Wednesday Lecture
Time By The Sun—Mean Time, Solar Time, Conversion, Etc.
There is nothing more important in all Navigation than the subject of Time. Every calculation for determining the position of your ship at sea must take into consideration some kind of time. Put in your Note-Book:
There are three kinds of time:
1. Apparent or solar time, i.e., time by the sun.
2. Mean Time, i.e., clock time.
3. Sidereal Time, or time by the stars.
So far as this lecture is concerned, we will omit any mention of sidereal time, i.e., time by the stars. We will devote this morning to sun time, i.e., apparent time, and mean time.
Apparent or Solar Time is, as stated before, nothing more than sun time or time by the sun. The hour angle of the center of the sun is the measure of apparent or solar time. An apparent or solar day is the interval of time it takes for the earth to revolve completely around on its axis every 24 hours. It is apparent noon at the place where you are when the center of the sun is directly on your meridian, i.e., on the meridian of longitude which runs through the North and South poles and also intersects your zenith. This is the most natural and the most accurate measure of time for the navigator at sea and the unit of time adopted by the mariner is the apparent solar day. Apparent noon is the time when the latitude of your position can be most easily and most exactly determined and on the latitude by observation just secured we can get data which will be of great value to us for longitude sights taken later in the day.
Now it would be very easy for the mariner if he could measure apparent time directly so that his clock or other instrument would always tell him just what the sun time was. It is impossible, however, to do this because the earth does not revolve at a uniform rate of speed. Consequently the sun is sometimes a little ahead and sometimes a little behind any average time. You cannot manufacture a clock which will run that way because the hours of a clock must be all of exactly the same length and it must make noon at precisely 12 o'clock every day. Hence we distinguish clock time from sun time by calling clock time, mean (or average) time and sun time, apparent or solar time. From this explanation you are ready to understand such expressions as Local Mean Time, which, in untechnical language, signifies clock time at the place where you are; Greenwich Mean Time which signifies clock time at Greenwich; Local Apparent Time, which signifies sun time at the place where you are; Greenwich Apparent Time, which signifies sun time at Greenwich.
Now the difference between apparent time and mean time can be found for any minute of the day by reference to the Nautical Almanac which we will take up later in more detail. This difference is called the Equation of Time.
There is one more fact to remember in regard to apparent and mean time. It is the relation of the sun's hour angle to apparent time. In the first place, what is a definition of the sun's HA? It is the angle at the celestial pole between the meridian intersecting any given point and the meridian intersecting the center of the sun. It is measured by the arc of the celestial equator intersected between the meridian of any point and the meridian intersecting the center of the sun.
Hour Angle of Greenwich
For instance, in the above diagram, suppose PG is the meridian at Greenwich, and PS the meridian intersecting the sun. Then the angle at the pole GPS, measured by the arc GS would be the Hour Angle of Greenwich, or the Greenwich Hour Angle. And now you notice that this angular measure is exactly the same as apparent time at Greenwich or Greenwich Apparent Time, for Greenwich Apparent Time is nothing more than the distance in time Greenwich, England, or the meridian at Greenwich is from the sun, i.e., the time it takes the earth to revolve from Greenwich to the sun; and that distance is exactly measured by the Greenwich Hour Angle or the arc on the celestial equator, GS.
The same is correspondingly true of Local Apparent Time and the ship's Hour Angle. Suppose, for instance, PL is the meridian intersecting the place where your ship is. Then your ship's hour angle would be the angle at the pole intersecting the meridian of your ship and the meridian of the sun or LPS and measured by the arc LS. And you will note that this distance is exactly the same as apparent time at the ship, for Apparent Time at ship is nothing more than the distance in time which the ship is from the sun. We can sum up all this information in a few simple rules, which put in your Note-Book:
Mean Time = Clock Time.
G.M.T. = Greenwich Mean Time.
L.M.T. = Local Mean Time.
Apparent Time = Actual or Sun Time.
G.A.T. (G.H.A.) = Greenwich Apparent Time or Greenwich Hour Angle.
L.A.T. (S.H.A.) = Local Apparent Time or Ship's Hour Angle.
Difference between apparent and mean time or mean and apparent time - Equation of Time.
Right under this in your Note-Book put the following diagram, which I will explain:
Twelve and Twentyfour Hour Clocks
You will see from this diagram that civil time commences at midnight and runs through 12 hours to noon. It then commences again and runs through 12 hours to midnight. The Civil Day, then, is from midnight to midnight, divided into two periods of 12 hours each.
The astronomical day commences at noon of the civil day of the same date. It comprises 24 hours, reckoned from O to 24, from noon of one day to noon of the next. Astronomical time, either apparent or mean, is the hour angle of the true or mean sun respectively, measured to the westward throughout its entire daily circuit.
Since the civil day begins 12 hours before the astronomical day and ends 12 hours before it, A.M. of a new civil day is P.M. of the astronomical day preceding. For instance, 6 hours A.M., April 15th civil time is equivalent to 18 hours April 14th, astronomical time.
