The Atomic Theory of Lucretius
I know not whether this inquiry I speak of concerning the first condition of seeds or atoms be not the most useful of all." — BACON.
THE popular conception of any philosophical doctrine is necessarily imperfect, and very generally unjust. Lucretius is often alluded to as an atheistical writer, who held the silly opinion that the universe was the result of a fortuitous concourse of atoms readers are asked to consider how long letters must be shaken in a bag before a complete annotated edition of Shakespeare could result from the process; and after being reminded how much more complex the universe is than the works of Shakespeare, they are expected to hold Lucretius, with his teachers and his followers, in derision. A nickname which sticks has generally some truth in it, and so has the above view, but it would be unjust to form our judgment of a man from his nickname alone, and we may profitably consider what the real tenets of Lucretius were, especially now that men of science are beginning, after a long pause in the inquiry, once more eagerly to attempt some explanation of the ultimate constitution of matter.
This problem, a favourite one with many great men, has come to be looked upon by most persons as insoluble nay, the attempt to solve it is sometimes treated as impious; but knowing that all the phenomena of light are explained by particular motions of a medium constituted according to simple laws, and so perfectly explained that the exact motions corresponding to all the colours of the spectrum, with their modifications due to reflection, refraction, and polarization, can be defined in form, speed, and magnitude, — knowing this, we may reasonably expect that the other complex attributes of inorganic matter may be deduced from some simple theory, involving only as an assumption the existence of some original material possessing properties far less complex than those of the gross matter apparent to our senses. It is only in this sense that we can hope ever to understand the ultimate constitution of matter; but as the undulatory theory of light has both suggested the discovery of new facts, and has connected all known facts concerning light into one intelligible series of logical deductions, so any true theory of the constitution of matter would suggest new inquiries, and would group the apparently disjointed fragments of knowledge, now called the various branches of science, into one intelligible whole. To frame some such theory as this was the first aim of Greek philosophers, and to establish the true theory will be the greatest triumph of modern science. Of all the  subtle guesses made by the Greeks at this enigma, one only, we think, has been fruitful, and that the one expounded by Lucretius, but learnt by him from Epicurus, who in his turn seems to have derived his most valuable conceptions from Democritus and Leucippus. As, however, we possess fragments only of these earlier writers, it is convenient to speak of the theory as that of Lucretius, though he seems to have been simply the eloquent and clear expounder of a doctrine wholly invented by others.
Before explaining how far the views of Lucretius are still held by naturalists, and how far they contain the germs of many modern theories, we must endeavour to give a clear account of what his views really were, in which attempt we shall be much aided by the admirable edition and translation of his works by Mr. Munro.
The principles of the atomic theory are all contained in the first two books attention being generally called in the original to each new proposition by a "nunc age" or some such expression. Lucretius begins by stating that " nothing is ever begotten of nothing." To this principle, which is assumed as true in all physical treatises of the present day, he unnecessarily adds, that this is not done even by divine power, about which he could know nothing. Lucretius felt little reverence for the Pagan divinities, and states this principle so roundly as at first to shock our feelings but if we limit the application of the principle to matter once created, and such as we can observe, his principle is true, and invariably acted upon. Not even by divine power is matter now created out of nothing — nor does any effect happen without what we call a natural cause. Lucretius seizes the opportunity of stating that men think things are done by divine power because they do not understand how they happen, whereas he will show how all things are done without the hand of the gods — a bold proposition truly, but one which, translated into modern language, means simply that natural phenomena are subject to definite laws, and are not unintelligible miracles. Lucretius fails to perceive that definite physical laws are consistent with the work of God and the difficulty of reconciling the two ideas, unreal as it seems to us, has been felt by able men even now-a- days, when the conception of divine power is very different from any present to the mind of Lucretius. To most of us the very conception of a law suggests a lawgiver, while he, to prove the existence of laws, thought it necessary to deny the action of beings who could set those laws at nought. The demonstration  which he gives of his first principle is loose, and goes rather to establish the fact that natural phenomena occur according to definite rules than to prove that no matter is created out of nothing, except in so far as this creation would, he thinks, disturb the order of nature. This first principle, as to the creation of matter, cannot indeed be otherwise than loosely stated by Lucretius, for no definition is given of what should measure the quantity of matter, and until we have defined how this quantity is to be measured, we cannot experimentally determine whether matter is being created or not. But Lucretius meant his proposition to include the statement that nothing happens without a cause, and without a material cause, and his proof of this is precisely that which we should still adduce, being the perfect regularity with which in nature similar effects follow similar causes.
The next proposition is, that " nothing is ever annihilated, but simply dissolved into its first bodies," or, as we should say, components. This statement is complementary to the first. Together, the two propositions affirm that constancy in the total quantity of matter which is a commonplace truth now, but which to Lucretius must have been unsupported by any rigorous proof. His own arguments in support of the law go no further than to show that we have no proof of the destruction of any portion of matter. He shows that rain when it falls is not lost, but produces leaves and trees, that " by them in turn our race and the race of wild beasts is fed" but he makes no effort to measure accurately the quantity of matter apparently disappearing, but reappearing in the new form, and without that measurement his proposition could not be rigorously proved moreover, in the mind of Lucretius, the indestructibility referred to all kinds of causes, so that, to make our proposition co-extensive with his, we must interpret it to mean that matter is indestructible, and that no cause fails to produce an equivalent effect, though Lucretius probably did not conceive these two parts of his proposition separate one from the other.
Occasion is taken at this point to state that the components into which bodies are resolved, or out of which they are built, may be invisible. The third distinct proposition states that " all things are not on all sides jammed together and kept in by body : there is also void in things." Lucretius thought that, in order to explain the properties of matter, it was absolutely necessary to admit the existence of vacuum, or empty space containing nothing whatever. If there were not void, he says, things could not move at all ! And it does seem, at first sight, that in a universe absolutely full, like a barrel full of herrings,  so shaped as to leave not a cranny between them, no motion whatever would be possible but reflection shows us that what is called re-entering motion is possible, even under those circumstances, provided we do not suppose our fish to stick to one another there may be an eddy in which the fish swim round and round one after the other, without leaving any vacant space between them or on either side, and yet without enlarging, diminishing, or disturbing the barrel as they move. Lucretius either failed to perceive this, or declined to admit the possibility that all the movements of gross matter could be of this class but he has another argument in favour of a vacuum : " Why do we see one thing surpass another in weight, though not larger in size ? " How can things be of various densities unless we admit empty pores in bodies ? His proof is insufficient but here again modern research has confirmed his conclusion, so far as it affects gross matter only, and Lucretius conceived no other. His explanation of varying density is that which is universally received and taught, and even the modern disbelievers in a vacuum do not deny that some space may be unoccupied by gross matter, but simply affirm, on grounds to be hereafter stated, that all space is full of something, though not of ponderable matter. In support of his proposition, Lucretius points to the pores found in all bodies, and uses the following ingenious though fallacious argument to prove a vacuum : — :" If two broad bodies after contact quickly spring asunder, the air must surely fill all the void which is formed between the bodies. Well, however rapidly it stream together with swift circling currents, yet the whole space will not be able to be filled up in one moment; for it must occupy first one spot, and then another, until the whole is taken up" therefore in the middle a void must have existed for a sensible time.
We are next informed by our author that matter exists, or, in the language of Lucretius, " all nature then, as it exists by itself, has been founded on two things : there are bodies, and there is void in which these bodies are placed, and through which they move about." In his first and second propositions, Lucretius uses the word thing, res, which, as we have already explained, comprehended all kinds of things, such as matter, force, motion, thought, life, etc. He now states the existence of matter, and few will be disposed to contradict him indeed, he appeals to the general feeling of mankind in proof of his assumption. Unless you grant this, he says, " there will be nothing to which we can appeal to prove anything by reasoning."
