Molecules 分子：在英国科学促进会的讲演 詹姆斯·克拉克·麦克斯韦 James Clerk Maxwell（1831–1879） 1873 年 9 月在布拉德福德的讲演 冷冻图书馆 · 开架书库 · S-006017 · https://coldlibrary.com/s/006017 权利：1873 年讲演，1873–74 年刊印；作者卒于 1879 年。所引丁尼生《卢克莱修》诗句发表于 1868 年，丁尼生卒于 1892 年。已按澳大利亚、欧盟、英国、中国大陆和美国的规则核对（截至 2026 年 10 月 11 日）。仅供参考，不是法律意见。 来源：Wikisource，https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_4/January_1874/The_Theory_of_Molecules（取于 2026-10-11） 中文译文：Claude（AI），2026 · CC0 1.0 生成于 2026-10-14，来自 https://coldlibrary.com/open-stacks/maxwell-molecules ---- An atom is a body which cannot be cut in two. A molecule is the smallest possible portion of a particular substance. No one has ever seen or handled a single molecule. Molecular science, therefore, is one of those branches of study which deal with things invisible and imperceptible by our senses, and which cannot be subjected to direct experiment. The mind of man has perplexed itself with many hard questions. Is space infinite, and if so in what sense? Is the material world infinite in extent, and are all places within that extent equally full of matter? Do atoms exist, or is matter infinitely divisible? The discussion of questions of this kind has been going on ever since men began to reason, and to each of us, as soon as we obtain the use of our faculties, the same old questions arise as fresh as ever. They form as essential a part of the science of the nineteenth century of our era, as of that of the fifth century before it. We do not know much about the science organization of Thrace twenty-two centuries ago, or of the machinery then employed for diffusing an interest in physical research. There were men, however, in those days, who devoted their lives to the pursuit of knowledge with an ardor worthy of the most distinguished members of the British Association; and the lectures in which Democritus explained the atomic theory to his fellow-citizens of Abdera realized, not in golden opinions only, but in golden talents, a sum hardly equaled even in America. To another very eminent philosopher, Anaxagoras, best known to the world as the teacher of Socrates, we are indebted for the most important service to the atomic theory, which, after its statement by Democritus, remained to be done. Anaxagoras, in fact, stated a theory which so exactly contradicts the atomic theory of Democritus that the truth or falsehood of the one theory implies the falsehood or truth of the other. The question of the existence or non-existence of atoms cannot be presented to us this evening with greater clearness than in the alternative theories of these two philosophers. Take any portion of matter, say a drop of water, and observe its properties. Like every other portion of matter we have ever seen, it is divisible. Divide it in two, each portion appears to retain all the properties of the original drop, and among others that of being divisible. The parts are similar to the whole in every respect except in absolute size. Now go on repeating the process of division till the separate portions of water are so small that we can no longer perceive or handle them. Still we have no doubt that the subdivision might be carried further, if our senses were more acute and our instruments more delicate. Thus far all are agreed, but now the question arises, Can this subdivision be repeated forever? According to Democritus and the atomic school, we must answer in the negative. After a certain number of subdivisions, the drop would be divided into a number of parts each of which is incapable of further subdivision. We should thus, in imagination, arrive at the atom, which, as its name literally signifies, cannot be cut in two. This is the atomic doctrine of Democritus, Epicurus, and Lucretius, and, I may add, of your lecturer. According to Anaxagoras, on the other hand, the parts into which the drop is divided are in all respects similar to the whole drop, the mere size of a body counting for nothing as regards the nature of its substance. Hence if the whole drop is divisible, so are its parts down to the minutest subdivisions, and that without end. The essence of the doctrine of Anaxagoras is, that the parts of a body are in all respects similar to the whole. It was therefore called the doctrine of Homoiomereia. Anaxagoras did not of course assert this of the parts of organized bodies such as men and animals, but he maintained that those inorganic substances which appear to us homogeneous are really so, and that the universal experience of mankind testifies that every material body, without exception, is divisible. The doctrine of atoms and that of homogeneity are thus in direct contradiction. But we must now go on to molecules. Molecule is a modern word. It does not occur in Johnson's "Dictionary." The ideas it embodies are those belonging to modern chemistry. A drop of water, to return to our former example, may be divided into a certain number, and no more, of portions similar to each other. Each of these the modern chemist calls a molecule of water. But it is by no means an atom, for it contains two different substances, oxygen and hydrogen, and by a certain process the molecule may be actually divided into two parts, one consisting of oxygen and the other of hydrogen. According to the received doctrine, in each molecule of water there are two molecules of hydrogen and one of oxygen. Whether these are or are not ultimate atoms I shall not attempt to decide. We now see what a molecule is, as distinguished from an atom. A molecule of a substance is a small body such that if, on the one hand, a number of similar molecules were assembled together they would form a mass of that substance, while on the other hand, if any portion of this molecule were removed, it would no longer be able, along with an assemblage of other molecules similarly treated, to make up a mass of the original substance. Every substance, simple or compound, has its own molecule. It this molecule be divided, its parts are molecules of a different substance or substances from that of which the whole is a molecule. An atom, if there is such a thing, must be a molecule of an elementary-substance. Since, therefore, every molecule is not an atom, but every atom is a molecule, I shall use the word molecule as the more general term. I have no intention of taking up your time by expounding the doctrines of modern chemistry with respect to the molecules of different substances. It is not the special but the universal interest of molecular science which encourages me to address you. It is not because we happen to be chemists or physicists or specialists of any kind that we are attracted toward this centre of all material existence, but because we all belong to a race endowed