# Humanities Units of Volume

The modern “gallon” of 231 cubic inches dates as far back as the late 14th century when King Richard III proclaimed the wine puncheon as a cask holding 84 gallons and a tierce as a cask holding 42 gallons. The gallon itself was formally codified into English law around 1706-1707 under Queen Anne and was often referred to as the “wine gallon”. Up until then, there were several different “gallon” measures in use; but the Roman gallon was by far the oldest and one of the most common. Being exactly 1/8th cubic foot, it measures just 216 cubic inches and thus is a little smaller than the modern gallon.

The obvious “difference” between these two volumes is 15 cubic inches. This can be considered the “overt” explanation. But there are covert mathematical relationships. A simple example of one of the most obvious of these is by expressing 15 cubic inches as 1.0 / .0666… cubic inches. In this way, the difference between the two gallons is simply:

216 + [ 1/.0666…] = 231

These covert explanations will reveal this difference in manners that clearly show why these volume quantities were chosen. They will show as well, why these quantities are also an inseparable part of the previously exposed 27mg weight system based on whole unit cubical assemblages. Artifacts of this system’s imprint on the gallon measures can be seen in the following equation:

231 ― 231[ 27 6400 ]1/2 = 216

What this equation shows us is that the volume of the Roman gallon differs from the modern gallon only by a [ 276400 ]1/2 portion of the modern gallon. Here the number 27 obviously relates to the geometry of the weight measures; and as we will soon see, the number 6400 and its’ powers is inextricably woven into land measures.

Compare the last simple equation above with this simple ratio:

1/32 : [1/32] + [ (27) 1/2 / 640 ]

This ratio compares humanities’ two measures of length, i.e. the “inchmeasure” and the “metermeasure”. The unit of length which we all call an “inch” contains either 32 one-thirty-secondths of an inch, or 25.4one-twenty-five.fourths” of an inch, which is one millimeter. Obviously the millimeter is the larger of the two measures. So how do they compare? They relate like the simple quantities expressed in the ratio immediately above: 1/32nd of an inch (the “inchmeasure”) to 1/32nd + [ (27) 1/2 / 640 ], the “metermeasure”.

Now look at the two equations above. The first (231 ― 231[27 6400]1/2 = 216) described the relationship between the modern gallon and ancient Roman gallon; and the second 1/32 : [1/32] + [(27) ½ 640] between the ancient inch measure and modern meter measure. (Note that even the numbers patterning 1/32 = 231 backwards.)

Nobody can deny that these two (overtly) vastly different systems of measures appear to have been derived from the same foundational mathematics. And it is obvious they are in conformance with the 27 milligram system of weight measures already exposed in the previous chapters.There can be no denying that all of this turns “history” upside-down! So hold on. What follows is unequivocal, and completely defies the historical record.

In this system of volume accounting the fundamental unit of account is the cubic inch. Both of these gallons can be modeled by perfectly complete cuboids assembled from cubes measuring 1 cubic inch. The Roman gallon, for example, as an eighth of a cubic foot is a 6 X 6 X 6 inch cube in its most natural modeling form. But a 2 X 2 X 54 assemblage works; so does 2 X 4 X 27; or 3 X 4 X 18; or 3 X 6 X 12, etc. However, with respect to the modern gallon of 231 cubic inches there is only one combination that will assemble into a perfectly complete cuboid: 3 X 7 X 11. Because these quantities are all “prime numbers” there can be no other workable combination. This limits the modeling of the modern gallon to just this one form.

To the casual observer, and to history itself for that matter, there is really no relationship between these two gallon measures let alone between them and the ounce measures. This is because the geometry that was used to determine the sizes of these measures has never been disclosed and is still, up until now, a closely guarded secret.

Now keep in mind that prior to the introduction of the avoirdupois ounce and the modern gallon there was already the troy ounce and Roman gallon. A few pages back, the reader was shown (in a photo) how the two ounces actually share a common core from which either ounce can be made by adding one complete additional layer of cubes on one or another face. This identical modeling transformation likewise characterizes the two gallon measures. Depicted below are these two gallons along with their “common core”.

