I would guess that the first careful measurements that are ever referenced were performed by Jacques Charles. In 1787 he did an experiment where he filled 5 balloons with with equal volumes of oxygen, hydrogen, nitrogen, carbon dioxide, and air and he heated them all to 80oC. He noticed that all five balloons increased in volume by the exact same amount, but never published his results. Charles' law (which describes the relationship between the volume of a gas and its temperature) was actually developed by Guy-Lussac, but named after Charles because of this initial unpublished experiment.
It could also be Boyle.
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