Lucretius now affirms that nothing exists but matter and void, or, as put in Mr. Munro's translation, " there is nothing which you can affirm to be at once separate from all body and quite  distinct from void, which would, so to speak, count as the discovery of a third nature." Here at last we reach debateable ground. Lucretius hardly adduces a single argument in support of this proposition, contenting himself with showing, first, that no tangible thing but matter exists, — a mere begging the question and, secondly, that properties and accidents are not entities distinct from matter, — which is true, but little to the point. As examples of properties, he gives weight, heat, fluidity as examples of accidents, poverty, riches, liberty, etc. Time, he says, exists not by itself, but simply from the things which happen actions do not exist by themselves, but may be fairly called accidents of matter, and of the space in which they severally go on. Even if all this be granted, we shall not necessarily concede that matter and void have alone a separate existence but we must not complain that Lucretius does not support his proposition more strongly at this point, for indeed his six books form one long argument in support of his proposition. Lucretius undertakes to show that every fact in the world can be explained by the properties of matter, and that matter itself may be conceived as possessed of but a very few simple properties, from the construction of which the complex facts we see may follow. Of course he fails to do this, but if the proposition be restricted to what are called physical phenomena, it becomes, if not certainly true, nevertheless an hypothesis well worthy of consideration, and not yet proved false. Lucretius admits no subtle ethers, no variety of elements with fiery, watery, light, heavy principles he does not suppose light to be one thing, fire another, — electricity a fluid, magnetism a vital principle, — but treats all phenomena as mere properties or accidents of simple matter, and produced in simple ways but to understand what he meant by matter, or " bodies," we must pass on.
The next proposition of Lucretius describes the composition of matter as we perceive it. Bodies are either atoms, or compounded of atoms and void, or, more at length, they " are partly first beginnings of things, partly those which are formed of a union of first beginnings." The words which Mr. Munro here translates as " first beginnings of things" describe the Lucretian atoms Lucretius does not use the word atoms, but calls these "primordia," or "seminarerum." These atoms are necessarily solid, or they could not mark off void space from full. They cannot be broken, because they have no void within them to admit a cutting body, or wet or cold or fire, therefore they must be everlasting and indestructible. Lucretius, too, is so persuaded of the great wear and tear that is going on, that he remarks, if atoms had not been indestructible, everything would have been destroyed by this time. The constancy of all phenomena is a very good  argument in favour of the indivisible atom, for unless the component parts of a machine are unchanged, how can the results produced be constant ? unless there be really something indestructible and indivisible in sodium, how can it happen that every little fragment shall retain every physical property of sodium, so that, for instance, when glowing with heat, it shall continually, as it were, ring out the same notes of light, imparting such vibrations to our eye as paint the well-known double yellow line ? If we could divide the little bodies which, vibrating at those special speeds prove sodium to be glowing in the flame, they would no more vibrate at those speeds than a cut violin-string would give out the true note to which it had been tuned. By such division sodium would be destroyed whatever might be the result, the body named sodium would exist no longer but as yet no man has been able thus to divide the sodium atom, and no one expects that bodies will ever be decomposed into elements simpler than such as would ring out a single note, a single line in the spectrum. In other words, all men of science believe, consciously or not, in atoms indivisible and imperishable. Lucretius certainly knew nothing of spectrum analysis, nor of the law owing to which chemical compounds have forced an atomic theory into daily language but the arguments drawn from these sources are simply special applications of his general theorem if matter really obeys definite unchangeable laws, the ultimate materials employed to make matter must themselves be definite and unchangeable. Newton's exposition of this argument, quoted by Mr. Munro to illustrate our author, is admirably clear : —
"While the particles continue entire they may compose bodies of one and the same nature and texture in all ages but should they wear away or break in pieces, the nature of things depending on them would be changed. Water and earth composed of old worn-out particles would not be of the same nature and texture now with water and earth composed of entire particles in the beginning. And, therefore, that nature may be lasting, the changes of corporeal things are to be placed only in various separations and new associations and motions of these permanent particles, compound bodies being apt to break, not in the midst of solid particles, but where those particles are laid together and only touch in a few points."
We confess that these arguments seem to us unanswerable, as proving the existence of some inalterable basis of matter. Lucretius described his atoms as small, but not infinitely small, nay, having parts, yet " strong in everlasting singleness," impenetrably hard, indivisible, unalterable, eternal.
Having reached his atom, before proceeding with the consequences of his assumption, Lucretius pauses to demolish rival theorists, but though he does this very well, we prefer to follow  out his own propositions in their natural order, remarking, however, that the next proposition occurs incidentally, as it were, while refuting his antagonists, and is to the effect that the differences between all bodies may be accounted for by the different arrangement of the atoms, and the different way in which they move, or, more literally, "the motions which they mutually impart and receive." Lucretius conceived matter as formed by atoms in continual motion, rebounding as it were from one another. His conception is most remarkable, as being very far removed from the impression produced by inert matter on our own senses, and yet almost indisputably true. Arguments drawn from the laws of the elasticity of gases and from the diffusion of fluids go far to prove the proposition. The former laws may be deduced from the assumption of atoms rebounding in a void; and it is hard to conceive why different fluids or liquids should mix with extraordinary rapidity whenever placed in contact one with its neighbour, unless molecules were continually fluttering as it were, at the limits of each fluid, restrained only from continuing their course by the opposition of other atoms. If these arguments seem insufficient, we may refer to the conception of heat as a mode of motion. If heat be a mode of motion of gross matter, then, as all bodies are more or less hot, the molecules of all bodies will be moving with more or less speed,- — precisely what Lucretius taught. Lucretius was led to his conception by considerations very analogous to those which lead us to consider heat and other forms of energy as modes of motion. Probably the reason why he does not state this seventh proposition as a dogma by itself, is, that the proof could not as yet be given but in discussing rival doctrines he is led to anticipate his own views.
He proceeds to assert that there is no limit to space, nor yet to the total quantity of matter but these are rather metaphysical than physical questions, although he seems to think that, unless infinite space were full of matter, the universe could not hold together, for he will not hear of gravitation, by which " all things press to the centre of the sum." He is almost comically unfortunate in denouncing the idea, that heavy bodies which are beneath the earth shall press upwards, or that living things walk head downwards, and that when these see the sun we behold the stars of night but although it is very interesting to observe that these doctrines were then held, we will examine only the propositions strictly necessary for his theory of matter, passing over also his assertion that atoms were not arranged by design, until we examine how he himself conceived that they were arranged. This explanation is given in the Second Book, containing what we should term the Kinetic branch of his theory, or, to use his own language, he next explains " by what  motion the begetting bodies of matter do beget different things, and, after they are begotten, again break them up, and by what they are compelled so to do." The book opens with the proposition that matter does not " cohere inseparably massed together;" it does not stick together as a mere inert mass. Lucretius infers this from the continual change which we perceive, and by which all things wax and wane, although the sum remains constant.
A modern physical treatise would attribute these changes to chemical affinity, heat, gravitation, etc., or possibly, in more general terms, to the various forms of what we term Energy. Lucretius can only suppose this energy to be represented by atoms in motion and if this be not universally true, it is probably true for many cases. This perpetual motion of the atoms is next reasserted as a distinct proposition^ " No atom," he says, " can ever stop, giving up its motion to its neighbour." At first sight, nothing can be more contrary to our ideas of the laws of motion. We repeatedly see a ball strike another, and set it in motion, remaining itself apparently quiescent after the blow but nevertheless it is quite impossible that the relative motion of two perfectly hard elastic bodies, such as Lucretius imagined, can ever be altered by knocking one against the other. Motion is essentially relative we only know that a body moves by observing that it changes its position relatively to another. When, therefore, treating of two isolated bodies only, we need only speak of their relative velocity. The motion of the centre of gravity of any system of bodies remains quite unaffected by their collision one with another, and, in considering our two isolated atoms, we may as well, for simplicity's sake, assume the motion of their joint centre of gravity to be nil, though this is not necessary to our argument. Moreover, it is found that a certain quantity, sometimes called vis viva, sometimes the kinetic energy of the system, is also constant after and before any collision. This quantity is proportional for each body to the mass of the body, and to the square of its velocity. It must be remembered that we are now speaking of two simple bodies which have only the properties of hardness and elasticity, not being compressible, hot, or susceptible of vibration, so that the transformation of energy due to motion into other forms of energy such as heat is excluded by hypothesis.
