II.] EQUIVALENT PROPORTIONS. 19 chemical attraction of the chlorine for the copper than for the mercury; a portion of the copper is dissolved, cupric chloride is formed, and a corresponding quantity of mercury is deposited. On making the experiment with suitable care, it is found that for each 3i"74 milligrammes of copper dissolved, ioo of mercury are separated in globules. In a similar way, when a strip of zinc is placed in a solution of cupric chloride, a deposit of metallic copper is separated, and for every 3174 mgrms. of copper thrown down, the zinc will lose 32-5 mgrms. in weight, whilst a corresponding amount of zinc chloride is formed in the liquid. Finally, if into a solution of hydrochloric acid a rod of zinc be introduced, hydrogen will be set free; and if the volume of the gas be measured, it will be found that i mgrm. of hydrogen is liberated for every 32*5 mgrms. of zinc dissolved. From this series of experiments we learn that different but definite amounts of the various metals are capable of displacing each other; for it appears that 100 parts of mercury, 31-74 of copper, 32"5 of zinc, and 1 of hydrogen, are each capable of exactly supplying the place of the other, in combination with one uniform amount (35*5 parts) of chlorine; and these different quantities of the metals are said to be chemically equivalent to each other, and the numbers obtained in this way form the combining ratios of the different elements. For the purpose of conveniently comparing together the quantities of the different elements which are thus equivalent to each other, it is necessary to select one element as the unit or standard of comparison. With this view chemists have agreed to take hydrogen as their unit or starting-point, since it is the element which enters into combination with a smaller equivalent part than any other. It must not, however, be supposed that the equivalent quantities of the elements can usually be ascertained by direct substitution for a given quantity of hydrogen: recourse is had therefore to indirect processes, such as the determination of the ratio in which each element unites with a fixed quantity of some other element, such as chlorine or oxygen. It is important to distinguish between the ideas chemical equivalent and combining proportion, or more correctly, combining ratio. Bodies can only be said to be equivalent to each other when they can be substituted for each other in combination, and form compounds more or less analogous; the proportion in which they thus displace each other, constitutes their equivalent proportion or numerical chemical equivalent. Definite quantities of silver, copper, iron, zinc, and potassium, for example, may be substituted one for the other in combination 20 EQUIVALENT PROPORTIONS. [il. with a given quantity of chlorine. In like manner, certain quantities of chlorine, of bromine, and of iodine, may be made to combine with a given quantity of silver; the quantity of bromine which will displace the iodine, or that of chlorine which will displace the bromine, being the true equivalent quantities of these elements, when compared with each other. It must not be supposed that this equivalence implies any equivalence of chemical energy of the different elements. This energy may be, to some extent, measured by the quantity of heat evolved during the combination of the elements with one another, and this is by no means the same when equivalents of different elements are employed (199 et (12) Tables of Equivalent Numbers.—Chemists are in the habit of referring the results obtained by analysis to the quantity contained in 100 parts of the body submitted to experiment. For instance, it has been ascertained by analysis that 100 parts of hydrochloric acid contain 97*26 of chlorine, and 2*74 of hydrogen; that 100 parts of zinc chloride contain 52*21 of chlorine, and 4779 of zinc; that 100 of cupric chloride contain 52*80 of chlorine, and 47*20 of copper; that 100 of mercuric chloride contain 26-20 of chlorine, and 73*80 of mercury; and that 100 of argentic chloride contain 2474 of chlorine, and 75*26 of silver. These illustrations are sufficient to prove that the quantity of chlorine is not the same in the compounds which it forms with the several elements; but this method of stating the result is not adapted to exhibit the numerical relations of these quantities in their simplest form. These relations are rendered much more evident in the following way. Having ascertained the quantity of each constituent in 100 parts of the various compounds which each elementary body forms when it combines with chlorine, let us determine by calculation that ratio in which each element unites with the same fixed quantity of chlorine, and let us take for our fixed quantity of chlorine the quantity of it which enters into combination with 1 part (say 1 gramme) of hydrogen. This is easily calculated, since we know that 100 parts of hydrochloric T2.] SCALE OF EQUIVALENTS. 21 acid contain 97*26 of chlorine, and 2*74 of hydrogen; consequently 274 : 97-26 :: 1 : 35-5 or $y$ grms. of chlorine are united in hydrochloric acid with 1 grm. of hydrogen. Now, it is easy to ascertain, by similar calculations, the quantity of each of the elements enumerated in the foregoing series of chlorides which is combined with 35-5 grms. of chlorine. In zincic chloride, for example, 3 2'5 grms. of zinc are united with 3j5 of chlorine; for 52-21 : 47-79 :: 35-5 : 325 In cupric chloride 35*5 of chlorine are united with 31-74 grms. of copper; for 52"8 •■ 47"2 = ■ 35'5 : 3I74 In mercuric chloride 35-5 grms. of chlorine are united with 100 of mercury; for 26-2 :73-8 :: 35-5 : 100 whilst in argentic chloride 35-5 of chlorine are united with 108 grms. of silver; since 2474 ■ 75"26 :: 35"5 : i°8 consequently one part of hydrogen, 32-5 parts of zinc, 31-74 of copper, 100 of mercury, and 108 of silver are chemically equivalent to each other, since they each combine with the same quantity (355 parts) of chlorine. But results, when obtained by experiments conducted on this plan, are