This common core is modeled on what was known at the time of the Romans as a “mason’s perch”. From Roman times on, the “perch” was a unit of volume containing 24.75 cubic feet. Since the perch was also a unit of length equal to 16.5 feet, the traditional volumetric perch most commonly measured 1.0 X 1.5 X 16.5 feet. If one regards the volume of the perch as being comprised of Roman gallons, then the traditional perch can be modeled by 198 cubes with each cube measuring 6 X 6 X 6 inches. This particular “unit” of masonry is depicted in the photo below. Notice that its “natural” vertical sub-divisioning is into two 99 cube assemblages; and horizontally into three 66 cube assemblages.

As mentioned, the cubes comprising the “perch” in the above photo can be viewed as each being a Roman gallon of 216 cubic inches. And again, as previously mentioned, this “perch model” is also the model of the core of both gallons; but only if the cubes are rescaled to represent “cubic inches” (instead of Roman gallons). Then this volume is simply reconfigured into a cuboid measuring 3 X 6 X 11 inches (as depicted in the first photo standing aside the two gallons). Later we will see how the perch, as a 16.5 foot measure of length, further incorporates the geometric and mathematical properties of the gallon measures into land survey and surfaceareaunit sub-divisioning (as well as monetary and weight measures).

One good example of this transition from the gallon (volume) measures to those of land (area) measures is seen when we convert the 198 Roman gallons that comprise the perch into cubic inches:

198 X 216 cu.in. = 42,768 cu.in.

and

43,560 in. – 792 in. = 42,768 in.

Without going into details here, since we are presently looking at the volume measures, we see that in terms of the quantity of cubic inches that are in a perch, that there is a direct and exact correspondence to the quantity of square feet in an “acre” (43,560) and the quantity of inches in the surveyor’s chain of 66 feet (since 66 X 12” = 792 in.).

So clearly it is no accident that the models of these gallons and their common core mirror the same geometry and transformations that we saw when modeling the troy and avoirdupois ounces. And just as the previously exposed geometry clearly answered the question as to why there is 12 and 16 ounces in each of the respective pounds, geometry will likewise prove why there are 42 gallons in the old tierce and its’ modern version, the “ petro barrel”.

## “The Modern “Petro-Barrel”

The history of “barrel-size” containers predates King Richard III’s proclamation in the late 1400’s that a tierce would contain precisely 42 gallons (of 231 cubic inches). So we do know for certain that the 42 gallon container has been with us for a very long time. By 1700 many of the American colonies had legislated this 42 gallon tierce as the standard shipping container for a variety of bulk commodities. This all happened long before the fledgling oil industry ever shipped a barrel of oil. Despite the conflicting historical mythology surrounding the oil industry they simply adopted the most abundant and readily available container of their day.

Obviously the question here is “why 42 gallons”? Is that volume special, or simply one that evolved through practical application on a human’s scale, just as our history leads us to believed? The conclusion that this is a “special” and very carefully “chosen” quantity, designed to conform to the Illuminati’s occult system of mathematics and geometry, will be unequivocally and indisputably proven by the following simple math and geometry.

When we looked at the picture of the modeled volume of the modern gallon unit, we saw a perfect cuboid comprised of 231 one-cubic-inch sub-divisions. They arrange in layers with 3 cubes by 7 cubes, and these stack 11 layers high. Remember, since they are all primes, there is no other arrangement of these cubes possible that will create a perfectly complete cuboid. Now let’s arrange 42 of these cuboids into one single form and see what we get.

First, the base of the modern gallon’s cuboid is a rectangle 3 inches by 7 inches; and, 3 X 7 = 21. This means that precisely 21 of these gallon cuboids fit “perfectly” in a square measuring exactly 21” X 21”. This is done by arranging them into three rows with each row containing seven gallons; their 3” X 11” faces combine to form one 21” long by 11” high rectangular plane. When the three rows are snuggled-up together, another 21” long by 11” high rectangular plane is created. When an additional layer of these 21 tightly arranged gallon cuboids is set atop the 21 already arranged as described (bringing the total to 42 gallons) we now have a new very special cuboid, as is pictured below.