Now, in the case of two such bodies striking one another, since their mass will not change, it is impossible that this quantity should remain constant unless each body kept its own velocity. The one cannot hand over a part of its velocity to the other, for in that case the centre of gravity of the system would acquire motion. The velocity of the two cannot  increase or decrease simultaneously, or the vis viva of the system would alter, so the bodies have no choice but to bound back or to glance aside with their original velocity. In the latter case a spinning motion might represent the vis viva, but this would not be rest. If it be asked how it is that we do see the relative motion of bodies alter after striking one another, we answer that heat and other forms of energy have been found equivalent to vis viva, which may therefore pass into these forms, and so allow a change in the relative velocities of bodies. Had Lucretius known this he would >:have answered, that heat can only be equivalent to vis viva inasmuch as it substitutes the motion of small parts for the motion of the whole — this being the very answer given by Leibnitz to the above objection, urged as fatal to the doctrine of vis viva which he had enounced.
It may be seen that our two bodies need not continue to move in straight lines after striking they may glance off, so as to spin round. The vis viva, or energy, will be perfectly represented by the velocity of the rotating masses, and the centre of gravity may remain undisturbed. When two actual bodies strike and come to rest, it is probable that their atoms do acquire some periodic motion, such as spinning, which motion produces the appearance of heat, but is on so small a scale as to be otherwise invisible to our senses. When we consider the collision of a multitude of bodies, innumerable changes may take place in their relative velocities without violating the two principles, that the motion of the centre of gravity and the energy of the system shall both remain unchanged. Among these combinations some will admit of one or more parts of the system coming wholly to rest, contrary to Lucre- tius's views, but the following consideration shows that it is difficult to see how this would be brought about if we adhered strictly to his assumption, that the motion of a hard mass is the sole form of energy. He almost unconsciously, and certainly without any express statement, assumes elasticity as a property of his atoms, which he describes as rebounding one from another; but, reverting to our two hard bodies, if they do strike and rebound they must gradually slacken speed, stop for an inconceivably short time, and then gradually resume their pace in an opposite direction, so that, if they rebound, they must stop and pass through all speeds intermediate between zero and their original velocity so that if we admit no form of energy but a hard mass in motion, we must conclude that no two bodies ever could strike one another, and yet, as neither we nor Lucretius have assumed anything to keep them apart, we find ourselves in a droll dilemma, which seems to prove the impossibility of the existence of a universe containing  simple hard atoms in motion. We moderns jump out of the difficulty at once by saying that the hard bodies are elastic, and elasticity is a form of energy, so that the energy or vis viva which at one time was represented by the body in motion, is at another time represented by the potential energy of elasticity. Lucretius would have shaken his head at this explanation, and would have much preferred the theory just started by Sir William Thomson, and long since vaguely suggested by Hobbes, that the elasticity of atoms may be due to the motion of their parts, — a proposition exemplified by one smoke-ring bounding away from another in virtue of the relative motions of their parts, these not being necessarily themselves elastic. The energy of the molecule at that point where it strikes its neighbour and changes velocity is on this theory transferred to another part of the molecule which moves faster as the first part moves more slowly. If the molecules of gross matter are made up of atoms in rapid motion, as Lucretius believed, or of a portion of whirling fluid, as Sir William Thomson suggests, and if elasticity itself be only a secondary property, not possessed by the primordia rerum at all, then the proposition that a molecule never can come to rest is undoubtedly true — such rest would be equivalent to the destruction of matter. Lucretius could not have proved this, nor even have understood the proof. He did not know the laws of motion even of two elastic bodies, but it is singular to find modern science returning to the never-ending motion of the old Greek atom.
The next proposition of our author explains the varying density of bodies. He says that the greater or less density of bodies depends on the smaller or greater distance to which the atoms in each continue to rebound after striking one another. They never stop striking and rebounding they are in perpetual motion, tossed about by blows. Mr. Munro's translation fails, it seems to us, to convey this view, reading as though the atoms struck, rebounded and remained quiet afterwards, hooked as it were together but Lucretius> in many passages describes the never-ending restlessness of his atoms, tossed like motes in a sunbeam, which he describes to illustrate the motion of the atoms in void. This explanation of the varying density of matter is still commonly received, and will be found in all popular text-books the density of the ultimate particles of gravitating matter is very generally assumed to be the same, the greater or less density of gross matter being supposed due to empty pores, of greater or smaller magnitude, separating the molecules. At first sight it is very difficult to see how any other explanation of varying density can be given, since we find that by compression we actually can increase the  density of bodies without altering their weight or mass in any way. Now, unless there were a void space separating the molecules, where can these go to when squeezed ? Most men will find a difficulty in conceiving that space absolutely full of matter, soft or hard, can be made to hold more but the same space does hold sometimes more and sometimes less gross matter, so that in the latter case it cannot be quite full, or, in other words, the body it contains is composed in part of empty pores. The proof is incomplete, and, if molecules be formed by the motion of a fluid, greater density may possibly be due to a modification in the motion of molecules, and not only to the greater frequency of the eddying molecules in a given space.
Lucretius next points out that his atoms must move very rapidly. In vacuum atoms travel faster than light. His proof of this is extremely vague. He says the light and the heat of the sun (which he calls " vapours " ) are forced to travel slowly, cleaving the waves of air, and several minute bodies of the heat ( vapour) are entangled together and impede one another, but atoms of solid singleness can go ahead wholly unimpeded in a vacuum — not a very satisfactory proof. The idea running in the mind of the writer seems to have been that any matter moving in a medium would be impeded by friction, and therefore necessarily move more slowly than a free atom moving in a void he may also have felt that, if all the power of the universe depended on the motion of exceedingly small particles, it was necessary to suppose them endowed with great velocity but we do not find this argument used, although it has led the modern believers in atoms to the conviction that if their motion does represent energy, their velocity must be enormous. Lucretius would be glad to know that Herapath, Joule, Krönig, Clausius, and Clerk Maxwell have been able to calculate it 1/400000 inch is the distance named by Maxwell.
The nature of the original motion of atoms is next defined. Atoms which have not struck one another move in straight parallel lines, sheer downwards gravitation is the evidence of this. An infinite number of atoms eternally pour from infinite space above to infinite space below with enormous velocity. This velocity is conceived as the explanation of the power or energy of the universe. Gravitation thus understood was a property of all matter. The apparent exceptions are correctly explained by Lucretius. The idea of his eternal infinite rain of atoms is enough to turn one giddy it can be best discussed after we have stated the next most singular proposition. The atoms, at quite uncertain times and uncertain places, swerve a  very little from the straight line, then they strike, and from their clashing, matter and all natural phenomena are produced. As Mr. Munro translates it, " When bodies are borne downwards sheer through void at quite uncertain times and uncertain points of space, they swerve a little from their equal poise, you just and only just can call it a change of inclination. If they were not used to swerve, they would all fall down like drops of rain through the deep void, and no clashing would have been begotten nor blow produced among the first beginnings thus nature never would have produced aught."
