I had to think a couple of seconds, but I came up with 640.

A lot of the western US was surveyed so they would have something to put in
deeds.  A township is 6 by 6 miles divided up into 36 sections a mile on a
side.  The section boundaries appear on our topo maps where a sensible system
would have a sq-km grid.

The lines on the maps are often quite non-square.  They are leftover from
where the early surveyors actually put the markers rather than what they
should have done.
http://en.wikipedia.org/wiki/Section_(land)
It's common to find survey markers on trees while hiking.  They are yellow
(easy to spot) with a 6x6 grid on them and a nail at the you-are-here point
which is usually where the trail crosses one of the lines.

When the pioneers moved west, they got land surveyed by that system.  (A lot
of it was given away if you settled in and stayed there for N years.)
Children's stories of farmers often refer to things like "the back 40" so the
40 sticks in my head.  That was a quarter of a quarter of a square mile.
I'm not sure how I remember that.  It's the part I had to think about.

I think the land grants were often 1/4 square mile and chopped up into 4
chunks for the convenience of the farmer.
http://en.wikipedia.org/wiki/Homestead_Act
It's a big part of our culture, right next to cowboys and indians and fur
trappers.

--
These are my opinions, not necessarily my employer's.  I hate spam.

On 8/20/09 4:13 PM, "Hal Murray" hmurray@megapathdsl.net wrote:

Getting back to a more timenuts-y vein.. And since I was explaining this to
my daughter last night. A lot of topo maps these days have UTM (universal
transverse mercator) gridding which is in meters.  The whole Public Lands
Survey System (range and township) is pretty interesting.. They had to come
up with a way to survey stuff in the great plains, where there
A) wasn't a lot of existing property boundaries
B) there weren't natural boundaries like footpaths, streams, etc.

In the Eastern US, boundaries are done and recorded much the same way as in
England (or Europe in general, I imagine), by "metes and bounds", using
reference points and landmarks.  But out in the great wide open west, the
advance of technology  helped start with a gridded scheme: by this time,
decent equipment was available inexpensively to do celestial nav, so you
could measure time astronomically, and measure lat/lon.  The need to do
things like survey railroads helped too (although the RR came after the
PLSS)

SO they establish primary monuments (here in Southern California, everything
is referenced to San Bernardino Peak. In the bay area, it's Mt. Diablo)..
They draw an accurate east west line (a BaseLine.. Which anyone who lives
out in the inland Empire will recognize as a street name) and an accurate
north south line (a Meridian) through that point, and start counting.
Ranges are used to count townships (the 6x6 mile chunk) going east and west,
and townships count north and south.  So a township might be identified as
Township 3 north, range 2 east, which would tell you that the SW corner of
the square is 12 miles north of the baseline, and 6 miles east of the
meridian.  The square miles within the township are called sections, and
numbered starting in the NE corner, running across (west), and then down,
and running east, and soforth back and forth (so section 6 is above section
7, section 12 is above section 13, etc... Google range/township and
something will turn up)

The township is surveyed assuming a flat earth, and the earth is curved, so
some of those sections aren't full square miles, but have pieces sliced off
the edge. I can't remember the rule for where and what gets sliced.  This
"large area surveying" is done with a lot of celestial measurements, and
assumptions about sphereoids, etc.  It's really quite interesting, while
perhaps not as spectacular as the Great Trigonometric Survey in India (but
it was done at about the same time).

Relating back to time-nuts.. To do good celestial nav, you need good time,
and so a lot of the later surveys used telegraph signals (along the
railroads) to get their time hack. There's a whole fascinating (to some of
us) literature about how they distributed accurate time, some of which
presages modern schemes like NTP (e.g. Measuring the round trip time, and
using that to estimate the latency, etc., accounting for the human reaction
time, etc.)

Roads in rural areas often follow the section or township boundaries, and
where the discontinuity is, the road has one too.

Not always.  There are non-square section lines because of the flat earth
approximation used to survey a 6x6 mile township. What makes life miserable
for surveyors is that the monument controls over the measurement. If the
land record says "the steel pipe at the corner of sections 1,2,11, and 12",
you go find that steel pipe.  You could resurvey from the reference point or
use GPS to get you to the right area, but the actual monument is what you
use, except in very rare cases.

There are some notorious examples of surveyors who were incompetent and
placed monuments in error 150 years ago, and everyone has to live with it.
This is what you pay for when you hire a licensed surveyor (after all, these
days, the technical skill to put a mark "right there" within a few
centimeters is easy to come by).

Yes. Those guys were tough. Imagine setting out with your plane table,
theodolite, and a couple mules to survey the Great Basin in Nevada and Utah,
or the Sierra Nevada.  Their names live on in landmarks like Mt. Whitney and
Mt. Clarence King