Molecule (Fr. molecule, diminutive of Lat. moles, a mass), a small mass of matter. The word came into use in France in the early part of the last century, and was adopted by Buff on in describing his remarkable theory of the constitution of organized beings. Later it was used by Laplace in his Systeme du monde, and also by Lavoisier, Fourcroy, and other chemists, at the period of the French revolution. The writers of this period distinguish between molecules integrantes and molecules constituantes. By their definitions the former were simply small particles differing from a mass of the same substance only in magnitude; the latter were the more minute particles of the elementary substances, of which the former may be regarded as composed. The molecules constituantes corresponded very closely to the atoms of modern chemistry, and by more recent authors the words molecule and atom were frequently used as synonymous. Into the English language the word molecule does not seem to have been readily received. Although the organic molecules of Buffon are referred to by Paley, the word is not found in Johnson's dictionary, and was not generally used by English writers on chemistry and physics until within a few years.

Indeed, in England the influence of Dalton's theory has given such authority to the word atom that it is still frequently used to denote both the true chemical atom and the physical molecule, and it is therefore the more important for us to carefully distinguish between them. - The term molecule, as used in the modern schools of physics and chemistry, implies more than the molecules integrants of the French writers just referred to. The molecules of a substance are not merely small particles of that substance, but they are isolated masses, or, to use the words of Sir William Thomson, "pieces of matter of measurable dimensions, with shape, motion, and laws of action, intelligible subjects of scientific investigation." The term therefore involves the conception that the molecules of a substance are as definite magnitudes as the stars, and that every mass of matter is a collection of such bodies, just as a stellar cluster is a collection of suns. The molecules of any one substance, however, are supposed to be alike in all respects. There are many phenomena, both of physics and chemistry, which indicate that this conception is just and accurate. We will only refer to two of the most familiar.

When by boiling under the atmospheric pressure water changes into steam, it expands, as compared with its volume at the point of maximum density, 1,700 times; or in other words, one cubic inch of water yields nearly one cubic foot of steam. Two suppositions are possible as modes of explaining this change. The first is, that in expanding the material of the water becomes diffused through the cubic foot so as to fill the space with the substance we call water as completely as before, and leaving no space within the cubic foot which does not contain its proper proportion of water. The second is, that the cubic inch of water consists of a certain number of isolated particles, the cubic foot of steam containing the same particles as the cubic inch of water, and the conversion of the one into the other depending simply on the action of heat in separating these particles to a greater distance. Hence the steam is not absolutely homogeneous; for, if we consider spaces sufficiently minute, we can distinguish between such as contain a particle of water and those which lie between the particles.

These assumed particles, which are thus supposed to be separated by the heat, are the molecules of the water; and the molecular theory of the constitution of matter explains the change of volume in the manner last described. That this is probably the true explanation will be evident from a consideration of the familiar phenomena which appear when by pressure we condense steam back to water. Conceive of a cylinder filled with rarefied steam at some temperature above the boiling point of water. If into such a cylinder we press a piston, the volume of the steam will be diminished in proportion to the pressure, according to the well known law of Mariotte, up to a certain limit; but as we increase the pressure a point will be reached, sooner or later, at which this law of compression .vases abruptly, and the steam without any intermediate transition takes a volume many hundred times less than before changing of course into liquid water. Now' if there was a perfect continuity in the steam, we cannot conceive why there should not be a similar continuity in the law of expansion; and on the other hand, this sudden break is perfectly explained if we are really crowding together a mass of impenetrable particles, and the whole order of the phenomena suggests this conception.

Again, if the space occupied by a mass of steam is really packed close with the material we call water, if there is no break in the continuity of this aqueous mass, we should expect that the vapor would fill the space to the exclusion of everything else, or, at least, would fill it with a certain degree of energy which must be overcome before any other vapor could be forced in. But the facts are the very reverse of this. Conceive of two globes at some temperature above the boiling point of water, one filled with steam, the other completely exhausted. Let these globes be so arranged that we can introduce into each the same quantity of alcohol, and we shall find not only that the alcohol will evaporate in both, but that just as much alcohol vapor will form in the globe filled with steam as in the vacuous space, and will exert precisely the same pressure against the sides of the two vessels. The presence of the steam does not interfere in the least degree with the expansion of liquid alcohol into alcohol vapor. The only difference which we observe is that the alcohol expands more slowly into the aqueous vapor than it does into a vacuum.

The final result however is the same in both cases, and thus we may have two different vapors filling the same space without interfering with each other; and more than this, so far as we know, any number of vapors, which do not act chemically on each other, may occupy the same space at the same time, each preserving its individuality so completely that its relations would not be essentially altered if the associated materials were removed. Evidently then no vapor completely fills the space which it occupies, although equally distributed through it; and we can give no satisfactory explanation of the phenomena of evaporation except on the assumption that each substance is an aggregate of particles or units, which by the action of heat become so widely separated that they leave very large interstices in which the particles of an almost indefinite number of other vapors can find room. - A study of the phenomena of evaporation leads to a definition of molecules, which, although not comprehensive, is for the cases it covers the most precise that can be given: Molecules are those small particles of a substance which are not subdivided when the body is expanded by heat, and which move as units under the influence of this agent.

As the above statement implies, the modern molecular theory assumes, not only that the molecules are isolated masses, but also that they are in active motion, and the phenomena of heat are regarded as manifestations of this motion. The idea that the ultimate particles of matter are in motion is as old as Democritus, but this idea was never precisely formulated until modern times. Now, however, it is one of the most pregnant theories of science; and it is evident that such motion, if it exists, must be a most important factor in nature. The circumstance that these molecular motions are limited by the boundaries of the mass of matter to which the molecules belong, and that the system remains in equilibrium with relation to external objects, because the amount of motion in opposite directions is usually equal, must not of course affect our estimate of the moving power, and this power is no less than that which would be shown in a motion of translation of the same mass with a velocity equal to the mean velocity of the several molecules; and, since the facts compel us to assign to this velocity a value commensurable with the velocities obtained in artillery practice, it is evident that the total moving power, even in a small mass of matter, must be enormous.

