During the following months he returned to the study of those cases in which the same elements combine to form more than one compound. We have seen that oxygen unites with nitric oxide to form two compounds, and that into the one compound twice as much nitric oxide (by weight) enters as into the other. A like relation was found in the weight of oxygen combining with carbon in the two compounds carbon monoxide and carbonic acid. In the summer of 1804 he investigated the composition of two compounds of hydrogen and carbon, marsh gas (methane) and olefiant gas (ethylene), and found that the first contained just twice as much hydrogen in relation to the carbon as the second compound contained. In a series of compounds of the same two elements one atom of one unites with one, two, three, or more atoms of the other; that is, a simple ratio exists between the weights in which the second element enters into combination with the first. This law of multiple proportions afforded confirmation of Dalton's atomic theory, or chemical theory of definite proportions.
"Without such a theory," says Sir Henry Roscoe, "modern chemistry would be a chaos; with it, order reigns supreme, and every apparently contradictory discovery only marks out more distinctly the value and importance of Dalton's work." In 1826 Sir Humphry Davy recognized Dalton's services to science in the following terms: "Finding that in certain compounds of gaseous bodies the same elements always combined in the same proportions, and that when there was more than one combination the quantity of the elements always had a constant relation,—such as 1 to 2, or 1 to 3, or 1 to 4,—he explained this fact on the Newtonian doctrine of indivisible atoms; and contended that, the relative weight of one atom to that of any other atom being known, its proportions or weight in all its combinations might be ascertained, thus making the statics of chemistry depend upon simple questions in subtraction or multiplication and enabling the student to deduce an immense number of facts from a few well-authenticated experimental results. Mr. Dalton's permanent reputation will rest upon his having discovered a simple principle universally applicable to the facts of chemistry, in fixing the proportions in which bodies combine, and thus laying the foundation for future labors respecting the sublime and transcendental parts of the science of corpuscular motion. His merits in this respect resemble those of Kepler in astronomy."
In 1808 Dalton's atomic theory received striking confirmation through the investigations of the French scientist Gay-Lussac, who showed that gases, under similar circumstances of temperature and pressure, always combine in simple proportions by volume when they act on one another, and that when the result of the union is a gas, its volume also is in a simple ratio to the volumes of its components. One of Dalton's friends summed up the result of Gay-Lussac's research in this simple fashion: "His paper is on the combination of gases. He finds that all unite in equal bulks, or two bulks of one to one of another, or three bulks of one to one of another." When Dalton had investigated the relative weights with which elements combine, he had found no simple arithmetical relationship between atomic weight and atomic weight. When two or more compounds of the same elements are formed, Dalton found, however, as we have seen, that the proportion of the element added to form the second or third compound is a multiple by weight of the first quantity. Gay-Lussac now showed that gases, "in whatever proportions they may combine, always give rise to compounds whose elements by volume are multiples of each other."
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 H2O.
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.
For James Prescott Joule (1818-1889), who came of a family of brewers and was early engaged himself in the brewing industry, was reserved, however, the distinction of discovering the exact relation between heat and mechanical energy. After having studied chemistry under Dalton at Manchester, he became engrossed in physical experimentation. In 1843 he prepared a paper On the Calorific Effects of Magneto-Electricity and on the Mechanical Value of Heat. In this he dealt with the relations between heat and the ordinary forms of mechanical power, and demonstrated that the mechanical energy spent "in turning a magneto-electrical machine is converted into the heat evolved by the passage of the currents of induction through its coils; and, on the other hand, that the motive power of the electro-magnetic engine is obtained at the expense of the heat due to the chemical reactions of the battery by which it is worked." In 1844 he proceeded to apply the principles maintained in his earlier study to changes of temperature as related to changes in the density of gases. He was conscious of the practical, as well as the theoretical, import of his investigation. Indeed, it was through the determination by this illustrious pupil of Dalton's of the amount of heat produced by the compression of gases that one of the greatest improvements of the steam engine was later effected. Joule felt that his investigation at the same time confirmed the dynamical theory of heat which originated with Bacon, and had at a subsequent period been so well supported by the experiments of Rumford, Davy, and others.
Already, in this paper of June, 1844, Joule had expressed the hope of ascertaining the mechanical equivalent of heat with the accuracy that its importance for physical science demanded. He returned to this question again and again. According to his final result the quantity of heat required to raise one pound of water in temperature by one degree Fahrenheit is equivalent to the mechanical energy required to raise 772.55 pounds through a distance of one foot. Heat was thus demonstrated to be a form of energy, the relation being constant between it and mechanical energy. Mechanical energy may be converted into heat; if heat disappears, some other form of energy, equivalent in amount to the heat lost, must replace it. The doctrine that a certain quantity of heat is always equivalent to a certain amount of mechanical energy is only a special case of the Law of the Conservation of Energy, first clearly enunciated by Joule and Helmholtz in 1847, and generally regarded as the most important scientific discovery of the nineteenth century.