Now, all astronomical calculations in which time is a necessary fact to be known, must be expressed in astronomical time. As chronometers have their face marked only from 0 to 12 as in the case of an ordinary watch, it is necessary to transpose this watch or chronometer time into astronomical time. No transposing is necessary if the time is P.M., as you can see from the diagram that both civil and astronomical times up to 12 P.M. are the same. But in A.M. time, such transposing is necessary. Put in your Note-Book:
Whenever local or chronometer time is A.M., deduct 12 hours from such time to get the correct astronomical time:
| CT | 15d 9h 10m 30s A.M. | |
| - 12 | ||
| ———————————— | ||
| CT | 14d 21h 10m 30s | |
| ——— | ||
| L.M.T. | 10d 4h 40m 16s A.M. | |
| - 12 | ||
| ———————————— | ||
| L.M.T. | 9d 16h 40m 16s |
Now we come to a very important application of time. You will remember that in one of the former lectures we stated that to find our latitude, we had to find how far North or South of the equator we were, and to find our longitude, we had to find how far East or West of the meridian at Greenwich we were. Never mind about latitude for the present. We can find our longitude exactly if we know our Greenwich time and our time at ship. For instance, in the accompanying diagram:
East and West Longitude
Suppose PG is the meridian at Greenwich, then anything to the west of PG is West longitude and anything to the East of PG is East longitude. Now suppose GPS is the H.A. of G. or G.A.T. - i.e., the distance in time G. is from the sun. And L P S is the H.A. of the ship or L.A.T. - i.e., the distance in time the ship is from the sun. Then the difference between G P S and L P S is G P L, measured by the arc L G, and that is the difference that the ship, represented by its meridian PL, is from the Greenwich meridian PG. In other words, that is the ship's longitude for, as mentioned before, longitude is the distance East or West of Greenwich that any point is, measured on the arc of the celestial equator. The longitude is West, for you can see LPG or the arc LG is west of the meridian PG.
Likewise if P E is the meridian of your ship, the Longitude in time is the S.H.A. or L.A.T., E P S (the distance your ship is from the sun) less the G.H.A. or G.A.T., G P S (the distance Greenwich is from the sun) which is the angle G P E measured by the arc G E. And this Longitude is East for you can see G P E, measured by G E, is east of the Greenwich meridian, P G.
In both these cases, however, the longitude is expressed in time, i.e., so many hours, minutes and seconds from the Greenwich meridian and we wish to express this distance in degrees, minutes and seconds of arc. The earth describes a circle of 360° every 24 hours. Then if you are 1 hour from Greenwich, you are 1/24 of 360° or 15° from Greenwich and if you are 12 hours from Greenwich, you are ½ of 360° or 180° from Greenwich. By keeping this in mind, you should be able to transpose time into degrees, minutes and seconds of arc for any fraction of time. It is, however, all worked out in Table 7 of Bowditch which turn to. (Note to Instructor: Explain this table carefully). Put in your Note-Book:
89° 24' 26" = (89°) 5h 56m
(24') 1m 36s
(26") 1 44/60s
——————————
5h 57m 37s 44/60s = 38s
4h 42m 26s
4h 40m = 70°
2m 24s = 36'
2s = 30"
—————
70° 36' 30"
Also put in your Note-Book this diagram and these formulas: (For diagram use illustration on p. 40.)
| L.M.T. + West Lo. = G.M.T. | L.A.T. + West Lo. = G.A.T. | |
| L.M.T. - East Lo. = G.M.T. | L.A.T. - East Lo. = G.A.T. | |
| G.M.T. - West Lo. = L.M.T. | G.A.T. - West Lo. = L.A.T. | |
| G.M.T. + East Lo. = L.M.T. | G.A.T. + East Lo. = L.A.T. |
If G.M.T. or G.A.T. is greater than L.M.T. or L.A.T. respectively, Lo. is West.
If G.M.T. or G.A.T. is less than L.M.T. or L.A.T. respectively, Lo. is East.
Example:
In longitude 81° 15' W, L.M.T. is April 15d 10h 17m 30s A.M. What is G.M.T.?
L.M.T. 15d 10h 17m 30s A.M.
- 12
—————————
L.M.T. 14d 22h 17m 30s
5 25 W +
—————————
G.M.T. 15d 3h 42m 30s
————
G.M.T. April 15d 3h 42m 30s
L.M.T. April 15d 10h 17m 30s A.M.
In what Lo. is ship?
G.M.T. 15d 3h 42m 30s
L.M.T. 14d 22h 17m 30s
—————————
Lo. in T 5h 25m 00s W
Lo. = 81° 15'W
Assign also for Night Work reading the following articles in Bowditch: 276-278-279-226-228-286-287-288-290-291-294 (omitting everything on page 114.)