Most people will think nature would not have produced much had she started in this way, and they are probably right this is the head and front of our philosopher's offending, and, indeed, there is not much to be said in his defence. Let us, nevertheless, in spite of the ridicule which from Cicero's time downwards has been heaped on this unhappy doctrine of the " Declination of Atoms," try to enter into the mind of Lucretius, and to understand what he sought for and thought he had found. As already said, he sought for power in the velocity of the atoms, power which, deflected hither and thither by obstacles of all kinds, should be the origin of every motion, every force observed on earth. Gravitation in its apparent action seemed to show a universal tendency in one direction this, then, he claimed as an inherent property of his atoms, — a claim no broader than the claim made by Newton, that every atom of matter should attract all other atoms at whatever distance they might be — and at first sight much more conceivable at first sight only, for, indeed, atoms pouring onward, as imagined by our author, could be no source of power. Motion in mechanics has no meaning except as denoting a change of relative position all atoms moving, as Lucretius fancied, at one speed, and in parallel lines, would relatively to one another have been in perfect rest. A bag of marbles in a railway train could not be employed as a source of energy in the train they lie at rest and it is only when brought into collision with something moving at a different pace from the train that they can develop any power, which may then be considerable. But more than this : How are we to conceive direction in space except relatively to something ?— what is up and what is down in space ? If it be answered, The place atoms come from is up above us, we answer, How, when all atoms are all one relatively to one another in a perfectly similar position, are we poor atoms to know that they are coming from anywhere ? So far as we can see, an absolute motion in space is devoid of all meaning. We must conceive a shape or position for space before we can conceive of motion relatively to space, and as we are at perfect  liberty to conceive any shape or position, or none at all, it follows that absolute motion in space is anything you please, that is to say, a mere fancy. Lucretius unconsciously assumed the world as his basis by which to measure direction and velocity. The direction in which things fall on the earth was sheer down in void but really his assumption was meaningless, or, at least, explained in no way the power or force which he wished to explain. Not so, by the way, the older conception of Democritus, who thought atoms moved in all directions freely and indifferently — a universe so constituted originally might at least contain all the energy we require. One atom would then exert its force on another, but the Lucretian atoms would have remained in profound stillness, except for that occasional swerve at quite uncertain times and places, the cause of which he leaves wholly unaccounted for. This swerving seems but a silly fancy, and yet consider this : — It is a principle of mechanics that a force acting at right angles to the direction in which a body is moving does no work, although it may continually and continuously alter the direction in which the body moves. No power, no energy, is required to deflect a bullet from its path, provided the deflecting force acts always at right angles to that path — an apparent paradox, which is, nevertheless, quite true and familiar to the engineer. It is clear to us that Epicurus, when he devised his doctrine of a little swerving from the straight path of an atom, had an imperfect perception of this mechanical doctrine a little swerving would bring his atoms into contact, and a modern mechanician would tell him you require no power to make them swerve. With what triumph Epicurus, and Lucretius his scholar, would have hailed the demonstration but, alas ! their triumph would have been short-lived they would soon have perceived that their atoms were described as in deadly stillness,— a death from which no life could spring, a rest from which they could never swerve until inspired with power from a source of life. Still we can see that their conception was not stupid, it was simply false, as all physical explanations of the origin of energy and matter must be. There is little to be said for the further conception that matter with its present properties would result from the mere accidental clashing of atoms this one doctrine of Lucretius is so well known and so little valued, that we will waste no further time on it, merely pointing out that the worthlessness of these ideas as an explanation of the origin of things does not impair the value of the conception of moving atoms as the constituent parts of gross matter as it exists.
The motive for devising the curious doctrine that atoms might swerve now and then from the straight path without being  acted upon by other atoms, was/ as Mr. Munro observes, undoubtedly the desire to devise an explanation of Free-will. Lucretius believed in free-will. If you believe in free-will and in atoms, you have two courses open to you. The first alternative may be put as follows : Something which is not atoms must be allowed an existence, and must be supposed capable of acting on the atoms. The atoms may, as Democritus believed, build up a huge mechanical structure, each wheel of which drives its neighbour in one long inevitable sequence of causation but you may assume that beyond this ever-grinding wheelwork there exists a power not subject to but partly master of the machine; you may believe that man possesses such a power, and if so, no better conception of the manner of its action could be devised than the idea of its deflecting the atoms in their onward path to the right or left of that line in which they would naturally move. The will, if it so acted, would add nothing sensible to nor take anything sensible from the energy of the universe. The modern believer in free-will will probably adopt this view, which is certainly consistent with observation, although not proved by it. Such a power of moulding circumstances, of turning the torrent to the right, where it shall fertilize, or to the left, where it shall overwhelm, but in nowise of arresting the torrent, adding nothing to it, taking nothing from it, — such is precisely the apparent action of man's will; and though we must allow that possibly the deflecting action does but result from some smaller subtler stream of circumstance, yet if we may trust to our direct perception of free-will, the above theory, involving a power in man beyond that of atoms, would probably be our choice. Lucretius chose the second alternative as an exit from the difficulty : Atoms with strict causation did exist, and free-will too. We will then grant free-will to atoms, one and all, not in perpetual exercise, but at quite uncertain times. The idea is startling, but not illogical, and the form in which atoms are supposed to exercise their free-will is quite unexceptionable. We cannot but admire the audacity of the man who, called upon to grant freewill as a tertium quid, either to man or to atoms, chooses the atoms without a qualm. We do not agree with him, because observation has detected no such action on the part of atoms, or the constituents of matter.
We cannot hope that natural science will ever lend the least assistance towards answering the Free-will and Necessity question. The doctrines of the indestructibility of matter and of the conservation of energy seem at first sight to help the Necessitarians, for they might argue that if free-will acts it must add something to or take something from the physical universe, and  if experiment shows that nothing of the kind occurs, away goes free-will but this argument is worthless, for if mind or will simply deflects matter as it moves, it may produce all the consequences claimed by the Wilful school, and yet it will neither add energy nor matter to the universe. Lucretius thought atoms acted thus we do not, because we observe no action of the kind in matter, but, on the contrary, strict causation or sequence of phenomena. Whether what we call mind act so or not must also be a matter of observation, but as people have not been able to agree as to the results of observation about free-will made during a great many centuries, we fear the path of observation will lead us no further than we have already come.
We beg pardon for this little digression, which was really necessary to the understanding of our author's physical theory. Lucretius proceeds to state that atoms have always moved and always will move with the same velocity, or, as translated by Mr. Munro, " The bodies of the first beginnings in time gone by moved in the same way in which they now move, and will ever hereafter be borne along in like manner, and the things which have been wont to be begotten, will be begotten after the same law," for there is nothing " extra," nothing outside and beyond the atoms which can either add to or take away from what we should call the energy of the universe. This proposition foreshadows the doctrine of conservation of energy. It is coupled with the assertion that the sum of matter was never denser or rarer than it now is, a proposition which we may admit, in the sense that the mean density of the universe is constant, but the connexion of this proposition with what may be called the constancy of the total amount of motion in the universe escapes us. But it is clear, in all his work, that Lucretius conceived two things as quite constant: atoms were neither created nor destroyed, and their motion could neither be created nor destroyed. He believed that each atom kept its velocity unaltered. The modern doctrine is that the total energy of the universe is constant, but may be variously distributed, and is possibly due to motion alone ultimately, though this last point has not been yet proved. Many a fierce battle has been waged over the question, whether what was called the " quantity of motion" in the universe was constant. Newton, with perfect accuracy, declared that it was not, defining the quantity of motion in a body as the product of mass and velocity. Leibnitz declared that it was constant, defining the quantity of motion as the product of the mass and the square of its velocity, but observing that when apparently the quantity of motion diminished, it was simply transferred to the molecules of the body, so as to escape our observation as motion. Davy and Joule have  proved him right in some cases, and shown that our senses still detect the motion as heat. It is conceivable, but not yet proved, that Leibnitz may be right in all cases, and that what we call the potential energy of gravitation, elasticity, etc., may really be due to the motion either of the atoms of gross matter, or of their constituent parts. If matter in motion be conceived as the sole ultimate form of energy, Leibnitz's proposition is absolutely true, and Lucretius must be allowed great merit in having taught that the motion of matter was as indestructible as its material existence, although he knew neither the laws of momentum nor of vis viva. If energy, as he believed, be due solely to motion, then his doctrine is true.
It is unnecessary further to state our author's theory in distinct propositions. He proceeds to explain the necessary properties of atoms. It is not odd, he says, that though they are in continual motion, their sum (i.e., gross matter) seems to rest in supreme repose. Atoms are too minute to be perceived; their forms, he says, are various, but the number of these forms are finite. This doctrine corresponds to the modern idea of simple or elementary chemical substances, each with its special atom, but limited in number. There are, he thinks, an infinite number of similar atoms. Infinite or not, the chemical theory requires that there shall be a great many similar atoms, but nothing, thought Lucretius, is formed of simple atoms all bodies, however minute, are compounds. Atoms have no colour, nor are they hot or cold in themselves they have neither sound, scent, nor moisture as properties. All these properties Lucretius believed to be dependent on the shape, motion, and relative position of his atoms, but he makes only the most feeble attempt to explain how these various properties can be thus conferred, nor could this be done with the slightest hope of success until the laws of these properties had been established by long series of experiments. Something may now be done in this direction, but it remains to be done, with one exception. The motions producing the phenomenon of light are known, but we do not know what moves.
Of course, Lucretius believed organic bodies to be made of atoms, and atoms only. Sentient beings, he thought, did not require to be built up of sentient materials but we need not discuss this conclusion, which follows of course from his assumption that nothing but atoms and void exists, a mere assumption, until the manner how atoms can build sentient beings be discovered. He determines in favour of a plurality of worlds, for what has chanced to happen here must certainly have chanced to happen elsewhere.
