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George Huxtable wrote:

>Replying to my posting stating-
>|
>| >The locus of an observer who was somewhere unknown on that circle becomes,
>| >after that displacement, not a circle at all. It's distorted, and the
>| >greatest distortion occurs in directions at 45 degrees (and 135, 225,
>| >315 degrees) to the direction of travel.
>
>Herbert Prinz replied-
>
>| I don't understand this. Shifting the circles in an east-westerly
>| direction does not distort them at all. Therefore shifting them
>| north-south must distort them the most. No?
>
>Not so, Herbert. If you shift every point on a circle (or any other
>geometrical figure) in an East-West direction by a certain number of
>DEGREES, then its shape and size remain quite unaltered; that's true.
>But it's not what we are doing here. We are shifting by a certain
>number of MILES, East or West, ...
>
George,

Of course! I moved a penny across a celestial globe to visualize
Zevering's procedure and forgot for a moment that this was exactly what
I had argued against earlier!

Where the use of Mercator is concerned, your proof of the deformation of
the circle of equal altitude is correct. It is sufficient to refute
Zevering's method by one counter example in a trivial case in which you
don't need Mercator. But I wanted to go beyond this by outlining a
constructive solution to Michael Dorl's problem for the general case. It
was in this context that I brought up Mercator. This projection
facilitates the advancement of a position along a loxodrome on a sphere.
Therefore I think that it is intrinsically related to the nature of the
deformation that any geometrical figure undergoes when shifted along a
loxodrome. (It's this "scale ~ sec latitude" thing.) Or it could be that
I am just hung up on this.

Herbert Prinz

   

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