To make some sense of this, notice that the distance from the point with latitude φ
and longitude λ to the Greenwich meridian (longitude zero) along the latitude line is
λ cos φ. Therefore, the distance to the Greenwich meridian (along lines of constant
latitude) averaged over the entire population is (1/k)
i λi cos φi. This needs to be
converted to a longitude value. If we use the average cosine of the latitude of the
population in order to convert, then we get the formula of the Census Bureau: