Feet
Message #69 Posted by James M. Prange (Michigan) on 3 June 2007, 6:34 p.m.,
in response to message #62 by blurdybloop
Quote:
Wrong. You're thinking about "survey feet", which has nothing to
do with state laws.
Before 1959, there was no standard defintion of the meter vis a
vis the foot, or vice versa.
Wrong. In 1866, the U.S. Congress defined the relationship of 1
meter being equivalent to 39.37 inches. See
http://lamar.colostate.edu/~hillger/laws/metric-act.html.
So (within the U.S.) 1 meter would be 3937/100 inches, and if we
accept that 1 foot is 12 inches, then it follows that 1 meter
would be 3937/1200 feet, and if we also accept that 1 yard is 3
feet, then it also follows that 1 meter would be 3937/3600 yard.
In 1866, the U.S. foot and inch would've been defined in terms of
the U.S. yard, first adopted by the Treasury department in 1832
and then slightly changed to agree with new standards in 1856.
This U.S. yard was intended to be equal to the British Imperial
yard.
Eventually, Congress delegated its power to fix the standard of
weights and measures to federal agencies. Judging from its
performance regarding weights and measures other than coinage, it
was probably a relief to shift its responsibility elsewhere.
In 1875, the U.S. was one of the 17 countries signing the Metric
Convention, which founded the International Bureau of Weights and
Measures. In 1890, the U.S. received its copies of the
international meter standard, and a comparison against the U.S.
standard didn't show the legal definition of 1866 to be incorrect;
that is, they agreed within the error of measurement.
In 1893, the "Mendenhall Order" established the meter as the
fundamental unit of length for the U.S., so, based on the 1866
legal relationship, the U.S. yard was redefined as 3600/3937
meter, and therefore the U.S. foot became 1200/3937 meter, and the
U.S inch became 100/3937 meter, and for a time, any attempts to
maintain the U.S. yard as equal to the British Imperial yard were
abandoned.
Quote:
In that time, surveying was done with the definition of a foot
being 1200/3937 meter.
Well, presumably, until the U.S. yard was adopted in 1832, the
definition of a foot would've been 1/3 British yard, and then
would've been 1/3 U.S. yard from its adoption until 1893, and even
then still 1/3 U.S. yard, but with the U.S yard being redefined as
3600/3937 meter, the foot would be 1200/3937 meter.
Quote:
In modern times, the foot is defined as
exactly .3048 meters (30.48cm, 304.8mm, take your pick).
Well, English-speaking countries which used them had slightly
different definitions for the yard and avoirdupois pound and units
based on them, which, with the increasing needs for accuracy,
increasingly caused difficulties, until in 1959, the directors of
the national standards laboratories of Australia, Canada, New
Zealand, South Africa, the United Kingdom, and the United States
entered into an agreement establishing uniformity for them. The
equivalents 1 yard=0.9144 meter and 1 avoirdupois
pound=0.453449237 kilogram were adopted for each of these national
laboratories, effective July 1st, 1959. So based on that, 1
international foot=0.3048 meter and 1 international inch=0.0254
meter.
But an exception was made for the definitions for the U.S. Coast
and Geodetic Survey. I don't know whether other countries made
such exceptions.
Measurements expressed in feet and published as a result of
geodetic surveys in the U.S. would retain the relationship of 1
foot=1200/3937 meter, and this foot would be referred to as the
U.S survey foot, and continue to be used for that purpose until
such a time as it becomes desirable and expedient to readjust the
basic geodetic survey networks in the U.S., after which the ratio
of a yard, equal to 0.9144 meter, would apply.
Has such a time arrived? Or maybe it's already past, and it would
be more desirable and expedient to just skip to always using the
meter itself for those purposes?
Quote:
The difference between the two is small; 6.09601e-7 meters.
Approximately; the exact difference is 3/4921250 meter. Another
way of looking at it is that 1 international foot is exactly
499999/500000 (or .999998) U.S. survey foot.
Quote:
But when you take into account that surveys cover large areas,
that microscopic difference actually makes a difference.
Hence the survey foot.
Quite so. Converting all land records from the "old" foot defined
as 1200/3937 meter to the "new" foot defined as 0.3048 meter would
be an awful lot of work (especially before computers or even
electronic calculators were generally available), so the old foot
was designated the "U.S. survey foot" and the new foot was
designated the "international foot", and such units as the rod (or
pole or perch), chain, furlong, U.S. survey mile ("statute mile"),
acre, and fathom still retain their definitions based on the U.S.
survey foot (at least, within the U.S.).
Note that there isn't a "U.S. survey inch" or a "U.S. survey
yard".
For more on the relationship between the U.S. survey foot and the
international foot, search within
http://physics.nist.gov/Document/sp811.pdf, and good
references for the history of the relationship of the metric
system to the U.S. customary units include
http://lamar.colostate.edu/~hillger/ and
http://physics.nist.gov/Pubs/SP447/.
Quote:
Now, some states have survey feet specified for their plane
coordinate system, and a few have standard feet, leading to the
myth that the foot is different in different US states. A foot is
.3048 meters in every US state; the question of survey feet is
only on SPCs.
Hmm, in every state, and anywhere else in the world for that
matter, a "U.S. survey foot" is always 1200/3937 meter, and an
"international foot" is always 0.3048 meter; these definitions
don't vary. But just a "foot" can leave me wondering which
definition of foot is intended, at least when it's used in land
measurement.
It seems to have been left up to the various states to choose
which units to use within their own state plane coordinate
systems, and apparently some haven't even bothered to choose.
Quote:
The federal government only publishes SPCs in metric, so feet are
calculated from the metric values. It's trivial to determine
whether these are survey feet or standard feet. I haven't seen
much usage of survey feet in new work.
I thought that it was up to the various states to choose which
unit to use? It seems bad enough that the states use different
units, but surely it would be madness for different surveys within
a state to use different definitions of a "foot".
Actually, as Norris wrote, the standard U.S. definition of the
acre is still based on the survey foot, and since land area is
normally stated in acres in the U.S., it strikes me as rather
insane to use international feet for land measurement. Let's see,
1 acre is exactly equivalent to 660 by 66 U.S survey feet, thus
43560 square U.S. survey feet. So 1 acre equals exactly
43560*(500000/499999)^2 square international feet, which works out
to exactly 10890000000000000/249999000001 (about
43560.174240522721) square international feet; who wants to work
with a crazy conversion factor like that?
Suppose that I'm looking at a property description; how do I know
which definition of "foot" is being used? But I grant that for the
size of a property, I wouldn't be too worried about the
difference; after all, 1 square international foot would be
exactly 249999000001/250000000000 (or .999996000004) square U.S.
survey foot, not enough of a difference for me to lose much sleep
over.
Note that the definition of the meter has changed over time too;
see http://physics.nist.gov/cuu/Units/meter.html. That said,
as far as I can tell, each new definition of the meter merely
reduced the uncertainty in its realization, rather than actually
changing its length.
Regards,
James
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