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=tFitzroy Barometer Correction

Hi! I've had a Fitzroy barometer for a few years which I've prized... but mainly as an ornament and I'd like to start using it.

Would anyone be able to help me with the correction procedure for a Fitzroy barometer as I'm not sure I'm doing it right. There seems to be some inconsistency with the signs for the adjustments online and I'm not sure which source to trust. I've included a passage from a book which I'm trying to follow.

So the source data I've got is that my barometer read 30.09", he attached thermometer read 66F, the outside air temperature was 12C, my latitude is 51 deg North in the UK, and my barometer is 38 metres above sea level.

Using a combination of tables online I looked up an altitude correction of +0.14", gravity correction of +0.02", temperature correction of -0.10" and I don't know what the index correction is but I want to assume it's small.

This takes me to 30.15" 1021 hPa but the Met Office said that at the time of my reading my local pressure was 1013 hPa. Do you think I've done anything wrong, or maybe I just have too high ambitions for my level of accuracy!
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