TM series for X and Y(from P. D. Thomas)

For

and where is a small parameter of the ERM,

the series expansion for X is given by,

where

and

where

and where Sø is the arc length along the meridian through P from the

origin. Sø is given in a series and is a function of latitude (ø) only.

COM computations for TM and UTM involve inversion of this series

to get the footpoint latitude.

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