Time, according to the position of the mean sun is called Greenwich Mean Time (GMT). Time using the central meridians of various time zones is called Zone Time (ZT). And time using the observer's meridian as a reference is called Local Mean Time (LMT).
Local mean time, is the relationship of the mean sun with the observer's meridian. When the mean sun is at lower transit of the observer's meridian, meaning that it is passing over the lower branch of his meridian, the LMT is midnight. At upper transit of the mean sun, when the upper branch of the observer's meridian is crossed, it is noon in LMT. Local mean time does not have much importance in celestial navigation, but the relationship of local mean time with local zone time and with Greenwich mean time is important in determining times of sunrise and sunset, moonrise and moonset, and local apparent noon.
Local mean time differs from zone time by the amount of time required for the mean sun to traverse the difference in longitude between the observer's meridian and the standard meridian of his time zone. The sun moves around the earth at a rate of 15° of arc (longitude) per hour, or 1 ° every four minutes. The difference in longitude, can be converted into differences in time. The Nautical Almanac has a Conversion Of Arc To Time Table.
Example - if you are located at longitude 64 ° 13.3' W and wanted to find the time required for the mean sun to travel from the central meridian of his time zone 60° W, to his meridian. The difference in longitude is 64° 13.3' - 60° = 4° 13.3'. Entering the first column of the table, a time of 0 hours 16 minutes is first extracted for 4 °. To find the additional time increment for the remaining 13.3 minutes of arc, the right-hand portion of the table is used. First the horizontal row containing entries for 13' is located, then the value under the column heading closest to the decimal fraction desired is read. Since .3 is closest to .25, the value for 13.3' of 0 minutes 53 seconds is taken. This result is then added to the value of time for 4 ° to get a final figure of 0 hours, 16 minutes, 53 seconds for the conversion of 4 ° 13.3' of arc to time. Rounding off to the nearest minute, which would be 17 minutes for the mean sun to travel that arc distance. You must remember when applying arc to time differences that if you are east of another you have a later time and if you are west of another you have a earlier time.
Example - Suppose you are located at the 64 ° W meridian and want to convert the local mean time of apparent noon at his meridian, say 1157 to the local zone time of apparent noon (LAN) for this time zone.
Since the 60° W meridian is the standard meridian of the + 4 time zone, and that the zone time of apparent noon at all meridians within the +4 zone to the east of the 60° W meridian will see local apparent noon (LAN) earlier than zone time 1157, and all meridians within the zone to the west will experience LAN at a later zone time. Use the arc-time conversion table, the time required for the mean sun to transit the four degrees of longitude between 60 W and 64 ° W is 16 minutes. At longitude 64 ° W, apparent noon will occur on at 1157 + 16 or 1213 zone time. Or if you were at 57° 45' W, local apparent noon will occur at 1157 - 9 (2° 15' of arc converted to time) or 1148 zone time.
When writing time expressed in hours, minutes, and seconds, Hours, minutes, and seconds are expressed using two digits, and each quantity is separated from the others by a dash.
Example of a written time, if the apparent sun had crossed the central 60° W meridian at 1200 zone time, it would cross an observer's meridian at 64 ° 13.3' W at 12-16-53 zone time. If any quantities to be written are less than 10 in value, zeros are used to fill in the blank spaces 01-02-03 for 1 hour, 2 minutes, and 3 seconds. Whenever celestial observations are made, they are always recorded to the nearest second.