The Second Book concludes by a contrast between the miserable  inefficiency of the gods, who pass a calm time in tranquil peace, and the mighty power of the infinite sum of clashing atoms, now building up new worlds, now slowly but inevitably crumbling heaven and earth to dust by the unceasing aggression of their never-ending flood.
He thinks Memmius his friend ought to be very glad when this conclusion is reached, and if fine poetry could please Memmius he probably enjoyed the peroration; otherwise it is doubtful how far looking upon himself as a curious and complicated result of the accidental collision of little bits of hard stuff is calculated to make a man cheerful.
We do not propose to follow Lucretius further. The applications which he makes of his theory are no doubt curious and amusing, but they contain little that is true, while any criticism of them would lead us to consider the whole field of physical research nor do they add much to the clearness of his doctrine as to the constitution of matter. Let us rather reconsider what that doctrine was, and what merit it can claim. We shall find that almost all the propositions which refer simply to the constitution of matter are worthy of the highest admiration, as either certainly true, or as foreshadowing in a remarkable way doctrines since held by most eminent naturalists. Confine the following statements to matter as we can observe it, to physical science in fact, and they form a basis which even now would require but little modification to be acceptable to a modern student of physics.
Nothing is made out of nothing, nor can anything perish both matter and vacuum have a real existence, and gross matter, such as we perceive, contains absolutely solid particles separated by empty spaces. The absolutely solid particles are atoms. These are impenetrable, hard, indivisible, indestructible. These atoms are in continual motion, and the difference between various bodies consists, first, in the difference of the shapes of original atoms, and, secondly, in their arrangement and their motion. The velocity with which atoms move is exceedingly great, and their motion is indestructible it can neither increase nor diminish. This motion escapes our senses only because atoms are very small. But they are not infinitely small. Atoms have no colour, nor are they of themselves hot, cold, noisy, moist, coloured, or scented. These properties are given by motion, shape, and arrangement. We shall better understand the extraordinary merit and good sense of these propositions after considering some rival theories.
Where Lucretius breaks down is in the attempt to account for the origin of the power found in the universe, and for the various regulated motions required to explain what we observe  and for the apparent anomaly between the strict causation required and perceived in inanimate nature, and the free-will of which he was conscious. Here he fails entirely, and many others have failed too. Although he would have cared little for our commendation of his physics, coupled with a rejection of his proud claim to have set free mankind from grovelling superstition, by explaining the mystery of the existence of matter and man's mind, we may derive sincere pleasure in recognising the early germs of discoveries which have required two thousand years to reach their present development. Let us not be too indignant at his scornful rejection of divine agency. Divinity to him meant either the old Pagan gods or the pale abstract idea of a First Cause, which explained nothing, being but one form of statement that something was left to be explained. What wonder that he rejected both ? We may admire those old philosophers who could clothe divinity with noble attributes, and find in their own hearts the motive for their faith, but we need not therefore despise those who, smitten with the great truth that nature's laws are constant, fancied that in this constancy they saw the proof that nature's laws are self-existent. But we are diverging from our subject.
We will not compare our author's views with other ancient theories at any great length these at first sight seem greatly inferior to the atomic doctrine. Of the idea that the universe is composed of four elements, earth, fire, air, and water, no trace remains except in language, but careful investigation might show that the believers in these elements, or in some one or more of them, as the material of the universe, meant something very different and much more sensible than the vulgar interpretation of their doctrine. Lucretius abuses these philosophers, some because they denied a vacuum, a denial which he thought inconsistent with motion, some because their material wanted the character of indestructibility which he thought essential, some because he quite failed to perceive how all things could be made out of the element chosen, — fire, for instance but we must not take Lucretius's account of rival theories as fair we may with the exercise of a good deal of fancy see in the doctrine of homœomeria, which taught that all things contained the materials of everything else in a latent state, a foreshadowing of the chemical theory which proves that our bodies are made of the same chemical materials as peas, cabbages, etc., but it requires an elastic imagination to link the old and new creed together. Any explanation of the metaphysical conceptions of matter would also be out of place here. To Aristotle the existence of an atom with any properties at all, and the nature of motion, were mysteries demanding, as he says, speculation of a far  deeper kind than Democritus and the atomic school attempted. This is true enough, but we think Aristotle and his followers got entangled in the " snares of words," to use Hobbes's language, and their teaching led to little or no progress in what we call science. Let us then pass on some two thousand years, and see at the revival of philosophy what some modern great men have taught and written on the possible constitution of matter. We need choose no smaller men than Leibnitz and Descartes to serve as foils to our author.
Descartes, after a hypocritical flourish to the effect that he knew the complete fallacy of all he was going to say, since it did not agree with the orthodox theory of creation, but still that it would be interesting to consider how God might have created the world if he had been of Descartes's mind as to the simplest way of proceeding, propounds the following plan : —
The universe at first was quite full of something it was all alike, and there was no void anywhere. This universal plenum by and by was broken up into pieces. The pieces of plenum rubbed against one another till they became quite round the dust rubbed off their angles filled up the interstices, — for of course no void could possibly occur once the universe was quite full. The dust and round balls he calls the first and second kind of materials of which the universe, as we know it, is composed but besides the dust and balls there is a third material all the edges of the first fragments of plenum did not get ground into dust a fair number were merely rubbed into a kind of snake-shape of triangular section, — such a shape as would slip through the interstices in a pile of cannon-balls. These snake- shaped pieces sometimes got entangled, and when so entangled they composed the solid matter which is apparent to our senses. The balls and dust fill all space, the dust forms the great vortices which carry the planets round the sun, the balls are light and go flying about, so do the snakes, which, getting entangled, form gross matter. It is far more interesting to endeavour to understand the views of great men, however removed they may be from our own, than to look merely on the ludicrous side which their ideas may happen to present but we are unable in all Descartes's theory of matter to perceive anything beyond the most childish fancy. It does not seem to have occurred to him that there would be any difficulty in breaking up an absolute plenum what would be the nature of the separation between the fragments, what could define the boundary, he nowhere says he sends his balls, dust, and snakes flying about in any direction he may think convenient the balls and dust are imponderable, the knotted snakes, made of the same stuff, and intermediate between the two other kinds, are  ponderable. Why three kinds — balls, dust, and snakes ? Why not rather fragments of infinite variety of shape and size, from big bits of plenum to dust ? No answer to all this, but long dissertation on the knotting of snakes to form spots on the sun. His laws of motion are false, and he knew it, but says we must not judge from our experience of gross matter; and yet, this man insisted on clear conceptions as the very test of truth.
Leibnitz about the same time declared against atoms, against a vacuum, and against Descartes. He will have it to be inconsistent with the perfection of God that a vacuum can exist. It is out of the question that God should leave any part of space unemployed. John Bernoulli, in whose correspondence with Leibnitz these questions are treated with much dexterity, very properly replies that vacuum may be useful, since it may be a condition without which matter would not have its present properties if so, the void could not properly be called unemployed. Still, Bernoulli admitting that a void is not necessary to the theory of matter, gives it up. We must of course remember that these men did not mean by void the absence of gross matter — the Torricellian vacuum was then known, — they meant absolute emptiness. This argument about what God could or could not do, because it was derogatory to his dignity or wisdom, was at this time pulled in upon all occasions, and led to the strangest paradoxes about his free-will and omnipotence. We do not use the argument now in support of the laws of mechanics we do not speak of circles as more perfect than other figures, and therefore more consistent with divine wisdom, but in morals a claim of the kind is still frequently made, and Darwin applies this argument to stripes on horses' legs, which he thinks God would not have stooped to create. We are far from saying that an appeal of the kind is without meaning. The argument may be turned thus, when it will no longer seem altogether foolish : — We observe great regularity and very perfect adaptation of means to ends throughout creation, so that what we do understand seems to be perfectly done, and we infer that the contrivances we do not understand are equally perfect. Any contrivance which we can show to be bad or imperfect will therefore by that very fact be proved impossible as a part of creation. The main proposition will very generally be granted the difficulty lies in applying the minor premiss. When a man says that a vacuum is an imperfect contrivance, he only means that he dislikes it; and the application of the argument to moral questions is generally open to like criticism. Bernoulli asked Leibnitz how he accounted for the existence of moral evil as part of a perfect universe. Leibnitz returned Bernoulli's own argument about a  vacuum. Evil may be necessary to allow of good, just as Bernoulli thought a vacuum might be necessary to allow of matter.
