There are 4 messages replying to this question compiled together below.
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Check out "The Center Seat" at http://www.ussalaric.org/cc/cc0205.htm
It is supposed to be funny; I gave a version of it at Toastmasters over
two meetings.  They didn't think the part about so many different places
in Europe claiming to be the geographic center was funny at all,
although when I said "Lambert Azimuthal," they thought that was hilarious.

The "geographic center" of any geographical entity is the centroid.  One
nice property of the centroid is that if you have disjoint polygons, the
centroid of the region (Arc/Info terminology) is equal to the sum of the
area of a polygon times its centroid, summed over all polygons.  So it's
actually not too hard to figure out that the geographic center of the
USA is near Castle Rock, SD.

For a city it should be calculated the same way, but I suspect that the
Census Bureau or whatever source you're using, may take a few shortcuts.

I had a discussion from someone from Middle Tennessee State University
in Murfreesboro, TN.  She told me that Murfreesboro was the geographic
center of Tennessee.  I went into A/I, crunched the centroid, and what
do you know, it sure was.

Joe McCollum
Information Technology Specialist
Forest Inventory and Analysis
Knoxville, TN  37919

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I can't speak to any current "official" definitions, but one of the
things I have spent some time on is looking at "city centers" while
travelling.  Nearly always, the "distance" to the city center as defined
by highway directional signs winds up being a distance that approximates
to what might be considered the "traditional" CBD of a city.
Let me explain in terms of Los Angeles.  When I'm appoaching Los Angeles
from far, far away (such as The Frozen North), the distance on I5 is
expressed in terms that approximate the location of the Los Angeles City
Hall (famous from Dragnet and Badge 714 if you're over the age of 45 or
watch a lot of reruns).  Tuesday, I happened  to be driving from the San
Fernando Valley, which inside the corporate boundary of the City of Los
Angeles to Long Beach.  I was went on the 101 Freeway to the I-5 and
found the signs and corresponding arrows said Los Angeles until I got to
the 4-level, aka the East DeeLA, interchange.  After passing the
4-level, the signs and corresponding arrows began to say Santa Ana
rather than Los Angeles.
I remember several months ago driving down down the I-5 through Burbank
and Glendale where the signs and corresponding arrows said Los Angeles
until I got to the interchange with the I-10 where they change to say
Santa Ana.

Finally, back in the day when I was teaching urban geography at the
University of Florida, I watched for the AAA signs on non-Interstate
highways and found they generally corresponded to the downtowns (read
CBDs) as they existed in the 1920s and 1930s when the AAA was putting up
directional signs.  If you'd like to see an actual one still standing
and performing its duty, go northbound on Sepulveda Boulevard in West
Los Angeles where you'll find such a sign just before you reach Wilshire
(you're likely to get hung up at the stop light to cross Wilshire and
can admire the sign while you wait).

HTH.

virginia

--
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Colin,

        It depends on which resource you use. If you use the Census
gazetteer, the center is the center of population for the city. If you
use GNIS, it is city hall or whatever they call it in each city. I
believe that highway mileage markers to cities are also measured to the
city hall as well. Linda Zellmer

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Linda Zellmer
Head, Geology Library
Geology Building, Room 601
1001 E. 10th Street
Bloomington, Indiana 47405-1405
Phone: (812) 855-2275 Fax: (812) 855-6614
[log in to unmask]

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The following is quoted from the GNIS Users Guide on the GNIS website.

  If the location of the geographic center of a large populated place was
difficult to identify, additional guidelines were used to determine the
placement of the primary geographic coordinates such as the location of
the city or town hall, main post office, main library, central business
district, or main intersection.

Daniel T. Seldin
Map Cataloger
Technical Services Department
Indiana University
Main Library E350
1320 E. 10th St.
Bloomington, IN  47405-3907
(812)855-2059
[log in to unmask]

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There is no official means of determining the center of a "city", and by
the way, there are no official definitions of city, town, etc., just as
there is no official definition of mountain vs. hill, etc.

Anyway, we at the Geographic Names Information System (GNIS), the nation's
official geographic names repository determine the primary coordinates of a
community at the approximate center of the "original" community by
selecting City or Town Hall, main post office, principal intersection, etc.
So, the primary coordinates in GNIS associated wit a community might not be
anywhere near today's centroid?  By the way, Topozone uses GNIS.

Roger L. Payne
Manager GNIS
703.648.4544

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