There are conditions, however, under which the molecules may communicate their motion to masses and thus produce mechanical effects; and our theory refers the tension of aeriform matter, and the mechanical work which it may be made to do, to the bombardment of the sides of the containing vessel by molecular projectiles. In a solid or a liquid it is assumed that the extent of the motion of the molecules is limited by internal forces, but in a gas this motion is supposed to be unrestrained, so that the molecules beat freely against any surface with which the aeriform mass may be in contact, and thus the molecules of water in the cylinder of a steam engine produce their well known effects. - The molecular theory has established on a firm foundation the great physical doctrine of the conservation of energy, by explaining a class of phenomena which, as viewed by the old physicists, were apparently wholly at variance with this truth. When two elastic billiard balls strike each other, although the balls may change their velocities, the total moving power will be nearly the same after the collision as before it; but when two inelastic balls of lead strike, there is always an apparent destruction of motion.

It was no answer to say that the power which had disappeared as motion had done its work in changing the shape of the balls; for since these bodies cannot recover their figure, and therefore have not the potential energy of elastic bodies under the same conditions, there must be an annihilation of power if the external phenomena are the only effects produced. But if, as our theory assumes, the motion is simply transferred from molar to molecular masses, all is clear; and since we have been able to prove that the change of temperature produced in the masses is the exact mechanical equivalent of the motion lost, we think we are justified in concluding that the effects ascribed to what we call heat are simply manifestations of molecular motion. - When we come to conceive of matter as consisting of elastic molecules which are ever in motion and colliding with each other, we see that motion must be readily communicated from one part of such a system to another; that any excess of energy acquired by any part must be rapidly dissipated; and that the tendency must be to bring all the molecules to the same condition.

Moreover, we see that the motion must spread not only through the molecules of the same body, but also from one body to another; for everywhere in nature the atmosphere or some other medium furnishes lines of molecules along which the energy can pass. Now exactly this is true of heat. When a heated body is brought into a room, the heat immediately begins to spread through surrounding objects, and the process goes on until all are reduced to what we call a uniform temperature, that is, to a condition in which there is no tendency of heat to pass from one to the other; and we must remember that our knowledge of temperature and our means of measuring it depend wholly on this motion of heat. We say that one body has a higher temperature or is hotter than another, if when brought in contact heat passes from the first to the second; and we measure the temperature of a body by bringing in contact with it a thermometer, a small bulb filled with mercury, whose narrow neck enables us to detect the slightest change in the volume of the enclosed liquid.

As this volume increases when the mercury is heated, and diminishes when it is cooled, a fixed position of the mer-curv column indicates that the thermometer is in equilibrium with the body to be tested, and then the artificial scale enables us to compare its thermal condition with freezing and boiling water. - Consider next what must be the mechanical condition of the molecules of two bodies at the same temperature, that is, in thermal equilibrium. The molecular theory assumes that all the molecules of the same substance are alike in every respect, and therefore have the same weight; and hence, in considering the mutual action between different portions of the same substance, we have to deal solely with the collision of small elastic masses of equal weight. Now it follows from the well known laws which govern the collision of elastic bodies, that by the exchanges of velocity which follow each collision the different portions which we are considering would soon be reduced to a state in which the mean velocity of the molecules in each part must be equal. Of course the mutual interchange of velocities must continue after the equilibrium is established, but the loss and gain on either side are then exactly balanced.

It follows from this that when two portions of the same substance are in thermal equilibrium, that is, at the same temperature, the molecules of each portion have the same mean velocity. It will be seen however that, although the molecules of a substance in a state of thermal equilibrium have a certain constant mean velocity, the velocity of the individual molecules may vary verv greatly. Indeed, this must result from the"fortuitous collisions, which will cause velocity to accumulate sometimes in one molecule and sometimes in another, while contiguous molecules suffer a corresponding loss. - When we come to consider next the mutual action between masses of different substances, consisting therefore of unlike molecules having different weights, the problem becomes more difficult, because we have now to deal with the collisions of unequal masses. Still the same laws as before give us the key to the solution; and it has been shown by Maxwell and Boltz-mann that in all cases, when the condition of equilibrium is reached, the mean value of the moving power of the molecules of any masses must be equal.

That is, in general, when any two bodies have the same temperature, 1/2mV2=1/2m'V/2, m and m' representing the weights of the several molecules of the two bodies, while V2 and V3 represent the mean of the squares of the velocities in each system. If the molecular weights are equal, then of course the mean velocities must be equal, as just stated; but if the weights are unequal, then the lighter molecules will have on the average a greater velocity. In any case V: V'= √m': √m; and since we can determine the relative values of the molecular weights, we can calculate the ratio between these mean values of the molecular velocities, turning of course that the two substances compared are of the same temperature. For example, as the molecules of oxygen gas are 16 times heavier than those of hydrogen gas, the mean value for the velocity of the hydrogen molecules at any given temperature will be four times as great as that for the oxygen molecules. It thus appears that temperature is a condition determined by molecular motion, and that the mean value of 1/2mV2 is the same for all bodies at the same temperature, a definite value corresponding to each temperature, and becoming greater or less as the temperature rises or falls.

