It is evident that Viking ships, amongst many others from the ancient Mediterranean, Continental European seaboard and Britain, sailed successfully to the Antipodean Isles of New Zealand at the very ends of the Earth in antiquity. If these early mariners could reach such a remote place, the most distant habitable country in the world from Europe, then every other part of the globe lay within their reach.

To the left is seen a belt buckle, retrieved from a Viking burial ship at Sutton Hoo in England. To New Zealanders and others of the South Pacific Islands, the face is very recognisable as "Tiki" or "Rongo". He is seen to be wearing the "high hat", so typically displayed on the statuettes or totems of the Pacific Islands, ranging from Hawaii to Tahiti to the Cook Islands. Although the elongated forehead or high hat design aspect is sometimes seen in New Zealand, "Tiki" or "Rongo" is generally depicted locally without his hat, as in the old photo to the right. Note how the Maori individual in the photo emulates the bulging eyes, protruding tongue and facial grimace of the totem figure and also holds a "mere" club (shaped like the Egyptian "SA" symbol hieroglyph, meaning "protection"). The origin of this cultural-religious expression is very ancient and, for both Scandinavia or the South Pacific totems, goes back to the dwarf god, Bes, of Egypt... who became Pan of Greece, Puck of Britain and Puge of Scandinavia. Maori oral tradition states that the arts of carving, facial tattooing and (haka) dance were taught to them by the earlier inhabitants of New Zealand, who they described as kiri puwhero (light complexion, reddish skinned) and uru-kehu (light coloured, golden tinged or reddish hair). For more information on the "world's-apart" relationship between "Bes" of Egypt and "Tiki"of the South Pacific or evidence of "Thor" in an ancient New Zealand totem and volcano, CLICK HERE.

By about 5000 BC and thereafter, the forebears of the European nations abandoned their increasingly arid homelands in Egypt and its environs and moved to the verdant new territories of Europe. In doing so, they brought their Weights, Measures and Volumes standards with them, as well as all of their astronomical and navigational sciences. These sciences they had encoded (by way of distance, area and angle numerical codes) into their early-epoch great edifices, like the many pyramids that they built in Egypt. It must be realised that the Egyptian pyramids of the Giza Plateau or those at Saqqara are far older than "officially" recognised. The measurement standards found encoded onto these "Bureau of Standards" edifices survived for further millennia within the European nations and were, over time, carried abroad to far-flung locations like New Zealand, by European explorers and settlers such as the Vikings.


The commonly known and preserved measurements of ancient Europe, despite their wide variety, are a part of a single and widely versatile integrated mathematical system, with traceable root origins and pedigrees extending back to Egypt and its former Caucasoid ethnicity peoples, who occupied Egypt and surrounding countries for many thousands of years. Skeletons, mummies, busts, etc., of the forebears to the Nordic Europeans, are still found there in profusion beneath the desert sands, attesting to their long occupation of the region.

Let us now look at the mathematical fingerprints of but one of the many European nations, the Swedish, and demonstrate how their oldest known Weights, Measures and Volumes standards have a direct pedigree to the Great Pyramid of Egypt or to its slightly smaller counterparts, the Khafre Pyramid, which was Egypt's Pyramid of the Moon, and Menkaure Pyramid.


It's very inportant to realise that the British Standard inch is not British at all, but has a very ancient pedigree back to the Eastern Mediterranean and beyond to yet more ancient Caucasian homelands. The so-called British Standard inch became the basis of many ancient "cubits" or "foot" measurements, ranging from Northern India to Egypt or wherever the forebears to the European nations settled and established long-term civilisations.


A Swedish "mil" (Sw. mile) was in the old days = 6000 "famn" (fathoms) = 18000 "aln" (ells) = 36000 "fot" (feet) = 10688 meters = 6.64 miles (Hans Högman).

Hans Hogman speaks of a length equating to 10,688 metres as representing one of the many increments called "the mile" in use in various parts of old Scandinavia. The, now, slightly drifted length identified would translate to 35,066 British Standard feet.

By comparative analysis to a wide range of other Swedish measurements, which would all have been in direct ratio or factorable, smaller expressions of the larger increment, it is evident that the original intended distance of this particular "Mil" or "Mile" was 35000 standard British feet. Three such "Mils" equated to 105000 feet or 20 Greek miles of 5250 feet each. Alternatively, three such "Mils" (105000 feet) equated to 10,000 Hebrew Reeds of 10.5 feet each or 100,000 Greek feet of 12.6-inches each.

Note: The Great Pyramid was built to be 756 feet in length, which is 72 Hebrew Reeds or 720 Greek feet. This length also equates to 360 Assyrian cubits of 25.2-inches each.

Hogman states that the Swedish "Mil" was divided up into 6000 Famn, which would mean that a Famn was 5.83333 feet or 70-inches. This increment is related to the well known Roman "Pace" increment of 58.33333-inches (58 & 1/3rd). Therefore, 1.2 Roman Paces would equate to 1 Swedish Famn. At the same time there would be 7200 Roman Paces in a Swedish "Mil" or 36000 Roman feet of 11.66666-inches each. There would be 777.6 Roman feet in the 756 feet length of the Great Pyramid or 5400 Roman feet in a Greek Mile of 5250 feet.

Note: There were two readings of the Roman foot, depending on the calculation requirements. For certain calculations it was read as 11.664-inches, making a Pace, under that second system, equate to 58.32-inches. This second reading was used for lunar cycle calculations, as well as some volume measures

The Roman foot was found to be 11.664 inches by John Greaves, professor of geometry, who in 1639 went to Rome specifically to ascertain the length of an ancient Roman foot. Greaves located a monument of Roman architect, Stalius Asper and measured bas relief instruments used by him in the first century A. D. Greaves concluded, after careful investigation, that the Roman foot, 'contained 1944 such parts as the English foot contains 2000'. This means a Roman foot of 11.664 inches (11 & 83/125ths).

