# [Proj] How to convert a sphere to ellipsoid with correct datum?

OvV_HN ovv at hetnet.nl
Tue Sep 7 12:35:37 EST 2010

```In the mean time I've found a contemporary reference about the modified
Flamsteed projection.

Traité de topographique, d'arpentage et de nivellement, L. Puissant, 2ème
edition, Paris, 1820.
Chapitre III: Théorie analytique de la projection modifiée de Flamsteed, pp.
114 f.f.

This chapter gives a mathematical description of said projection. It's
probably worth checking this projection against the (current interpretation
of the) Bonne projection you used.

Oscar van Vlijmen

From: Jan Hartmann <j.l.h.hartmann <at> uva.nl>
Subject: Re: How to convert a sphere to ellipsoid with correct datum?
Date: 2010-09-07 10:10:24 GMT

Thanks Mikkael, I'll follow that road too. I corresponded over this with a
Dutch geodesist who programmed a datum conversion tool (Jan Hendrikse,
http://members.home.nl/hendrikse/), but the results were not as good as
transforming the triangulation points using the original PROJ formula, and
afterwards rubbersheeting them to their exact modern position. There was a
problem wit GDAL, though: it's not possible to rubbersheet an already
georeferenced map, due to a limitation in the Geotiff format. I think now
that it can be done by using the VRT format.

And there remains the question of proof. I can (and will) compute the datum
shift, and can get a map that is within 10m accuracy, about the theoretical
maximum, but is a datum shift really the reason for the deviation? Did they
really use an ellipsoid with a different center and location in 1850? I find
it hard to believe, at least I never found an indication for that, and I
read the handbooks used in 1850. And Cliff Mugnier doesn't think it either
(http://lists.maptools.org/pipermail/proj/2008-November/004042.html).

So, while I know now how to solve the problem computationally  and get a map
that is as exact as can be (thanks to all you input, thanks!), I am still
wondering about the reasons for the deviation. There could be some legal
issues (although I am not much afraid of those, it's too long ago), but for
the most I don't wont to be right for the wrong reasons. I'm not a great
believer in statistical "proofs" where the underlying law or model is
unknown.

Thanks again for all your responses,

Jan

```