Leibnitz, though he protested against atoms, himself devised what must be called an atomic theory, though his atoms were not separated by a vacuum. They were a kind of bubble (bulla), with a glassy shell containing ether. They were of various composition, containing more or less fire, earth, air, or water not the gross things known by that name, but essences of some kind. Leibnitz does not think his bubbles existed from all eternity, but gives the strangest account of their formation in his "Theoria motus concreti." He sets the sun and earth spinning in the midst of a universal ether. Molecules of the sun's mass, too, had a special motion of their own, which impelled some thing or some action, we are not sure which, along the ether, producing light this light, striking the earthy, airy, watery globe of the earth, sets the whole in fermentation the dense parts formed in hollow bubbles containing ether these spun round and so acquired consistency. (This idea of giving consistency by motion, taken by Leibnitz from Hobbes, was in opposition to Descartes, who derived consistency from rest.) Leibnitz explains his meaning by a metaphor : In a glass- blower's, glasses of a simple artificial form result from the straight motion of breath, combined with the circular motion of fire, and so "bullae" were produced from the straight motion of light and the circular motion of the earth. These bubbles are the seeds of things — Lucretius's own phrase — the origin of various kinds of things, the receptacles of ether, the basis of bodies, the cause of the force we admire in motions.
The bubbles varied in "contents through density;" in "contents through size" in emptiness, or perfect fulness, and in more or less emptiness and fulness. He explains how bubbles for the animal, vegetable, and mineral reigns, of sterile or productive qualities salt, sulphurous, mercurial bubbles, etc. etc., are formed, and gives the special combination of qualities wanted for each. Thus, one of his bubbles is empty-extraordinary- alkaline-colourable-feminiue, another full-extraordinary-acid- coloured-masculine — these two kinds of seeds differ in their way of acting. This seems like idiocy to persons not familiar with the scholastic habit of bracketing off qualities and categories, distinguishing and dividing things into a kind of verbal Chinese pattern. We have not made out the constitution of Leibnitz's ether, or his earthy, watery, airy globe, out of which he blew his bubbles, but we have found enough to show a very unfavourable contrast with Lucretius, even omitting monads, pre-established harmony, and many other interesting ideas,  proposed by the man who claimed to have run a race with Newton in inventing the higher calculus of mathematics, and who enounced the doctrine of vis viva.
Adhesion, he thought, was obtained by motion, but how, we fail to understand. His explanation runs somewhat thus — that two bodies in motion, one after the other, are both trying to be in the same place at once, and as they cannot accomplish this, stick together. Even Bernoulli, familiar with the views and terms of the day, found Leibnitz's theory extremely difficult to understand; as found in his Hypothesis Physica Nova, it is, contained in a series of short dogmatic sentences with very little elucidation we may therefore be unjust to him in our ignorance, but his criticism contained in his correspondence with Bernoulli seems to us much more valuable than this blowing of little complex bubbles. Thus he would not hear of the usual explanation of solidity, by the supposition that particles were hooked together or entangled by their shape, as taught both by Lucretius and Descartes. What, he asks, is to keep the hook together ? and he got no answer. He refused to admit Lucretius's postulate of infinitely hard bodies and infinitely elastic bodies indeed, the two properties do seem incompatible. The elasticity which we observe is given by a change of position of the parts of the body, and if the parts never change position it is hard to see by what the energy required for elasticity can be represented. He further objected to the assumption that atoms were indivisible, since, however small we conceive a particle to be, we can invariably think of its parts. Leibnitz was not to be satisfied with the idea which Lucretius seems to hold, that a thing may exist just big enough to have parts too small in themselves for independent existence. John Bernoulli, however, did not quite abandon atoms in consequence of this attack; like a sensible man he does not like assumptions of infinite hardness and infinite elasticity, but he replies to Leibnitz that atoms may be so constituted that they may be really indivisible by any process to which they can be subjected by other atoms, although they may have an infinity of parts such as the mind can conceive.
We will now endeavour to trace the development of the school which, discarding the hard solid elastic atoms of Lucretius, attempts to deduce the properties of matter from the motion of an all-pervading fluid endowed with comparatively simple qualities. This conception of matter probably differs little from the tenets of those ancient philosophers who held that the universe was built of some one element, such as air, fire, or water. Descartes, who has at least the merit of reviving the idea, in opposition to Gassendi and others who followed Lucretius, could  devise no rational hypothesis from this assumption; but Hobbes, contemporary with Descartes, held views which bear a striking resemblance to those recently broached by Sir William Thomson. Hobbes thought that a moist fluid ether fills the universe, so that it left no empty space at all. He understood by fluidity that which is made such by nature equally in every part of the fluid body, — not as dust is fluid, for so a house which is falling in pieces may be called fluid, — but in such manner as water seems fluid he defines " a hard body to be 'that whereof no part can be sensibly moved unless the whole be moved" and in explanation how a fluid can compose a hard body, he says, " Whatsoever, therefore, is soft or fluid can never be made hard, but by such motion as makes many of the parts together stop the motion of some one part by resisting the same" — -an admirable explanation of a recent discovery due to Helmholtz, described below, contrasting most favourably with Leibnitz's subsequent mere verbal quibble on the same point. More than this, Hobbes perceived that elasticity need not be a primary quality of matter, but might be conferred by motion. " If the cause of this restitution (elasticity) be asked, I say it may be in this manner, namely, that the particles of the bended body, whilst it is held bent, do nevertheless retain their motion, and by this motion they restore it as soon as the force is removed by which it is bent." These are most remarkable propositions, and, should Thomson's ideas be established, will entitle Hobbes to a very high position as the precursor of the true theory. Unfortunately, Hobbes did not compose an harmonious system out of the above ideas. He missed the conception of vortices of ether as atoms, and introduced particles of gross matter distinct from ether, which may after all be true. He also could not get free from the old nomenclature of elements, and even devised those same glassy bubbles full of ether, which now serve chiefly to prove that Leibnitz took (without acknowledgment which we can find) the best of Hobbes's ideas, without being able to leave the dross behind. Hobbes has a kind of undulating theory of light, which he thought was produced by the motion of an ether Leibnitz took that too but Galileo might perhaps claim this, as well as the notion that it was the action of this ether which was meant by the spirit brooding on the waters at creation. Leibnitz took that too, and altogether he seems to have been a great hand at appropriation.
Malebranche, who followed Descartes in most things, gave up to a great extent the balls and dust and snakes, and broached the idea that gross matter was made up of molecules, each of which was an eddy or vortex of the primeval fluid. Here  we reach an intelligible conception, greatly in advance of the crude and somewhat confused views of Hobbes. The molecule is separated from the surrounding medium by the motion of its parts, it has a distinct existence, and may have very different properties from all the rest of the medium or fluid. If the parts of this fluid do not cohere in any way, but move frictionless, our little vortex-atom may have qurte a sharp boundary, and if inertia be granted as an original property in our fluid, the little vortex may go on spinning for ever. Moreover, if it goes at a very great rate it may contain almost infinitely more energy or power than other parts of the medium, even when these are displaced by the motion of the vortex-atom, or a congeries of these, through the medium, which must of course then form a comparatively slow eddy coming in behind our vortex-atoms as fast as it is shoved away in front. The vortex plays the part of the Lucretian atom, the medium of the Lucretian void. A few vortices in a given space constitute a rare body a dense body contains many vortices in the same space. The idea is one of remarkable merit, and has received several recent developments. Malebranche conceives the medium itself as full of vortices, almost infinitely small as compared with those constituting gross matter. He thought that cohesion was the result of pressure from this elastic medium against gross matter, as the two halves of a Magdeburg sphere were pressed together by the elastic air outside when the air inside is removed. Here we have a fresh explanation of hardness, as due to the motion of a fluid, — an idea adopted in an unintelligible form by Leibnitz from Hobbes, and also by John Bernoulli, who further argues that this property may be given by re-entering motion.
