* to the *geometry* *of* *form* being a creature derived from the geometry of the *fundamental* *unit* and the mathematical and geometric constant π. Confirming this *special*-ness is the fact that:

**13**,000(.**007615435**…*inch*) = **99.****000**66142…*inches*

and that **99** inches has previously been shown to be a “natural” sub-unit of the surveyor’s chain of **66** feet; i.e., 8 times **99** inches equals **66** feet. In this case,

8(**99.****000**66142…*inches*) equals **66**.**000**44095… feet

which is .**99999**… the actual measure of **66** feet.

If instead of **99.****000**66142… “*inches*” in the above equations we *name* the measure “*square inches*”, then the visual geometry resulting from the equation can be seen as a line consisting of **99** one inch “squares”. Each of these squares consist of a bit more than 131 sub-units of area with each measuring **1.0** inch on one side and **.007615435… **inch on the other. It is **13,000** of these units that together create this **99.****000**66142… measure. Repeat this **98** more times and one will arrive at a larger square measuring **99** inches per side (or, two times **4.125**027559… feet). This square contains **9,8**01.065481… “*square inches*”. Just as **99** inches is the “survey chain’s” designed *occulted* sub-unit, the square of this measure is the sub-unit of **1.0** “square chain” in that there are **8** of these per side, **64** all together. **10** of these “square chain” measures constitute **1.0** acre measuring 43,560 square feet. And **64**0 acres constitute **1.0** square mile. Once again, here *they* are, the western world’s (pre-metric) measures of land.

All of the above quantities were derived directly from agglomerations of a *more fundamental* geometric measure: **.007615435**. . . In this example, we’ve “named” it either *inch*, or *square* *inch*. The square described above, with the two times **4.125**027559… foot edge-length (**99.****000**66142… “*inches*”), contains *exactly* **1,287,000** units each measuring **.007615435**. . . square inch. Another way of describing this is that each of these **.007615435**. . . square inch units is **1/1,287,000** the area of the greater (**99**” X **99**”) square of which it is a part. Each of these *units* is a

# .000000**777**000**777**000**777**0…

portion of the entire **99.****000**66142… inch square.

By its structural appearance alone this is a very interesting looking number. That it is a repetition of the quantity **777** gives it a particular mystic, since throughout history the triple seven has had an inseparable *spiritual* connotation. For what it is worth, to many religious sects **777 **is *The Number of God**.*

There is something else too, along these lines, with respect to this special unit of area derived from the properties of the *fundamental* *unit*. In the example above this area was modeled by the **1.0”** X **.007615435…**” rectangle; but when reconfigured into a square, once again its *divine* property shines forth. Have a look.

(**.007615435**. . .)^{1/2 } = **.0872664**. . . **and**

** ****30**(**.0872664**. . .) = **2.617993878**. . . **and**

**2.617993878**. . . = (**φ**)^{2 }, or (**φ** + **1.0**)

The first equation above reads: the square root of the .**007615435. . . ***area* is a *length* measure equal to **.0872664**. . . The middle equation then shows that *every* **30** of these measures equal a length of **2.617993878**. . .units; and the third equation equates this quantity to the mathematically essential **phi** proportion . . . which is more popularly known as *The Divine Proportion**, *as well as the *Fibonacci ratio* and is found throughout all of nature’s constructs. Specifically, **2.617993878**. . .***** is the second power, or “square” of **φ**, which as we see is also (**φ** + **1.0**).

*Note: **φ **is equal to [(5)^{1/2} + 1.0] / 2, which equals **1.618033989**…; and (**φ**)^{2} = **2.618033989**… The quantity **2.617993878**. . . derived from the above geometry, compares to the implied ideal as:

**2.617993878**. . . / **2.618033989**… = .**99998**46

And lastly, and again for what its worth, in the *cosmology* which parallels “The Geometry of Form”, *the inherent potential of Unity is the release of seven others identical to itself*. Together, the *eight* of them combine to form the next power of the “Original Unit”. In the beginning of geometry, **7** “others” is the potential of **1**.

