[OSRS-PROJ] Re: Lambert Conformal Conic 1SP
Clifford J Mugnier
cjmce at lsu.edu
Mon Feb 10 21:28:16 EST 2003
Gerald,
You must have an earlier edition of 251 than me. In my edition, the Fifth
Printing of 1968, that term is indeed printed as 3298.
Congratulations on backing that out! However, in comparative terms of
masochism, Oscar S. Adams beats them all in Special Publication Number 57,
"Latitude Functions." He derived each function five different ways!
Cliff Mugnier
LOUISIANA STATE UNIVERSITY
251 is a useful book and a dog-eared copy sit on my shelf.
I also found a suspicious coefficient for the expression for
x in Tmerc on page 96. For eqn 289, and the first row of
the expression for the lamda^7 term, the 6th term reads
"3,262". I believe the value should be "3,298".
This was found when comparing extended precision Gauss
quadrature integrations, Thomas's expanded coefficients and
various "standard" versions of Tmerc.
What was a very interesting part of this endeavor is that
numerical integration allowed me to empirically determine
the correct 4 digit number that, when used in the evaluation,
the comparison was exact to 15 digits. Just changing the
"8" up or down 1 would significantly alter the comparison.
There was no way I would carry out a re-derivation! Thomas
was a masochist.
On Sun, 2003-02-09 at 22:45, Clifford J Mugnier wrote:
>
> It's USC&GS Special Publcation 251, dated 1952. "Conformal Projection in
> Geodesy and Cartography." No, he did not offer guidance on such. He
> presented the math with proofs and gave a few brief statement on usage
> throughout the world as he could apparently find out about in the USC&GS
> Library. It was quite limited in comparison to what Army Map Service
had,
> but that was mainly classified at the time and AMS was busy with the EU50
> Datum adjustment. It is rumored that Paul D. Thomas did the math and
> derivations on contract to AMS for the UTM.
>
> Cliff Mugnier
> LOUISIANA STATE UNIVERSITY
>
> I don't have Thomas 1952. Out of curiosity, did he tender recommendations
> for choice of standard parallels?
>
> Regards,
>
> daan Strebe
> Geocart author
>
>
>
>
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