with faculties which urge us on to search deep and ever deeper into the nature of things. We find that now, as in the days of the earliest physical speculations, all physical researches appear to converge toward the same point, and every inquirer, as he looks forward into the dim region toward which the path of discovery is leading him, sees, each according to his sight, the vision of the same quest. One may see the atom as a material. point, invested and surrounded by potential forces. Another sees no garment of force, but only the bare and utter hardness of mere impenetrability. But though many a speculator, as he has seen the vision recede before him into the innermost sanctuary of the inconceivably little, has had to confess that the quest was not for him, and though philosophers in every age have been exhorting each other to direct their minds to some more useful and attainable aim, each generation, from the earliest dawn of science to the present time, has contributed a due proportion of its ablest intellects to the quest of the ultimate atom. Our business this evening is to describe some researches in molecular science, and in particular to place before you any definite information which has been obtained respecting the molecules themselves. The old atomic theory, as described by Lucretius and revived in modern times, asserts that the molecules of all bodies are in motion, even when the body itself appears to be at rest. These motions of molecules are, in the case of solid bodies, confined within so narrow a range that even with our best microscopes we cannot detect that they alter their places at all. In liquids and gases, however, the molecules are not confined within any definite limits, but work their way through the whole mass, even when that mass is not disturbed by any visible motion. This process of diffusion, as it is called, which goes on in gases and liquids and even in some solids, can be subjected to experiment, and forms one of the most convincing proofs of the motion of molecules. Now, the recent progress of molecular science began with the study of the mechanical effect of the impact of these moving molecules when they strike against any solid body. Of course these flying molecules must beat against whatever is placed among them, and the constant succession of these strokes is, according to our theory, the sole cause of what is called the pressure of air and other gases. This appears to have been first suspected by Daniel Bernoulli, but he had not the means which we now have of verifying the theory. The same theory was afterward brought forward independently by Lesage, of Geneva, who, however, devoted most of his labor to the explanation of gravitation by the impact of atoms. Then Herapath, in his "Mathematical Physics," published in 1847, made a much more extensive application of the theory to gases; and Dr. Joule, whose absence from our meeting we must all regret, calculated the actual velocity of the molecules of hydrogen. The further development of the theory is generally supposed to have been begun with a paper by Krönig, which does not, however, so far as I can see, contain any improvement on what had gone before. It seems, however, to have drawn the attention of Prof. Clausius to the subject, and to him we owe a very large part of what has been since accomplished. We all know that air or any other gas placed in a vessel presses against the sides of the vessel, and against the surface of any body placed within it. On the kinetic theory this pressure is entirely due to the molecules striking against these surfaces, and thereby communicating to them a series of impulses which follow each other in such rapid succession that they produce an effect which cannot be distinguished from that of a continuous pressure. If the velocity of the molecules is given, and the number varied, thence since each molecule, on an average, strikes the side of the vessel the same number of times, and with an impulse of the same magnitude, each will contribute an equal share to the whole pressure. The pressure in a vessel of given size is therefore proportional to the number of molecules in it, that is, to the quantity of gas in it. This is the complete dynamical explanation of the fact discovered by Robert Boyle, that the pressure of air is proportional to its density. It shows also that, of different portions of gas forced into a vessel, each produces its own part of the pressure independently of the rest, and this whether these portions be of the same gas or not. Let us next suppose that the velocity of the molecules is increased. Each molecule will now strike the sides of the vessel a greater number of times in a second, but besides this, the impulse of each blow will be increased in the same proportion, so that the part of the pressure due to each molecule will vary as the square of the velocity. Now, the increase of the square of velocity corresponds, in our theory, to a rise of temperature, and in this way we can explain the effect of warming the gas, and also the law discovered by Charles, that the proportional expansion of all gases between given temperatures is the same. The dynamical theory also tells us what will happen if molecules of different masses are allowed to knock about together. The greater masses will go slower than the smaller ones, so that, on an average, every molecule, great or small, will have the same energy of motion. The proof of this dynamical theorem, in which I claim the priority, has recently been greatly developed and improved by Dr. Ludwig Boltzmann. The most important consequence which flows from it is, that a cubic centimetre of every gas at standard temperature and pressure contains the same number of molecules. This is the dynamical explanation of Gay-Lussac's law of the equivalent volumes of gases. But we must now descend to particulars, and calculate the actual velocity of a molecule of hydrogen. A cubic centimetre of hydrogen, at the temperature of melting ice and at a pressure of one atmosphere, weighs 0.00008954 gramme. We have to find at what rate this small mass must move (whether altogether or in separate molecules makes no difference) so as to produce the observed pressure on the sides of the cubic centimetre. This is the calculation which was first made by Dr. Joule, and the result is 1,859 metres per second. This is what we are accustomed to call a great velocity. It is greater than any velocity obtained in artillery practice. The velocity of other gases is less, as you will see by the table, but in all cases it is very great as compared with that of bullets. We have now to conceive the molecules of the air in this hall flying about in all directions, at