Lengths of sections on the chosen parallels therefore have the same length on the globe and the same length on the same segments in the Sinusoidal projection. In the Sinusoidal projection the lengths of all parallels and lengths of segments on parallels are true to local scale--by definition.
To be specific, suppose the parallel mid-way between ([[phi].sub.B],[[phi].sub.T]) is considered and set [delta][lambda] = [lambda] - [[lambda].sub.0] then the difference between where the [lambda] meridian is in the Trapezoidal and where it would be in a Sinusoidal projection will be:
The result of the fit of a sinusoidal projection is given in Table 3.
The parameter [[lambda].sub.0] (Eq 3) is again the standard (or central) meridian for the Sinusoidal projection. In this case it is not a fitted parameter but fixed at the longitude of Beijing.
The parameter [[lambda].sub.0] (Eq 3) is once more the central meridian for the Sinusoidal projection at Beijing.