This new 42 gallon cuboid is described as follows: one perfect cube (assembled from 1-cubic-inch sub-unit cubes) measuring 21” X 21” X 21”, with one additional complete layer of sub-unit cubes added to any one of its faces. This is the model after which is patterned the late medieval tierce, the 18th-19th centuries standard shipping container for practically any commodity, and which is today commonly referred to as a petro-barrel.

When studying the next photograph, it is essential that the reader understand this older 42 gallon tierce, and its’ twice volumed puncheon were standardized and written into English statute at about the same time in the late fourteen-hundreds as the new avoirdupois ounce and pound. This is an important correlation since in the previous chapter, the photograph of the avoirdupois pound likewise depicted two “cuboids” with each comprised of a perfect cube measuring 20 X 20 X 20 cubets per edge with one additional complete layer of sub-unit cubes added to any one of its faces.

These same two ½ pound cuboids are again pictured (on the left) in the next photograph. In this same photo (on the right) is the puncheon, modeled as two tierce. Its geometry is practically indistinguishable from the nearly identically modeled AV pound. These two vastly different measures . . . i.e., one of weight, the other volume, seem to defy their history which makes no claim of any relationship between the two. On the Left are two ½ Pound Avoirdupois Units Modeled With 27 Milligram Cubets. And on the Right, Modeled With 1 Inch Cubes, is the Puncheon; or Two Tierce; or Two 42 Gallon Petro-Barrels.

So now we clearly see with our own eyes, that there is a shared geometry between humanities two ounces of weight measure, and the two “gallon” units of volume measure. These have manifest and taken precedence during the evolution of western civilization. And even though the fundamental unit of the ounces is the grain, and the fundamental unit of the gallons is the cubic inch, both can still be modeled by the same geometry using simple cubes, and whole-unit geometric assemblages of these cubes.

This next modeling should further dispel any notion that this could in any way be attributed to coincidence since it too eloquently answers the same simple question as to why there is 42 gallons in the tierce and petro-barrel in the first place rather than an even 40, or some other quantity? Remember, history tells us these are measures of convenience which are scaled to this size so as to be comfortably handled by the average workman. Obviously that’s not what was going on here. And further proof that the true answer is found in the geometry of form is again seen in the petro-barrel itself.

In the next illustration a petro-barrel of 42 gallons has been disassembled into its constituent 1.0 cubic inch cubets. Since there is 231 cubic inches per gallon, the 42 gallons must total 9,702 cubic inches. If we arrange these 1” cubets 2-dimensionally on a flat surface, and package them in the most geometrically economical manner, we’ll arrive at a “perfectly” imperfect square measuring 99 cubets by 98 cubets. Each of the white squares in the illustration represents one cubic inch; and, 99 X 98 equals 9,702 cubic inches, which is 42 gallons. 42 Modern Gallons Disassembled Into Their 9,702 Constituent Cubic Inch Sub-Units. It makes a Perfect 99 Unit Square, Minus One Complete Line, And Holds The Barrel’s “Contents”. The One Missing Line of Cubic Inch Cubets (in red) is The “Space” Required For Expansion of The Barrel’s Contents In Practical Real World Applications

The “perfectly complete” square, 99 cubic inches by 99 cubic inches, depicted in the illustration above, is likely to be the true ideal maximum “volume” of the petro-barrel’s“capacity. The barrel’s “content” of 42 gallons is this perfect square less the one line of cubits highlighted in red. These 99 empty cubic inches would allow for the expansion of the fluid contents within the barrel due to changes in temperature and pressure. If this same ratio of air space per barrel content were applied to a single gallon unit (measuring 3 inches, by 7 inches, by 11 inches tall) 11.112244 . . . inches would be the container’s inside measure. This is less than one 1/8th of an inch between the top of the fluid and the top of the container to allow for expansion due to changes in temperature.