a rate of about seventeen miles in a minute. If all these molecules were flying in the same direction, they would constitute a wind blowing at the rate of seventeen miles a minute, and the only wind which approaches this velocity is that which proceeds from the mouth of a cannon. How, then, are you and I able to stand here? Only because the molecules happen to be flying in different directions, so that those which strike against our backs enable us to support the storm which is beating against our faces. Indeed, if this molecular bombardment were to cease, even for an instant, our veins would swell, our breath would leave us, and we should, literally, expire. But it is not only against us or against the walls of the room that the molecules are striking. Consider the immense number of them, and the fact that they are flying in every possible direction, and you will see that they cannot avoid striking each other. Every time that two molecules come into collision, the paths of both are changed, and they go off in new directions. Thus each molecule is continually getting its course altered, so that in spite of its great velocity it may be a long time before it reaches any great distance from the point at which it set out. I have here a bottle containing ammonia. Ammonia is a gas which you can recognize by its smell. Its molecules have a velocity of six hundred metres per second, so that, if their course had not been interrupted by striking against the molecules of air in the hall, every one in the most distant gallery would have smelt ammonia before I was able to pronounce the name of the gas. But, instead of this, each molecule of ammonia is so jostled about by the molecules of air, that it is sometimes going one way and sometimes another. It is like a hare which is always doubling, and, though it goes a great pace, it makes very little progress. Nevertheless, the smell of ammonia is now beginning to be perceptible at some distance from the bottle. The gas does diffuse itself through the air, though the process is a slow one, and, if we could close up every opening of this hall so as to make it air-tight, and leave every thing to itself for some weeks, the ammonia would become uniformly mixed through every part of the air in the hall. This property of gases, that they diffuse through each other, was first remarked by Priestley. Dalton showed that it takes place quite independently of any chemical action between the inter-diffusing gases. Graham, whose researches were especially directed toward those phenomena which seem to throw light on molecular motions, made a careful study of diffusion, and obtained the first results from which the rate of diffusion can be calculated. Still more recently, the rates of diffusion of gases into each other have been measured with great precision by Prof. Loschmidt, of Vienna. He placed the two gases in two similar vertical tubes, the lighter gas being placed above the heavier, so as to avoid the formation of currents. He then opened a sliding-valve, so as to make the two tubes into one, and, after leaving the gases to themselves for an hour or so, he shut the valve, and determined how much of each gas had diffused into the other. As most gases are invisible, I shall exhibit gaseous diffusion to you by means of two gases, ammonia and hydrochloric acid, which, when they meet, form a solid product. The ammonia, being the lighter gas, is placed above the hydrochloric acid, with a stratum of air between, but you will soon see that the gases can diffuse through this stratum of air, and produce a cloud of white smoke when they meet. During the whole of this process, no currents or any other visible motion can be detected. Every part of the vessel appears as calm as a jar of undisturbed air. But, according to our theory, the same kind of motion is going on in calm air as in the inter-diffusing gases, the only difference being that we can trace the molecules from one place to another more easily when they are of a different nature from those through which they are diffusing. If we wish to form a mental representation of what is going on among the molecules in calm air, we cannot do better than observe a swarm of bees, when every individual bee is flying furiously, first in one direction, and then in another, while the swarm, as a whole, either remains at rest, or sails slowly through the air. In certain seasons, swarms of bees are apt to fly off to a great distance, and the owners, in order to identify their property when they find them on other people's ground, sometimes throw handfuls of flour at the swarm. Now, let us suppose that the flour thrown at the flying swarm has whitened those bees only which happened to be in the lower half of the swarm, leaving those in the upper half free from flour. If the bees still go on flying hither and thither in an irregular manner, the floury bees will be found in continually increasing proportions in the upper part of the swarm, till they have become equally diffused through every part of it. But the reason of this diffusion is not because the bees were marked with flour, but because they are flying about. The only effect of the marking is to enable us to identify certain bees. We have no means of marking a select number of molecules of air, so as to trace them after they have become diffused among others, but we may communicate to them some property by which we may obtain evidence of their diffusion. For instance, if an horizontal stratum of air is moving horizontally, molecules diffusing out of this stratum, into those above and below, will carry their horizontal motion with them, and so tend to communicate motion to the neighboring strata, while molecules diffusing out of the neighboring strata into the moving one will tend to bring it to rest. The action between the strata is somewhat like that of two rough surfaces, one of which slides over the other, rubbing on it. Friction is the name given to this action between solid bodies; in the case of fluids it is called internal friction or viscosity. It is in fact only another kind of diffusion—a lateral diffusion of momentum, and its amount can be calculated from data derived from observations of the first kind of diffusion, that of matter. The comparative values of the viscosity of different gases were determined by Graham in his researches on the transpiration of gases through long, narrow tubes, and their absolute values have been deduced from experiments on the oscillation of disks by Oscar Meyer and myself. Another way of tracing the diffusion of molecules through calm air is to heat the upper stratum of the air in a vessel, and so observe the rate at which this heat is communicated to