This product is the true measure of temperature, and, as will soon appear, this measure corresponds to that obtained with an air thermometer. - We know as yet but little in regard to the molecular structure cither of solids or liquids, but the three great laws which define the aeriform condition of matter may be shown to be necessary consequences of the mode of motion which our theory assigns to the molecules of gases. Gas molecules, as we have seen, move with perfect freedom until their motion is altered by collisions either with each other or against some surface; and our theory refers the pressure of a gas against the surfaces with which it is in contact to a very rapid succession of small impulses which produce the effect of a continuous pressure. Now if a mass of oxygen, for example is confined in a vessel, each of the oxvgen molecules must on an average strike the sides of the vessel the same number of times; and so long as the temperature is constant, it must strike with an impulse of the same average momentum. Hence each must contribute an equal share to the whole pressure, and this pressure must be proportional to the number of oxygen molecules in the vessel, or in other words to the density of the gas.

Next let us assume that we have two similar vessels of equal capacity containing different gases, both at the same temperature and tension, one filled for example with hydrogen and the other with oxygen gas. According to our theory, if the temperatures are the same, the moving power of the hydrogen and oxygen molecules must be the same; that is, 1/2mV2= 1/2m'V'2, as above. Hence mV: m'V'=V': V, or the momentum of the two kinds of molecules, which is the measure of the pressures they exert, must be inversely proportional to their respective velocities. But, on the other hand, the swifter molecules will strike the sides of the vessels a greater number of times in a second, the number of impulses in a given time being proportional to the respective velocities; or n: n'=V: V. Hence, nmY=n,m'V; that is, each molecule of hydrogen will produce in a given time the same effect as each molecule of oxygen, the less momentum being compensated by the greater frequency of the impulses. But if the molecule of hydrogen thus becomes the mechanical equivalent of the molecule of oxygen in producing pressure, then the same effect can be produced in the two vessels only by the same number of molecules.

In other words, equal volumes of two gases at the same temperature and tension must contain the same number of molecules; and this is the very important law first announced by Avogadro and afterward confirmed by Ampere. - Next consider what must be the effect on a confined mass of gas of an increase of temperature. Assume that we begin with a closed vessel filled with air at the temperature of melting ice, and with a tension measured by a column of mercury 273 millimetres high in a connecting barometer. An increase of temperature will augment the velocity of the molecule, and the effect of each molecular impulse upon the exposed surface of mercury will bo increased in proportion to the velocity; but besides this, each molecule will now strike the mercury a greater number of times in a second, greater again in proportion to its velocity, so that the part of the pressure due to each molecule will vary as the square of the velocity. As the total effect is but the aggregate of these molecular impulses, and the number of molecules acting is assumed to be constant, it is evident that the mercury column, which is the measure of the pressure or tension of this confined gas, must rise in proportion as the product 1/2mV2 increases; and since, as we have seen, all gas molecules are mechanically equivalent, the effect must be the same whether our vessel bo filled with air or with any other gas.

Now this product is our theoretical measure of temperature, and the assumed apparatus is a possible form of air thermometer, which is the most accurate measure of temperature we employ; and thus it appears that our best practice is in harmony with our theory. Evidently, if we could reduce the temperature of the confined gas indefinitely, we should at last bring the molecules to rest. They would then exert no pressure, and the mercury column in our barometer would fall to its lowest level. This condition would be theoretically the absolute zero, and our air thermometer shows what the relation of this point must be to our ordinary standard of temperature, the centigrade scale. - Beginning with the apparatus in the condition described above, the temperature of the air being that of melting ice or 0° C, and the tension 273 millimetres, let us heat it to the temperature of boiling water, 100° 0. We know by experiment that if the volume of the air is kept constant the mercury column, which measures the tension, would rise to 373 millimetres. Hence, under the conditions assumed and according to our method of graduating thermometers, each centigrade degree corresponds to one millimetre in the height of this mercury column.

If the instrument is now cooled through 100° C, that is, if the temperature is reduced again to 0° C, the mercury column will of course fall 100 millimetres; and therefore if cooled 373° C, that is, 273° below the centigrade zero, the tension should become nothing. Or if, according to our mode of estimating temperature by the air thermometer, we define a centrigrade degree as a difference of temperature, which at any part of the scale determines in a confined mass of gas a difference of tension equal to 1/273 of the tension at the temperature of melting ice, then the absolute zero of heat is at - 273° on the scale so defined. Such a definition, however, gives us no positive knowledge of the relations of the absolute zero to natural phenomena, as a simple consideration will show. - Starting from the self-evident proposi-' tion that the quantity of heat liberated by burning fuel under constant conditions is proportional to the amount of fuel burned, we may use the weight of some combustible of constant nature, like hydrogen, as a measure of quantities of heat.

Now taking the case we have assumed of a confined mass of air having a tension of 237 millimetres at the temperature of melting ice, we can say in general that, so far as accurate observations have been made, equal increments of heat measured by the fuel standard cause equal increments of tension, and equal decrements of heat equal decrements of tension. Moreover, it would be possible in a given case to calculate from experimental data, at least approximately, the amount of combustible which would be required to increase the tension of a confined mass of air one millimetre; and the theory of the air thermometer, our standard of temperatures, is based on the conclusion that twice this amount of combustible would increase the tension two millimetres, three times the amount three millimetres and so on. If this is true indefinitely, and if the tension actually increases or diminishes by a constant quantity, through all parts of the scale, on the addition or subtraction of the same quantity of heat (measured by the fuel standard), then we have real knowledge of the relations of the absolute zero.

We can say of a mass of matter that it contains as much heat as would be generated by burning a given weight of hydrogen gas, and that if this limited amount of heat were removed its temperature would be reduced to absolute zero. But unfortunately the accurate experiments on the expansion of gases by heat have been confined within such narrow limits of temperature, and our means of connecting the observed effects with the amount of fuel burned, the only legitimate measure of thermal differences, are so indirect, that we must generalize very cautiously; and it is possible that the law to which our observations appear to point would totally fail when the differences of temperature became extreme. Still there are several independent phenomena which seem to confirm this law, and indicate that the absolute zero, as defined above, is a reality and not an assumption. But even as an assumption the absolute zero is on many accounts a more convenient point to count from than the temperature of melting ice. By adding 273° to temperatures expressed in centigrade degrees, we obtain what we may call the absolute temperature; and we find by experiment, as our theory requires, that the tension of a confined mass of any gas is proportional to the absolute temperature thus expressed.

