Use Formula (27) to show that if the length of the equatorialline on a Mercator

Chapter 7, Problem 63

(choose chapter or problem)

Use Formula (27) to show that if the length of the equatorial line on a Mercator projection is \(L\), then the vertical distance \(D\) between the latitude lines at \(\alpha^{0}\) and \(\beta^{0}\) on the same side of the equator (where \(\alpha<\beta\) ) is

                  \(D=\frac{L}{2 \pi} \ln \left|\frac{\sec \beta^{0}+\tan \beta^{0}}{\sec \alpha^{\circ}+\tan \alpha^{\circ}}\right|\)

Equation Transcription:

Test Transcription:

L

D

alpha^0

beta^0

alpha< beta

D=L/2pi ln |⁡sec beta^0⁡ +tan beta^0/⁡ sec alpha^0⁡ +tan alpha^0|⁡

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