There are other properties of this 99 inch square that make it very “special” within this geometric hierarchy of weights and measures. For example, its 99 X 99 = 9,801 cubic inches is also 42 3/7 gallons. When this is re-written as 297.0 / 7 gallons; and again as [(371.25) X 8] / 7 gallons, we can see the U.S. monetary measures distilled from the barrel’s capacity: 29.70 inches was the width of the full sheets of paper on which the old large paper notes were printed. And again, it is the 371.25 grains of pure silver that gives the dollar coin its inherent value.

The silver dollar coin’s gross weight of 412.5 grains is also a sub-unit of this 99 inch square derived from the petro-barrel’s capacity. We can note first of all, that 99 inches is also two times 4.125 feet. This means that it (a 99” square) naturally sub-divides into square quarter-sections with each edge measuring 4.125 feet.

Overtly, the area of this 4.125 foot square is 2,450.25 square inches. But covertly it is either 99 times 24.75 square inches (mirroring the 247.5 grains of pure gold in the \$10 dollar eagle coin); or, 66 times 371.25 square inches. So we can see in this one square, this quarter-section of the larger 99 inch square, three of the primary monetary measures defining the American system of coinage. And let’s not forget, that this system of areal measures just exposed (based on the square inch) came from us looking at square inch units representing the “cubic” inch units associated with the petro-barrel and its predecessors, the tierce and puncheon.

Thus far we’ve seen America’s (and much of the world’s) customary units of volume evolve into quantitative expressions of area. These, we’ve since discovered, are themselves reflections of America’s monetary units of weight. And now we find that exactly 640 of these 99 inch squares, laid out in a single line edge-to-edge, measures exactly 5,280 feet, or 1 statute mile. Moreover, these 640 “tiles”, 99 inches on a side, exactly covers an area that we’ve come to know as 1.0 acre; and 1.0 square mile, 1.0 section of a township, contains 640 acres. And remember that the difference between the ancient Roman gallon and the (comparatively) modern gallon unit of volume measures can simply be expressed (to a .99998…degree of perfection) as:

1 : 1 [27 (640 X 10)]1/2 =   231 cu.in. : 216 cu.in.

There is much more to be seen regarding the volume measures and their relationship to the eternal ideal forms of geometry. But that is for a later chapter or book explaining the source and mechanism by which these ideals were infused into geometry, nature, and ultimately the various manifestations of human weights and measures. But as a segway into a later chapter on the measures of geographical distance and area we’ll look once more at this 4.125 foot unit and its fundamental relationship to the Surveyor’s Chain. Until the 1960’s, in America and elsewhere, the surveyor’s chain was the “yard stick” for land measurement. Overtly, it is 66 feet in length and divided into 100 “links”. Property lines were recorded in “chains and links” as opposed to feet and inches.

But to the initiated, the length of the surveyor’s chain is eight times 99 inches; or sixteen times 4.125 feet; or thirty-two times 24.75 inches. And each of its 100 links is eight times .99 inch. From this perspective, the length of the surveyor’s chain is

800 X .99”

and is divisible by powers of two and ten. The idea back in the early 1600s, that’s when Edmund Gunter first introduced his measuring chain, was to slowly and subtly introduce a “base ten” system into humanity. Today we know it as the “metric system”.

## Measuring Agricultural Produce

### And it’s Derivative Units

Why is a “bushel” the size that it is? According to accepted history, it’s really anybody’s guess. What I mean by this is that history at least gives us a “story” about the meter’s origin from a French measurement of the earth’s quadrant in the 1790’s, but there is no comparable record for the system of volume units culminating in the “Winchester bushel” and its derivative sub-units.

This system of measuring agricultural produce goes back at least to the time of King Henry VII at the end of the 15th century. It was first codified into English law by an Act of Parliament around 1697. It was defined as a cylinder 18.5 inches in diameter and 8 inches deep. This comes out to be 2150.42028… cubic inches. The United States formally adopted the Winchester bushel for measuring wheat in 1836 and refined the measure to exactly 2150.42 cubic inches.

Now, it’s worth asking why, in 1836, those in charge didn’t choose to just round off the measure even further to make it an even number of cubic inches. Why did they choose to leave less than a half of a cubic inch remnant, especially if originally its size was simply determined by subjective factors of human strength and convenience, rather than some conscious adherence to an occult geometry?