This is a modern way of expressing the law discovered by Charles that equal changes of temperature cause the same relative changes of volume or tension in all aeriform bodies. Thus it is that the molecular theory explains, and indeed predicts, the mechanical condition of aeriform bodies. We have only been able to give the general features of the reasoning. The mathematical demonstration of the several theorems is based on a beautiful application of the doctrine of averages in the calculus of probabilities, and for this we must refer the mathematical reader to the classical works of Clausius. - Let us next consider some of the qualities or relations of molecules of different kinds, which can be deduced by a similar course of reasoning. In the first place, it is evident that if equal volumes of two gases contain the same number of molecules, the relative weights of these molecules must be the same as the relative weights of the equal gas volumes. Thus, a cubic centimetre of oxygen weighs 16 times as much as a cubic centimetre of hydrogen under the same conditions; and if there is in each cubic centimetre the same number of molecules, each molecule of oxygen must weigh 16 times as much as each molecule of hydrogen.

In general, the number which expresses the specific gravity of a gas with reference to hydrogen, expresses also tho weight of a molecule of that substance with reference to the hydrogen molecule. It must be remembered moreover that as the molecule of hydrogen is a definite mass, its weight must be a definite quantity, however small, and may therefore be used as a standard of weight like a grain or a gramme. When therefore we determine the specific gravity of a gas with reference to hydrogen, we thereby determine the weight of a molecule of that aeriform substance in terms of this molecular unit. For reasons based on chemical relations we have actually adopted as the unit of molecular weight one half of a hydrogen molecule, which we call a hydrogen atom; and hence in the system in use the molecular weight of a substance is equal to twice its specific gravity in the state of gas referred to hydrogen. As this unit of molecular weight, although a magnitude of a very different order, is as definite a mass of matter as a grain or a gramme, we shall aid our conceptions by giving to it a definite name; and since the mass of a cubic decimetre of hydrogen has been called a crith, the word microcrith will suggest both the nature of the molecular unit and the order of its magnitude.

Remembering then that the microcrith is the weight of the hydrogen atom, and that this is one half of the hydrogen molecule, we shall be understood when for the future we estimate molecular weights in microcriths. In the second place, it is evident that the known pressure which a gas exerts against the sides of the containing ves-sel gives data from which we can calculate the mean velocity of the molecular motion under determinate conditions. Consider for example a cubic metre of hydrogen gas at the temperature of melting ice and under a pressure of one atmosphere. This aeriform mass weighs 0.08954 of a kilogramme, and exerts a pressure of 10,332.90 kilogrammes against each face of the cubic enclosure. This pressure balances the molecular bombardment, and the momentum of the bombardment thus resisted during one second must be equal to that which the pressure would produce during the same period if acting on a mass of matter free to move. If the force of gravity at the place of observation imparts to one kilogramme of matter a velocity of 9.8083 metres a second, then this momentum must be equal to 9.8088 x 10,332.96 = 101.354. To find the momentum of the molecular bombardment against the cube face, we must conceive of the mass of hydrogen divided by planes parallel to the face in question into very thin sections, which are not thicker than the length of the mean path of a molecule, and between which the motion maybe regarded as uniform.

Let V represent the mean velocity of the molecules, moving of course in all directions, and u one of the components of this velocity resolved perpendicularly to the face of the cube we are considering, and estimated of course as so many metres a second. Limiting our attention to this component, it is evident that we may regard the whole number of the hydrogen molecules within the enclosure as moving at any instant with the mean velocity u on lines normal to the face of the cube we are considering, and directed either toward this face or its opposite; and, since equilibrium is maintained, it is evident that the two opposite molecular volleys must be equal to each other. It it also further evident that the pressure against the face of the cube must bo the sum of these two molecular streams, that from the face as well as that toward it. If the molecules moved only one metro each second, it is manifest that each molecule would on the average move through the length of the cube in a second, were it not that the direction of its motion is continually being altered by collision with other molecules.

But although the path of any one molecule may bo very short, yet, as the molecules perfectly transmit their motion at each collision, and as the motion is always carried forward by a series of perfectly similar masses, the result is the same as if the same one had moved through the whole distance. There is therefore constantly passing between the small sections we have assumed, and also boating against the opposite faces of the cube, the same number of molecules as if the two streams were continuous. If the velocity were only a metre a second, there must pass every section in one or the other direction, and beat against one or the other of the two opposite faces of the cube during each second, a number of molecules, which we will represent by n, equal to the whole number of molecules in the cube; and since the velocity we are considering isu, the number of molecules thus passing on striking must be nu. If now m represents the weight of each molecule, then the total momentum resisted by the cube face each second must bo mnu2, which is equal, as we have before seen, to 101,354. But in tho expression wmw2=101,354 the value mn is simply the weight of the cubic metre of hydrogen at the temperature of melting ice and at a pressure of one atmosphere, or 0.08954 of a kilogramme; so that u2=101,354 /0.08954=1,131,940. It must bo remembered, however, that u is only one of the components of the molecular velocity, that perpendicular to one pair of the cube faces; and in order to determine the actual velocity, V, we must take into consideration the other two components, which are normal to the other two pairs of the cube faces; for V2=u2+ v2 + w2. Now, although the values of these components for individual molecules may vary between the widest limits, yet their average values must bo equal; for otherwise the pressure of the gas could not be, as it is, equal in the directions of these components.

If then our letters represent these average values, V2 =3u2=3,395,820, and V=l,843 metres a second. The absolute velocity of the hydrogen molecules being now known at the temperature of melting ice, we can readily calculate the velocity for any other temperature. For if the temperatures are estimated on the absolute scale, we have, as has been shown, T: T' =1/2mV2: 1/2mV'2, and hence V: V'= √T: √T' For example, the velocity of the hydrogen molecules at the temperature of boiling water would be found by the proportion 1,843: V = √273: √373. Knowing now the velocity of the hydrogen molecule at any temperature, we can find the velocity of every other molecule whose molecular weight is known. Since for any given temperature 1/2mV2=1/2m'V/2, we have V: V'= √m': √m. For the oxygen molecules which weigh 32 microcriths we have at the temperature of melting ice 1,843: V'= √32:√2, and V'=461 metres a second. The velocity of the molecules of the heavier gases is still less, but in all cases it is very great as compared with that obtained with projectiles. - The weight and velocity of the molecules of. different gases are known with great precision, because the data from which they have been calculated are very well determined.

But the molecular relations we have next to consider cannot be ascertained with the same accuracy, and must be regarded as only rough approximations. Morever, the methods by which they have been calculated cannot be described in a few words, and we can therefore only state here the general results. As we have shown, the molecules of a gas are flying about in all directions with great velocity; those of the air, for example, about 17 miles a minute. Could we by any means turn into one direction the actual motion in the molecules of what we call still air, this air would at once become a wind blowing 17 miles a minute, and exerting a destructive power compared with which that of the most violent tornado is feeble. We are unconscious of the molecular storm which is constantly beating around us only because it beats equally in all directions at once. Obviously, however, an immense number of small masses of matter cannot be flying in every possible direction without constantly striking each other, and every time two molecules come into collision the paths of both are changed, and frequently reversed; so that although they move with such great velocity they make very slow progress. "When a jar of ammonia gas, for example, is opened in a lecture room, a sensible time elapses before its pungent odor is perceived even at a distance of a few feet, and a long time passes before it reaches the distant end of the hall.

Nevertheless, the molecules of ammonia at the ordinary temperature move over 20 miles a minute, and would flash over the hall were they not jostled about by the molecules of air. Still, although the process is a slow one, the gas does diffuse itself through the air, and we can easily devise experiments to test the rate of progress. The phenomena of which our illustration is a single example are among the most instructive effects of molecular motion, and under the name diffusion of gases they have long been studied.

It was discovered by the late Dr. Graham that two gases diffuse through each other at rates which are inversely proportional to the square roots of their densities, and this empirical law strongly confirms the molecular theory; for, as we have seen, the molecular velocities, which must determine the relative rates of diffusion, are also proportional to the square root- of the densities. More recently the diffusion of gases has been studied by Loschmidt of Vienna, who measured the absolute as well as the relative rates. He placed the two gases in -irnilar portions of the same vertical tube, the lighter over the heavier, and after allowing them to diffuse during an observed time closed a sliding valve which divided the two portions, and then by chemical analysis determined the amount of gas which had passed in the two directions. According to our theory, the molecules of still air must also travel from place to place in the same halting manner as the gases; only we have not the means of noting their progress.

Nevertheless, by communicating momentum or heat to one portion of a mass of air, under such conditions as to avoid the effect of currents, and observing the rates at which the momentum or heat spread by means of phenomena depending on these effects, we obtain data by which we can estimate approximately the travelling power of the molecules. Such phenomena depend on modes of diffusion, and Maxwell distinguishes between what he terms the diffusion of mass, the diffusion of momentum, and the diffusion of energy. Taking then into consideration the obvious principle that the greater the velocity of the molecules and the longer their path between successive collisions the faster they must travel, and remembering that we know the velocity of their actual motion, it can readily be seen that experiments on the three kinds of diffusion would give us the means of calculating what Clausius calls the mean path of a molecule, that is, the average distance travelled by a molecule between one collision and another; and further, that from the velocity and mean path we can estimate the number of collisions in a second. Of course the mean path varies for different molecules and under different conditions.

That these paths should be very short we should expect, but our calculations surprise us by showing that they are of the same order of magnitude as the waves of light, and that the number of collisions in a second is to be numbered by thousands of millions. No wonder that although the molecules move so swiftly, they make so little progress. - As has already been said, the phenomena attending the condensation of a gas to a liquid have the appearance of the crowding together of hard masses, and suggest the conception that in the liquid state the molecules are as near together as when they come into collision in the state of gas. If this conception is accurate, the specific gravity of a liquid is the specific gravity of its molecules, and the diameter of a molecule is the distance between the centres of two adjacent masses in the liquid state. It is generally assumed that the perfect elasticity of the molecules results from an elastic atmosphere, perhaps the ether, which surrounds them, and in a gas we distinguish between what we call the free path of the molecule and that portion of its motion during which the path is changed by collision; and the principal difference between a gas and a liquid seems to be, that while in a gas the molecules are almost all the time on the wing, in a liquid they are always in a state of close encounter with each other, and have hardly any free path.

When therefore we define the diameter of a molecule as the distance between the centres of two adjacent molecules in the liquid state, we of course include the molecular atmosphere, or at least so much of it as produces an appreciable effect in the collision. If then we thus define the diameter of a molecule, it is evident that we can determine the relative diameters of molecules of different substances by comparing their densities in the aeriform and liquid states. For the densities of the gases give us the relative weights of these molecules, and the densities of the liquids the weights of the unit volume of the liquids. Hence, by dividing the latter by the former, we learn the relative number of molecules in these equal volumes, and from this we at once deduce the relative volumes of the molecules and their relative diameters. Moreover, as these results agree very remarkably with those obtained by other means, we feel great confidence in the assumption on which they are based; and if our knowledge in regard to them is not precise, it is at least approximate. - We next come to a class of molecular data of which our knowledge is not only not precise, but not even definite, and whose assigned values can only be regarded as probable conjectures.