The Swedish "Aln" was 1.94444 feet or 23.3333-inches (23 & 1/3rd). This is very consistent with the report concerning the Rydaholmsalm:

'The first unit of length to all parts of Sweden was the Rydaholmsalm (the length of a prototype kept in the church of Rydaholm, Smaland, now lost. It is thought to have been 0.593 m.'

At exactly .593 m., the Rydaholmsalm would translate to 1.945 feet or 23.34-inches. We can safely call this a very slightly "drifted" increment that was known elsewhere as the "Aln", which was related to both the Swedish Famn and the Roman Pace. The degree of error at the estimated .593 m is so negligible that the 1.944444 feet (23 & 1/3rd inches) proves to be the intended value of the ancient measurement.

Hogman further states:

'The "mil" was divided into 4 "fjärdingsväg" (4 quarters) of 2672 meters or 4500 "aln" (ells).'

From this we can safely assign an original value of 8750 feet to a "fjärdingsväg" or 1.66666 (1 & 2/3rds) Greek miles of 5250 feet each.

'1 "steg" = 1/2 "famn" (fathom).'

A "Steg" was, therefore, 35-inches.

'1 " famn" = 6 "fot" (Sw. feet) = 3 "aln" (Sw. ells).'

From the above statement by Hogman, we get further verification that the ancient Swedish "foot" was 11.66666 (11 & 2/3rds) inches and was exactly the same length as the Roman foot.

It is significant that one ancient means for easily remembering the equatorial size of the Earth was to apply the formula:

12 x 12 x 12 x 12 x 1.2 = 24883.2-miles. If navigating by the Swedish-Roman-Greek method, those miles would be 5250 feet each (6&7 number family). If navigating by the British method, those miles would be 5280 feet each (11 number family). The length of the Great Pyramid is 756 British feet or 777.6 Swedish feet. If the Earth is considered, by the above formula, to be 24883.2-miles in equatorial circumference, then 777.6-miles would represent 1/32nd segment. Therefore, one of the inbuilt codes of the Great Pyramid, extractable by use of a Swedish foot of 11.6666-inches (representing miles), would be to consider that 1 circumnavigation of the Pyramid mnemonically identified the distance value for 1/8th of the equatorial circumference of the Earth or 45-degrees of arc.

Hogman states:

'In the beginning 1 "kabellängd" [cable length] = 100 "famn".'

This means that the original "kabellängd" was 58.33333 feet or 60 Roman & Swedish feet. This also equates to 12 Roman Paces.

One of the concepts of ancient metrology, which survived into mediaeval times, was that 75 Roman miles represented 1-degree of arc for the world. The Scandinavian system was, undoubtedly, adopted by the Romans and has its root origins much further back in remote antiquity. Under this system, the equatorial size of the Earth was considered to be, for navigational purposes, 25000-Greek miles in circumference or 131250000 British Standard feet of 12-inches. This distance would also be 135000000 Swedish-Roman feet of 11.6666 (11 & 2/3rds) inches.

Under this system, 1-degree of arc (1/360th of the equatorial circumference) was 375000 Swedish-Roman feet. Therefore, according to the oral tradition handed down from mediaeval times, the Roman mile should have been 5000 Roman feet or 1000 Roman Paces of 58.3333-inches. This equated to 3000 Swedish Alns of 19.4444-inches each.
Under this system 1-minute of arc (1/60th of a degree) was 6250 Swedish-Roman feet. This equated to 375 Swedish Alns.
Under this system, 1-second of arc (1/60th of 1-minute of arc) was 62.5 Swedish Aln's.

Hogman states:

1 "fot" = 2 "kvarter" = 12 "tum" (verktum) = 1/2 "aln"

From this we see yet further divisions to the Swedish foot and aln. There was also the "tvärhand", which was 4 "tum".It would appear that 1/16th part of the Swedish foot was the "fingerbredd".

As stated, both the Swedish and the Romans appear to have used two separate, but almost identical, "foot" rules. One "occasional use" calibration of the foot, set to 11.664-inches (1458/125ths) for lunar cycle tracking, was marginally shorter than the navigational foot rule of 11.6666-inches. The difference in the two rules would have been visually difficult to detect.


When sailing, one is at the mercy of the wind to a large degree and must tack at angles to the breeze to make forward progress. The preferred course is not always directly or easily achievable and tacking, first one way then another at an angle to the wind, is often the only way to stay on course. It was the ominous responsibility of the navigators to always be aware of the ship's position and distance from both point of departure or destination. The navigators had to be constantly aware of boat speed through the water, as well as heading. Distances covered could be measured under several systems, such as the "11" family of numbers (leagues, miles, furlongs, etc.) or other increments of length within a "6&7" family of special navigational numbers. The Swedish, Romans and Greeks seemed to prefer the "6&7" family of numbers for "linear distances" covered or legs completed during a voyage.

The navigators would maintain a vigilant watch on boat speed and could, from time to time, feed out a knotted rope over the stern and count the time lapse between knots crossing the barrier aft. There would be tremendous co-operation between the helmsman and the navigator, who would work together to maintain the same course heading until a sought after distance had been travelled. The goal of the ever watchful navigator would be to complete segments of a voyage according to whole number distances for each leg in, say, Greek miles at known degree angles around from north. If full attention, related to boat speed and heading, as well as angle of tack and distance travelled were maintained, then relatively accurate "positional plotting" was mathematically achievable. The navigator would have a very good idea where the boat sat in the vastness of the ocean at all times.