This very idea, first due, we think, to Hobbes, and now proved possible by rigid mathematics, is perhaps the latest contribution to our subject. Helmholtz has proved that in a perfect fluid one vortex or whirlpool cannot destroy another, cannot cut through it or divide in any way from the outside — so that a ring-shaped vortex, for instance, would be quite indestructible by other vortices by a ring-vortex we do not mean one in which the fluid moves round in a simple circle, but a ring built up of a series of such little circles side by side each little circle placed as a circlet of thread tied on a marriage ring would be. Such a ring-vortex as this, once set going in a perfect fluid, in which no friction occurs, would go on for ever, if we suppose our fluid endowed with inertia. Our ring-vortex might be stretched, squeezed, even knotted by other similar vortices, but it could never be pierced by them, never destroyed, and would, in all its metamorphoses, retain some of its original characteristics, depending on the velocity of its particles and its magnitude. Sir William Thomson  at once pounced on this indestructible vortex as possibly fulfilling the conditions required for a practicable atom. Each vortex would be indestructible, since we could never bring to bear on it anything but other like vortices. It would be elastic, in virtue of the motion of its parts only, without any assumption of elasticity in its materials — an idea this hard to grasp, but to be practically felt by any one who tries to upset a good heavy top. He will find that, as he pushes it over, it resists, and will come upright again, exerting what we may call a kind of elasticity due to motion only. Moreover, Thomson shows that these very vortices have necessary modes of .vibration, which may correspond to the special waves of light which the chemical atom of each elementary substance is capable of exciting or receiving knotted, or even knitted, they would explain cohesion and chemical properties without any supposition of attraction or repulsion between atoms. By their impact they may explain the elasticity of gases in the manner proposed by a later Bernoulli by other motions, such as those treated of by Thomson himself and Clerk Maxwell, they may cause magnetism and electricity. Nor is more required for the explanation of heat; and although it cannot be said that we yet know with any certainty what motions are required for the explanation of these phenomena, we do begin to know some of the relations which must exist between the several motions nor need we despair even of explaining light and gravitation with the same machinery. Having traced the theory of a continuous fluid to its development in the hands of Thomson, we find that this school too has arrived at indestructible elastic atoms as the secondary constituents of gross matter, though they reject the crude atoms of Lucretius as a primary material.
Bacon was very cautious about atomic theories, but on the whole believed in atoms. He devised the idea of groups or knots of atoms, saying, in reference to the argument of Democritus, that if only one kind of atom existed, all things could be made out of all things " there is no doubt but that the seeds of things though equal, as soon as they have thrown themselves into certain groups or knots, completely assume the nature of dissimilar bodies till those groups or knots are dissolved." Newton, while approving of some form of the atomic theory, was very guarded in expressing his opinions but his discovery of the laws of gravitation exercised great influence on most subsequent hypotheses as to the constitution of matter. The conception of atoms having the property of exerting various forces across a void space, followed as a matter of course from the idea of universal gravitation. A school arose which taught  that atoms might have the property of exerting force at a distance, and that this property might be inherent in the atoms, just as Lucretius taught that hardness and elasticity were original indefeasible properties of the seeds of things. Force came to be considered as having a real existence apart from matter but this idea, though very popular now, was not established without a hard struggle, and may yet have to be abandoned.
This view is in direct contradiction with the old axiom that matter could not act where it was not, or, as Hobbes put it, " there can be no cause of motion except a body contiguous and moved," — no unnatural idea, but, on the contrary, universally or almost universally believed till Newton's time. We do not think that the fact of gravitation justifies the assumption that atoms can exert a force upon one another across a void, but Newton spoke of gravitation as an action between two distant bodies, and since then we have got quite accustomed to the idea of finite molecules of matter acting everywhere in the universe, and that, too, without any material medium of communication. This to Leibnitz was either miraculous or absurd. But, in fact, Newton did not teach this he stated a fact, he did not devise hypotheses he found that from the law of gravitation the vast mass of facts observed about falling bodies and planetary motions could be logically deduced. The one statement comprehended all the others his great discovery was the short statement with its proof he invented no explanation of how the law of gravitation could be brought about, and neither asserted nor denied that some medium of communication must exist. Leibnitz and other doubters said, How can this be, this attraction at a distance ? We cannot see how it can be done, so we will not believe it it is miraculous or absurd. Newton could only reply it was a fact, and we have been so satisfied with the answer as to be somewhat in danger of forgetting that the question, " How can it be ?" deserves consideration that the statement of the law of gravitation, though a wonderful discovery, does not set a bound to further inquiry.
The law of gravitation considered as a result is beautifully simple in a few words it expresses a fact from which most numerous and complex results may be deduced by mere reasoning, results found invariably to agree with the records of observation but this same law of gravitation looked upon as an axiom or first principle is so astoundingly far removed from all ordinary experience as to be almost incredible. What ! every particle in the whole universe is actively attracting every other particle through void without the aid of any communication by means of matter or otherwise — each particle unchecked by distance, unimpeded by obstacles, throws this miraculous influence to infinite distance without the employment of any  means ! No particle interferes with its neighbour, but all these wonderful influences are co-existent in every point of space ! The result is apparent at each particle, but the condition of this intermediate space is exactly the same as though no such influence were being transmitted across it! Earth attracts Sirius across space, and yet the space between is as if neither Earth nor Sirius existed ! Can these things be ? We think not and Newton himself did not affirm this his work was to prove a fact, and he neither affirmed nor denied the possibility of a medium of communication. That was a secondary question then, but now that the fact of the attraction is established the secondary question has risen to the first rank, and we must consider whether the intermediate space really contains nothing which plays a part in gravitation.
Analogy is against such a supposition. The influence exerted at a distance by electricity, magnetism, heat, and light, is effected by the substances filling intermediate space. For every one of these influences we suppose some intermediate material, and the existence of this material, often called an ether, is almost demonstrated. Faraday, by proving the influence of the intermediate material in the case of electrical action, by his discovery of magneto-optic rotation, and by showing how lines of force arose in media, rudely shook the theory of attraction and repulsion, exerted at a distance across a perfect void. Light gives us a very perfect analogy to illustrate our assertion that the law of gravitation is not an hypothesis, but a result capable of and requiring further explanation. Gravitation is not perceived directly by the senses, except in the case of the attraction of the earth. We have a special sense for the perception of light, yet many phenomena of radiation are not detected by the eye. Similarly, some of the phenomena of gravitation may escape our observation. Newton detected some of these. Suppose we had all been blind, Newton, instead of discovering universal gravitation, might have discovered light and its laws. From observations on the growth of vegetation, the sensation of heat, chemical decomposition, and other facts perceptible to blind creatures, he with vast genius might have discovered that a body existed at a great distance from the earth, from which a peculiar influence was periodically rained upon the earth that this influence could also be produced by fire and in other ways by men living on the earth, and was in a given medium inversely proportional to the square of the distance from the source of light, as we call it. He might have discovered the transparency and opacity of bodies, and the simpler laws of refraction and reflection. To any one of his blind compeers who objected that such a supposition as an influence starting from an amazing distance, occupying no sensible  time in the traject, transmitted, reflected and refracted without the interference of one ray with another, was either miraculous or absurd, and wholly unworthy of consideration as a physical hypothesis, he would have answered Light exists for all that, and its laws I can prove to you by mathematical reasoning from experiment. He would have been perfectly right, as he was about gravitation, but that need not have prevented subsequent philosophers from devising the undulatory theory of light if they had been clever enough; quite similarly, the fact that gravitation as discovered by Newton does exist need not prevent our trying to devise a scheme which shall explain its action, starting from much simpler postulates than that of an universal influence of each atom on all others at a distance.
The action of a body on its neighbour can be explained without the idea of a force acting even across a small void, by the simple assumption that two bodies cannot be in the same place at the same time, an assumption only tacitly made by Lucretius, and generally received as undeniable, though it admits of rational doubt, for experiment is by no means conclusive as to its certainty. Still, most people will be and have been unable to doubt it. With this assumption, motion and influence of all kinds can be transmitted either through a fluid constituting a plenum, or from one atom to another, as they clash in a vacuum. By successive blows or extended currents action can produce results at a great distance from its origin upon either of these hypotheses, without the assumption that matter can act where it is not. Some explanation of gravity may be found requiring only the above assumption, coupled with the other dogma, that matter once in motion will continue to move till stopped, and no atomic theory can be received as complete which does not explain gravitation as one of its consequences.
