Jim Alison presents what he calls "A grid aligned to the cardinal directions, with lengths in even units of 900, 1200 and 1800 meters, (which) provides
a simple and accurate key to the location of the main buildings and monuments in the city", meaning Washington, DC. The grid that he refers to is
rectagonal. His description of the map with the grid can be found in at least two places (see above). Here is a copy of the image that he uses.
Click for larger image
Please note that I agree with his 1200 meter east-west divisions, but disagree with the 900 meter north-south division number. I will explain why
soon, but first I would like to make some comments about the general nature of his method.
Three Decimal Points
At the outset, I would like to say that (having worked both as a rod person and instrument person on surveying teams) I question the wisdom of attempting
to establish the quantity of angles to three decimal points using measurements from maps found on the internet.
For instance, he determines that the orientation of the line from the Kennedy Memorial through the Lincoln Memorial to the Ellipse as 26.565 degrees north
of due east. He does this by presumimg that the Ken Mem lies at the bottom left corner of his 1800 meter block A, and that the Linc Mem lies at the top
right corner of that. If you look closely at his image, you will see that the corner of the block does not appear to coincide with the center of the
LM, and the Kennedy Memorial is impossible to detect.
In order to be able to proclaim angles to 3 decimals, I would recommend measurements to within a part of an inch, the way surveyors do it. It is
more than a fraction of an inch from the center of the LM to the corner of his grid, which calls his measurements from there into question. The red lines
that he is using are several feet wide in the image.
Just for fun, enlarge the map image and put a measuring device on that line segment and see if you get 26.565 degrees? Remember that for every degree that
our 'measurement' is off, there is an error of 92.4 feet at a mile's distance, and the diagonal of the 1800/900 box is 1.25 miles long. That's 115.5 feet of
error per degree between the Ken Mem and the L Mem.
Now put that image in a paint program and extend that line until it runs beside NY Ave heading northeast from the WH. Jim determines the angles of the
diagonals in the pentagram to be 24.228, about 2 degree difference, but it doesn't appear in the map to vary that much. As a matter of fact it appears
to parallel NYA.
And what's up with making one grid block a time and a half as wide as the others? He does this, he says, because both the KM and the National
Cathedral fall on this line, at corners of his 900 meter vertical blocks.
If he were to use 600 meter wide horizontal blocks, both of these locations, as well as Logan and DuPont Circles would fall on grid lines without
having an odd divisor. This would also add a north-south line 2400 meters west of the WH, which would fall very near the light colored area on
Roosevelt Island.
The Capitol Building
Looking at the Capitol Building (below right) you can clearly see that the center of that lies a good distance north of the red line yet he describes it
as "at the south-east corner of zone 5D". [The CB is over 600 feet wide.] The red line that you see below is his line that is 900 meters south of the WH,
while the blue line is an approximation of the east west axis from the center of the Capitol Building. As you can see, the (purple) line that
runs from the CB through the Wash Mmt and on to the LM, runs down hill (south of due west).
According to Alison, "the main east west axis of the city is through the Capitol" (and Wash Mmt to the Lincoln Memorial). The fact of the matter is that
this line is not 'due' east and west since (as he tells us) the Washington Monument was "constructed to the east and slightly to the south of it's
originally intended location".
The 'intended' location was the spot where the N-S axis through the WH crossed the E-W axis through the CB (where the blue line crosses the red line
above, and where the Jefferson Pier is located today). In the "Secret Architecture of our Nation's Capital", we read that the monument was displaced 371+
feet east and 123+ feet to the south (a ratio of 1:3).
Jim suggests that the CB is 2400 meters east of the WH. If the Wash Mmt is 371+ feet (113.1 meters) east of the WH, then it is 2286.9 meters west of
the CB. This means that at 2287 meters from the CB, the Wash Mmt is 37.5 meters south of the due west line from the center of that building.
37.5/2287 = .01639. This is a little bit less than one degree because the sine and tangent of one degree are both .0175.
2400 meters, the east west distance between the CB and WH, is 1.49 miles. The Wash Mmt is 1.42 miles from the CB. The Lincoln Memorial is 2.235 miles from
the CB, on the same line as the monument. Remember that two line segments 1 degree apart are seperated by 92.4 feet at the distance of a mile (5280 feet,
1609.4 meters). While our angle is a little bit less than 1 degree, we know the 'exact' ratio to be .01639, so we can determine the offset from the 'true'
E-W axis, which turns out to be 193 feet at the LM.
