To begin, then, with the sextant itself. It is nothing but an
instrument with which we can measure how high up the sun is in the
sky. Now, everyone knows that the sun slowly climbs the sky in
the morning, reaches its greatest height at noon, and then slowly
sinks again in the afternoon. The captain simply begins to watch
the sun through the sextant shortly before noon, and keeps at it
until he discovers that the sun is just beginning to descend. That
is the instant of noon on the ship. The captain quickly glances
at the chronometer, or calls out "noon" to an officer who is near
that instrument. And so the error of the chronometer becomes known
then and there without any further astronomical calculations
whatever. Navigators can also find the chronometer error by sextant
observations when the sun is a long way from noon. The methods of
doing this are somewhat less simple than for the noon observation;
they belong to the details of navigation, into which we cannot
enter here.
Incidentally, the captain also notes with the sextant how high
the sun was in the sky at the noon observation. He has in his
mysterious "chart-room" some printed astronomical tables,
which tell him in what terrestrial latitude the sun will have
precisely that height on that particular day of the year. Thus the
terrestrial latitude becomes known easily enough, and if only the
captain could get his longitude too, he would know just where his
ship was that day at noon.
We have seen that the sextant observations furnish the error of
the chronometer according to ship's time. In other words, the
captain is in possession of the correct local time in the place
where the ship actually is. Now, if he also had the correct time
at that moment of some well-known place on shore, he would know
the difference in time between that place on shore and the ship.
But every traveller by land or sea is aware that there are always
differences of time between different places on the earth. If a
watch be right on leaving New York, for instance, it will be much
too fast on arriving at Chicago or San Francisco; the farther you
go the larger becomes the error of your watch. In fact, if you
could find out how much your watch had gone into error, you would
in a sense know how far east or west you had travelled.
Public-domain text, read in full here on John Shaqi.
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