I am currently writing a function on geodetic datum transformation in Hong Kong by referring to the Explanatory Notes on Geodetic Datums in Hong Kong by the Survey & Mapping Office of the Lands Department.
On p. C7,
upsilon_s = radius of curvature in the prime vertical = a / (1 - e^2 * (sin(phi))^2)^(1/2)
rho_s = radius of curvature in the meridian = a * (1 - e^2) / (1 - e^2 * (sin(phi))^2)^(3/2)
a = semi-major axis of the reference ellipsoid
e^2 = the first eccentricity of the reference ellipsoid
On p. C9, you can find the value of these parameters in the table "Parameters for Projection Formulae", and below the table, there is a note that
upsilon_s, rho_s and psi_s are parameters of a point near the centroid of Hong Kong and given to simplify the transformation.
What I am interested is to find the phi (the latitude) of the centroid, the default value of my function calculating the parameters.
Using the radius of curvature in the prime vertical = 6381480.500, I got phi = 0.38942 (in radian);
While using the radius of curvature in the meridian = 6359840.760, I obtained phi = 0.6638568 (in radian, corrected).
asin(sqrt((1 - (6378388 / 6381480.500)^2) / (2/297 - 1/297^2))) = 0.38942
asin(sqrt((1 - (6378388 * (1 - (2/297 - 1/297^2)) / 6359840.760)^(2/3)) / (2/297 - 1/297^2))) = 0.6638568
The difference is considerable. So, I am wondering if I mis-calculated the centroid or the wrong values are put in the document.