Loschmidt has deduced from the principles of molecular mechanics the following theorem: "As the volume of a gas is to the combined volume of all the molecules contained in it, so is the mean path of a molecule to one eighth of its diameter." Since we know at least approximately the other three quantities, we ought to be able by this proportion to calculated absolute molecular diameters. Accordingly, Maxwell has calculated from Loschmidt's data that "the size of the molecules of hydrogen is such that two million of them in a row would occupy a millimetre, and a million million million million of them would weigh between four and five grammes;" and further, that "in a cubic ntirnetre of any gas at standard pressure and temperature there are about 19 million million million molecules." Striking as these results are, they depend on so many uncertain elements that they must be accepted with caution. Still if should be added that from several wholly independent data, such as the lengths of luminous waves, the thickness of soap bubbles, and the electric properties of metals.

Sir William Thomson has deduced values of the molecular magnitudes which are consistent with the numbers just given, and has proved that these magnitudes must fall within certain limits, which, though too wide to secure entire confidence in his methods, at least fix the order of the magnitudes. - In preparing this article we have been greatly indebted to the lecture on molecules delivered before the British association at Bradford in September, 1873, by Prof. Maxwell, and to sum up what we have said of the physical relations of molecules we reproduce from this lecture the table of molecular magnitudes, in which the values are classed according to the completeness of our knowledge in regard to them:

Table Of Molecular Data. Rank I





Mass of molecule, in microcriths...





Velocity at 0° C. (from mean square), in metres a second...





Rank II

Mean path, in (10)-10 of a meter...





Collisions in a second, in millions...





Rank III

Diameter, in (10)-10 meters...





Mass, in (10)-25 ofa gramme





Number of molecules in one cubic centimetre of any pas under normal conditions..............

19 million million millions, or 19x1018.

" These considerations will show how definite the idea of the molecule has become in the mind of the physicist. It is no longer a metaphysical abstraction, but a reality about which he reasons as confidently and as successfully as he does about the planets. He no longer connects with this term the ideas of infinite hardness, absolute rigidity, and other incredible assumptions which have brought the idea of a limited divisibility into disrepute. His molecules are definite masses of matter, exceedingly small but still not immeasurable; and they are the points of application to which he traces the action of the forces with which he has to deal. These molecules are to the physicist real magnitudes, which are no further removed from our ordinary experience on the one side than are the magnitudes of astronomy on the other. The old metaphysical question in regard to the infinite divisibility of matter, which was such a subject of controversy in the last century, has nothing to do with the present conception.

Were wo small enough to be able to grasp the molecules, we might be able to split them, and so were we large enough we might be able to crack the earth; but we have made sufficient advance since the days of the old controversy to know that questions of this sort, in the present state of knowledge, are both irrelevant and absurd. The geologist tears the earth to pieces, and so does the chemist deal with the molecules; but to the astronomer the earth is a unit, and so is the molecule to the physicist. The word molecule, which means simply a small mass of matter, expresses our modern conception far better than the old word atom, which is derived from the Greek a privative andMolecule 1100341 and means therefore indivisible. In the paper just referred to, Sir W. Thomson used the word atom in the sense of molecule, and this confusion of the two terms is still common. We shall give to the word atom an utterly different signification, which we must be careful not to confound with that of molecule. In our modern chemistry the two terms stand for wholly different ideas, and, as we shall see, the atom is the unit of the chemist in the same sense that the molecule is the unit of the physicist." (The writer of this article, in "The New Chemistry," page 35, New York, 1874.) - The chemist studies the molecular theory from a point of view quite different from that of the physicist. To the physicist the molecules are the points of application of those forces which determine or modify the physical condition of bodies, and he defines molecules as the small particles of matter which under the influence of these forces act as units. To the chemist, on the other hand, the molecules determine those differences which distinguish substances. Sugar, for example, has the qualities which we associate with that name, because it is an aggregate of molecules which have those qualities.

Divide up a lump of sugar as small as you please: the smallest mass that you can recognize still has the qualities of sugar; and so it must be if you continue the division down to the molecules; and so is it with every substance. It is the molecules in which the qualities inhere. Hence the chemist's definition of a molecule: The smallest particles of a substance in which its qualities inhere. By no physical process, that is, by no process which leaves the qualities of a substance essentially unchanged, is subdivision carried beyond the molecules. The molecules can however be divided, but by the division you destroy the substance; new substances result, and you have what is called a chemical process. The distinguishing feature of a chemical change is simply this: From one or more substances one or more new substances are produced, and according to the molecular theory these changes depend on the reciprocal action of different kinds of molecules on each other. The molecules become subdivided, and new molecules are formed by a new grouping of the fragments. And here chemistry comes in to substantiate the molecular theory with most important evidence.

If in a chemical change the reaction takes place between molecules, then we should expect that the weights of the substances involved in the process would bear some simple relation to the weights of their molecules, as determined by physical methods. Now this is exactly what we find to be true. It is the great law of chemistry that in every chemical process definite proportions are preserved between the weights both of the factors and of the products of the change; and wherever observation is possible it has been found that these weights bear a simple relation to the specific gravities of the substances in the state of gas, which, as will be remembered, are the measures of the molecular weights of these substances. A few examples will illustrate this point. "When hydrochloric acid gas combines with ammonia to form amnionic chloride (sal ammoniac), 36.5 parts by weight of the former unite with 17 parts of the latter. Now the specific gravities of these two gases with reference to hydrogen are by observation 18.32 and 8.53 respectively, and the molecular weights 36.5 and 17 microcriths, very nearly. When water is decomposed, 9 parts by weight of water yield 8 parts of oxygen gas and 1 part of hydrogen.

