Lectures in Navigation

by Ernest Gallaudet Draper

CT	15d 9h 10m 30s A.M.
	- 12
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CT	14d 21h 10m 30s
	———
L.M.T.	10d 4h 40m 16s A.M.
	- 12
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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:

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
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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.