pressions similarity of chemical composition' and 'similarity of crystalline form.' The following example will indicate how the so-called law of isomorphism has been used as an aid in determining the atomic weight of gallium.

2

4

Gallium sulphate was found to form a double salt with ammonium sulphate; the crystalline form of this double sulphate was identical with that of ordinary ammonia-alum. Therefore the double sulphate in question doubtless belonged to the class of alums. Now the composition of the alums is expressed by the general formula M,3SO. N2SO. 24H2O where M-AI, Fe, Cr, or Mn, and N-Na, K, Cs, Rb, or NH, In the case of common ammonia-alum M ̧ = Al ̧ = 2 × 27·02 parts by weight of aluminium; in the double sulphate of gallium and ammonium M, was found to represent 138 parts by weight of gallium. Hence, as 2 atoms of aluminium have been replaced by 138 parts by weight of gallium without altering the crystalline form or the general chemical type of the compound, it was concluded that the atomic weight of gallium was 138-69. This number was afterwards verified by the application of the law of Avogadro, and also by the specific heat method*.

There are then two generally applicable methods whereby 307 values may be found for the atomic weights of the elements; the method founded on the law of Avogadro; and the method based on the specific heats of solid elements. Besides these, there is another method, arising out of the relations between the chemical composition and crystalline forms of similar compounds, which is useful as a guide in determinations of atomic weights. The first method is applicable to determinations of the atomic and molecular weights of elements, and the molecular weights of compounds, but it is restricted to bodies which are gasifiable without decomposition. The second and third methods can be strictly applied only to find values for the atomic weights of solid elements, and to some extent of elements which form solid compounds. All the methods are essentially physical; they are based on physical conceptions, and they are to a great extent developed by physical reasoning. Thus the image of the molecule which is called up in the mind by the statement “ equal volumes of gases contain equal numbers of molecules" is that of a very small, definite,

*We do not propose to go more fully into the method of isomorphism here. The study of this subject is more suited to the advanced student of chemistry.

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portion of matter, moving about without separation into parts, colliding with other like particles of matter, and rebounding after collision. The application of this conception to chemical changes obliges us to admit that in many of these changes the molecule is shattered into parts. Thus we are led to the chemical conception of the atom, as a portion of matter smaller than the molecule, and either itself without parts, or else composed of parts which, so far as we know at present, do not part company during any of the changes which the atom undergoes. The study of the properties of atoms leads to the generalisation that the atoms of all solid elements, at certain temperatures, have equal capacities for heat.

The molecular and atomic theory regards the molecule of a gas as the smallest portion of it in which the properties of the gas inhere. Chemical change, it looks on as an interaction between molecules; in most cases of chemical change the interacting molecules are separated into parts and these parts are rearranged to form new molecules; but in some cases it is probable that one kind of molecules combines with other kinds to form more complex molecules.

The Daltonian atomic theory applied the term atom to elements and compounds alike; but the atom of an element was supposed to have no parts, whereas the atom of a compound was separable into unlike parts. The molecular and atomic theory applies the term molecule to elements and compounds alike; but the molecule whether of an element or a compound is regarded as built up of parts which may be either all of one kind, or of different kinds.

The atomic weights of most of the elements have been determined by one or other of the physical methods arising out of the molecular and atomic theory. But there are a few elements no compounds of which have yet been gasified, and the specific heats of which have not yet been determined. The values assigned to the atomic weights of these elements have been gained by studying the chemical analogies between these elements and others to which the methods of the molecular and atomic theory are directly applicable.

The metal rubidium is a case in point. No compound of this metal has been gasified; hence the molecular weights of rubidium compounds are not known; and hence the atomic weight of the element has not been determined by the application of the law of Avogadro. Nor has the specific heat

of rubidium been determined. The value given to the atomic weight of rubidium is 85.2; how has this number been obtained?

