There is one term I have used which does not appear in the illustration. It is the Earth's Central Progress (
.C.P.). The astronomical day based on the sun, is 24 hours long, as said before. The sidereal day, however, is only 23h 56m 04s long. This is due to the fact that whereas the earth is moving in its ecliptic track around the sun while revolving on its own axis, the First Point of Aries is a fixed point and hence never moves. The correction, then, for the difference in the length of time between a sidereal day and a mean solar day is called the Earth's Central Progress and, of course, has to be figured for all amounts of time after mean noon at Greenwich, since the Sun's Right Ascension tables in the Nautical Almanac are based on time at mean noon at Greenwich.
Now you have a formula for practically all kinds of conversion except for converting L.M.T. into L.S.T. You could do it by the formula
L.M.T. + W.Lo. = G.M.T. +
.R.A. +
.C.P. = G.S.T. - W.Lo. = L.S.T.
- E.Lo. + E.Lo.