compounds of only 42 elements have been prepared and analysed. Hence the application of the method based on the law of Avogadro is limited. This method is at present the only general method for determining the relative weights of the gaseous molecules of elements and compounds. But there is another general method whereby values may be found for the atomic weights of elements. This method is contained in the statement ; The products of the specific heats of solid elements, determined in each case at the temperature-interval for which specific heat is nearly constant, into the atomic weights of these elements, approach a constant, the mean value of which is 6·4. This statement is a modification of the so-called law of Dulong and Petit. From their study of the specific heats of 13 solid elements in the year 1819, these naturalists announced that "the atoms of all simple bodies have exactly the same capacity for heat." Investigation has shewn that this statement was too absolute. The specific heats of some solid elements, e.g. carbon, boron, silicon, beryllium, vary much with variations of temperature, and become approximately constant only at high temperatures. The specific heat of a solid also varies to some extent with variations in the greater or less compactness of the specimen. The product specific heat of solid element × atomic weight is usually called the atomic heat of the element. The specific heats of a few elements have not yet been 303 determined. Values which may be approximately correct, have been indirectly obtained for some of these; but too great stress must not be laid on these values. The indirect method in question is based on the assumption, to some extent verified by facts, that the 'molecular heat' of a solid compound, i.e. the product of the specific heat into the mass of the compound expressed by its formula, is equal to the sum of the atomic heats of the elements in the compound; therefore if the 'molecular heat' (as thus defined) of a solid compound is known, and the atomic heats of all the elements in the compound except one are known, the atomic heat of the remaining one element can be calculated. The following statements summarise the present state of knowledge with regard to the atomic heats of the 42 elements maximum values for the atomic weights of which have been determined by applying the law of Avogadro (par. 301). I. Solid elements, 28 in number, the specific heats of which 304 305 306 have been directly determined, and the atomic heats of which are approximately equal to 6·4 :-P, S, K, Ti, Cr, Al, Zn, As, Se, Br, Zr, Mo, Fe, Cd, In, Sn, Sb, Te, I, Cu, W, Os, Hg, Tl, Pb, Bi, Th, U. II. Solid elements, 6 in number, the specific heats of which have been directly determined, and the atomic heats of which are approximately equal to 5.5-Be, B, C, Si, Ga, Ge. III. One solid element, the atomic heat of which has been indirectly determined and is probably equal to 6·4:-Vanadium. IV. Five gaseous elements, the specific heats of which in solid form have only been determined indirectly and are extremely doubtful :-H, N, O, F, Cl. V. Two solid elements the specific heats of which have not been determined directly or indirectly:-Nb, Ta. These data establish a very fair probability in favour of the statement made in par. 302 regarding the constant value of the atomic heat of the solid elements. If this statement is granted, then an approximate value may be found for the atomic weight of an element by dividing 64 by the specific heat of that element in the solid form. The maximum values found for the atomic weights of aluminium, iron, copper, and gallium, by the use of Avogadro's law were 54-04, 111-8, 126-8, and 138, respectively (s. Table, par. 301). Now the spec. heats of these elements are ·225, 114, 097, and 08, respectively; dividing 6·4 by each of these numbers we get the quotients, 28.5, 56.1, 65.9, and 80. Therefore we conclude that the maximum values found for the atomic weights of these elements by applying Avogadro's law must be halved, and we adopt the numbers 27.02, 55.9, 63.4 and 69, as very probably the true atomic weights of aluminium, iron, copper, and gallium, respectively. There is another physical method which has sometimes been found useful in determinations of atomic weights, but which can only be used as a guide to point the way to experimental inquiries. This method is founded on the generalisation, that similarity of chemical composition is usually associated with close similarity of crystalline form. In some cases marked similarity of composition is accompanied by identity of crystalline form; e.g. the oxides of arsenic and antimony, As., and Sb,O,, crystallise in identical forms; they are isomorphous. 2 3 2 The difficulties in applying this method-generally known as the method of isomorphism-lie in the vagueness of the ex 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. 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 M2 = 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*. 2 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. 308 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 either all of one kind, or of different kinds. be 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? = 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 x 2367, and •166 × 39 6·5. 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 M2O, MCI, M2SO,, M,CO2, &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,, RыCO,, &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 ticles of a solid are supposed to oscillate about positions of |