John Rowland wrote:
"Larry Lard" wrote in message
oups.com...
Stephen Osborn wrote:
John Rowland wrote:
"Stephen Osborn" wrote in
message
...

However the contours on an OS map
(and AFAIK isobars on a weather chart)
never touch let alone cross.

They can touch, but they can't cross.

I think you are wrong there.

Contours mark places of equal height. If two contours
touch at any one point then, de definito, they have to
touch at *all* points, so the two
contours become one contour.

This is a correct argument that two contours
_indicating the same height_ must be coincident
if they have at least one point in common;

No. There are many "saddle" points in the landscape where, say, the
land is
lower to the north and south, and higher to the east and west. The
contour
which marks the height of the saddle point runs away from the saddle
point
in 4 directions. It would be perverse to describe the contour as
crossing
itself, but the contour could meaningfully be described as touching
itself
at this one point. This is as true for a map of isochrones or
isobars.

Like this, yes? :

[fixed width font needed]
numbers are heights

0 -1 -2 -3 -2 -1 0
1 0 -1 -2 -1 0 1
2 1 0 -1 0 1 2
3 2 1 0 1 2 3
2 1 0 -1 0 1 2
1 0 -1 -2 -1 0 1
0 -1 -2 -3 -2 -1 0

Surely in this situation there is only one contour, though, and it is
X-shaped. If you want to argue that there are two contours meeting in
the middle, how do you decide whether it's a meeting a , or a ^
meeting a v ?

Anyway, I'm not really sure this branch of this thread (?) has anything
useful to say about the original problem, as raised by Michael Dolbear:
"I think it can't be done on a flat map without rearranging the order
of
stations on each line."


--
Larry Lard
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