Latitude - Numerical Comparison of Auxiliary Latitudes

Numerical Comparison of Auxiliary Latitudes

The following plot shows the magnitude of the difference between the geodetic latitude, (denoted as the 'common' latitude on the plot), and the auxiliary latitudes other than the isometric latitude (which diverges to infinity at the poles). In every case the geodetic latitude is the greater. The differences shown on the plot are in arc minutes. The horizontal resolution of the plot fails to make clear that the maxima of the curves are not at 45° but calculation shows that they are within a few arc minutes of 45°. Some representative data points are given in the table following the plot. Note the closeness of the conformal and geocentric latitudes. This was exploited in the days of hand calculators to expedite the construction of map projections. (Snyder, page 108).

Approximate difference from geodetic latitude ( )
	Reduced	Authalic	Rectifying	Conformal	Geocentric
0°	0.00′	0.00′	0.00′	0.00′	0.00′
15°	2.91′	3.89′	4.37′	5.82′	5.82′
30°	5.05′	6.73′	7.57′	10.09′	10.09′
45°	5.84′	7.78′	8.76′	11.67′	11.67′
60°	5.06′	6.75′	7.59′	10.12′	10.13′
75°	2.92′	3.90′	4.39′	5.85′	5.85′
90°	0.00′	0.00′	0.00′	0.00′	0.00′