While the WM is 123 feet south of the Capitol's E-W axis, the Lincoln Momument is 193 feet south of there.
In determining the positions of buildings on the 'east-west' axis, Alison claims that, "The White House is 900 meters north of the east-west axis of the
Capitol". By that he means the point to the left of the Wash Mmt in the McMillan Plan below, while we can now calculate that that point is 39.35 meters
south of the Capitol axis. If the 900 meter point does lie at the red line, then we know that the 'true' E-W axis is 900 - 39.35 meters south of the
WH.
So it is Not True that -
"From the White House to the Capitol Building, Pennsylvania Avenue travels 2400 meters east and 900 meters south". At the CB it is
only 860 meters south of the WH, so instead of a 2400/900 ratio that produces an angle of 20.556 degrees south of due east, the ratio is 2400/860, or less
than 20 degrees. (The number is about 0.35833 and the tangent of 20 degrees is 0.3640. His number is 0.375, 900/2400.)
"From the intersection point of the e-w axis and the n-s axis, the distance to the Lincoln Memorial is 1200 meters and the distance to the White House
is 900 meters. These two lengths are the sides of a 3-4-5 right triangle." While it is true that those are the lengths of a right triangle, that triangle
in the map does not have a 90 degree angle in the corner. The Lincoln Memorial is actually 70 feet further south of the E-W Capitol axis than the Wash Mmt
is, 58.7 meters as a matter of fact. The angle is about 91 degrees. If one is going to calculate angles to three decimal points, one should not call 91
degrees a right angle, eh?
"The intersection point, the Lincoln Memorial and the Jefferson Memorial also form a 3-4-5 right triangle", because the line from
the 'intersection point' to the LM Is running 1 degree south of due west. This angle is about 89 degrees. [Note that the diagonals of his grid blocks
form 3-4-5 triangles with 900 and 1200 meter sides.]
The Great Pyramid
By means of his map measurements he determines the angle of New Hampshire Avenue as 53.47 north of due east. Try putting a measuring device on his map
image and see what you get for that.
Personally, I am going with Don Barone and Gary Osborn on this one, and suggest that the planners' intention was to depict the ~ 52 degree and 23+ degree
angles inherent in the pyramid form, that is, that the triangle in the map was meant as a silhouette of the Great Pyramid's cross-section.
We should remember that this image from John Greaves' book "Pyramidographia" was probably the model that the planners used for the map. Try NOT
thinking about a pyramid when you look at the 50 something degree triangle in the map.
The Grid
Horizontally, the grid depends on the positions of the points of the pentagon/gram centered on 16th Street, one of the axes of symmetry in the map
(another being East Capitol Street east of the CB). At the bottom point we see the WH; Logan and DuPont Circles (the top points) are each 600 meters removed
from the WH (east and west of 16th), while Washington Circle and Mt Vernon Square (the wide points) are each 1200 meters removed; the CB is 2400 meters east
of 16th, but he chooses to leave off a grid line 2400 meters west of the WH.
While I am not sure why Jim chose to have a different sized grid block in the far west of the image, for the sake of symmetry I use a circle to place a
north-south line 2400 meters to the west of 16th Street. I have also added N-S axes at both Logan and DuPont Circles. [Please forgive me for not having a
better paint program.]
Another circle shows that the map grid is defined vertically by the fact that the HOT and Jeff Mml are equidistant from the WH (at the center of the
circles). Each is 1800 meters removed from there, the total distance between the two being 3600 feet, which Alison has divided into four 900 meter blocks.
Since two 900 meter blocks are the same as three 600 meter ones, the circle marking the HOT and JM also marks the third N-S line from the WH. We now have
eight 600 meter wide blocks between the 0 and 32 lines.
Notice that the line 900 meters south of the WH falls roughly on the line from the CB to the Lincoln Memorial, while the line 900 meters north of the WH
falls on the intersection of two sets of lines in the pentaram/gon (Mass and Vermont, and Rhode Island and Connecticut), although there are no monuments
there.
Talk of the peak of the triangle in the map and Scott Circle (both blue above) is conspicuously absent from Alisons posts. I would like to argue that the
vertical component of the map grid should be determined by these two positions, and that the north and south sections of the map are radically different
from one another, as are the east and west.
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