Hi Tony and all
No you are not wrong. And happily for your heliochronometer you were not
half asleep. There was indeed a french expedition in Lapland in 1736 sent
by the then french king Louis XV and lead by P de Maupertuis. He found that
the length of a degree of the meridian was longer in Lapland (66° latitude)
than in France (46°). He found 57437 french "toises" in Lapland instead of
57030 found in France by Abbé Picard. For information 57030 toises are equal
to 111,153 km; a toise is 1,95 m. At the same time another expedition was
sent to Peru for the same job, lead by M. Bouguer. He found a length of
56750 "toises" for a degree at Equator.
The result is not surprising. As Bill Gottesman recalls, an arc of one
degree is defined by the distance of two points of a meridian such that the
angle between vertical lines at these points is 1 degree. As the Earth globe
is a ellipsoid flattened at the pole the vertical lines do not always
intersect at the center.
Near the pole they intersect beyond the center, ("radius of curvature" of
earth surface is larger) ; at the equator they intersect between center and
surface, ("radius of curvature" is smaller). Distance between intersection
points and earth center is about 30 km in both cases. So the meridian arc
between two points 1 degree apart is shorter at the equator than at the
pole. Have a look for instance at J. Meus book "Astronomical algorithms"
chapter 10 for more technical details. Or draw a very very flat ellipse to
convince yourself.
Regards
Jean-Paul Cornec
----- Original Message -----
From: "tony moss" <[EMAIL PROTECTED]>
To: "Sundial Mail List" <[email protected]>
Sent: Tuesday, February 03, 2004 1:32 PM
Subject: Was I half asleep?
> Fellow Shadow Watchers,
> There was a programme on UK Discovery yesterday -
> 2nd Feb - with some excellent material covering a thousand years of
> history. I must admit that I wan't paying 100% attention but one
> sequence caught my immediate attention. This described a French??
> expedition to northern latitudes to determine the true shape of the earth
> which, as we now know, is an 'oblate spheroid' which is flattened near
> the poles. The whole thing was expensively restaged in costume with
> elegantly attired gentlemen trudging through deep snow on a frozen lake
> laying wooden poles end to end to measure surface distances.
>
> By comparing accurate astronomical positioning with linear measurements
> made on the surface they proved - accoding to the programme - that the
> distance between lines of latitude is GREATER at the poles. This
> 'concept' was supported by using a graphical representation of the earth
> with a superimposed protractor BOTH of which stretched as the earth was
> distorted. As the protractor stretched or rather distorted, with the
> earth image this point *appeared* to be true.
>
> Have I got it wrong? Surely the linear distance between lines of
> latitude will be decreased by flattening a sphere at its poles? Or had I
> missed something important by simultaneously watching TV and designing a
> heliochronometer base casting on my computer? Back on topic - ish.
>
> Tony Moss
>
>
>
> -
-
