Journal of Geomancy vol. 4 no. 2, January 1980
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Reprinted from “Melton Mowbray Times,” February 19th, 1909.
The question is often asked, why do the coal wagons on the London and North-Western railway have two white diamonds painted thereon? The diamond is a most ancient and scientific method of calculation, and was one of the great trade secrets so carefully preserved by an early guild. The method is based upon the well-known triangle having its three sides respectively 3, 4, 5 in length, and containing an area of 6, the angle at the junction of the 3 and the 4 sides forming an angle of 90 degrees, or the fourth part of a square. The unit, of course, may be inches, feet, cubits, miles or thousands of miles, and the method has been in use in Egypt for thousands of years to measure the land after the River Nile goes down. The system is illustrated by being cut on stone in Egypt, and it is also found in India. If four of these 3, 4, 5, angles be placed together with the 90 degree angles in the centre they form a diamond 6 by 8 having its four sides each 5, and its area equal to 24. In 1836 Mr. Joseph Locke, the engineer of the Grand Junction Railway decided to have a “Trade Mark” so that the Grand Junction trains could be distinguished from those of other companies. Mr. Locke at that time was a member of a guild or company of Freemasons by whom the ancient diamond of Egypt was preserved, and he decided to adopt it, and it was painted on the buffer-beams of each of the Grand Junction engines, also on the back of the tender tank and upon the vehicles. At Newton East and West Junctions in 1837, the signalmen had instructions to keep a sharp look-out for the “Diamond” trains approaching from either Liverpool or from Manchester, and to turn them on to the Warrington—that is the Grand Junction line, which at that period ran from Newton to Birmingham, Curzon Street. Mr. John Ramsbottom, when he took charge at Crewe, 1st August, 1857, continued the practice, and placed the diamond upon all the engines he built down to the time of the 1862 exhibition, when the “Lady of the Lake” was the first engine to be built without the diamond. In 1837 Mr. Gooch (afterwards Sir Daniel) placed two of the Egyptian diamonds vertically upon the buffer-beams of the Great Western engines. Many years ago the wagons of the Haydock Colliery Company, Lancashire, also had the diamond of the Masons painted in black upon them. It is hardly necessary to say that the 3, 4, 5 angle forms the centre of the 47th Prop. of Euclid, and is of great practical use. If we take a sheet of paper 12 inches by 8, and set out the 3, 4, 5 angle at each corner, and draw the diagonal lines, we obtain two diamonds, two side positions, and four corners. The area of the corners, 4 at 6 equal 24, the area of the diamonds, 2 at 24 equal 48, the area of the sides, 2 at 12 equal 24, total 96. The two diamonds, 48, are equal in area to the two sides and the four corners together. By this ancient method the Egyptians performed their calculations without the use of decimals or fractions. To this day in all parts of the world engineers and surveyors use the 3, 4, 5, angle to set out an angle of 90 degrees upon the ground, however, some thousands of years ago the method was only known to three people in the world, and they were sworn to keep the information in their own possession. To do this they adopted what was termed “the three rod method,” which consisted of three rods of wood, cut respectively 3, 4, and 5 cubits in length; there was no mark or measure on either rod—simply the name of the person to whom it was handed, and who was responsible for its safe keeping, it therefore followed that unless the three people met together, each having his rod with him, it was impossible for the angle of 90 degrees to be formed. Our old friend Euclid, about whom we heard so much in our school days, was a most scientific man, and also a Guild Mason. In his first book Prop. 47, he clearly published to the whole world the three rod method which previously had been so carefully protected by the use of the 3, 4, 5 “rods.”
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An investigation of the uses of this figure shows that it has been popular as a trademark in past years. The diamond on
Double Diamond beers, recently revived as a mark for an ‘export strength’ brew, has two Egyptian Diamonds
drawn centre to centre. The film manufacturer Agfa also has its name within such a figure. Old petrol pumps of National
Benzole used the Diamond, as did the station nameplates on the Madrid Metro. No doubt other uses may be found. Clement
E. Stretton’s note opposite showing a Masonic connexion dating back to Egyptian and Pythagorean times is yet
another example of the esoteric in modern life, be it applied to objects as prosaic as railway wagons and beer bottles.
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There is another way of dealing with these 3.4.5‘s which also has Egyptian connexions, on a square of 196 or 142. Such a square within a square was recently shown by Professor Zeeman in his book Catastrophe Theory. He mentioned it came from a book by Hogben where it was shown as an ancient Chinese method of demonstrating what afterwards came to be known as the Pythagoras Theorem. I always used to show this diagram in my first papers. Of course this diagram also brings in the 1 × 7 diagonal that was sacred to the Egyptians and further extensions of the same diagram show how the 1 × 7 diagonal is equal to 5 diagonals of a square of 5 and also makes 1/8 angles with the hypotenuse of the 3 × 4 triangle on the principle of a × b & a + b × a − b always make an 1/8 angle when placed in the right position. I don’t think that these obvious facts of life are enough appreciated by mathematicians and yet they were clearly known and worked with in the distant past.
In Keith Critchlow’s new book Time Stands Still he goes into further detail of two subjects I have
always been going on about: the Plimpton tablet and that gold geometrical ‘pendant’ found near Stonehenge.
The Clandon Barrow breastplate in the Dorset County Museum measures as a near perfect example of the Egyptian Diamond,
3.4.5. triangles back to back. There is a little central diamond and this is treated differently, in keeping with the
Bush Barrow specimen it is I suggest based on 2/9 and 5/18. I don’t think that there is a 2/7 angle in sight, if
there is, it’s there by chance because it is all just a bit difficult to detect. The thing is that the angles of a
3.4.5 triangle are near to 53° and 37°, therefore near to 106° and the 5/18 = 100 are both near the 2/7 at
102.85714… Of course the object may have been to show how near together all these angles are. I’m all for
1/7 angles as you know but I don’t think this is the template to find them in. I do wish someone could go into
this more thoroughly because it will get labelled as a template to make 2/7‘s as it is already depicted in
Critchlow’s book, and noone will ever dare look into it again. I don’t think it is that, I think
that it is the Egyptian Diamond.
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The Double Diamond trademark referred to by Mr Pennick was adopted by the Burton brewery in 1876. Additionally, the mystic connexion of the beer is that the water which goes into it is drawn from a former holy well at Burton-on-Trent.