1737 in science
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- May 28 – The planet Venus passes in front of Mercury. The event is witnessed during the evening by amateur astronomer John Bevis at the Royal Greenwich Observatory in England. As of 2006, it is still the only such planet/planet occultation that has been directly observed.
- Elizabeth Blackwell's A Curious Herbal, with her own colour illustrations, is published in London.
- Francesco Serao is the first person to use the word lava in connection with extruded magma in a short account of the eruption of Mount Vesuvius which took place between May 14 and June 4.
- October 11 – An earthquake in Calcutta, India is said to have caused 300,000 deaths; this is now in question: it was probably a cyclone, with deaths estimated at 3,000.
- October 16 – An earthquake with an estimated magnitude of 8.3 strikes offshore of the Kamchatka Peninsula.
- John Harrison is given an award from the longitude prize to continue his work on development of a stable marine chronometer.