NavList:

Mercator sailings take into account the differences between the difference in longitude and latitude as latitude varies.  The issue that you are finding is that the earth isn't a sphere, but an oblate spheroid.  The very long formula takes into account such things as eccentricity and flattening.  As time has passed, these "constants" have been refined.  The meridional parts tables have been adjusted to reflect these changes in knowledge in various editions of navigational tables.  You need to pay attention to what WGS ellipsoid is being referenced.  If you were to use modern MP tables, they will likely not exactly match your father's calculations.

Mercator sailings are used for longer distance calculations when mid-latitude sailings start to become inaccurate.  We rarely use plane sailings as their accuracy rapidly diminished with distance.  I tend to use Mercator sailings on rhumb line courses over about 100 miles.  We use great circle sailings when taking that route.

M= 7915.704 log tan b (45+L/2) - 23.013 sin L-.051 sin^3L-.000206 sin^5L.  I am sure the "log" in there is causing the change in the rate of change, but I'm a simple sailor and know more about using the tables than the mathmatics behind them.  I am sure others on here can be more exacting.

Jeremy