the lower strata. This, in fact, is a third kind of diffusion—that of energy, and the rate at which it must take place was calculated from data derived from experiments on viscosity before any direct experiments on the conduction of heat had been made. Prof. Stefan, of Vienna, has recently, by a very delicate method, succeeded in determining the conductivity of air, and he finds it, as he tells us, in striking agreement with the value predicted by the theory. All these three kinds of diffusion—the diffusion of matter, of momentum, and of energy—are carried on by the motion of the molecules. The greater the velocity of the molecules, and the farther they travel before their paths are altered by collision with other molecules, the more rapid will be the diffusion. Now, we know already the velocity of the molecules, and therefore by experiments on diffusion we can determine how far, on an average, a molecule travels without striking another. Prof. Clausius, of Bonn, who first gave us precise ideas about the motion of agitation of molecules, calls this distance the mean path of a molecule. I have calculated, from Prof. Loschmidt's diffusion experiments, the mean path of the molecules of four well-known gases. The average distance traveled by a molecule between one collision and another is given in the table. It is a very small distance, quite imperceptible to us even with our best microscopes. Roughly speaking, it is about the tenth part of the length of a wave of light, which you know is a very small quantity. Of course the time spent on so short a path by such swift molecules must be very small. I have calculated the number of collisions which each must undergo in a second. They are given in the table, and are reckoned by thousands of millions. No wonder that the traveling power of the swiftest molecule is but small, when its course is completely changed thousands of millions of times in a second. The three kinds of diffusion also take place in liquids, but the relation between the rates at which they take place is not so simple as in the case of gases. The dynamical theory of liquids is not so well understood as that of gases, but the principal difference between a gas and a liquid seems to be that, in a gas each molecule spends the greater part of its time in describing its free path, and is for a very small portion of its time engaged in encounters with other molecules, whereas in a liquid the molecule has hardly any free path, and is always in a state of close encounter with other molecules. Hence, in a liquid, the diffusion of motion from one molecule to another takes place much more rapidly than the diffusion of the molecules themselves, for the same reason that it is more expeditious in a dense crowd to pass on a letter from hand to hand than to give it to a special messenger to work his way through the crowd. I have here a jar, the lower part of which contains a solution of copper sulphate, while the upper part contains pure water. It has been standing here since Friday, and you see how little progress the blue liquid has made in diffusing itself through the water above. The rate of diffusion of a solution of sugar has been carefully observed by Voit. Comparing his results with those of Loschmidt on gases, we find that about as much diffusion takes place in a second in gases as requires a day in liquids. The rate of diffusion of momentum is also slower in liquids than in gases, but by no means in the same proportion. The same amount of motion takes about ten times as long to subside in water as in air, as you will see by what takes place when I stir these two jars, one containing water and the other air. There is still less difference between the rates at which a rise of temperature is propagated through a liquid and through a gas. In solids the molecules are still in motion, but their motions are confined within very narrow limits. Hence, the diffusion of matter does not take place in solid bodies, though that of motion and heat takes place very freely. Nevertheless, certain liquids can diffuse through colloid solids, such as jelly and gum, and hydrogen can make its way through iron and palladium. We have no time to do more than mention that most wonderful molecular motion which is called electrolysis. Here is an electric current passing through acidulated water, and causing oxygen to appear at one electrode, and hydrogen at the other. In the space between, the water is perfectly calm, and yet two opposite currents of oxygen and of hydrogen must be passing through it. The physical theory of this process has been studied by Clausius, who has given reasons for asserting that in ordinary water the molecules are not only moving, but every now and then striking each other with such violence that the oxygen and hydrogen of the molecules part company, and dance about through the crowd, seeking partners which have become dissociated in the same way. In water these exchanges produce, on the whole, no observable effect, but no sooner does the electromotive force begin to act, than it exerts its guiding influence on the unattached molecules, and bends the course of each toward its proper electrode, till the moment when, meeting with an unappropriated molecule of the opposite kind, it enters again into a more or less permanent union with it till it is again dissociated by another shock. Electrolysis, therefore, is a kind of diffusion assisted by electromotive force. Another branch of molecular science is that which relates to the exchange of molecules between a liquid and a gas. It includes the theory of evaporation and condensation, in which the gas in question is the vapor of the liquid, and also the theory of the absorption of a gas by a liquid of a different substance. The researches of Dr. Andrews on the relations between the liquid and the gaseous state have shown us that, though the statements in our own elementary textbooks may be so neatly expressed that they appear almost self-evident, their true interpretation may involve some principle so profound that, till the right man has laid hold of it, no one ever suspects that any thing is left to be discovered. These, then, are, some of the fields from which the data of molecular science are gathered. We may divide the ultimate results into three ranks, according to the completeness of our knowledge of them. To the first rank belong the relative masses of the molecules of different gases, and their velocities in metres per second. These data are obtained from experiments on the pressure and density of gases, and are known to a high degree of precision. In the second rank we must place the relative size of the molecules of different gases, the length of their mean paths, and the number of collisions in a second. These quantities are deduced from experiments on the three kinds of diffusion. Their received values must be regarded as rough approximations till the methods of experimenting are greatly improved. There is another set of quantities which we must place in the third rank, because our knowledge of them is neither precise, as in the first rank, nor approximate, as in the second, but is only as yet of the nature of a probable conjecture. These are the absolute mass of a molecule, its absolute diameter, and the number of molecules in a cubic centimetre. We know the relative masses of different molecules with great accuracy, and we know their relative diameters approximately. From these we can deduce the relative densities of the molecules themselves. So far we are on firm ground. The great resistance of liquids to compression makes it probable that their molecules must be at about the same distance from each other as that at which two molecules of the same substance in the gaseous form act on each other during an encounter. This conjecture has been put to the test by Lorenz Meyer, who has compared the densities of different liquids with the calculated relative densities of the molecules of their vapors, and has found a remarkable correspondence between them. Now, Loschmidt has deduced from the dynamical theory the following remarkable proportion: 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 the diameter of a molecule. Assuming that the volume of the substance, when reduced to the liquid form, is not much greater than the combined volume of the molecules, we obtain from this proportion the diameter of a molecule. In this way Loschmidt, in 1865, made the first estimate of the diameter of a molecule. Independently of him and of each other, Mr. Stoney in 1868, and Sir W. Thomson, in 1870, published results of a similar kind, those of Thomson being deduced not only in this way, but from considerations derived from the thickness of soap-bubbles, and from the electric properties of metals. According to the table, which I have calculated from Loschmidt's data, the size of the molecules of hydrogen is such that about 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! In a cubic centimetre of any gas at standard pressure and temperature, there are about nineteen million million million molecules. All these numbers of the third rank are, I need not tell you, to be regarded as at present conjectural. In order to warrant us in putting any confidence in numbers obtained in this way, we should have to compare together a greater number of independent data than we have as yet obtained, and to show that they lead to consistent results. Thus far, we have been considering molecular science as an inquiry into natural phenomena. But, though the professed aim of all scientific work, is to unravel the secrets of Nature, it has another effect, not less valuable, on the mind of the worker. It leaves him in possession of methods which nothing but scientific work could have led him to invent, and it places him in a position from which many regions of Nature, besides that which he has been studying, appear under a new aspect. The study of molecules has developed a method of its own, and it has also opened up new views of Nature. When Lucretius wishes us to form a mental representation of the motion of atoms, he tells us to look at a sunbeam shining through a darkened room (the same instrument of research by which Dr. Tyndall makes visible to us the dust we breathe), and to observe the motes which chase each other in all directions through it. This motion of the visible motes, he tells us, is but a result of the far more complicated motion of the invisible atoms which knock the motes about. In his dream of Nature, as Tennyson tells us, he "saw the flaring atom-streams / And torrents of her myriad universe, / Running along the illimitable inane, / Fly on to clash together again, and make / Another and another frame of things / Forever." And it is no wonder that he should have attempted to burst the bonds of Fate by making his atoms deviate from their courses at quite uncertain times and places, thus attributing to them a kind of irrational free-will, which on his materialistic theory is the only explanation of that power of voluntary action of which we ourselves are conscious. As long as we have to deal with only two molecules, and have all the data given us, we can calculate the result of their encounter; but when we have to deal with millions of molecules, each of which has millions of encounters in a second, the complexity of the problem seems to shut out all hope of a legitimate solution. The modern atomists have therefore adopted a method which is, I believe, new in the department of mathematical physics, though it has long been in use in the section of statistics. When the working members of Section F get hold of a report of the census, or any other document containing the numerical data of Economic and Social Science, they begin by distributing the whole population into groups, according to age, income-tax, education, religious belief, or criminal convictions. The number of individuals is far too great to allow of their tracing the history of each separately, so that, in order to reduce their labor within human limits, they concentrate their attention on a small number of artificial groups. The varying number of individuals in each group, and not the varying state of each individual, is the primary datum from which they work. This, of course, is not the only method of studying human nature. We may observe the conduct of individual men and compare it with that conduct which their previous character, and their present circumstances, according to the best existing theory, would lead us to expect. Those who practise this method endeavor to improve their knowledge of the elements of human nature in much the same way as an astronomer corrects the elements of a planet by comparing its actual position with that deduced from the received elements. The study of human nature by parents and school-masters, by historians and statesmen, is therefore to be distinguished from that carried on by registrars and tabulators, and by those statesmen who put their faith in figures. The one may be called the historical, and the other the statistical method. The equations of dynamics completely express the laws of the historical method as applied to matter, but the application of these equations implies a perfect knowledge of all the data. But the smallest portion of matter which we can subject to experiment consists of millions of molecules, not one of which ever becomes individually sensible to us. We cannot, therefore, ascertain the actual motion of any one of these molecules, so that we are obliged to abandon the strict historical method, and to adopt the statistical method of dealing with large groups of molecules. The data of the statistical method as applied to molecular science are the sums of large numbers of molecular quantities. In studying the relations between quantities of this kind, we meet with a new kind of regularity, the regularity of averages, which we can depend upon quite sufficiently for all practical purposes, but which can make no claim to that character of absolute precision which belongs to the laws of abstract dynamics. Thus molecular science teaches us that our experiments can never give us any thing more than statistical information, and that no law deduced from them can pretend to absolute precision. But, when we pass from the contemplation of our experiments to that of the molecules themselves, we leave the world of chance and change, and enter a region where every thing is certain and immutable. The molecules are conformed to a constant type with a precision which is not to be found in the sensible properties of the bodies which they constitute. In the first place, the mass of each individual molecule, and all its other properties, are absolutely unalterable. In the second place, the properties of all molecules of the same kind are absolutely identical. Let us consider the properties of two kinds of molecules, those of oxygen and those of hydrogen. We can procure specimens of oxygen from very different sources—from the air, from water, from rocks of every geological epoch. The history of these specimens has been very different, and, if, during thousands of years, difference of circumstances could produce difference of properties, these specimens of oxygen would show it. In like manner we may procure hydrogen from water, from coal, or, as Graham did, from meteoric iron. Take two litres of any specimen of hydrogen, it will combine with exactly one litre of any specimen of oxygen, and will form exactly two litres of the vapor of water. Now, if, during the whole previous history of either specimen, whether imprisoned in the rocks, flowing in the sea, or careering through unknown regions with the meteorites, any modification of the molecules had taken place, these relations would no longer be preserved. But we have another and an entirely different method of comparing the properties of molecules. The molecule, though indestructible, is not a hard, rigid body, but is capable of internal movements, and when these are excited it emits rays, the wave-length of which is a measure of the time of vibration of the molecule. By means of the spectroscope the wave-lengths of different kinds of light may be computed to within one ten-thousandth part. In this way it has been ascertained, not only that molecules taken from every specimen of hydrogen in our laboratories have the same set of periods of vibration, but that light, having the same set of periods of vibration, is emitted from the sun and from the fixed stars. We are thus assured that molecules of the same nature as those of our hydrogen exist in those distant regions, or at least did exist when the light by which we see them was emitted. From a comparison of the dimensions of the buildings of the Egyptians with those of the Greeks, it appears that they have a common measure. Hence, even if no ancient author had recorded the fact that the two nations employed the same cubit as a standard of length, we might prove it from the buildings themselves. We should also be justified in asserting that at some time or other a material standard of length must have been carried from one country to the other, or that both countries had obtained their standards from a common source. But in the heavens we discover by their light, and by their light alone, stars so distant from each other, that no material thing can ever have passed from one to another; and yet this light, which is to us the sole evidence of the existence of these distant worlds, tells us also that each of them is built up of molecules of the same kinds as those which we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time. Each molecule, therefore, throughout the universe, bears impressed on it the stamp of a metric system as distinctly as does the metre of the Archives of Paris, or the double royal cubit of the Temple of Karnac. No theory of evolution can be formed to account for the similarity of molecules, for evolution necessarily implies continuous change, and the molecule is incapable of growth or decay, of generation or destruction. None of the processes of Nature, since the time when Nature began, have produced the slightest difference in the properties of any molecule. We are therefore unable to ascribe either the existence of the molecules, or the identity of their properties, to the operation of any of the causes which we call natural. On the other hand, the exact equality of each molecule to all others of the same kind gives it, as Sir John Herschel has well said, the essential character of a manufactured article, and precludes the idea of its being eternal and self-existent. Thus we have been led, along a strictly scientific path, very near to the point at which Science must stop. Not that Science is debarred from studying the internal mechanism of a molecule which she cannot take to pieces, any more than from investigating an organism which she cannot put together. But, in tracing back the history of matter, Science is arrested when she assures herself, on the one hand, that the molecule has been made, and on the other that it has not been made by any of the processes we call natural. Science is incompetent to reason upon the creation of matter itself out of nothing. We have reached the utmost limit of our thinking faculties when we have admitted that because matter cannot be eternal and self-existent it must have been created. It is only when we contemplate, not matter in itself, but the form in which it actually exists, that our mind finds something on which it can lay hold. That matter, as such, should have certain fundamental properties—that it should exist in space and be capable of motion, that its motion should be persistent, and so on, are truths which may, for any thing we know, be of the kind which metaphysicians call necessary. We may use our knowledge of such truths for purposes of deduction, but we have no data for speculating as to their origin. But that there should be exactly so much matter and no more in every molecule of hydrogen is a fact of a very different order. We have here a particular distribution of matter—a collocation—to use the expression of Dr. Chalmers, of things which we have no difficulty in imagining to have been arranged otherwise. The form and dimensions of the orbits of the planets, for instance, are not determined by any law of Nature, but depend upon a particular collocation of matter. The same is the case with respect to the size of the earth, from which the standard of what is called the metrical system has been derived. But these astronomical and terrestrial magnitudes are far inferior in scientific importance to that most fundamental of all standards which forms the base of the molecular system. Natural causes, as we know, are at work, which tend to modify, if they do not at length destroy, all the arrangements and dimensions of the earth and the whole solar system. But though in the course of ages catastrophes have occurred, and may yet occur, in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules out of which these systems are built—the foundation-stones of the material universe—remain unbroken and unworn. They continue this day as they were created, perfect in number, and measure, and weight, and, from the ineffaceable characters impressed on them, we may learn that those aspirations after accuracy in measurement, truth in statement, and justice in action, which we reckon among our noblest attributes as men, are ours, because they are essential constituents of the image of Him who in the beginning created, not only the heaven and the earth, but the materials of which heaven and earth consist. ---- 中文译文 · Claude（AI）译 原子是不能被切成两半的物体。分子是一种特定物质的最小可能的部分。从来没有人见过或摸过单个的分子。因此，分子科学属于这样一类研究：它所处理的东西是我们的感官看不见、觉察不到的，也无法对它们进行直接的实验。 人的心智曾为许多难题而困惑。空间是无限的吗？如果是，在什么意义上无限？物质世界在广延上是无限的吗？在这一广延之内，所有地方都同样充满了物质吗？原子存在吗？还是物质可以无限分割？ 自从人类开始推理以来，这类问题的讨论就一直在进行；而对我们每一个人来说，一旦能够运用自己的官能，这些古老的问题就又像从前一样新鲜地出现了。它们是我们纪元十九世纪科学的根本组成部分，正如它们是纪元前五世纪科学的根本组成部分一样。 对于二十二个世纪以前色雷斯的科学组织，或者当时用来传播对物理研究之兴趣的机构，我们所知不多。然而，那时就有一些人以一种无愧于不列颠科学促进会最杰出会员的热忱，把一生献给了对知识的追求；德谟克利特向他的阿布德拉同胞讲解原子论的那些讲座，赢得的不只是如金的口碑，还有真金的塔兰特，其数目即使在美国也难有人能比。 另一位非常杰出的哲学家阿那克萨哥拉——世人最熟知他是苏格拉底的老师——为原子论作出了在德谟克利特提出它之后尚待完成的最重要的贡献。事实上，阿那克萨哥拉提出了一种与德谟克利特的原子论截然相反的理论，以致其中一种理论的真或假，意味着另一种理论的假或真。原子存在与否的问题，今晚不可能比用这两位哲学家针锋相对的理论更清楚地摆在我们面前了。 取任何一部分物质，比如一滴水，观察它的性质。像我们见过的其他任何一部分物质一样，它是可分的。把它分成两半，每一部分似乎都保留着原来那滴水的一切性质，其中也包括可分性。各部分除了绝对大小之外，在一切方面都与整体相似。 现在继续重复分割的过程，直到分开的一份份水小得我们再也觉察不到、摸不着它们。我们仍然毫不怀疑，如果我们的感官更敏锐，仪器更精细，分割还可以继续下去。到这里为止，大家都意见一致，但这时问题就出现了：这种分割能不能永远重复下去？ 按照德谟克利特和原子学派的看法，我们必须作否定的回答。经过一定次数的分割之后，那滴水会被分成许多部分，每一部分都不能再分割。这样，在想象中，我们就会到达原子——正如它的名字字面上所表示的，它是不能被切成两半的。这就是德谟克利特、伊壁鸠鲁和卢克莱修的原子学说，我还可以补充一句，这也是诸位的讲演人的学说。 另一方面，按照阿那克萨哥拉的看法，那滴水被分成的各部分在一切方面都与整滴水相似，一个物体单纯的大小，对于它的物质本性来说毫无意义。因此，如果整滴水是可分的，它的各部分也是可分的，一直分到最微小的部分，而且永无止境。 阿那克萨哥拉学说的要义是：一个物体的各部分在一切方面都与整体相似。因此它被称为“同素体”学说。阿那克萨哥拉当然没有对有机体——如人和动物——的各部分这样断言，但他主张，那些在我们看来是均匀的无机物质确实是均匀的，而且人类的普遍经验证明，每一个物质物体都毫无例外是可分的。 这样，原子学说与均匀性学说就是直接矛盾的。 但现在我们必须接着谈分子。“分子”是一个现代的词。约翰逊的《词典》里没有这个词。它所体现的观念属于现代化学。 回到我们前面的例子，一滴水可以被分成一定数目——不能再多——彼此相似的部分。现代化学家把其中的每一部分叫作一个水分子。但它绝不是原子，因为它含有两种不同的物质，氧和氢，而且通过某种过程，这个分子确实可以被分成两部分，一部分由氧组成，另一部分由氢组成。按照公认的学说，每一个水分子中有两个氢分子和一个氧分子。它们是不是终极的原子，我不打算去判定。 现在我们明白了，与原子相区别的分子是什么。 一种物质的分子，是这样一种小物体：一方面，如果把许多相似的分子聚集在一起，它们就会形成一团这种物质；另一方面，如果把这个分子的任何一部分去掉，它就不再能够与一群经过同样处理的其他分子一起，组成一团原来的物质。 每一种物质，无论是单质还是化合物，都有它自己的分子。如果把这个分子分开，它的各部分就是另一种或另几种物质的分子，而不是整个分子所属的那种物质的分子。原子，如果真有这种东西的话，必定是一种元素物质的分子。因此，既然并非每个分子都是原子，而每个原子都是分子，我就把“分子”这个词作为较一般的术语来使用。 我无意占用诸位的时间，去阐述现代化学关于各种物质之分子的学说。鼓励我向诸位讲话的，不是分子科学的专门趣味，而是它的普遍趣味。我们之所以被吸引到这个一切物质存在的中心来，不是因为我们恰好是化学家、物理学家或者别的什么专家，而是因为我们都属于一个被赋予了某些官能的族类，这些官能催促我们深入、再深入地探究事物的本性。 我们发现，如今，正如在最早的物理思辨的年代一样，一切物理研究似乎都向同一点汇聚；每一个探索者，当他向前眺望发现之路正把他引向的那片朦胧地带时，都依各自的眼力，看见了同一场追寻的异象。 有人可能把原子看作一个物质点，被势力所包裹、所环绕。另一个人则看不到什么力的外衣，只看到单纯的不可入性那赤裸而绝对的坚硬。 然而，尽管许多思辨者眼看着那个异象在他面前退入不可思议之微小的至深圣所，不得不承认这场追寻不属于他；尽管每个时代的哲学家都在互相劝勉，要把心思转向某个更有用、更可企及的目标；从科学最早的黎明直到今天，每一代人都贡献出了他们最有才智的头脑中应有的一份，去追寻那终极的原子。 我们今晚的任务，是介绍分子科学中的一些研究，特别是把关于分子本身已经获得的任何确定的知识摆在诸位面前。古老的原子论，正如卢克莱修所描述、并在近代复兴的那样，断言一切物体的分子都在运动，即使物体本身看上去是静止的。在固体中，分子的这些运动被限制在如此狭窄的范围之内，即使用我们最好的显微镜，也根本察觉不出它们改变了位置。然而，在液体和气体中，分子不受任何确定界限的约束，而是在整团物质中穿行，即使那团物质没有受到任何可见运动的扰动。 这一过程叫作扩散，它在气体和液体中进行，甚至在某些固体中也进行；它可以付诸实验，是分子运动最有说服力的证据之一。 分子科学近来的进展，始于研究这些运动着的分子撞击任何固体时所产生的力学效应。这些飞行的分子当然一定会撞击放在它们中间的任何东西，而按照我们的理论，这些撞击的持续不断，就是所谓空气和其他气体压强的唯一原因。 最早猜到这一点的，似乎是丹尼尔·伯努利，但他没有我们今天所拥有的验证这一理论的手段。后来日内瓦的勒萨日独立地提出了同样的理论，不过他把大部分精力用在了用原子的撞击来解释引力上。接着，赫拉帕斯在 1847 年出版的《数学物理学》中，把这一理论更广泛地应用于气体；而焦耳博士——他没能出席我们的大会，我们都深感遗憾——计算出了氢分子的实际速度。 人们一般认为，这一理论的进一步发展始于克吕尼希的一篇论文，不过在我看来，那篇论文并没有对前人的工作作出任何改进。然而，它似乎引起了克劳修斯教授对这个问题的注意，此后所取得的成就，很大一部分要归功于他。 我们都知道，放在容器中的空气或任何其他气体，会压着容器的器壁，也压着放在其中的任何物体的表面。按照分子运动论，这种压强完全是由于分子撞击这些表面，从而给它们一连串的冲击，这些冲击一个接一个，快得使它们产生的效果与连续压力的效果无法区分。 如果分子的速度给定，而改变分子的数目，那么，由于平均说来，每个分子撞击器壁的次数相同，冲击的大小也相同，每个分子都会为总压强贡献相等的一份。因此，在一个给定大小的容器中，压强与其中的分子数目成正比，也就是与其中气体的量成正比。 这就是对罗伯特·玻意耳所发现的事实——空气的压强与它的密度成正比——完整的动力学解释。它还表明，压进一个容器的不同份的气体，各自独立于其余部分而产生它自己那一份压强，无论这些份气体是不是同一种气体。 其次，我们假设分子的速度增加了。现在每个分子每秒撞击器壁的次数会更多，而且除此之外，每次撞击的冲量也按同样的比例增加，因此每个分子所贡献的那一份压强，将随速度的平方而变化。而按照我们的理论，速度平方的增加对应于温度的升高；这样我们就能解释给气体加热的效果，也能解释查理所发现的定律：在给定的温度之间，一切气体膨胀的比例都相同。 动力学理论还告诉我们，如果让质量不同的分子混在一起相互碰撞，会发生什么。质量较大的分子会比质量较小的分子走得慢，结果平均说来，每个分子，无论大小，都具有相同的运动能量。 这条动力学定理的证明——我要求承认我在这上面的优先权——最近由路德维希·玻尔兹曼博士大大地发展和改进了。由它得出的最重要的推论是：在标准温度和压强下，每种气体的一立方厘米都含有相同数目的分子。这就是盖-吕萨克气体当量体积定律的动力学解释。不过现在我们必须深入到具体细节，计算一个氢分子的实际速度。 在冰的熔点温度和一个大气压下，一立方厘米的氢重 0.00008954 克。我们要求出，这一小团质量必须以多大的速率运动（是整体运动还是分成一个个分子运动，没有区别），才能在这一立方厘米的各个面上产生观测到的压强。这个计算最早是焦耳博士做的，结果是每秒 1859 米。这就是我们惯常所说的高速度。它比炮兵射击中得到的任何速度都大。其他气体的速度要小一些，诸位从表中可以看到，但无论哪种情况，与子弹的速度相比，它都非常大。 所以我们现在必须设想，这个大厅里的空气分子正以大约每分钟十七英里的速率向四面八方飞去。 如果所有这些分子都朝同一个方向飞，它们就会形成一股以每分钟十七英里的速率吹刮的风，而唯一接近这种速度的风，是从炮口喷出的那股风。那么，你我怎么还能站在这里呢？只是因为分子碰巧朝不同的方向飞，所以撞击我们后背的那些分子，使我们能够抵挡住扑向我们脸上的风暴。的确，如果这种分子轰击停止，哪怕只停一刹那，我们的血管就会膨胀，呼吸就会离我们而去，我们就会名副其实地“咽了气”。但分子并不只撞击我们，撞击这间屋子的墙壁。想想它们的数目之巨大，想想它们朝一切可能的方向飞行，你们就会明白，它们不可避免地要相互碰撞。每当两个分子相撞，两者的路径都会改变，朝新的方向飞去。因此，每个分子的路线都在不断地被改变，所以尽管它速度极大，可能要过很长时间，它才能到达离出发点很远的地方。 我这里有一瓶氨。氨是一种你们能凭气味辨认出来的气体。它的分子速度为每秒六百米，所以，如果它们的路线没有因撞击大厅里的空气分子而被打断，那么在我还没来得及说出这种气体的名字之前，最远的楼座上的每一个人就都会闻到氨味了。可实际上，每个氨分子都被空气分子挤来撞去，一会儿往这边走，一会儿往那边走。它就像一只总在折返兜圈的野兔，虽然跑得飞快，却进展甚微。尽管如此，在离瓶子有一段距离的地方，现在已经开始能闻到氨的气味了。这种气体确实在空气中扩散，只是过程很慢；如果我们能把这个大厅的每一个开口都封住，使它不透气，然后让一切听其自然几个星期，氨就会均匀地混合在大厅里各处的空气中。 气体相互扩散的这种性质，最早是普里斯特利注意到的。道尔顿表明，它的发生与相互扩散的气体之间的任何化学作用完全无关。格雷厄姆的研究专门针对那些似乎能揭示分子运动的现象，他仔细研究了扩散，得到了最早的一批可以据以计算扩散速率的结果。 更近一些时候，维也纳的洛施密特教授非常精确地测量了气体相互扩散的速率。 他把两种气体放在两根相似的竖直管子里，较轻的气体放在较重的气体上方，以免形成对流。然后他打开一个滑阀，使两根管子连成一根；让气体自行扩散一个小时左右之后，他关上阀门，测定每种气体有多少扩散到了另一种气体中。 由于大多数气体是看不见的，我要用两种气体——氨和氯化氢——来向诸位展示气体的扩散；这两种气体相遇时会形成一种固体产物。氨较轻，放在氯化氢的上方，中间隔着一层空气；但你们很快就会看到，这两种气体能够穿过这层空气扩散，相遇时生成一团白烟。在整个过程中，察觉不到任何气流或别的可见运动。容器的每一部分看上去都和一罐未受扰动的空气一样平静。 但是，按照我们的理论，在平静的空气中进行着的，是与相互扩散的气体中同一种运动，唯一的区别是：当分子与它们穿过的那些分子性质不同时，我们更容易追踪它们从一处到另一处。如果我们想在心里描绘平静的空气中分子之间发生的事情，最好的办法莫过于观察一群蜜蜂：每一只蜜蜂都在疯狂地飞，一会儿朝这个方向，一会儿朝那个方向，而整个蜂群要么停在原处，要么在空中缓缓飘移。 在某些季节，蜂群往往会飞到很远的地方去，蜂主为了在别人的地界上找到它们时能认出自己的财产，有时会朝蜂群撒几把面粉。现在，我们假定撒向飞行蜂群的面粉，只把碰巧位于蜂群下半部的那些蜜蜂染白了，而上半部的蜜蜂没有沾上面粉。 