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.

Whereas, in the example that Mike gave,
the isochrones will have to cross.

No, they won't. It's just the same as a weather map, it's just a map where
every point has a real number associated with it. Draw two isochrones
crossing each other, write various times on the isochrones and on the spaces
between them, and you'll see that it can't happen.

I was accepting Mike's point that "I think it can't be done on a flat
map without rearranging the order of stations on each line."

Using Mike's example, a 'railway straight line' runs Wimbledon, Raynes
Park & Surbiton in that order. The isochrone passes through Wimbledon &
Surbiton (ignoring the 1 minute difference) but not through Raynes Park.

That arrangement is possible on an OS map or weather chart as, say, two
maxima (M) can be separated by a minimum (m) so there will be places
with the same value but they are not linked by a contour / isobar. For
example a1 & a2 in the diagram below:

a b a
a a b b a a

a M a1 b m b a2 M a

a a b b a a
a b a

Here the contours / isobars that a1 & a2 sit on have different centres.

For a travel map to be of use, every point on it has to share share the
same centre.

regards

Stephen