Once a "straight-line" leg was completed, the navigator would rule a line on the chart and the end of the scaled line would represent the position where the boat now sat in the ocean. Each time a long or short leg was completed, this had to be done and a mathematical means had to exist to determine anew the degree angle back to the point of departure or onward to the port of destination

If the Viking navigators wished to achieve a "Mil" of travel (35000 British feet or 36000 Swedish feet) for each leg before changing to a new tack angle, then the result, in turning this linear distance leg (diameter) into a circle (using PI @ 22/7 or 3.142857143) would be: 35000 feet X PI = 110000 feet.

So, the navigator could now rule a much scaled down line representing 35000 feet of travel onto the plotting chart, then, using half the length of the line (radius), draw a circle at the end of the line at the position where the boat was estimated to be situated in the ocean. The circle created accurately depicted a circumference of 110000 British feet, in which 1/360th part (1-degree of arc) was 305.55555 feet (305 & 5/9ths feet) or 55.5555 British fathoms of 5.5 feet each.

Note: the original British fathom was 5.5 feet and not 6 feet).

Another metrologist (reseacher of measurement standards), Gary Anderson, who devoted 10-years to researching Viking measurements, states:

'Fot*: In doing the research for this I found that there were actually two measurements for the Fot. One was very early and ran at exactly 11 inches, the other was almost 1.03 feet.'

So, with this in mind, the navigator, using a scaled rule representing "11" inches would know that 333.3333 such increments would represent 1-degree of arc on the plotting chart for the circumference of a circle with a diameter of 1 Mil (35000 British feet). By this means, accurate angle fixing back to the point of departure or onward to the destination could always be known, despite many zigzag course changes during the voyage.

Alternatively, the legs of the voyage could be accomplished in multiples of "Greek miles" of 5250 feet, if desired. A circle based upon a diameter of 1 Greek mile would achieve a circumference of 16500 feet (1 ancient British league...3.125-British standard miles of 5280 feet each). In this circle, 1-degree of arc would equate to 550-inches (50 X 11 inches) or 8 & 1/3rd British fathoms per degree of arc. The so-called Greek mile was fully an increment within the ancient Swedish navigational system.

From the above, we can see that the Vikings, along with many other cousin nations, were in full possession of sophisticated manual methods to do accurate positional plotting at sea. They used one set of measurement increments, based upon a 6&7 family of numbers, for all of their linear distance calculations. After the PI formula was used to turn a leg of travel from a diameter into a circle, the circumference value achieved was easily divisible by 360-degrees and accurate angle determinations could then be made for positional plotting. The measurements known to have been used in ancient Scandinavia show that they knew the equatorial circumference of the Earth and could grid reference it for accurate navigation and safe traversal using highly factorable numbers.

This basic rule applies: When travelling by the Swedish-Greek-Roman 6&7 number family, the circle derived therefrom will be based upon the number "11". When travelling by the British "11" family of numbers (League @ 16500 feet, Mile @ 5280 feet, Furlong @ 660 feet, Chain @ 66 feet, Rod or Perch @ 16.5 feet, Fathom @ 5.5 feet, Link @ 7.92-inches), the circle derived therefrom will be perfectly sexagesimal and divisible by 360-degrees. These otherwise strange numbers, like 5250 feet for a Greek mile or 5280 feet for an English mile, were specifically created because of PI, so that a linear distance would convert to a very meaningful circumference that broke down easily into 360-degree divisions.


Few things can cause more public discontent than "short measures" at the market place. When the buying public made a purchase of a "fjärding" of grain, they expected a full measure for their money. The "fjärding" had to be the correct cubic inch capacity. Right up until the middle of the 19th century one could face the death penalty in Sweden for falsifying weights and measures. It is probably for this reason that there were traditions like "the baker's dozen", which meant that when one purchased 12 bread rolls, the baker would include an extra roll to bring the tally up to 13. By such means there could be no argument that one had been "short changed" or "ripped off" by the deceitful merchant.

Like all of the other European cousin nations, the Swedish had a "volume" system with root origins that extended all the way back to the former homeland of Egypt. Every volume had to encode scientific information in the numerical value of its cubic capacity. These special inbuilt numbers, to do with navigation or astronomy, had to be remembered at all cost, as the concept of civilisation and abundant society depended on them. If everybody was using the special numbers every day in a length, volume or area calculation, based upon the selfsame inch, or in weights based upon counts of healthy wheat grains, then the sciences would never be forgotten. The old adage applies: "You either use it or lose it".

Hogman speaks of a Tunna (Barrel):

1 "tunna" = 2 "spann" = 8 "fjärding" = 32 "kappar" = 56 "kannor" (pitchers) = 146.6 liters levelled measure (struket mått).

Hogman also says that there was a slightly larger capacity Tunna.

'...or 164.9 liters full (good) measure (fast mått or med råge).'

So, there was a larger and a smaller Tunna, one at 164.9 litres capacity and another at 146.6 litres capacity. Let's now convert these ancient volumes back to cubic inches in an effort to identify the inbuilt, original codes obscured by metrification.

The larger Tunna, said to have been 164.9 litres would translate to 10062 cubic inches.
The smaller Tunna, said to have been 146.6 litres would translate to 8945.5 cubic inches.

These values are very close to highly significant numbers from the ancient parcel of scientific codes. It is quite obvious that the latter era "Tunna" values had drifted slightly off the accurate capacity numbers that the ancient forebears put in place. This can be demonstrated in a very practical sense in consideration of the smaller divisions or breakdown capacities associated with the Tunna.

