Larry Lard wrote:
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;
however consider contours marking _different_ heights; these can
coincide on a non-empty set of points (eg along a vertical cliff)
without necessarily coinciding everywhere.
--

That is true for a _literally_ vertical cliff, which does not actually
occur in nature.

Can you think of any other case that would be true (should "eg along a
vertical cliff" actually have been "ie along a vertical cliff")?


Also I still believe that, to make an accurate time map without
rearranging the order of stations on each line, the isochrones would
have to cross not just touch.


regards

Stephen