Well, the answer actually is an “occult geometry” and the relationship it discloses between the fundamental units of surface area and volume. But first it is helpful to understand that in the Winchester System the base-unit called a “pint” relates to the full “bushel” measure, in the same way that the “inch” measure relates to the “yard”. In this manner, twelve inches make a foot; three feet make a yard, and so on. In the Winchester system of dry measures two pints make a quart, four quarts make a gallon, two gallons make a peck, and four pecks make a bushel.

But, just how did they (yes, the illuminati) come up with this unit of measure if in fact it is derived from geometry’s fundamental units of surface area and volume? It turns out that their process was not only very clever but very simple as well. But before I explain what geometry they used to create this system of customary dry measures, let’s first see a few of the ways it relates to some of their other units of measure.

It starts with the Roman gallon of exactly one-eighth cubic foot (216 cu. in.). This gallon most certainly pre-dates the bushel’s sub-unit dry gallon (268.8025 cu. in.). Its possible the gallon measure we most commonly use today in America (231 cu. in.), and in the past throughout the British Empire, came into existence at about the same time as the dry gallon. This might help explain why these three different gallon measures of volume quantities are related when they shouldn’t be . . . according to “history”. Of course, one wouldn’t be able to recognize these connections without first having some level of familiarity with the rest of the illuminati’s handiwork. America’s monetary system in 1792 is a good example for comparison.

Here is what I mean in simple mathematical expressions. First, compare the standard gallon measure with the dry gallon using the following ratios:

Stnd. gal / Dry gal = 231 cu.in. / 268.8025 cu.in. = .859367008… / 1.000

And

Wt. silver \$ / Wt. troy oz. = 412.5 grains  /  480 grains = .859375 / 1.000

And

.859375 / .859367008… = .999990700…

The equations above show that the American silver dollar coin’s weight in grains compared to the precious metals’ standard unit of measure, the troy ounce, is the same ratio or relative proportioning as that between the cubic inches in these two gallon measures. One way of looking at this is if we divided a single silver dollar coin into 231 equal parts, then a troy ounce of the same silver alloy will divide into 268.8025 such parts. The last equation above shows that the two different measurement systems are perfectly commensurate through better than five decimal places.

Earlier it was pointed out that it was in 1836 that the dry gallon was “officially” incorporated into American law. And it was in 1837 that Congress authorized the reduction in the gross weight of the dollar coin from 416 grains to the 412.5 grains (which it remained until the last coin was struck in 1935). Even though the new coins weighed slightly less, the original mandate specifying that each silver dollar contain 371.25 grains pure silver was maintained by adjusting the standard silver alloy.

Now history says nothing about legislation purposely relating these two gallons, or the gallons and the weight of the coin. But common sense would indicate a strong probability that these measures were relatedly conceived, given the timing of the legislation. But better than probability is confirmatory evidence found in America’s new “fractional” dollar (dimes, quarters, and halves) foisted on the unwitting American public in 1873. Twenty years earlier, in the 1853 Coinage Act, Congress authorized the intentional debasing (reducing the silver content) of the fractional silver coins. In 1873 the weight of these previously debased coins, now weighing 24.882… grams per dollar amount, was slightly increased to an even 25 grams. This was allegedly done to bring the U.S. coinage system more into line with their European counterparts and their “metric system”. But was this the only reason? Have a look at the following equations.

Roman gal / Dry gal = 216 cu.in. / 268.8025 cu.in. = .80356395… / 1.000

Wt. fractional \$ / Wt. troy oz. = 25 gms / 31.1047… gms = .8037686… / 1.000

.80356395… / .8037686… = .9997453

The above equations show that the Roman gallon relates to the Dry gallon in the same proportions as the weight of a fractional dollar and a troy ounce. In fact, a troy ounce is 1.244139… times the weight of 1.0 fractional dollar; and, the bushel itself measures 1.244456… times a base “unit” of 1.0 cubic foot. And it should be pointed out that between 1853 and 1873 one half-dollar; or, two quarters; or, five dimes weighed 12.44139…grams.