It must be realised that the original architects of these cubic inch or cubic foot volume systems used highly factorable numbers. A smaller capacity was an exact division of a larger one. Moreover, the capacity system of one nation would be in an exact and easily calculable ratio to that of a trading cousin nation. Everything could be calculated out and transactions done with exactitude by applying simple ratios or fractions. By looking at the smaller divisions of the Swedish Tunna, we can easily see what the original volumes were supposed to be, despite small "drift" that has occurred to the standard within the last 2000 years.

Hogman states that the capacities of the smaller divisions were:

1 "fjärding" = 18.32 liters (117.9 cubic inches), 1 "kappe" = 4.58 liters (279.47 cubic inches), 1 "kanna" (pitcher) = 2.617 liters (159.69 cubic inches).

Hogman further states:

"Skäppa" is a very old measurement that was abandoned in Sweden in 1735. The size of a "skäppa" could be different in different parts of Sweden. In the province of Småland a "skäppa" was 1/6 of a "tunna" (barrel) but in the province of Bohuslän it was only 1/4 of a "tunna" (36.6 liters) and in the province of Västergötland it was 1/5 of a "tunna".

From this we can see that the Bohuslän "Skäppa" was approximately 36.6 litres (2233.3 cubic inches).

From this abundant accumulation of evidence, we are able to make the very minor adjustments necessary to restore the intended values put in place by the original architects of the system. We know full well that they would never have used such utterly meaningless and arbitrary values as 279.47 cubic inches for a "kappe", when the highly factorable and full number, 280 cubic inches was available. Likewise, the value of the "kanna" was not chosen by the Swedish forbears to be the non-factorable and non-divisible value of 159.69 cubic inches, but was set at the highly usable value of 160 cubic inches, etc.

So, let's now restore the original system:

Swedish dry volumes (Heavy)Swedish wet volumes (Heavy)
Large Tunna = 10080 cubic inches.Fat (Barrel) = 9600 cubic inches.
Large Fjärding = 1260 cubic inches.Tunna = 7680 cubic inches.
Large Kappe = 315 cubic inches.Ankare = 2400 cubic inches.*
Large Kanna = 180 cubic inches.Fjärding = 1920 cubic inches.
Large Skäppa (Bohuslän) = 2520 cubic inches.Kannor = 160 cubic inches.
Large Skäppa (Västergötland) = 2016 cubic inches. 
Large Skäppa (Småland) = 168 cubic inches. 


Swedish dry volumes (Light)Swedish wet volumes (Light)
Small Tunna = 8960 cubic inches.Fjärding = 1890 cubic inches.
Fjärding = 1120 cubic inches.Kanna =157.5 cubic inches.
Kappe = 280 cubic inches.Stop = 78.75 cubic inches.
Kanna = 160 cubic inches.Kvarter = 19.6875 cubic inches. (19 & 11/16ths).
Skäppa (Bohuslän) = 2240 cubic inches.Jungfru = 4.921875 cubic inches. (4 & 59/64ths).
Skäppa (Västergötland) = 1792 cubic inches. 
Skäppa (Småland) = 149.3333 cubic inches. 

Note: the Heavy Skäppa values are assumed to exist, based upon the Heavy Tunna value. This is consistent with the way many of the very ancient Mediterranean systems were structured, offering two differing capacities called "Heavy" & "Light" or "Single" & "Double" within a standard. The Skäppa was considered to be a Swedish "Bushel" and, for the most-part, hovered quite close to the British Bushel, which was, anciently, 2160 cubic inches. The astronomical coding placed within the British Bushel related to the duration of the Precession of the Equinoxes (25920-years) and how the sun spends 2160-years in each of the 12 houses of the zodiac during the precessional cycle.

*Footnote: Hogman tells us that the "Ankare" was for volumes of 'Liquor, Wine & Beer'.

By the description Hans Högman gives of what we could term as the "light" capacity wet volumes, the values given make a great deal of sense, despite their visual complexity. The value of 1890 cubic inches was for "navigation", as well as for very accurate calendar calculation determinations, especially lunar, and the length of the Great Pyramid is 189 feet X 4 (756 feet). The smaller division value of 19.6875 (19 & 11/16ths) was much used by the Egyptians, Greeks and Romans and their Beqa weight Standard for gold was set at 196.875 grains. Further verification and comparitive analysis will be necessary to fully determine if that family of navigational and lunar numbers was being used within the Swedish wet volumes standard, but it is certainly looking very encouraging so far.

Note: the "Stop" volume for the Wet "Light" series appears to be 78.75 cubic inches. The Viking longship found at Oseberg, Norway (circa 1904) had a length of 78.75 Swedish feet of 11.666666-inches (11 & 2/3rds). Half the base length of the Great Pyramid (378 feet) is in a ratio of .7875 to 1 to the height (based upon where lines running up the faces would converge at a single point above the flat floor altar at the top of the Pyramid & coded to be at 480 feet of vertical height). The width of the Oseberg longship was 17.5 Swedish feet, for a length to width ratio of 4.5 to 1.


To understand the significance of the numbers encoded into these cubic capacities, one must return to analysing the dimensions of the Great Pyramid of Egypt, situated in the former homeland of Nordic Europeans, but long ago abandoned to the encroachment of the desert sands.

