In 1811 Avogadro, in an essay on the relative masses of atoms, succeeded in further confirming Dalton's theory and in explaining the atomic basis of Gay-Lussac's discovery of simple volume relations in the formation of chemical compounds. According to the Italian scientist the _number_ of molecules in all gases is always the same for equal volumes, or always proportional to the volumes, it being taken for granted that the temperature and pressure are the same for each gas. Dalton had supposed that water is formed by the union of hydrogen and oxygen, atom for atom. Gay-Lussac found that two volumes of hydrogen combined with one volume of oxygen to produce two volumes of water vapor. According to Avogadro the water vapor contains twice as many atoms of hydrogen as of oxygen. One volume of hydrogen has the same number of molecules as one volume of oxygen. When the two volumes combine with one, the combination does not take place, as Dalton had supposed, atom for atom, but each half-molecule of oxygen combines with one molecule of hydrogen. The symbol for water is, therefore, not HO but H{2}O. Enough has been said to establish Dalton's claim to be styled a great lawgiver of chemical science. His influence in further advancing definitely formulated knowledge of physical phenomena can here be indicated only in part. In 1800 he wrote a paper _On the Heat and Cold produced by the Mechanical Condensation and Rarefaction of Air_. This contains, according to Dalton's biographer, the first quantitative statement of the heat evolved by compression and the heat evolved by dilatation. His contribution to the theory of heat has been stated thus: The volume of a gas under constant pressure expands when raised to the boiling temperature by the same fraction of itself, whatever be the nature of the gas. In 1798 Count Rumford had reported to the Royal Society his _Enquiry concerning the Source of Heat excited by Friction_, the data for which had been gathered at Munich. Interested as he was in the practical problem of providing heat for the homes of the city poor, Rumford had been struck by the amount of heat developed in the boring-out of cannon at the arsenal. He concluded that anything which could be created indefinitely by a process of friction could not be a substance, such as sulphur or hydrogen, but must be a mode of motion. In the same year the youthful Davy was following independently this line of investigation by rubbing two pieces of ice together, by clock-work, in a vacuum. The friction caused the ice to melt, although the experiment was undertaken in a temperature of 29° Fahrenheit.