** **We’ve already seen that when geometry’s *fundamental unit of length* is re-configured into the edges of a cube, each edge equals .0833333… and encompassed a volume of .000578707… We also know this volume as **1/1728** *cubic* *unit*, and that it requires exactly 1728 of these cubes’ volumes to perfectly fill a cube with a **1.0** “unit” edge-length; 12 cubes per edge. Since we’ve given this *unit* the name “foot”, its “cube” equals **1.0** *cubic* foot; and each of its **1728** natural sub-unit cubets (each one with edge-length-sums totaling **1.0** *lineal* unit, **1.0** foot) long ago we’ve come to call them *cubic* “inches”. There are twelve per edge; and we call *this* cube’s edge-length a *foot*. Each face of this larger cube measures **1.0** *square* foot.

Now, let’s make the *inch* the base unit of *length*. Again, look at the larger tetrahedron inspected earlier with the volume of **412.5**296124… *cubic* “inches”. Transform this volume into a perfect cube and it will have an edge-length equal to 7.444205890 *inches*. Now this is a very interesting

*****

cube. Agglomerations consisting of eight of these cubes…together form one larger cube and create the perfect size cube for embracing within the confines of its face-planes a very special *sphere* having a volume of __exactly__**1728** *cubic inches* . . . that’s

**1.0**

*cubic*

**foot**__exactly__! This sphere’s

*perfect*volume of

**1728**

*cubic*inches can then be re-package as a

*single*cube; its edges are divided “naturally” into

**12**units, each unit

**1.0**

*inch*in length.

In the light of the above described relationships this **1.0** *cubic* ** foot** unit has been exposed

*as a primal construct of geometry*;

__by whatever “name” you want to call it__. It is inherent to, and derives from,

*The Geometry of Form’s*fundamental unit of length (

**1.0**

*unit*) in its forms as both the six edges of a tetrahedron and the 12 edges of a cube. It is this cubical

*volume*of

**1.0**

*cubic foot*and any one of its individual face’s surface areas (of

**1.0**

*square foot*) that has

*patterned*all of humanity’s

*customary*

*units*of length, area, and volume.

**Measures of Length and Area**

Measures of *length* and *area* are synonymous with measures associated with *land* here on Earth. Appropriately, man’s measures of land have been derived from the geometric relationship between a sphere’s *volume* (like earth) and its *surface area*. To prove this, we must return to the cube equal to **1.0** *cubic foot*.

Any one square face-plane of this cube measures **1.0** *square foot*. Re-formed into a *sphere’s* surface it will encompass a volume of .094031597… cubic foot. This quantity is the __maximum__ *volume* that **1.0** *surface* unit is capable of enclosing. The relationship between this sphere’s surface and volume (1.0 / .0940…) is equally expressed as 10.63472310… / 1.0. Specifically,

**1.0 / .0940… = 10.63472310… / 1.0**

This means that for every unit of volume there is ten-*plus* units of surface. Specifically, there are **10 “**square surface units” with each square measuring 1.06347231 square “feet”. This *square* became man’s fundamental unit of land measurement. Let’s see why?

The edge-length of this square is 1.031247938… “foot”. This is 1.03125 foot (or, **33/32** foot) to a **.999998**00… degree of perfection. And [(2)^{9 }X **1.03125** foot = **5280** feet], which is one “mile”. In “inches”, 1.031247938… foot is 12.37497526*… inches; and (2)^{9} of these units measure 5279.989444… feet. Again, this is a “mile” to the same .**999998**00… degree of perfection.

* 123.7497526… X 3 = **371.2**492578… ; and, 123.7497526… / 3 = **41.24**991753…both of which are a .**999998**00… degree of congruence to America’s **371.25 ***grains* and **412.5** *grains* monetary measures.

But America’s prime coinage measures of *weight* make the behind the scenes manipulation even more blatant since as portions of a foot, show the same geometry at work: (.**2475′** + .**37125′** + .**4125′ **= **1.03125′). ***The Geometry of Money* (the predecessor of *this* book) proved beyond any doubt that this is by *design*.

This square base unit of land measurement aggregates, once again, like the classic chessboard: **8.0 **per edge, **64 **in all. Using the modeled *ideal* measure of **1.03125** feet/edge for this base unit, makes the edge-length of the next (now a composite) square measure 8.25 feet; which is also *both* 2(**4.125**) feet or, **99** inches. Again, **8.0 **of these **99**-inch squares form each edge comprising the next composite square unit of area. This square measures 792 inches per edge, which is also **66** feet. This is the length of the *surveyor’s chain*, which was the measuring rod in use from the early 1600’s right up into the 1960’s. One *square **chain* contains 4356 square feet, which is a tenth of an *acre*: thus **10 **square chains equal one *acre*. A square, **80 **chains per edge, is a square mile, and contains **64**00 square chains; which is also **64**0 acres.