The Great Pyramid was designed to be 756 feet per side length or 3024 feet for one circumnavigation. Under what, much later, became the Swedish-Greek-Roman method of world-traversing navigation, two circuits of the Great Pyramid were 6048 feet, which represented 1-minute of arc on the Earth's circumference. The full equatorial circumference under this method was 24883.2 "Greek" miles of 5250 feet each or 130636800 British standard feet. This meant that 1-degree of arc (1/360th of the Earth's circumference) was 362880 feet (note that one full circuit of the Great Pyramid, which means 756 feet x 4 or 3024 feet = 36288 inches). As stated, 1-minute of arc (1/60th of a degree) was 6048 feet and 1-second of arc (1/60th of 1-minute) was 100.8 feet. There would be 7.5 occurrences of 100.8 feet in one side length of the Great Pyramid.

Note: The Sarsen Circle at Stonehenge (made of upright Sarsen stones capped with lintels) was made slightly eliptical to achieve two sets of crossing codes. In one cross measurement the Sarsen Circle is 100.8 feet, or 1-second of arc diameter for the equatorial circumference of the world.

The value of 10080 cubic inches in the Swedish Heavy Tunna is a very important navigational value, alluding to the number used to describe 1-second of equatorial arc. It was placed into the standard for mnemonic recall of the size of the Earth. In each of the lesser divisions of the Large Tunna there are recurring progressions of numbers that can be exploited for world navigation.

There is insufficient room in this article to demonstrate all that these volume codes could do or mean and researchers are encouraged to refer to Weights, Measures and Volumes of the Ancient Mediterranean, within this website. To see that fuller article CLICK HERE.

A small glimpse of how far one could go in extracting meaningful codes is seen in the conversion of "1-second of arc" (100.8 British standard feet) into ancient Swedish units based upon their navigational foot of 11.6666-inches. Therefore, 100.8 feet x 12 = 1209.6 inches ÷ 11.6666 = 103.68.
Consider this: The ancient value for the equatorial size of the Earth was 24883.2-miles. There are 24 hours in a day so the rate of speed at which the Earth spins is 24883.2 ÷ 24 = 1036.8 Miles per hour.
Consider also: One half of 103.68 is 51.84. The slope angle of the Great Pyramid's 4 faces is 51.84-degrees. The azimuth angle from the altar of the huge Octagon earthworks complex of Newark, Ohio, dissecting the entire site in half and extending through the avenue out the end gate of the Octagon, is 51.84-degrees. The Precession of the Equinoxes endures for 25920-years, which is 51.84 x 500. When one travels 1 British league of 16500 feet (3.125-miles), it converts to a sexagesimal navigational circle of 51840 feet (divisible by 360-degrees).
Consider also: The "Stirling Jug" of Scotland, dating to 1457 and possibly much earlier, had a capacity very close to 103.68 cubic inches, which was the same as the ancient Hebrew liquid volume called the Jerusalem Cab (predating the Babylonian conquest), etc., etc.

The smaller Tunna is 1.125 to 1 less in size to the large Tunna, so it's a perfectly ratioed down expression of the bigger one.


As stated earlier, up until the middle of the 19th century, one could face the death penalty in Sweden for falsifying weights and measures or conspiring to deliberately defraud the buying public. This meant that merchants in the market place had to have perfect capacity vessels, such that anyone purchasing a "Tunna" of grain received exactly what they had paid for. Market place inspectors periodically checked the accuracy of the merchant's measuring tubs. So, how did the ancient Swedes produce round barrels or tubs that they knew, with certainty, were of perfect, internal cubic inch capacity?

The answer to that question lies in the fact that the ancient people of Scandinavia had yet another measurement rule of 1.030 British Standard feet, which functioned specifically for creating all of the various volume vessels or tubs. Gary Anderson, who researched Viking measurements for ten years, concluded that there was a very old "Fot" (foot) that would equate very closely to .314 metres. This would translate to 1.03018 feet.

The manner in which the ancient scientists configured these highly specialised rules for constructing round volume vessels, was to base them on the PHI ratio of 1.6180339 to 1. The same ratio exists between the area covered by the base of the Great Pyramid in comparison to the area of its 4 side faces, including a symbolic capstone on top.

If one uses simple trigonometry to work out the side length of the full pyramid, including the theoretical, non-existent capstone, the length to the centre apex would be (Adj. ÷ 51.84 Cos.) = 611.7894615 feet.
Alternatively, if one used a PHI method of Adj. (378 feet) X PHI (1.6180339) = 611.6168142 feet.
It will be observed that the calculated PHI length is only about 2 inches less than the length achieved by straight trigonometry. The ancient astronomer/ mathematicians were coding a PHI related angle for the Great Pyramid simultaneously to the standard angle of 51.84-degrees. The whole edifice was designed to clearly code PHI relationships. For example:

Let's consider the Great Pyramid on the basis of PHI and the ratio relationship (in pyramid acres) between the 4 faces, compared to the ground area that the Great Pyramid covers.
The surface area of each face of the theoretical full pyramid, complete with a (symbolic) pointed capstone, = 611.6168142 feet of side length X 378 feet (1/2 the base length) = 231191.11558 square feet.

Because there are 4 faces, their combined square footage amounts to 924764.6231 square feet. This translates to 32.10988275 pyramid acres of 28800 square feet each.
The base area measured 756 feet X 756 feet or 571536 square feet, which equated to 19.845 pyramid acres of 28800 sq. ft each. A perfect PHI relationship exists between this (symbolic capstone included) total side acreage and that of the base area that the Great Pyramid covers: 32.10988275 ÷ 19.845 = 1.6180339 (PHI).

Because the Great Pyramid was a static "Bureau of Standards" for the Caucasoid family of scattered nations and civilisations, it was absolutely essential that it strongly encode the PHI ratio, as this was central to fabricating very accurate, circular"volume vessels" or tubs with ease. Evidence shows that all of the most ancient volume vessels were made by this simple method. The use of the PHI formula persisted through the epoch of the Druids until the dawn of the "Dark Ages", spawned by the coming of Roman Christianity and its brutal introduction of backwards, dogmatic religion. Prior to that time, all volume vessels had to contain profound codes in (1) the square inch area of the base, (2) internal side height and (3) cubic inch volume, all of which related to astronomical cycles or world navigation.


