It has been abundantly proved that the 'atom* of the chemist and the °molecule of the physicist are (in general) different things, a molecule being a system formed by the union of a definite number of atoms, combined in a definite way. The molecules of a given sub stance are the smallest parts into which that substance can be conceived to be divided, with out changing its chemical character; while the atoms are the proximate constituents through whose immediate combination the molecule is formed. (The word "proximate* is employed here, because the atoms themselves are now believed to be composed, wholly or in part, of still smaller corpuscles, as will be explained subsequently). The molecules of most of the substances that are considered in elementary Inorganic chemistry are comparatively simple in structure. Hydrochloric acid gas, for ex ample, is composed of molecules which each contain one atom of hydrogen combined with one atom of chlorine, as indicated by the formula HO; and water (at least in the form of steam-gas) is composed of molecules which each contain one atom of oxygen combined with two atoms of hydrogen. as indicated by the formula H2O. In organic chemistry molecules occur which apparently contain hundreds of constituent atoms, and the comparative stability of such systems is hard to understand, on any hypothesis.
One of the most fundamental assumptions of the molecular theory in its usual form is that the molecules of any one chemical substance are identically alike in all respects. This point was tested by Graham, in the case of hydrogen, by passing the gas through a series of porous partitions, and comparing the final hydrogen, as it issued from the last partition, with the original gas. No difference could be observed, and hence it was concluded that hydrogen, at least, is not a mixture of dissimilar particles; because it is known that a mixture of different gases, whose molecules are different in size, can be partially separated by a diffusion process of this kind. Stas, the great Belgian chemist, investigated this question by determining the atomic weight of a given element as prepared in different ways and from different sources; and he found that the results obtained under these varying conditions were indistinguishable from one another, even when his work was so accurate that a variation in the atomic weight of the hundredth part of 1 per cent could hardly escape detection. It cannot be considered to be proved, however, that the molecules of any one substance are alike in every way, in the sense that a hundred standard machine screws are alike, for the question has not yet been tested exhaustively enough. Graham's method and Stas' method furnish evidence to which proper weight should be given, but they cannot be said to be conclusive. Neither can we admit the evidence of the spectroscope to be con clusive, although it indicates that the internal vibrations of a molecule of hydrogen (for ex ample) are performed with the same rapidity, whether the hydrogen is obtained from water, or from organic bodies, or from ti.e gases that are occluded by meteorites and brought to us from the depths of space. The identity of mole cules of the same substance is nevertheless a fundamental assumption of the usual molecular theory, and it will be assumed in the present article. In this connection the modern theory
of isotopes should be considered. According to Soddy (who coined the word "isotooen) it is possible, or perhaps probable, that many of the substances now considered to be homogeneous elements may prove to be heterogeneous when we know more about them. Each so-called ele ment may consist of several different sub stances, which are inseparable and indistinguish able by any means we now have. Such sub stances are said to be °isotopic° with one another, and among the radio-active elements several such bodies have already been recog nized. lonium, thorium and radio-thorium are isotopes, for example. Consult A. W. Stewart, 'Recent Advances in Physical and Inorganic Chemistry.) All matter may be classified, for present pur poses, as (1) gaseous, (2) liquid or (3) solid. (See MArrca). According to the kinetic theory, a gas consists of molecules which are distributed through the space occupied by the gas in such a manner that the average distance from one molecule to the next one is large in comparison with the diameter of any one mole cule. The molecules are all believed to he in rapid motion, so that from time to time they encounter one another; and when an encounter occurs it is believed that the molecules that come together rebound again as if they were per fectly elastic bodies. They have motions of rotation as well as of translation, and the col lisions affect both the rotative and the trans-. latory velocities of the colliding molecules. A system composed of a practically infinite num ber of bodies of this sort will have certain properties which are considered in the article GASES, KINETIC THEORY OF, and shown to be in general agreement with the properties of the actual gases of nature.
It may be shown, by the methods of the kinetic theory of gases, that the speed with which the molecules of a gas are moving may be determined by means of the formula = where V is the volume, in cubic centimeters, of one gramme of the gas, P is the pressure ex erted by the gas, in dynes per square centi meter, andN7 is the square root of the average value of the squares of the velocities of the molecules, each expressed in centimeters per second. In the case of hydrogen at atmos pheric pressure and the temperature of melting ice, we have V 11,160 and P ==. 1,012,000; and therefore v, for hydrogen molecules under the assumed conditions, is equal to 184,100 centi meters (or 1,841 meters) per second. The kinetic theory of gases shows that the true average (or arithmetic mean) of the velocities may be found by multiplying the so-called !mean-square velocity," (as obtained above), by the constant 0.9213. Hence the average velocity of the molecules of hydrogen, under the conditions here assumed, is 1,841 X 0.9213 1,696 meters (or 5,564 feet) per second. The mean (or average) velocity for any other gas, under these same conditions of tempera ture and pressure, may be found by dividing the velocity of the hydrogen molecules by the square root of the number that expresses the density of the other gas, when the density of hydrogen is taken as unity. Furthermore, the molecular velocity increases, in any given gas, in proportion to the square root of the absolute temperature.