By seeing how the water swirls and whirlpools when going down the drain in a washbasin is it possible to tell something about the longitude or latitude where the individual is?
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No. It is not possible. Coriolis force, if measured precisely, might give the latitude --- but is far to small to affect water going down a washbasin drain. You need a huge tank and weeks of waiting to see any effect. Longitude cannot be measured without a clock to give you Greenwich Mean Time.
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$\begingroup$ I'd love to see a calculation of the latitude. $\endgroup$ Commented Apr 14 at 16:03
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$\begingroup$ Use a Foucault pendulum to determine the lattitude. For water see: nature.com/articles/2071084a0 and nature.com/articles/1961080b0.pdf $\endgroup$ Commented Apr 14 at 16:10