How and when did scientists first determine that hydrogen was the lightest element?

Question

Cavendish first isolated hydrogen and recognized it for what it was; Lavoisier realized that water consisted of hydrogen and oxygen; Dalton used hydrogen as the basis for relative atomic weights by giving it the value of 1 and assuming that the atomic weight of all other elements would be, in relative terms, simple multiples of that value. But why did Dalton assume hydrogen was the lightest element? Who determined that, and when?

Answer 1

Cavendish was apparently the first to measure the density of hydrogen, then called inflammable air (air that can burn). It didn't have the identity of an element at the time, of course, and there were other varieties of inflammable air known, but these sorts of questions would be resolved before Dalton's time.

Inflammable air was observed by e.g. Boyle, among others, but it was Cavendish who measured the density and recorded some of its notable properties. This was in Three papers, containing experiments on factitious air (1766), available online. There's a few commentaries on this, e.g. here:

West JB. Henry Cavendish (1731-1810): hydrogen, carbon dioxide, water, and weighing the world. Am J Physiol Lung Cell Mol Physiol. 2014 Jul 1;307(1):L1-6. doi: 10.1152/ajplung.00067.2014. Epub 2014 May 2. PMID: 24793169.

I will quote Cavendish for the main result:

The specific gravity of each of the above-mentioned sorts of inflammable air, except the first, was tried in the following manner. A bladder holding about 100 ounce measures was filled with inflammable air, in the manner represented in Fig. 3. and the air pressed out again as perfectly as possible. By this means the small quantity of air remaining in the bladder was almost intirely of the inflammable kind. 80 ounce measures of the inflammable air, produced from zinc by the vitriolic acid, were then forced into the bladder in the same manner: after which, the pewter pipe was taken out of the wooden cap of the bladder, the orifice of the cap stopt up with a bit of lute, and the bladder weighed. A hole was then made in the lute, the air pressed out as perfectly as possible, and the bladder weighed again. It was found to have increased in weight $40 \frac{3}{4}$ grains. Therefore the air pressed out of the bladder weighs $40 \frac{3}{4}$ grains less than an equal quantity of common air: but the quantity of air pressed our of the bladder must be nearly the same as that which was forced into it, i.e. 80 ounce measures: consequently 80 ounce measures of this sort of inflammable air weight $40 \frac{3}{4}$ grains less than an equal bulk of common air. ...

... Taking a medium therefore of the different trials, 80 ounce measures of inflammable air weigh 41 grains less than an equal bulk of common air. Therefore, if the density of common air, at the time when this experiment was tried, was 800 times less than that of water, which, I imagine, must be near the truth, inflammable air must be 5490 times lighter than water, or near 7 times lighter than common air. But if the density of common air was 850 times less than that of water, then would inflammable air be 9200 times lighter than water, or $10 \frac{8}{10}$ lighter than common air.

(Emphasis mine.)

The value of 1/800 the density of water is commonly accepted even today, thus Cavendish is saying that the density of hydrogen (and, by Avogadro's law (1812), the atomic weight of hydrogen) is 1/7th that of air at standard temperature and pressure. The true ratio should be about 1/13th that of air (0.09 g/L to 1.2 g/L), about half of what Cavendish found.

I suppose no other gas would (or could) be found to have such a low density (and by extension, atomic weight; but this would come 6 years after Dalton's paper).