[56] From a calculation of the ratio in which the density of the atmosphere decreases with its altitude, and from that of the relative combustibility of different bodies, it follows that the taper would be extinguished at a height of between nine and ten miles--hydrogen, between twelve and thirteen--and sulphur, between fifteen and sixteen. Hitherto he had only considered the effects of rarefaction, when produced by the diminution of pressure; he had next to investigate the phenomena of rarefaction when occasioned by expansion from heat. The experiments of M. de Grotthus had apparently shown that rarefaction by heat destroys the combustibility of gaseous mixtures; those of Davy, however, proved that it enables them to explode at a lower temperature. In the progress of this research, while passing mixtures of hydrogen and oxygen through heated tubes, the heat being still below redness, he observed that steam was formed without any combustion. Here was a slow combination without combustion, as long since observed with respect to hydrogen and chlorine, and oxygen and metals; and he believes that such a phenomenon will happen at certain temperatures with most substances that unite by heat. On trying charcoal, he found that at a temperature which appeared to be a little above the boiling point of quicksilver, it converted oxygen pretty rapidly into carbonic acid, without any luminous appearance, and that, at a dull red-heat, the elements of olefiant gas combined in a similar manner with oxygen, slowly and without explosion. It occurred to Davy, in the progress of these experiments, that, during this species of slow combination, although the increase of temperature might not be sufficient to render the gaseous matters luminous, or to produce flame, it might still be adequate to ignite solid matters exposed to them. It was while engaged in devising experiments to ascertain this fact, that he was accidentally led to the discovery of the continued ignition of platinum wire, during the slow combination of coal gas with atmospheric air; the circumstances of which have been already related, as well as the curious invention to which the application of the fact gave origin.[57] [57] See page 100 of this volume. For this and his preceding papers on the subjects of flame and combustion, the President and Council of the Royal Society adjudged to Sir Humphry Davy the gold and silver medals, on the donation of Count Rumford;[58] and never, I will venture say, did a society in awarding a prize more faithfully comply with the intentions of its founder.