The specific gravities of the several substances in the state of gas are (by observation) 8.98, 15.95, and 1, and the weights of the molecules therefore 18, 32, and 2 microcriths, very nearly. Examples like these might be multiplied indefinitely. The relation is very simple. The chemical proportions are always very nearly either as the molecular weights, deduced from the gas densities, or as some simple whole multiples of these weights; a fact which wonderfully confirms the molecular theory. - But it may be asked, why is not the relation just described absolute? First, because a certain amount of error of observation is inherent in all measurement, and the determinations of gas densities are peculiarly exposed to errors of this kind; and secondly, and chiefly, because the vapors, on which we mostly experiment, are not in the condition of perfect gases. They do not perfectly obey the law of Mariotte, and, as the molecular theory shows, it is only when they exactly obey this law that they contain the same number of molecules in the unit volume, and that their densities are the measures of their molecular weights.

In the case of a few perfect gases the agreement between the two classes of observations is very close; but with most vapors, especially when near the point of condensation to liquids, we can only expect to find an approximation. It is evident moreover that the definite proportions of chemistry, which can be weighed with the greatest accuracy, are a far more exact measure of the molecular weights than the gas densities. Of course we cannot tell from these proportions alone whether they are the ratios between the weights of equal or of multiple numbers of molecules; but here the gas densities come to our aid, and fix approximately the values of the molecular weights, which we need only correct by the chemical evidence. When, as is most frequently the case, the substances with which we are dealing are incapable of existing in the state of gas, we are obliged to depend wholly on the combining proportions for fixing their molecular weights; but although in such cases we have various chemical means of controlling our results we are frequently in danger of assigning multiple values. - Chemistry has shown that all matter is composed of one or more of 64 substances, which we call elementary sub-stances or chemical elements, because as yet they have not been decomposed; and by the processes of chemical analysis we are able to determine with great accuracy the relative proportions of each element which a compound may contain.

Moreover, as the masses are aggregates of perfectly similar molecules, it is evident that in analyzing a substance we analyze also its molecules; and that when we learn, for example, that water, in every hundred parts, contains 88.89 parts of oxygen and 11.11 parts of hydrogen, we know that every molecule of water must consist of the same elements in the same proportions. The following tables contain lists of volatile compounds of four elementary substances. Opposite to the name of each substance is, first, the weight of its molecule in microcriths, and secondly, the amount in each molecule of the elementary substance common to the list. The molecular weights are deduced primarily from the gas or vapor densities, but are corrected by the known combining proportions of the compounds. The amount of the elementary substance which each molecule contains is calculated from the results of chemical analysis.

Atomic Weight Of Carbon


Weight of molecule.

Weight of carbon in molecule.

Marsh gas...

16 m.c.

12 m.c.

Olefiant gas...

28 "

24 "

Propylic alcohol.........

60 "

36 "


74 "

48 "

Amylic alcohol .

88 "

60 "


209 "

72 "


98 "

84 "

Oil of wintergrcen.......

152 "

96 "


120 "

108 "

Oil of turpentine........

136 "

120 "

Amyl benzole ......

148 "

132 "


169 "

144 "

Atomic Weight Of Hydrogen


Weight of molecule.

Weight of hydrogen in molecule.

Hydrochloric add.......

86.5 m.c.

1 m.c.

Hydrobromlc acid

81 "

1 "

Hydriodic acid....

129 "

1 "

Hydrocyanic acid...

27 "

1 "


18 "

2 "

Hydric sulphide..

34 "

2 "

Hydric selenide..

81.5 "

2 "

Formic acid.......

46 "

2 "

Ammonia gas...

17 "

8 "

Hydric phosphide___


3 "

Hydric arsenide....

78 "

3 "

Acetic acid.......

60 "

4 "

Olefiant gas...

23 "

4 "

Marsh gas...

16 "

4 "


46 "

6 "


74 "

10 "

Hydrogen gas...........

2 "

2 "

Atomic Weight Of Oxygen


Weight of molecule.

Weight of oxygen in molecule.


18 m.c.

16 m.c.

Carbon dioxide...

28 "

16 "

Nitric oxide...

30 "

16 "


46 "

16 "

Ether .................

74 "

16 "

Carbonic dioxide...

44 "

32 "

Nitric dioxide...

46 "

32 "

Sulphurous dioxide.....

64 "

32 "

Acetic acid...

60 "

48 "

Sulphuric trioxide...

80 "

48 "

Methylic borate...

104 "

48 "

Ethylic borate...

146 "

48 "

Ethylic silicate...

208 "

64 "

Osmic tetroxide...

263.2 "

64 "

Oxygen gas...

32 "

32 "

Atomic Weight Of Chlorine


Weight of molecule.

Weight of chlorine in molecule.

Hydrochloric acid...

36.5 m.c.

35.5 m.c.

Acetylic chloride...

78.5 "

35.5 "

Ethylic chloride...

64.5 "

35.5 "

Phosgene gas...

99 "

71 "

Dicarbonic dichloride___

95 "

71 "

Chromic oxychloride___

155.2 "

71 "

Arsenious chloride...

181.5 "

106.5 "

Boric chloride...

117.5 "

106.5 "

Phosphorous chloride....

137.5 "

106.5 "

Carbonic tetrachloride...

154 "

142 "

Dicarbonic tetrachloride.

166 "

142 "

Silicic chloride....

170 "

142 "

Tantalic chloride....

859.4 "

177.5 "

Columbic chloride...

271.4 "

177.5 ".

Aluminic chloride...

267.8 "

213 "

Dicarbonic hexachloride.

