[Proj] Relationship between transverse Mercator algorithms

Charles Karney ckarney at sarnoff.com
Thu Sep 11 14:20:41 EDT 2008

I've posted an update of


This contains a listing of the errors quoted as meters on the ground
(instead of meters in TM space).  This also includes the coefficients
for the 12th order series for the TM calculation and I say where the
extra terms go in Krueger's 1912 paper.

Finally, I've also posted 3 maxima files:

tmseries.mac -- maxima code to generate the coefficients for the series
    in UTM-fi.txt.

tmscale.mac -- maxima code to generate series approximations for the
    scale and meridian convergence in UTM-fi.txt.

revert.mac -- maxima code for the reversion of a series (used by

These were important for me because I never like coding up a series
solution unless I have some way of generating the general term in the

You'll need to have maxima installed to run these.  (This is easy if
you're running Linux.)  Sorry, but this code is neither pretty nor
efficient (nor is is documented).  Ask if you have questions...

Charles Karney <ckarney at sarnoff.com>
Sarnoff Corporation, Princeton, NJ 08543-5300

URL: http://charles.karney.info
Tel: +1 609 734 2312
Fax: +1 609 734 2662

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