At the beginning of this chapter I said that the source of this system of dry measures was found in geometry and the relationship between “the unit” as surface area and “the unit” as volume. But to do this a “name” must be assigned to the unit in order to give it scale, or substance, or some other quality such as weight. Regarding their system of dry measures, the illuminati chose the “foot” as the computational basis for its division into what became the Winchester bushel. Here is how they contrived these measures.

The fundamental units of area and volume can be modeled by the same form: 1.0 unit of volume in the form of a cube. This cube has six square faces, with each measuring exactly 1.0 surface unit. The illuminati’s technicians took the square 1.0 surface unit and reformed it into the surface area of a sphere. And the cubical volume unit they also reformed into the shape of a perfect sphere.

Since the sphere is geometry’s most economical form for packaging any given unit of volume (least surface/most volume), the 1.0 surface unit sphere encloses the maximum amount of volume possible: .09403159… “cubic” unit. And for the same reason, the 1.0 volume unit in the form of a sphere is enclosed by the very minimum amount of surface area allowed by geometry: 4.8359758… “square” units. These are the exact quantities from which our dry pint measure was created. And the dry pint is the fundamental sub-unit of the Winchester bushel. Here is how they did it.

Using the above quantities, the illuminati created the pint-to-bushel system of measures by dividing the volume of the spherical surface unit (.094031…) by the quantity defining the surface of the spherical volume unit (4.8359…):

.094031… cubic foot / 4.8359… = .019444… cubic foot

and since

1.0 cubic foot = 1728 cubic inches

therefore

.019444… X 1728 cubic inches = 33.5995… cubic inches

and

One Dry Pint = 33.6003125 cubic inches

So, just how closely do the measures created by man conform to those derived from the simplest and most fundamental geometric proportions?

33.5995… cubic inches / 33.6003125 cubic inches = .99997722…

For generations the illuminati’s “technicians” knew the significance of a quantity of “7.0 units”. In the geometry of form it is co-equal to 1.0, and represents the form of Unity’s potential. Its influence manifests throughout transformational geometry. It is more than just of interest that I point out that 7.0 cubic feet equals 45 dry gallons. To be exact, 7.0 cubic feet equals 44.999581… dry gallons. But these are the same measures to a .999990700… degree of “fineness”.

Another measure of volume is the “cord”, and “cord foot”. It is still used today, most popularly as a measure of timber, or especially firewood. A cord measures 4 feet, by 4 feet, by 8 feet (128 cubic feet). There are 8 “cord feet” in one cord, so a cord foot measures 16 cubic feet. These were important measures in our recent past, especially when most of the population was involved with agriculture to some degree or another. Then, both the Winchester bushel and the cord were in far more use than today. These were used in conjunction with the avoirdupois ounce, which itself was decreed the legal unit of weight measure for merchants at about the same time that the cord and bushel became measures of the realm. So when we find that 7.000 cubic feet measures exactly .4375 cord foot; i.e., a .4375 portion of 16 cubic feet . . . , then WE know that the illuminous technicians knew of this relationship. How do we know this? Look:

7.000 cu.ft. = .4375 cord. ft. X 16

and

7000 grains = 437.5 grains X 16

Of course 7000 grains is 1.0 pound avoirdupois. This pound is just like your pound of hamburger in the supermarket. And just like every “pound” today (excluding troy) it consists of 16 ounces, with each ounce containing 437.5 grains. So we can see as plain as day, that the “cord” volume measure and the “pound” weight measure share in the exact same mathematical structuring. Only the names have been changed, and the powers of the different quantities.

On the backdrop of the above relationships we will now look once more at the dry pint measure:

7.000 cu. ft. / 360 = .0194444444… cu.ft. = 33.6 cu. in.

and

1.0 dry pint = 33.6003125 cu. in.

Again, the measures of man and the measures derived from pure geometry are the same to a .999990700… degree of perfection.