To make perfect capacity, round volume vessels for the Swedish Tunna of 10080 cubic inches the formula was:

10-inches ÷ 1.6180339 (PHI) = 6.18034-inches (this increment became the standard length for making all of the circular market place volume tubs, of widely varying capacity, for all of the cousin European nations.

The width of the Bush Barrow Lozenge of Southern England was very close to 6.18034-inches (the lozenge has suffered some edge damage, slightly obscuring the original codes) and two such widths equated very visually close to 12.36068-inches or 1.0300566 feet, seemingly the same as a Swedish long "Fot". A primary purpose of the Bush Barrow Lozenge appears to have been for "market-place" inspectors to check the base width of "Bushel" barrels and tubs used by ancient merchants of the Neolithic Age. The very slightly "drifted" dimensions, for building a Bushel tub, are described in the old "English Winchester Standard". The base floor of the British Bushel was 270 square inches, with walls rising above the base floor a total of 8-inches, for a cubic capacity of 2160 cubic inches.

The increment of 6.18034 X 2 = 12.36068-inches. This value equates to 1.03005666 feet and is the measurement identified by researcher Gary Anderson as the largest "Fot" utilised by the Vikings.

In the following I will show numbers set at decimal point refinement and tolerances beyond what was visually or manually achievable by humans, but do so only to demonstrate how perfect the ancient mathematical method was.

To make the Tunna tub base, take a large thin slab of flat smooth timber or tightly edge-splice several planks together to form a single piece of sufficient size. Next take the 1.0300566 foot rule and mark double that length (2.0601132 feet) onto the wooden base. Now take a compass and create a circle of 2.0601132 feet diameter. Because you have used a rule derived directly from the PHI formula, your base is exactly 480 square inches of surface area. Your formula for determining the square inch area is PI x the radius squared, memorised by every schoolchild in the formative years of their education. So, the diameter of 2.0601132 feet ÷ 2 = 1.0300566 feet = 12.3606792-inches. This value "squared" = 152.7863903 x PI (3.14159) = 480 square inches of base.

The 480 number is a much used coded value of antiquity and all aspects of your tub must contain recognisable codes in the base surface area, internal side height and cubic capacity to be contained. Because you need to achieve a cubic capacity of 10800 cubic inches for this Swedish Tunna vessel, the internal height of the tub, from the top surface of the base to the brim of the side wall is 21-inches. This value (21-inches...sometimes called a Celtic Royal Cubit) is found in the base length of the Great Pyramid, which is 432 X 21-inches in length per side or 1728 X 21-inches for all four sides. Note: A cubic foot (12 x 12 x 12) is 1728 cubic inches.

It's as easy as that to make all of the old Swedish volume vessels listed and have them achieve a perfect capacity. You have the option to use 1, 2, 3 or more of the 6.18034-inch PHI-derived increments in the base. A tub can be more squat than tall or vis-versa. A perfect capacity is always easy to create by this simple ancient method, which was used in the production of, seemingly, all the tub-type standard volume vessels of the Caucasian (European) civilisations in antiquity.


The Scandinavian mariners are known to have used the Sun Shadow board of 32 calibrations for navigation and are theorised to have used a Sun Crystal for determining the sun's rise and set positions on cloudy days. Other than that not much has survived to tell us how they did "dead reakoning" or "positional plotting" to stay abreast of their location in the open sea. A very good clue, however, to the kinds of devices they would have used, is found in the Bush Barrow Lozenge or Clandon Barrow Lozenge artefacts of Southern England.

The Bush Barrow Lozenge and associated artefacts located in Southern England, very close to Stonehenge. The intricate pattern incising is far more than decorative and with a set of callipers and a precise rule, a wide variety of codes can be extracted from the main lozenge.

There were once, undoubtedly, a wide variety of "Lozenge" memory devices, used for a range of functions including navigation at sea. For the Viking navigator, remembering the coded dimensions and geometry of the Great Pyramid and that of the Khafre Pyramid, would have been sufficient. If those encoded principles were committed to memory and the lozenge mnemonic devices were fabricated as precisely "scaled" rules in their side lengths or other internal reducing diamond patterns, then accurate positional plotting at sea was very achievable to the experienced navigator.

Consider the following:


The Red segment accentuated in this image from a book on "Positional Astronomy" demonstrates exactly what the Great Pyramid triangle was supposed to encode. The Great Pyramid triangle taught spherical geometric and trigonometric principles for safe navigation, but also contained mathematically extractable information related to the EXACT equatorial circumference of the Earth. The following is what early pre-Christian European navigators had to commit to memory and what they handed on generation after generation to their progeny, until the Roman Christian Church finally destroyed their old scientific knowledge:

  1. In the coded navigational triangle of the Great Pyramid the "Adjacent" (half the base length) was 378 feet and this distance was 1/16th of 1-minute of arc under the Swedish-Greek-Roman method of reading the Earth's equatorial circumference.

  2. The Great Pyramid triangle, however, had to demonstrate to the student of navigation the ratio that existed between the earth's radius and its outer curved face. This was, quite obviously, taught (in view of the Great Pyramid's triangular design configuration, coupled with its scaled geodetic attributes) by using a quarter segment of the Earth's circumference, as shown in the red segment in the picture. The horizontal line X to C represents the radius of the Earth, from the equator to the centre of the Earth. On the Great Pyramid triangle this world dimensional radius was represented by the vertical height (Opposite), coded to be 480 feet. If we consider the Earth's diameter to be 7920-miles, then its radius is 3960-miles. The reduced sum of 480-miles would, therefore be in a scale of 1 to 8.25 against the true radius.