It’s clear to see that regardless of what “name” man assigns to the “unit” in the geometry unfolded above, to *geometry* it is simply the “unit”. The evolving geometric forms are always the same, and they will always have the same internal sub-structuring. There will always be a sphere, perfectly quanta-sized by a 1728 unit volume, resulting from a *radius* derived from the edge of a cube having a **412.5**296124… *cubic unit* volume. And the cubical form of this 1728 unit volume will always be sub-structured with a **12**-unit edge-length with each individual “unit” equal to the *fundamental unit of length* in its form as a tetrahedron. So regardless of the *name*, the *geometry* is the same.

The previous geometric units of *length*, *area*, and *volume* descended from the properties of a line equal to **1.0** lineal “unit”. Man’s customary units of *volume* (such as our various *gallons* and their derivatives) are based on the *cubic* *inch* . . . and the same occult geometry.

For example, the Roman gallon contains **216** cubic inches (**6x6x6)** and is *overtly* an eighth of a cubic foot. But its *occulted* genealogy is

(**1/6**)**π**(**412.5**296124…) cubic inches

The modern gallon of **231** cubic inches *overtly* is the Roman gallon with an additional 15 inches. But again, *covertly*, the modern gallon is:

(**1/6**)**π**(**412.5**296124…) + (**1.0**/.0**666**…) cubic inches

Clearly, the formative structural quantities of the fundamental unit of length combine along with **π **to create the Roman and modern gallons. And so too can the *dry gallon* (or *gallon dry*) measure (**268**.**8****025** cubic inches) be derived from a relationship between the two specific geometric forms noted above. These are the sphere with a **1.0** unit *surface area*, and the sphere with a **1.0** unit *volume*.

In *The Geometry of Money*, we saw man’s measures of *land* fittingly spawned from the geometric relationship between geometry’s fundamental unit of *surface area *and the spherical *volume* within its confines. Traditionally, *produce* __from the land__ has been measured in *bushels*. Beginning with two *dry pints* to one *quart dry*; then four *quarts dry* to one *dry gallon*; four *gallons dry* to one *peck*; and finally two *pecks* to a *bushel*. Thus like the *squares* of land measures above, the *bushel* essentially consists of **64** *pint dry* sub-unit measures.

The *dry pint* volume unit is a portion of *the volume unit contained by a ( 1.0) unit surface area in the form of a sphere’s surface*. This volume of .0940315… unit is then

*divided by the spherical surface area quantity containing (*: 4.835975… units. The resulting portion is the pint dry measure.

**1.0**) volume unit**.0940315… / 4.835975… = .019444183…**

** **Since this.0940315… *volume* measure is a portion of a cubic “foot”, this .019444183… quantity also is scaled to the cubic foot. Therefore,

**.019444183… X 1728 ****cubic inches = 33.59954… ****cubic inches**

Man’s *pint dry* measurement is **33.6** cubic inches; geometry’s measurement is **33.59954…** cubic “units”. They are the same measure to better than a **.99998…** correspondence.

**An Interesting Cube Indeed!**

GEOMETRY clearly shows that the *American monetary measures*, along with the *grain/gram* conversion quantity, to have been “borrowed” or “stolen” from the fundamental constructs of geometry! This is simple to prove.

The gross weight of the *silver dollar coin* is **412.5** *grains*. In this case this “number” is first and foremost a “quantity” of weight-standards; but to geometry, it is simply a “quantity”, devoid of *substance* leaving only *volume*. This quantity is most easily modeled *geometrically* by a simple cube with a volume equal to **412.5 ***units***.**

The American gold coin in circulation at the same time was the *eagle*. It was the equivalent in value to ten of these silver dollar coins. Therefore the gold *eagle* was worth the same as the **4125** grains of *coinage* *silver* comprising the ten silver dollars. This too is most easily modeled geometrically by a simple cube with a volume equal to **4125 ***units***. ***This is a very special cube*. We can see *why* I say this first by examining its remaining parameters:

Edge-length = **16.03767165**…

and

Surface area = **1543.241472**…

The quantity describing the length of this cube’s edge is the *same* quantity describing the *pure gold* content in the ten dollar *eagle* coin. But this quantity (of *grains* of pure gold, **247.5**) is here denominated in *grams*:

**16.03767165… **X 15.432358… grains/gram = **247.499**096… grains

and

**247.499**0960… / **247.5** = **.999996…**

Moreover, and of great significance, is the commensuration between the surface area *quantity* of this cube and the standard *quantity* for converting grains to grams, or grams to grains:

15.43235835… / **1543.241472**… = .00**999996…**

** ** Another example of this can be seen in the form of a regular tetrahedron. When it is *scaled* having an edge-length equal to 15.43235835… (once again, the *grain/gram* conversion quantity) then its surface-area will be **412.5**01209…

This is really quite remarkable since “history” tells us that these *human designed weight quantities* were arrived at *subjectively* and *arbitrarily*; and that the *gram* was a derivative of the meter measure, which was simply a ten-millionth part of the earth’s quadrant running through Paris France from the north pole to the equator. History does note, however, that the *birth of the metric system* amidst the French revolution in the 1790’s, and the *Coinage Act of 1792* in the USA, *both* occurred contemporaneously.

**Prior to this point in time**, the “quantities”

**15.432**…,

**16.037**…,

**412.5,**and

**247.5**existed

*only*in the eternal relationships among the forms of geometry.

** ****The Winchester Bushel**

** ****A “Natural” Unit of Account**

If one investigates the *bushel measure* (2150.42 cubic inches) it too will be found, contrary to the historical derivation, to be firmly embedded in the hierarchy of geometric form. Whereas we just saw the *pint dry* measure coming from the *surface* unit’s *volume* in the form of a “sphere’s” surface, in the case of the *bushel* *measure*, among other means, it can be derived directly from the primal geometric forms of both the “cube” and “tetrahedron”. Here’s how that works.

Start with **1.0** unit of *surface* in the form of a cube. In *The Geometry of Form* this is the “Unit” in its second-dimensional form (in contradistinction to Euclid’s two-dimensional square). If this cubical *surface*-unit is magnified by a factor of one-thousand then we have a cube with a **1000** unit surface area. The resulting cube will have a volume of 2151.6574…, which is the *bushel* measure above to better than .**999**4… fine. And a *tetrahedron* with a **1200** unit surface area has a volume of 2149.13986… which, like the cube, is the volume of the *bushel* to better than .**999**4… fine. When we find the *average volume* between these two very unique geometric forms *having* *essentially* *equal* *volumes* it is 2150.39863… This is .**99999**00…the *bushel* measure.

As mentioned earlier there are eight *dry* *gallons* in this *bushel* *measure* with each gallon equal to 268.8025 cubic inches. Not only is this “quantity” embedded in the geometric hierarchy, but it appears to be a quantity “natural” to our *physical* world relating directly to at least two of the elements: *silver* and *copper*, both prime *monetary* metals. Watch what happens when we “name” geometry’s *fundamental* *volume* *unit* (in the form of a cube) this time as “1.0 dry gallon”.

Since there are 268.8025 cubic inches within this cube its edge-*length* is the *cube-root* of this volume which is 6.45373476… inches; and, the *area* of any one of its six square facial planes is (6.45373476…)^{2} making its total surface area 249.90414…square inches. This is **250** square inches to .**999**6… fine. So in a very real sense, the “ideal” geometric forms on which the macro-modeling of the *bushel* *measure* is based views the **1000** square inch surface cube divided into eight gallon sub-cubes with each having a **250** square inch surface area. The original **1000** square inch surface becomes **2000** when the bushel divides into separate gallons. But here is what is most remarkable:

Take the edge-length of this cubical “Unit”, 6.45373476… inches, and reconfigure it into the twelve edges of a new cube. The volume of this new cube is .155557002… cubic inch. If this cube is filled with *pure* *silver* it will weigh exactly **412.6**65… *grains*. *This is the gross weight of 1.0 American silver dollar t*o .

**999**598… fine!

Now, make another *cube* with a *surface* *area* equal to any *one* of the six square faces of the *gallon* *dry* in its form as a cube. . . i.e., equal to the square of this Unit’s 6.45373476… inch edge-length. The edge-length of this new cube is 2.**63472**61…* inches; its volume is 18.28969351… cubic inches. If this cube is filled with *pure* *copper* it will weigh exactly **4125**7.6732 *grains*. Since there are **41.25 ***grains* of pure copper in each silver dollar coin, this cube of pure copper (derived from the geometry of the *Winchester* *dry gallon*) will make alloy for *exactly* **1000** of these coins to a precision of .**999**8… fine.