When I encountered the above relationships, I was reminded of 7’s role with 360 in forming what, in the Geometry of Form is called “the lowest common denominator of unity”. Without going into detail here, this quantity is 2520 and is the product of 7 times 360. In the equations immediately above, we saw how these two quantities divided to create the dry pint measure in cubic inches; and that 64 together creates 1.0 bushel. So by now when we see that 7.0 lineal inches times 360 equals 64 meters (yes, metric) to a fineness of .999875… we see once again man’s measures in sync with geometry’s.

Now, it has been obvious throughout this manuscript (The Geometry of Money) that the illuminati used the “geometry of form” as a template for a single system of weights and measures for the entire planet. Even more importantly, the “geometry of form” is literally Nature’s geometry, and actually reveals the process by which our universe (the only “universe”) came into existence from nothing. That is one of the reasons it is not taught, why it has been “occulted” and hidden from humanity for at least a thousand years or more.

Nature quanta-sizes its constructs in geometric units. Ultimately, when geometry is traced back to the Beginning, we find a specific “form” which gives rise to all of these quantities as it progresses through a series of transformations. This is the subject of another book in progress. But now, for purposes at hand, the following examples regarding this system of dry measures and its relationship to “natural” units should be noted here and for future reference:

One Dry Gallon of pure silver weighs 1485.95… troy ounces. Each Dry Quart of pure silver must therefore weigh 371.3952… troy ounces. The Coinage Act of 1792 specified there be precisely 371.25 grains of pure silver in every dollar coin; and that 1485 grains of pure silver be alloyed with 179 grains pure copper to formulate what this Act designates as “standard silver”. To geometry, all of these quantities are structural units derived from the same measuring rod. They are born from formal transformations of “the unit” and the relationships arising as a consequence. They manifest in nature, since ultimately, nature itself is a geometric construct subject to the rules of geometry.

The dry gallon is built from its sub-unit dry pint, which has been shown earlier in this chapter to have been derived from geometry’s fundamental units of surface area and volume. These were assigned a name; “1.0 square foot” and “1.0 cubic foot”. Now, let’s look at some of the quantitative properties of 1.0 cubic foot of pure silver.

For starters, a cubic foot of pure silver weighs 4,584,000.49 grains. The 371.25 grain pure silver content of America’s dollar coin is 90% of its 412.5 grain gross weight; 90% of 4,584,000.49 grains is 4,125,600 grains. There is also 297,043.24 grams in 1.0 cubic foot of pure silver. When it is divided into its 8.00 Roman gallon sub-units, each must weigh 37,130.4…grams. This means that if it is further sub-divided into 100 cubets, each cubet must weigh 371.304 grams. Of course, this leads to the inevitable conclusion that 1.0 cubic foot of pure silver renders into 800 cubets, each weighing 371.30… grams.

But the actual geometry producing the dry measures base unit, the dry pint, employs the 1.0 volume unit in its spherical form. Calculate the smallest cube within which this spherical unit of silver may be contained. The diameter of a 1.0 cubic foot sphere is 1.24070098… which is the edgelength of the smallest cube capable of embracing it. Convert this edgelength to inches and calculate the volume of the cube in inches. It is 3,300.236… cubic inches, and as pure silver weighs 1250 pounds (this is to a accuracy of 99.9%). This cube’s volume can also be expressed as 8.00 times 412.529612… cubic inches. And a cube of pure silver this size weighs 2300.1660… apothecaries’ ounces; or 2501.42403… avoirdupois ounces. An “even” 412.5 cubic inches weighs (an almost even) 2300.00097… apothecaries ounces; or, 2501.2444… avoirdupois ounces. And 1.2444 times 1.0 cubic foot equals 1.0 Winchester bushel measure.

There is one more sphere we should look at. It is the largest sphere within a cube having a volume of one cubic foot. Since the cube’s edge measures 1.0 foot so does the sphere’s diameter. This sphere’s volume is .523598…, or /6 cubic foot. If made of pure silver it has a “nominal” weight of 5000troy ounces, or 2,400,000 grains. These “nominal” weights correspond to the “actual” weights to a 99.99% approach to perfection! There is a principle at work, recognized in The Geometry of Form, and called “The Actual and the Ideal”. The last several paragraphs demonstrate clearly that this principle of geometry is present in nature’s compositions as well.