Measurement of Terrestrial Longitude

Theorem

To measure the (terrestrial) longitude of a position:

$(1): \quad$ Identify the exact moment of noon at the location in question

$(2): \quad$ Work out the precise time of day $t$ that this happens.

Let $N$ be the time of noon at the principal meridian on the day in question.

Let $x$ be the number of hours before $N$ at the principal meridian.

If $t$ is after $N$, then $x$ is treated as negative.

Then the (terrestrial) longitude is $15 x \degrees$.

If $x$ is positive, the (terrestrial) longitude is east.

If $x$ is negative, the (terrestrial) longitude is west.

Proof

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Sources

• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $6$: Curves and Coordinates: Coordinate geometry today