237 "

213 "



Chlorine gas............

71 "

71 "

An inspection of these tables will reveal one of the most remarkable facts in the whole range of physical science. The molecules of the compounds of any element always contain quantities of that element, which are simple whole multiples of a definite mass; and this mass, which is the smallest quantity of an element found in the molecules of any of its compounds, is what we call the atom of that element. Thus the atoms of the four elements oxygen, chlorine, carbon, and hydrogen weigh respectively 16, 35'5, 12, and 1 microcriths respectively. It will be noticed that this definition does not necessarily imply that the atoms are isolated masses like the molecules. When water is decomposed, two substances, which we call oxygen and hydrogen, are evolved from the aqueous mass, and from each molecule of water there must be evolved by the chemical processes the quantities of these elementary substances which we call one atom of oxygen and two atoms of hydrogen. Whether now these masses preexisted in the molecule, or are formed from it by some unknown and unconceived transformation of its substance, is a question about which we can only speculate.

Nevertheless these atoms are definite and invariable quantities whether preexisting as isolated masses in the molecules or not; and the only theory which has been advanced that gives an intelligible explanation of the facts assumes that the atoms are not only invariable quantities, but definite bodies, and that the molecules are congeries of atoms, except, of course, in those cases where the molecules consist of a single atom. The atom is the unit of the chemist in the same sense that the molecule is the unit of the physicist; and as the molecules are the limits which the subdivision of matter reaches in any physical process, so what we now regard as atoms are the limits of the subdivision in any known chemical process. The word atom, by which we designate these units of chemistry and which we have inherited from the past, is in some respects an unfortunate term, because its etymology suggests conceptions which are no longer associated with the small masses it designates. Although our chemical atoms have never as yet been divided, we do not regard them as necessarily indivisible. The atom of oxygen for example, weighing 16 microcriths, is simply the smallest quantity of this elementary substance known to exist in a molecule of any of its compounds.

It is by no means impossible that a compound of oxygen may be discovered whose molecule contains only 8 microcriths of the element; or in other words, that what we now call an oxygen atom may be divided, just as it is possible that the elementary substance may be decomposed; for the chemical atom, like the chemical element, is such only provisionally. - The distinction between atom and molecule is preserved in chemistry by the system of chemical symbols. The Latin initials which are used as the symbols of the chemical elements represent in every case one atom of the elementary substance, and the groups of these letters which are used as the symbols of chemical compounds stand in each case for one molecule of the compound. Thus 0 stands for one atom or 16 microcriths of oxygen, C for one atom or 12 microcriths of carbon, and H for one atom or one microcrith of hydrogen; H20 for one molecule of water, .C2H60 for one molecule of alcohol, C2H4O2 for one molecule of acetic acid. The figures below the symbol indicate the number of atoms of the corresponding element in the molecule, and the weight of the molecule is obviously the sum of the weights of the atoms which the symbols represent.

For example, the weights of the molecules of water, alcohol, and acetic acid are 18, 46, and 60 microcriths respectively. Several molecules of a compound may be indicated by placing figures before the group of symbols like an algebraic coefficient; thus 3H20 stands for three molecules of water, and 4C2H4O2 for four molecules of acetic acid. In order to determine the symbol of a molecule, we must know in the first place the molecular weight, and in the second place the percentage of composition. The molecular weight, as we have seen, is found approximately from the gas or rapor density, and corrected by the combining proportions of the substance. The percentage composition is determined by a quantitative chemical analysis. As an example, suppose we wished to determine the symbol of butyric acid. The specific gravity of the vapor of this volatile compound was determined by Cahours and found to be 44.3, hydrogen gas being unity. Hence the molecular weight would be 88.6 microcriths, but the combining proportions of the acid deduced from analyses of its salts prove that the more accurate value is 88 m. c.

An analysis of the acid published by Grtinzweig gives the following percentage composition, and from this we easily calculate the amount of each element in 88 m. c. or one molecule:


Analysis of butyric acid.

Composition of one molecule.

Atomic weight.

Number of atoms in one molecule.



47.97 m.c.=

12 x




8.15 " =



Oxygen ...


31.88 " =

16 X



88 "

Evidently in the molecule there are 4 atoms-of carbon, 8 atoms of hydrogen, and 2 atoms of oxgen, and the symbol is therefore C4LUO2. Thus we can fix the symbols of all volatile bodies. If the substance is non-volatile, we rely primarily on the combining proportion to fix the molecular weight, and, as has been said, there is frequently danger of assigning multiple values. But as a general rule the chemical relations of the substance enable us to determine which of the possible multiples should be taken; and if these leave us in doubt, we adopt provisionally as the symbol of the molecule that multiple which has the smallest number of whole atoms, and wait for the progress of science to correct any error. But even after weighing the molecules and determining the number and kind of atoms of which they consist, chemistry has gone forward still further in developing the molecular theory, and has discovered a large and important class of phenomena, which it refers to differences of arrangement in the grouping of the atoms of the molecules. Thus, there is a substance called acetic ether which has the same molecular weight and the same percentage of composition as butyric acid. Its molecules therefore contain the same number of the same kind of atoms as the other.

Yet the qualities of the two substances are utterly different, the acid having the disgusting smell of rancid butter and the ether the pleasant odor of apples, and chemistry attempts to explain this difference by showing that the atoms are arranged differently in the two classes of molecules, as the following diagrams indicate:

Butyric acid.

Butyric acid.

Acetic ether.

Acetic ether.

Substances so related are said to be isomeric, and these structural formulas, as they are called, so far from being vagaries of the imagination, are sober deductions from experimental evidence. It is impossible however, in a brief article, to render this evidence intelligible. The investigation of molecular structure is at present the chief aim of chemistry, and to works on this subject the reader is referred for further information.