  3. The 480 feet Opposite, however, had to be in a ratio of .7854 to 1 to the distance measurement of the face (Hypotenuse) of the Great Pyramid triangle. The PI ratio for converting a circle's diameter to a circumference is 1 to 3.1416, thus the .7854 to 1 value is 1/4th of PI. In the above picture the curve red line represents 1/4th part of the sphere or 1/4th PI.

  4. To achieve a distance on the Great Pyramid's Hypotenuse or face that demonstrated a ratio to the Earth's radius, compared to its curved outer or spherical surface, either a PHI (1.6180339 to 1) increase on the Adjacent was used or else the Opposite (480 feet) ÷ 1/4th PI (.7854) was used. So, 378 feet X 1.6180339 = 611.6168142 feet (the length of the Great Pyramid's faces to where all diagonally upward lines resolve to a common apex point). If this Hypotenuse length is multiplied by .7854 (1/4th PI @ 3.1416) then the value achieved for the Opposite or vertical height is 480.3638459 feet or very close to 480 & 4/11th feet. By this means a wonderful tutorial is available to teach the ratio difference between the radius of a sphere (like the Earth) and quarter of it's circumference. It should be noted that trigonometry dictates that the apex height of the Great Pyramid would have sat between 480 and 481 feet of vertical height, in consideration of a half base length of 378 feet and a slope angle of 51.84-degrees. There was, of course, never a capstone on the pyramid only an flat floor altar on top, but the geometric principles of a "full" pyramid still applied.

  5. The "Official" equatorial diameter of the Earth is 7926-miles of 5280 feet each. The radius of the Earth is, therefore, 3963-miles and its official equatorial circumference is 24,900.26337-miles.

  6. If the above 480 & 4/11th feet were called (coded as) miles, then that would be in a ratio of 1 to 16.5 on the Earth's diameter or 1: 8.25 to its radius. Therefore: 480.36363636-miles X 16.5 = 7926 miles for a precise reading of the Earth's equatorial circumference of 24900-miles.

  7. For navigational convenience, this value was anciently set at the highly factorable number of 24883.2-miles (12x12x12x12x1.2), which, depending on navigational method preference, could be miles of 5280 feet ("11" family) or 5250 feet (6&7 family). In all, there were several navigational methods, exploitable within different number families and the Great Pyramid geodetic or navigational geometry was adaptable and applicable to them all.

  8. In this study, we have seen how the PHI formula was used by ancient Caucasoid civilisations in a very dynamic way and practical sense for creating highly accurate volume vessels for the marketplace or tutorials in spherical geometry.

  9. The exactness of the Great Pyramid equatorial coding suggests a former age of very advanced technology that was lost because of a cataclysmic event, in the aftermath of which only some very specialised knowledge survived. The parcel of numbers describing the duration of cycles and the equatorial dimensions of the Earth was used to re-establish and preserve "civilisation".

Other Great Pyramid attributes that would be committed to memory include:

The Bush Barrow Lozenge centre section, based upon an accurately scaled drawing of the lozenge done within the exacting confines of AutoCAD. Scaling was completed by reference to dimensions supplied by Mr. Paul Robinson, Curator of the Devizes Museum, Wiltshire, England.

The foregoing represents just some of the coding that the Scandinavian navigator (or any late era Druidic Priest teaching navigation, for that matter) would have committed to memory for the fluid reading of navigational devices. He had the option of using a range of cubits or feet measures, including Hebrew Reeds of 10.5 feet, Assyrian cubits of 25.2-inches, Celtic or Hebrew Royal Cubits of 21-inches, Celtic common cubits of 18-inches, older Hebrew and Babylonian feet of 17.5-inches or 16.8-inches, Greek feet of 12.6-inches, Swedish-Roman feet of 11.6666-inches, a measurement identified by Egyptian Priests to Herodotus of 11.34-inches (lunar...3 sides of the Great Pyramid = 2268 feet or 1134 feet x 2), etc., all of which would fit the literal dimensions of the Great Pyramid. The Egyptian Royal Cubit (one of 3 types), which is simply a memory device for remembering the equatorial circumference of the Earth, is 1/440th of the Great Pyramid's length or 20.61818182-inches (20 & 34/55ths).

Without trying to confuse the issue, there was another geodetic system built into the Great Pyramid, which meant extending it's length by 3-inches (756.25 feet per side) by this means the equatorial circumference could be read in miles of 5280 feet (under an "11" family of numbers...League, 16500 feet, Mile , 5280 feet, Furlong or Furrowlong, 660 feet, Chain, 66 feet, Rod or Perch, 16.5 feet, Fathom, 5.5 feet, Link, 7.92-inches). This second method was preserved in Britain and Germany, but the existence of an "11"-inch rule amongst the Viking measurements attests to the fact that this navigational system was also used, at times, in Scandinavia.

This researcher apologises for the complexity of the presentation, but cautions any wannabe "Druids": This is what a Druid learnt, taught, maintained incorruptible, held sacred and passed to the ensuing generation. Getting yourself a nobbled staff and dressing up like a Druid, then watching the Solstice sunrise at Stonehenge while doing the "Hey derry derry down" two-step dance doesn't make a Druid... You have to serve the hard-slog apprenticeship and learn the cyclic and navigational maths!... unless you only aspire to be a "bard" or "inferior rhymer"... sorry to be the bearer of ill tidings.