如果蜜蜂继续不规则地飞来飞去，就会发现，沾了面粉的蜜蜂在蜂群上部所占的比例不断增加，直到它们均匀地分布在蜂群的每一部分。但这种扩散的原因，并不是蜜蜂被面粉做了记号，而是因为它们在飞来飞去。做记号唯一的作用，是使我们能认出某些蜜蜂。 我们没有办法给挑选出来的一部分空气分子做记号，以便在它们扩散到其他分子中间之后追踪它们；但我们可以把某种性质传给它们，借此获得它们扩散的证据。 例如，如果一层水平的空气在水平地运动，从这一层扩散到上下两层中去的分子，就会把它们的水平运动带过去，从而倾向于把运动传给相邻的层；而从相邻的层扩散到这一运动层中来的分子，则倾向于使它停下来。层与层之间的这种作用，有点像两个粗糙的表面，一个在另一个上面滑动、摩擦。固体之间的这种作用叫作摩擦；在流体中，它叫作内摩擦或黏滞性。 它实际上只是另一种扩散——动量的横向扩散；它的大小可以根据对第一种扩散，即物质扩散的观测所得的数据计算出来。各种气体黏滞性的相对数值，是格雷厄姆在研究气体通过细长管子的流逸时测定的；它们的绝对数值，则是奥斯卡·迈耶和我从圆盘振荡的实验中推算出来的。 另一种追踪分子在平静空气中扩散的方法，是把容器中上层的空气加热，然后观察这热量传到下层的速率。这实际上是第三种扩散——能量的扩散；在还没有做过任何直接的热传导实验之前，它必须以什么速率进行，就已经根据黏滞性实验所得的数据计算出来了。维也纳的斯特藩教授最近用一种非常精巧的方法，成功地测定了空气的导热率；据他告诉我们，他发现这个值与理论所预言的值惊人地吻合。 所有这三种扩散——物质的扩散、动量的扩散和能量的扩散——都是由分子的运动来进行的。分子的速度越大，它们在因与其他分子碰撞而改变路径之前走得越远，扩散就越快。我们已经知道分子的速度，因此通过扩散实验，就能测定一个分子平均走多远才撞上另一个分子。波恩的克劳修斯教授最早使我们对分子的骚动运动有了精确的概念，他把这段距离叫作分子的平均程。我根据洛施密特教授的扩散实验，计算了四种常见气体分子的平均程。一个分子在一次碰撞与下一次碰撞之间所走的平均距离，见表中所列。这是一段非常小的距离，即使用我们最好的显微镜，我们也完全察觉不到。粗略地说，它大约是光波波长的十分之一，诸位知道，光波波长已是一个非常小的量。当然，如此迅速的分子在如此短的路程上所花的时间，必定非常短。我计算了每个分子每秒必须经受的碰撞次数。它们也列在表中，是以几十亿次计的。一个分子的路线每秒要被彻底改变几十亿次，难怪即使最快的分子，行进的本领也很有限。 这三种扩散也在液体中进行，但它们进行的速率之间的关系，不像在气体中那样简单。液体的动力学理论不像气体的那样被人透彻理解，但气体和液体之间的主要区别似乎是：在气体中，每个分子把大部分时间用于走完它的自由路程，只有很小一部分时间与其他分子相遇；而在液体中，分子几乎没有自由路程，总是处于与其他分子紧密相遇的状态。 因此，在液体中，运动从一个分子到另一个分子的扩散，比分子本身的扩散快得多；道理就像在密集的人群中，把一封信一手一手地传过去，要比交给一个专门的信差让他挤过人群快一样。我这里有一个罐子，下部装着硫酸铜溶液，上部装着清水。它从星期五起就放在这里了，你们看，蓝色的液体在上面的水中扩散得多么少。福伊特曾仔细观察过糖溶液的扩散速率。把他的结果与洛施密特关于气体的结果相比较，我们发现，气体中一秒钟所发生的扩散，在液体中大约需要一天。 在液体中，动量扩散的速率也比在气体中慢，但远没有慢到同样的比例。同样多的运动，在水中平息下来所需的时间，大约是在空气中的十倍；我搅动这两个罐子——一个装水，一个装空气——时所发生的情形，会让你们看到这一点。至于温度的升高在液体中和在气体中传播的速率，两者的差别就更小了。 在固体中，分子仍在运动，但它们的运动被限制在非常狭窄的范围之内。因此，物质的扩散不在固体中发生，而运动和热的扩散却在固体中进行得非常自由。不过，某些液体能够扩散穿过胶体状的固体，比如果冻和树胶，而氢能够穿过铁和钯。 我们没有时间多讲，只能提一提那种最奇妙的分子运动，它叫作电解。这里有一股电流正通过酸化的水，使氧出现在一个电极上，氢出现在另一个电极上。在两极之间的空间里，水十分平静，然而必定有两股方向相反的氧流和氢流正在穿过它。克劳修斯研究过这一过程的物理理论，他给出了理由断言：在普通的水中，分子不仅在运动，而且时不时地彼此猛烈撞击，以致分子中的氧和氢分道扬镳，在人群中四处跳舞，寻找以同样方式离散了的舞伴。在水中，这些交换总的说来不产生任何可观察的效果；但电动势一开始起作用，它就对这些没有配对的分子施加引导性的影响，使每一个分子的路线都弯向它该去的电极，直到它遇上一个尚未被占有的异类分子，又与它结成一种或多或少持久的结合，直到再一次受到撞击而再次离散。因此，电解是一种由电动势辅助的扩散。 分子科学的另一个分支，涉及液体与气体之间的分子交换。它包括蒸发和凝结的理论——其中所说的气体就是该液体的蒸气——也包括一种气体被另一种物质的液体所吸收的理论。安德鲁斯博士关于液态与气态之间关系的研究向我们表明：尽管我们的初级教科书里的陈述可能表达得如此简洁，以致看上去几乎不言自明，但对它们的真正解释，可能涉及某个如此深刻的原理，以致在合适的人抓住它之前，谁也不曾怀疑那里还有什么有待发现。 这些，就是分子科学的数据所由采集的一些领域。我们可以根据我们对最终结果认识的完备程度，把它们分为三等。 属于第一等的，是不同气体分子的相对质量，以及它们以米每秒计的速度。这些数据是从气体压强和密度的实验中得到的，已知的精确度很高。 第二等中，我们必须放进不同气体分子的相对大小、它们平均程的长度，以及每秒钟碰撞的次数。这些量是从三种扩散的实验中推出来的。在实验方法得到大大改进之前，它们的公认值必须被看作粗略的近似值。 还有另一组量，我们必须把它们放在第三等，因为我们对它们的认识既不像第一等那样精确，也不像第二等那样近似，而至今只具有一种可能的推测的性质。这就是一个分子的绝对质量、它的绝对直径，以及一立方厘米中的分子数目。我们非常精确地知道不同分子的相对质量，也近似地知道它们的相对直径。由此我们可以推出分子本身的相对密度。到这里为止，我们站在坚实的地面上。 液体对压缩的巨大抵抗，使人觉得很可能：液体分子彼此之间的距离，大约等于同一物质的两个分子在气态下相遇时相互作用的距离。洛伦兹·迈耶检验了这个推测，他把不同液体的密度与计算出来的其蒸气分子的相对密度作了比较，发现二者之间有显著的对应。 洛施密特从动力学理论推出了如下这个了不起的比例：气体的体积与其中所含全部分子的总体积之比，等于一个分子的平均程与分子直径的八分之一之比。 假定物质在化为液态时的体积并不比分子的总体积大多少，我们就可以从这个比例得出分子的直径。洛施密特就是用这种方法，在 1865 年第一次估算了分子的直径。斯托尼先生在 1868 年、W. 汤姆孙爵士在 1870 年，各自独立地——既独立于洛施密特，也彼此独立——发表了类似的结果；汤姆孙的结果不仅是用这种方法推出的，还依据了从肥皂泡的厚度以及金属的电学性质得来的考虑。 根据我从洛施密特的数据计算出来的那张表，氢分子的大小是这样的：大约两百万个排成一行，才占一毫米；而一亿亿亿个氢分子，重量在四到五克之间！ 在标准压强和温度下，任何气体的一立方厘米中，大约有一千九百亿亿个分子。所有这些第三等的数字，不用我说，目前都只能看作推测。要使我们有理由对用这种方法得到的数字抱有任何信心，我们必须把比迄今所得更多的独立数据放在一起加以比较，并表明它们导致一致的结果。 到此为止，我们一直把分子科学当作对自然现象的一种探究来考察。但是，虽然一切科学工作公开宣称的目的是解开自然的秘密，它对工作者的心智还有另一种同样宝贵的效果。它使他掌握了一些方法，这些方法只有科学工作才能引导他发明出来；它还把他置于这样一个位置，从那里看去，除了他一直在研究的那片领域之外，自然的许多领域都呈现出新的面貌。对分子的研究发展出了一种它自己的方法，也打开了看待自然的新视野。 卢克莱修想让我们在心里描绘原子的运动时，告诉我们去看一束穿过暗室的阳光（廷德尔博士正是用这同一种研究工具，让我们看见我们呼吸的尘埃），观察其中向四面八方相互追逐的微尘。他告诉我们，这些看得见的微尘的运动，不过是那些看不见的原子远为复杂的运动的结果，是原子把微尘撞来撞去。正如丁尼生告诉我们的，在他关于自然的梦中，他 “看见那熊熊燃烧的原子流 / 和她万千宇宙的洪流， / 沿着无边的虚空奔涌， / 飞去又再度相撞，造出 / 一个又一个事物的构架， / 永无止息。” 难怪他要试图挣脱命运的束缚，让他的原子在完全不确定的时间和地点偏离它们的路线，从而赋予它们一种非理性的自由意志——按照他的唯物主义理论，这就是对我们自己所意识到的那种自主行动能力的唯一解释。 只要我们处理的只是两个分子，而且所有的数据都已给定，我们就能计算出它们相遇的结果；但当我们必须处理数以百万计的分子，而每个分子每秒又有数以百万计的相遇时，问题的复杂性似乎断绝了得到正当解答的一切希望。 因此，近代的原子论者采用了一种方法，我相信这种方法在数学物理学领域是新的，尽管它在统计学部门中早已使用。当 F 组的工作人员拿到一份人口普查报告，或者任何其他载有经济与社会科学数字资料的文件时，他们首先把全体人口按年龄、所得税、教育程度、宗教信仰或刑事定罪分成若干组。个人的数目实在太多，不可能一一追踪每个人的历史，所以，为了把工作量减到人力所能及的范围之内，他们把注意力集中在少数几个人为划分的组上。他们据以工作的原始数据，是每一组中个人数目的变化，而不是每个人状态的变化。 当然，这并不是研究人性的唯一方法。我们可以观察个人的行为，把它与根据现有最好的理论、由他们先前的性格和目前的境况会使我们预期的行为相比较。采用这种方法的人，努力改进他们对人性诸要素的认识，其方式与天文学家通过比较一颗行星的实际位置和由公认根数推算出来的位置来修正它的轨道根数大致相同。因此，父母和教师、历史学家和政治家对人性的研究，有别于登记员和制表员以及那些信赖数字的政治家所进行的研究。前一种可以叫作历史的方法，后一种可以叫作统计的方法。 动力学方程完全表达了应用于物质的历史方法的规律，但应用这些方程，意味着对一切数据有完全的认识。然而，我们能够付诸实验的最小一部分物质，也是由数以百万计的分子组成的，其中没有一个能单独被我们感觉到。因此，我们无法查明其中任何一个分子的实际运动，所以我们不得不放弃严格的历史方法，而采用统计方法来处理大群的分子。 应用于分子科学的统计方法，其数据是大量分子量值的总和。在研究这类量之间的关系时，我们遇到了一种新的规律性，即平均值的规律性；就一切实际目的而言，我们完全可以依赖它，但它不能自称具有抽象动力学定律所具有的那种绝对精确的特性。 因此，分子科学告诉我们：我们的实验所能给我们的，永远只不过是统计的信息，从实验中推出的任何定律都不能自称绝对精确。但是，当我们从思考我们的实验转向思考分子本身时，我们就离开了机遇与变化的世界，进入了一个一切都确定不移、永恒不变的领域。 分子符合一个恒定的类型，其精确程度是由它们构成的物体的可感性质中找不到的。首先，每一个分子的质量及其一切其他性质，都是绝对不可改变的。其次，同一种类的所有分子的性质，都是绝对相同的。 让我们来考察两种分子的性质：氧分子和氢分子。 我们可以从非常不同的来源获取氧的样品——从空气，从水，从每一个地质年代的岩石中。这些样品的历史很不相同；如果在几千年间，境遇的不同能够造成性质的不同，这些氧的样品就会显示出来。 同样，我们可以从水中、从煤中，或者像格雷厄姆那样，从陨铁中获取氢。取任何一份氢样品两升，它都会与任何一份氧样品恰好一升化合，生成恰好两升的水蒸气。 如果在任何一份样品以往的全部历史中——无论是被禁锢在岩石里，在海中流动，还是随着陨石在未知的区域里飞驰——分子发生过任何改变，这些关系就不会再保持下去了。 但我们还有另一种、完全不同的方法来比较分子的性质。分子虽然不可毁灭，却不是一个坚硬刚性的物体，而是能够进行内部运动的；当这些运动被激发时，它就发出光线，光线的波长是分子振动时间的一种量度。 借助分光镜，各种光的波长可以计算到万分之一以内。用这种方法已经查明，不仅从我们实验室里每一份氢样品中取出的分子都具有同一组振动周期，而且太阳和恒星也发出具有同一组振动周期的光。 这样我们就确信，与我们的氢分子性质相同的分子存在于那些遥远的区域，或者至少在发出我们借以看到它们的那道光时存在过。 把埃及人建筑的尺寸与希腊人建筑的尺寸加以比较，可以看出它们有一个共同的量度。因此，即使没有一位古代作者记载过这两个民族用同一种肘尺作为长度标准，我们也能从建筑本身证明这一点。我们还有理由断言：在某个时候，一定有一件实物的长度标准从一个国家被带到了另一个国家，或者两个国家的标准来自一个共同的源头。 可是在天上，我们凭借星光——而且仅仅凭借星光——发现了一些彼此相距如此遥远的星，任何实物都不可能从一颗星到达另一颗星；然而，这光，这我们得知那些遥远世界存在的唯一证据，也告诉我们：它们每一个都是由与我们在地球上所见的同样种类的分子构成的。比如一个氢分子，无论在天狼星上还是在大角星上，都以完全相同的时间振动。 所以，宇宙中的每一个分子，身上都印着一套度量制度的印记，就像巴黎档案馆里的米原器，或者卡纳克神庙里的双王室肘尺一样清楚。 没有一种演化理论能够解释分子之间的这种相似，因为演化必然意味着连续的变化，而分子既不能生长，也不会衰败，既不会产生，也不会毁灭。 自从自然开始以来，自然界的任何过程都没有使任何一个分子的性质产生过丝毫的差别。因此，无论是分子的存在，还是它们性质的同一，我们都不能归之于我们称为“自然的”任何原因的作用。 另一方面，正如约翰·赫歇耳爵士说得好，每个分子与同类的其他一切分子精确相等，这使它具有了一件制成品的根本特征，也排除了它是永恒的、自存的这种想法。 这样，沿着一条严格的科学道路，我们被引到了离科学必须止步之处非常近的地方。这并不是说，科学不许研究它无法拆开的分子的内部机制，正如它并没有被禁止研究它无法组装起来的有机体一样。但是，在追溯物质的历史时，科学一旦确信：一方面，分子是被造成的；另一方面，它又不是由我们称为“自然的”任何过程造成的——科学就停住了。 科学无力对物质本身从无中被创造出来这件事进行推理。当我们承认，因为物质不可能是永恒的、自存的，所以它必定是被创造的，我们就到达了我们思维能力的极限。 只有当我们所思考的不是物质本身，而是物质实际存在的形式时，我们的心智才找到了可以把握的东西。 物质作为物质，应当具有某些基本性质——它应当存在于空间之中，能够运动，它的运动应当持续不变，等等——就我们所知，这些可能是形而上学家所说的那种必然真理。我们可以利用对这类真理的认识来进行演绎，但我们没有任何资料可以用来推测它们的起源。 但是，每一个氢分子中，物质恰好就是这么多，不多也不少，这是一个性质完全不同的事实。在这里，我们面对的是物质的一种特殊分布——借用查默斯博士的说法，是一种“配置”——我们毫不困难就能想象，这些东西本来可以有别的安排。 比如，行星轨道的形状和大小，并不是由任何自然法则决定的，而取决于物质的一种特殊配置。地球的大小也是如此，所谓米制的标准就是从地球的大小得来的。但这些天文的和地上的量值，在科学上的重要性，远不及那个构成分子体系之基础的、一切标准中最根本的标准。我们知道，自然的原因正在起作用，它们倾向于改变——如果最终不是毁灭的话——地球和整个太阳系的一切排列和尺寸。但是，尽管在漫长的岁月里，天上发生过、并且还可能发生灾变，尽管古老的体系可能解体，新的体系从它们的废墟中演化出来，构成这些体系的分子——物质宇宙的基石——却始终完好无损，从不磨蚀。 它们直到今天仍然和被造之初一样，在数目、尺度和重量上都完美无缺；从印在它们身上、不可磨灭的特征中，我们可以领悟到：我们所认为的人类最高贵的品质——度量上求精确、陈述上求真实、行动上求公正——之所以为我们所有，是因为它们是那一位的形象的本质组成部分；太初之时，他不仅创造了天和地，还创造了构成天地的材料。