-------- Original Message --------
Subject: Re: Patron question regarding topo maps - square vs. rectangle
Date: Thu, 6 Mar 2008 22:36:11 GMT
From: [log in to unmask] <[log in to unmask]>
To: [log in to unmask]
Oh my goodness -- the one I'm looking at is projected in Universal Transverse Mercator, not geographic (Plate Carree). In the old days some of the topos were in polyconic. Whether you're in UTM or polyconic, one minute of longitude is not equal to one minute of latitude.
Joe McCollum
Information Technology Specialist
Forest Inventory and Analysis
Knoxville, TN 37919
Subject: Re: Patron question regarding topo maps - square vs. rectangle
Date: Thu, 06 Mar 2008 15:02:06 -0800
From: Mary Douglass <[log in to unmask]>
To: Air Photo & Geospatial Systems Forum Maps <[log in to unmask]>
Thanks to all! I received six responses within minutes of my question, and I pieced them together to respond to the patron with a brilliant, collective answer. Much better than I could have done.
Subject: Re: Patron question regarding topo maps - square vs. rectangle
Date: Thu, 06 Mar 2008 18:01:17 -0600
From: James R. Carter <[log in to unmask]>
To: Maps, Air Photo & Geospatial Systems Forum <[log in to unmask]>
CC: John Kostelnick <[log in to unmask]>
Mary: This is a very good question and I am certain it is a problem for
many people. On the Earth the lines of longitude, meridians, converge
at the Poles. Look at a globe to show this relationship. This leads
into the color of the bear question -- a hunter walks south 1 mile, then
due east 1 mile, then due north 1 mile and comes back at the starting
point. The hunter finds a bear there. What color is the bear?
White obviously, for this can only occur at the North Pole. Note the
question is based on the assumption ice is still continuous to the North
Pole. At the Equator the hunter would be 1 mile due east of the
starting point.
Now, if USGS topo sheets were based on the equirectangular, or Platte
Carree, projection the maps would be square. But, the topos are based
on a polyconic projection and as such the east-west spacing of the
meridians becomes ever narrower as one moves poleward. To illustrate,
fold the top edge of a topo sheet down to compare the width of the 7 1/2
minutes of longitude with the width at the bottom of the topo sheet. It
is a small difference but you will see that the width at the top is less
than it is at the bottom. The higher the latitude, the greater the
difference between top and bottom.
Anyone who has worked with a collection of topos for the whole U.S. has
probably observed that topo maps for Hawaii and souther Florida and
Texas are a tight fit in a drawer if they are filed two stacks in a
drawer. By contrast, the maps for the more northern states in the lower
48 fit very well in the drawer.
Note that degrees, minutes and seconds are angular measurements and not
linear measurements. If the topos were 7.5 miles on a side they would
be square, but they are not. They are instead based on an angular
measurement on a sphere, or more precisely an ellipsoid.
Jim Carter
At 3/6/2008, you wrote:
> -------- Original Message --------
> Subject: Patron question regarding topo maps
> Date: Thu, 6 Mar 2008 16:43:40 -0500
> From: Mary Douglass <[log in to unmask]>
> To: [log in to unmask]
>
> Hello folks,
> I think that some of you out there will be able to come up with a well
> thought out answer for this question before I can think of where to look!
> "Why on a 7.5 minute USGS Topo isn't the area map square? Since the map is
> 7.5 minutes X 7.5 minutes, it should be square. The map clearly is not
> square and appears rectangular. Can you help with this dilemma?"
> I've told the patron that I'm sending the question out to the "experts".
>
> Mary Douglass
> History, Travel and Maps Department at Seattle Public Library
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Dr. James R. "Jim" Carter, Emeritus Professor
Geography-Geology Department
Illinois State University, Normal, IL 61790-4400 USA
-- http://www.ilstu.edu/~jrcarter
<http://www.ilstu.edu/%7Ejrcarter> --
tel: (309) 438-2833 fax: (309) 438-5310
[log in to unmask]
Past President, Normal Rotary Club
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