Along with the main navigational triangle incorporating a scaled Adjacent that was .7875 the value of the Opposite and in a PHI relationship between the Adjacent and Hypotenuse, etc., there was yet another very important one for following the cycle of the moon.

Obviously, the moon's position every night is a very good indicator of ship's position, provided the navigator knows the cycle of the Moon on a daily basis during the lunar year or its larger duration cycle over 18.613 solar years (anciently set at 6804-days). All of the scientific information necessary is found on the Khafre Pyramid, Egypt's Pyramid of the Moon.

The way to find the exact intended dimensions of the Khafre Pyramid is to realise that it's 15/16ths the base length of the Great Pyramid. Therefore: 756 ÷ 16 = 47.25 feet x 15 = 708.75 feet. If one dissects the Pyramid in half from the centre base to the apex, then a 3,4,5 triangle is the result. Half the base length is therefore 354.375 feet and it just so happens that there are 354.375-days in a lunar year. The dimensions are Adjacent, 354.375 feet (3 x 118.125), Opposite, 472.5 feet (118.125 x 4) and Hypotenuse, 590.625 feet. All of these numbers are dynamic lunar values. The inch count around the pyramid is 708.75 x 4 x 12 = 34020-inches (1/2 of 68040 inches). Note there are 6804-days in the ancient calibration describing the lunar nutation cycle. Also the Adjacent value of 354.375 (354 & 3/8ths days) ÷ 12 = 29.53125-days (29 & 17/32nds days or 708 & 3/4ths hours). The lunar month is 29.53125-days to a precision of less than a minute.

It can be readily seen that merely by memorising the dimensions of these two edifices and then working from precisely scaled rules, that all or most of the essential navigational mathematics are known. Moreover, having scaled memory devices like the Bush Barrow Lozenge on hand would keep the special navigational knowledge at the forefront of memory. Added to that, the boat itself would be coded according to length and breadth with navigational measurements, so that a forgotten principle could be recalled by measurements on board. This would include the volumes contained within the food storage tubs and vessels, the dimensions of sailor's sea chests that they sat upon when rowing, the length of oars, the height of the dragon head prow, etc., etc. Rest assured that no opportunity to build codes into internal positions of the boat would be missed.

Added to the above, if a boat was swamped and wrecked, but the navigator and others survived, sufficient to build a raft or patched up boat on which to limp home, all of the navigational aids could be restored if the navigator retained a rule or even a belt buckle that was a true inch wide. The fact of the matter is that the ancient navigational methods are so sophisticated that, with the aid of an abacus, an adept, well trained, ever alert and clever navigator could work out Longitude with relatively good accuracy and Latitude with little else but a shadow pole.

Although it has been stated by several authors that nothing has survived to indicate Viking navigational knowledge and methods, a huge amount has, in fact, survived. The researchers, unfortunately, have been looking in the wrong places. They should have delved deeply into the most ancient "Weights, Measures & Volumes" used and preserved by the Scandinavians to find the navigational mathematics.

Swedish, Danish and Norwegian researchers are encouraged to experiment with the numbers and simple mathematical methods identified herein. After all, this is your long-term heritage, based upon your own ancient measurements. Only a very few of your oldest standards have been touched upon here, but rest assured that ALL weights, measures and volumes, originally configured for use in each of the ancient Provinces, would have been from the same wellspring of coded numbers.

As time permits, many more of the ancient Swedish standards can be identified, then categorised as to function and number family. The same processes identified herein will apply to all of the ancient German Weights, Measures and Volumes, as well as within the oldest standards used amidst any long-established European nations.

A Celtic Torque, taken from the grave of the Princess of Vix, (circa 5-600 BC). It weighs 480 grams, which converts fluidly to 16.875 ounces (16 & 7/8ths). Its carefully fabricated and coded weight is, therefore, in direct ratio to both the Greek Commercial Talent or Tridrachm (Beqa) gold standard Talent and it represents 1/80th of the Talent weight in both standards. The Torque depicts the rising and setting orb of either the Sun or Moon and shows a "Greek Pegasus" flying horse ascending upwards on the orb to the East (right) and downwards on the orb to the West (left). In terms of the grain weights inherent within the artefact or Greek Commercial & Tridrachm standards, the numbers produced are lunar and 16.875-days (504-hours) would be 1/21st-part of the lunar year of 354.375-days duration.

We will soon analyse the ancient Swedish "Weights" system, based upon "grains". A cursory assessment shows it to be using the same mathematical progression as the Hebrew "Desert Heavy Weight" standard, where the Talent, Mina and Shekel are in direct proportion to the ancient Swedish "Skeppspund". The internal coding of these related (ancient Hebrew & Swedish) systems of weights refers directly and dynamically to the lunar cycle and navigation.

Remember, no pre-Christian weights, measures and volumes standards used by the European nations were arbitrary and meaningless and all were in perfect ratio, either within the provinces of the same nation or to the standards of other cousin nations. The perfect ratios that existed between provincial or national standards allowed everyone to trade in the same market places around the Mediterranean or Atlantic and easily convert quantities mathematically. All original standards, put in place then maintained by overseer scientist-astronomers like the Druids or their forebears, always contained profound scientific information, very essential to continued abundant living and optimised society. That scientific information came from a solitary parcel of highly specialised numbers, handed down from remotest antiquity and it is still found in the geometry of standing stone circles or via the dimensions and angles found upon the most ancient edifices of the Mediterranean and Europe.

The sophisticated astronomical and navigational sciences embraced by your Swedish-Norwegian-Danish forebears allowed them to sail, at will, to any place on the globe where they chose to go...even unto the very ends of the Earth.

Martin Doutré, October 2006. ©

To be continued.