not always free from ambiguity, for there are cases in which the same metal appears to have more than one equivalent number. Mercury, for example, forms another chloride, calomel, which is quite different from the one above described; it contains twice the quantity of mercury combined with our standard quantity of chlorine, or 200 grms. of mercury with 355 of chlorine. In like manner copper forms another chloride, which contains twice as much copper as the one above described, or 63-4 grms. of copper combined with 35-5 grms. of chlorine. Which of these two proportions of mercury or of copper is to be taken as the equivalent of the metal? Each of the two numbers thus obtained is in fact the true equivalent under the particular circumstances; so that both mercury and copper have two equivalents; and the same thing is true of iron, of tin, of plati22 ATOMIC CONSTITUTION OF MATTER. [l2. num, and of several other elements. The ambiguity thus occasioned may, however, be removed by means of a conception known as the atomic hypothesis, first distinctly enunciated by Dalton, though it has since been in some degree modified. (12 a) Hypothesis of the Atomic Constitution of Matter.— Dalton's atomic theory is that every element is composed of ultimate particles or atoms, which cannot be further subdivided by chemical or mechanical means. That these atoms are, in the same element, exactly equal in size and in weight, and absolutely similar in all respects. That the atoms of any one element differ from those of all the other elements in mass and in chemical properties. And that whenever combination takes place between any two elements, union occurs between them atom to atom. If these assumptions-be admitted, we find— C. That the ratio in which combination occurs must, when the same compound is formed, always be definite; since that ratio is determined by the relative weights of the atoms of the combining elements, and the atom cannot be subdivided. z°. That when the same elements unite in several ratios, these ratios must vary according to the terms of a simple series of multiples, since each atom of one element must unite with the other element in the ratio of i, of 2, or of 3 atoms, or in some other ratio almost equally simple, inasmuch as the atom does not admit of subdivision. 30. That combination must occur also in equivalent proportion; since the equivalent amounts of each element must be in the proportion either of the weights of their atoms, or of a simple multiple of those weights. In order to elucidate these statements further, let us suppose, for example, that an atom of mercury weighs 200 times as much as the atom of hydrogen, that the atom of silver weighs 108 times as much, the atom of sodium 23 times as much, the atom of chlorine $$'5 times as much, and the atom of oxygen 16 times as much,—it follows that when chlorine and silver unite to form argentic chloride, if one atom of each element enters into each molecule of the compound, this chloride must necessarily and invariably contain, in 143*5 parts, be they grammes, grains, or pounds, 108 of silver, and 35*5 of chlorine. In like manner, if each of the molecules of sodic chloride be formed by the union of one atom of sodium with one atom of chlorine, then 585 parts will necessarily consist of 23 parts of sodium, and 35*5 of chlorine. So also, if each molecule of water consists of 2 atoms of 13 ■] SYMBOLIC NOTATION. 23 hydrogen and 1 atom of oxygen, it must happen that 18 parts of water will always contain 2 parts of hydrogen and 16 of oxygen. Again, if calomel be formed of 1 atom of mercury and 1 of chlorine, it is a matter of necessity that in 235^5 parts of calomel, 200 consist of mercury, and 35*5 of chlorine; while, if corrosive sublimate be formed by the union of 1 atom of mercury with 2 atoms of chlorine, 271 parts of this chloride must contain 200 parts of mercury, and 71 of chlorine, or twice as much chlorine as is found in calomel. Suppose now that into a solution of corrosive sublimate a slip of copper be introduced : the copper will displace the mercury; and if the weight of the atom of copper be 634 times that of the atom of hydrogen, and cupric chloride be formed by the union of 1 atom of copper and 2 atoms of chlorine, the mercury displaced must be in the proportion of 200 parts for every 6 3^4 parts of copper which enter into solution. In other words, 63^4 parts of copper are chemically equivalent to 200 parts of mercury. Dalton indeed supposed that the chemical equivalents of the elements always represented the relative weights of their atoms, and hence the term atomic weight has often been employed as synonymous with the term chemical equivalent. But the ideas involved in the two terms are essentially distinct. There can only be one atomic weight of a simple substance; but as we have seen in the case of mercury and of copper, there may be two chemical equivalents for the same element, and, in some cases, the equivalents may be even more numerous. The atomic weight of a body may coincide with its ordinary chemical equivalent, or it maybe a multiple of it. The equivalent number is necessarily a direct experimental result; whilst the number adopted for the atomic weight is arrived at from considerations often somewhat complicated, based partly on the law of gaseous volumes (14), partly on the experimental results upon the specific heat of the bodies under investigation (172), and partly on the isomorphism or similarity in crystalline form of bodies of analogous constitution (83). The table at pp. 24, 25, contains tr list of the elementary bodies at present known to chemists, with the atomic weights ascribed to them by the authorities mentioned, as well as the symbols by which each element is indicated in describing chemical changes. (13) Symbolic Notation.—Before proceeding further, it will be advantageous to describe the principles of notation, as applied to the construction of chemical formulae. This notation constitutes a kind of short-hand, which materially facilitates the representation |