##### *Note: This quantity of *length* is directly related to *1.0** surface unit in the form of a sphere* in that its .**63472**61… portion is also that amount over 10 units in the simple equation describing the surface/volume relationship in a sphere equal to **1.0** unit of surface area:

*1.0*

##### 1.0 / .094031… = 10.**63472**31… / 1.0

##### This can be translated to read “The ratio between 1.0 surface unit and the maximum amount of volume it can possibly contain, *is the same* ratio as that between 10.**63472**31… surface units and 1.0 unit of volume. Again, this is just another piece of blatant evidence revealing both the nature of geometric structure and its measurement basis, and the bushel measure’s geometric pedigree as well since this portion has been directly distilled from the cube made from one face of the *Winchester* *bushel’s gallon* *dry* when it is itself modeled as a cube.

I should point out that those who have read *The Geometry of Money* may remember that on page 247 we see that a perfect **1.0 **cubic foot of pure silver is actually comprised of **800** units with each one containing “**371.25** * grams*” (which same

*quantity*as “

**371.25**

*” is the pure silver content in the dollar coin). This metal embodies this geometry and mathematics to a .*

__grains__**9999**degree of perfection.

One can further reference page 169 in *The Geometry of Money* where I showed that today’s standard gallon of 231 cubic inches is .**85936**700 the capacity of the still in use 268.8025 cubic inch *gallon* *dry*. And, that this compared to the **412.5** grains comprising the silver dollar coin being .**85937**5 the weight of **1.000** *troy* *ounce*. These measures are in the *same* proportions to .**99999**0 fine! The much older Roman gallon of 216 cubic inches is only .**8035**63… the capacity of the *Bushel’s* gallon dry, but this too mirrors the much later 25 gram “fractional silver dollar’s” .**8037**68… portion of (again) **1.000** *troy* *ounce*. These are the same quantities to .**999**745… fine.

Referring back to the two cubes of metals derived from the edge and face measures of the *Winchester* *bushel* there is certainly *no* *coincidence* at work here. No other metals filling the voids of these two specific cubes (extracted from the geometric properties of the *Winchester* *Bushel*) will be *base-ten-denominated* in whole numbers of units comprising **412.5** grains each.

Here is further *evidence* that this geometry unites the natural properties of *mass* and *volume* for the element silver, with first the supposed “arbitrary” *monetary* *measures* devised by the men back in 1792; and second, in relation to other measures of weight and volume that became firmly established before and after that time. For we see that the *same* cubical *volume*–*measure* containing *exactly* **412.5 **grains of *pure* *silver* is also:

.0000**16027**3549… *barrel* *oil*; and, **16.037**730… *grams* of pure **gold **are in each $**10** eagle coin (different powers of the same quantity to .**999**3… fine).

.0000**723**121… *bushel* *dry*; and there is .**723**391… of **1.0** troy ounce of pure silver in America’s fractional dollar coins (.**999**6… fine).

.00000**562**379… *cord* *foot*; and .**562**5 *troy* *ounce* is the gross weight of the $10 dollar eagle coin (.**999**78… fine).

.0000**8998**690… *cubic* *foot*, which is a 1/10,000^{th} part of .**900** *cubic* *foot* to .**999**85… fine: and, American coinage silver is .**900 **pure silver.

.**1554**96… cubic inch; and a *pence* (a unit of weight used in the 1792 Coinage Act) is **1.555**17… *gram* (.**999**86… fine).

Maybe silver *is* special with respect to geometry and man’s systems of weights and measures. In the following section, the reader will be introduced to a new quantity and its powers and various forms of its expression. This *quantity* structures one of the most important conceptual relationships among the geometric forms. One of its powers is .000**37412297**…, and as a portion of **1.0** *barrel dry* this measure of volume *filled with pure silver* weighs **1.000**4231… *pound*. This is **1.0** *pound* __exact __to a precision greater than .**999**5… fine. . . *finer* than the purity of America’s gold and silver coinage. And if we have a complete **1.0** *barrel* *dry* of pure silver it will weigh **2674**.04899… *pounds*. This quantity as *grams* is the gross weight of 100 silver dollars (**26.729550**… X 100) again to a precision greater than .**999**5… fine. Why are *these* measures so special to geometry, to nature, and to man?

# BALANCE

## 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^{th }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 in the chapter on Measures of Land on page 180.

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__(

*grain/gram*conversion ratio**15.43235835**); and, what is arguably

*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…**