X

There can be no doubt that rubidium belongs to the class of elements which comprises sodium and potassium (for details of the properties of this group, s. Chap. XI. pars. 160-168). The atomic weights of sodium and potassium are 23 and 39 (in round numbers) respectively; 23 parts by weight of sodium and 39 parts by weight of potassium severally combine with (a) 8 parts by weight of oxygen, and (b) 35.5 parts by weight of chlorine; the specific heats of these metals are, for sodium 293, for potassium 166; now 293 × 23 = 6·7, and 166 × 396.5. But if 23 and 39 are the atomic weights of sodium and potassium, respectively, and if 16 is the atomic weight of oxygen, then analyses of the oxide, chloride, &c. &c. of these metals shew that the formulæ of these compounds must be MO, MCI, M2SO, M,CO,, &c. &c. where M = one atomic weight of sodium or potassium. Now the compounds of rubidium are very similar in their properties to the compounds of potassium and sodium, hence the oxide, chloride, &c. &c. of rubidium ought to be represented by the formulæ Rb,O, RbCl, Rb,SO,, RьCO,, &c. &c. where Rb = one atomic weight of rubidium. But in order to do this, the number 85.2 must be assigned to the atomic weight of rubidium.

The method based on a study of the analogies between the chemical properties of a specified element and those of other elements is also frequently used to check the results of the determinations of atomic weights gained by applying the two physical methods. But a fuller examination of this chemical method will be better made when we come to consider the periodic law (s. Chaps. XVIII. and XXVI.).

In the sketch which has been given of the molecular theory 309 of the structure of matter, the conception of the molecule has been applied only to gases. The theory regards liquids and solids also as built up of minute particles. It asserts that the minute particles of a liquid have less freedom of motion than the molecules of a gas, and that they are so frequently in collision with each other that the paths which they describe are far removed from being straight lines. The minute particles of a solid are supposed to oscillate about positions of equilibrium, and never to travel far from these positions. The particles of both liquids and solids, moreover, are probably aggregations of smaller particles; and the complexity of the

particles of a specified liquid or solid is probably not the same for all the particles, nor even for the same particle at different times. 310 It is customary to apply the term molecule to the particles of liquids and solids, as well as to the much more rigidly defined particles of gases. But no generalisations can at present be made, in terms of the molecular theory, regarding the properties of liquids and solids comparable with those which have been made for gases, and which are known as the laws of Boyle, Charles, and Avogadro. We cannot define the term molecule as applied to a liquid or solid body; we can define the term when applied to a gas.

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When therefore we speak of the molecular weight of an element or a compound we ought to mean the relative weight of the molecule of the gaseous element or compound. The expression molecular weight is not always used in chemistry in this strict meaning; it is frequently applied to what in former chapters we have called the reacting weight of a body.

To take an example. No compounds of sodium have been gasified; therefore we do not know the molecular weights of any compounds of this element. But the atomic weight of this metal has been determined by applying the method of specific heat. The simplest formula which can be given to the compounds of sodium, when we know that Na=23, are Na,O, NaCl, NaBr, NaNO,, Na,CO,, Na,SO,, &c. Moreover these formulæ enable us to express the chemical reactions of the compounds in a consistent and satisfactory manner. These formulæ are therefore adopted. But we must carefully observe that the formulæ do not necessarily express the atomic compositions of molecules of the compounds: indeed we cannot in strict accuracy speak of a molecule of sodium oxide, or sodium chloride, because these compounds are only known as solids and the term molecule corresponds to an accurately defined conception only when it is applied to gases.

We formerly used the term reacting weight of a compound; thus Na,O represents the composition of a reacting weight of sodium oxide. We may now, in the light thrown on chemical interactions by the molecular and atomic theory, widen the meaning we give to this term reacting weight. Although Na O does not certainly represent the atomic composition of a molecule of sodium oxide, yet it almost certainly represents the ratio of the number of atoms which constitute the reacting

weight of this oxide. The reacting weight of a compound may now mean for us a group or collocation of atoms which interacts chemically with other groups of atoms. The formula of a solid or liquid compound does not necessarily express the number of atoms in this chemically reacting group of atomsindeed the number may vary under different circumstancesbut in all probability it does represent the ratio between the number of atoms in this reacting group. The atomic composition of the reacting weight of sodium oxide may perhaps be better represented by one of the formulæ NaО,, Na ̧ ̧, Na,,O,, than by the simpler formula Na,O; but