Lesage, a Genevese, undertook to deduce the laws of gravitation as a necessary consequence of the atomic theory, reverting, however, to the chaotic motion of atoms in all directions taught by Democritus, instead of the rectilinear parallel motions of Lucretius. Lesage asked you to conceive two solid bodies in space, say the earth and sun, and atoms coming to assail them equally in all directions but one side of the earth would be partially screened by the sun, and the corresponding side of the sun would be partially screened by the earth, so what we would call the front faces of the earth and sun, which looked towards one another, would be less bombarded by the atoms than all the other faces. The atoms hitting at the back of the two bodies would push them together. The atoms hitting the sides would of course balance one another. The idea is ingenious, but requires some strong assumptions. The attraction of gravitation  is not as the surface of the bodies, but as their mass. Lesage had therefore to suppose his solid bodies not solid but excessively porous, built up of molecules like cages, so that an infinite number of atoms went through and through them, allowing the last layer of the sun or earth to be struck by just as many atoms as the first, otherwise clearly the back part of the sun and earth would gravitate more strongly than the front or nearer sides, which would be struck only by the siftings of the previous layers of matter. This notion involves a prodigious quantity of material in the shape of flying atoms, where we perceive no gross matter, but very little material in solid bodies where we do find gross matter, and it further requires that the accumulation of atoms which strike the solid bodies perpetually should be insensible, and on these grounds, independently of dynamical imperfections, we must reject the theory in its crude form, though it may prove fruitful some day. Meanwhile it serves to show that the school which denies action at a distance need not have recourse to an absolute plenum.
Three distinct atomic theories have now been discussed : we have found believers in atoms of " solid singleness," in atoms due to the motion of a continuous fluid, and in atoms having the property of exerting force at a distance. Naturally the three elementary conceptions have been compounded in a variety of ways. Leibnitz mentions with great disapproval a certain Hartsoeker who supposed that atoms moved in an ambient fluid, though the idea is not unlike his own. It is difficult to trace the origin of the hypothesis, but Galileo and Hobbes both speak of a subtle ether. The conception of an all-pervading imponderable fluid of this kind has formed part of many theories, and ether came to be very generally adopted as a favourite name for the fluid, but caloric was also much thought of as a medium. We even find half-a-dozen imponderable co-existent fluids regarded with favour, — one called heat, another electricity, another phlogiston, another light, and what not, with little hard atoms swimming about, each endowed with forces of repulsion and attraction of all sorts, as was thought desirable. This idea of the constitution of matter was perhaps the worst of all. These imponderable fluids were mere names, and these forces were suppositions, representing no observed facts. No attempt was made to show how or why the forces acted, but gravitation being taken as due to a mere " force," speculators thought themselves at liberty to imagine any number of forces, attractive or repulsive, or alternating, varying as the distance, or the square, cube, fifth power of the distance, etc. At last Boscovich got rid of atoms altogether, by supposing them to be the mere centres of forces exerted by a position or point only, where nothing existed but the power of exerting a force. A medium  composed of molecules flying in all directions has been shown by Maxwell to have certain properties in which it resembles a solid body rather than a fluid. The less the molecules interfere with each other's motion the more decided do these properties become, till in the ultimate case in which they do not interfere at all, Maxwell states that the elastic properties of the medium are precisely those deduced by French mathematicians from the hypothesis of centres of force at rest acting on one another at a distance. Thus the most opposite hypotheses sometimes conduct to the same result. Dalton, assuming that the idea of an atom with an ambient ether was generally believed in, gave an immense support to the atomic theory by his discovery of the simple relations in which substances combine chemically. Since then it has been heretical to doubt atoms, until Sir Benjamin Brodie the other day broached ideas which seem independent if not subversive of the simple atomic faith.
Reviewing the various doctrines, we find that the problem of the constitution of matter is yet unsolved but at least it can now be fairly stated. We know with much accuracy the conditions to be fulfilled by any hypothesis, and we possess a mathematical machinery by which we can test how completely any hypothesis does fulfil those conditions. The materials for the work are not wanting, though the architect has not appeared. Inertia and motion seem the most indispensable elements in the conception of the materia prima extended in space. Once in motion, it must continue in motion till stopped when at rest, it must not move without a cause when in motion, it represents energy, or power, and can exert force. How ? The simplest, but not the only mode conceivable, is by displacement, in virtue of the property that two parts of it cannot occupy one and the same part of space. The believers in displacement may assume that space is quite full, or that in parts it is wholly empty that it contains one, two, or more kinds of primary ingredients capable of displacing one another, or each its own products merely.
The most plausible suggestion yet made by this school is, that a single omnipresent fluid, ether, fills the universe that by various motions, of the nature of eddies, the qualities of cohesion, elasticity, hardness, weight, mass, or other universal properties of matter, are given to small portions of the fluid which constitute the chemical atoms that these, by modifications in their combination, form and motion, produce all the accidental phenomena of gross matter that the primary fluid, by other motions, transmits light, radiant heat, magnetism, and gravitation that in certain ways the portions of the fluid transmuted into gross matter can be acted upon by the primary  fluid which remains imponderable or very light but that these ways differ very much from those in which one part of gross matter acts upon another; that the transmutation of the primary fluid into gross matter, or of gross matter into primary fluid, is a creative action wholly denied to us, the sum of each remaining constant.
Gross matter, on this view, would be merely an assemblage of parts of the medium moving in a particular way groups of ring-vortices, for instance. There appears to be some difficulty in determining the fundamental properties to be assumed for our medium. We must grant it inertia or it would not continue in motion.
The believers in hard atoms can hardly restrict themselves to the combination and motion of atoms of gross matter these will not explain light, gravitation, and analogous phenomena, for which a second kind of very subtle matter is required but this may be supposed to consist of almost infinitely finer atoms. If the molecules of gross matter be supposed constructed from these finer atoms moving in certain special ways, this doctrine would be in accordance with that of Lucretius, and would differ little from the fluid theory, except that it would admit a void. Thus far the displacement school.
Those who believe in force exerted at a distance without a means of communication have more elbow-room. They may assume attractive and repelling forces, perhaps oblique and tangential forces they may assume that these forces vary according to laws, simple or very complex they may wholly deny the existence of anything but force, and grant extension and inertia to a field of force regulated in a special fashion. This little field of force, or a combination of such fields, may build their chemical atom, and the motions of these atoms in their turn as above, produce some of the properties or accidents of gross matter they may believe in a plenum or a partial vacuum, and in one or more kinds of matter, precisely as the other school may do and, indeed, it is impossible to set a limit to their conjectures because when once the mind admits this conception of an abstract force, such as that of gravitation as popularly understood, it will not refuse to entertain the idea of any other kind of force varying according to infinitely different laws, nor is there any mental limit to the possible set of co-existent forces.
Let each party try. Mathematics provide a sure test of success, though impotent to suggest a theory. The existence of the chemical atom, already quite a complex little world, seems very probable, and the description of the Lucretian atom is wonderfully applicable to it. We are not wholly without hope that the  real weight of each such atom may some day be known, not merely the relative weight of the several atoms, but the number in a given volume of any material that the form and motion of the parts of each atom, and the distance by which they are separated, may be calculated that the motions by which they produce heat, electricity, and light may be illustrated by exact geometrical diagrams and that the fundamental properties of the intermediate and possibly constituent medium may be arrived at. Then the motion of planets and music of the spheres will be neglected for a while in admiration of the maze in which the tiny atoms turn. Those who doubt the possibility of this achievement should read the writings of Thomson, Clausius, Rankine, and Clerk Maxwell. They will there gain some insight into what is meant by an explanation of such things as heat, electricity, and magnetism, as caused by the motion of matter, ponderable or imponderable. They will also perceive the vast difference between the old hazy speculations and the endeavours of modern science. Yet when we have found a mechanical theory by which the phenomena of inorganic matter can be mathematically deduced from the motion of materials endowed with a few simple properties, we must not forget that Democritus, Leucippus, and Epicurus began the work, and we may even now recognise their merits, and acknowledge Lucretius not only as a great poet, but as the clear expositor of a very remarkable theory of the constitution of matter, though we must admit that he failed in his bolder attempts to abolish the gods, and dispense with creation, or even to reconcile universal causation with free-will.
- T. Lucreti Cart De Rerum Natura, Libri sex. With Notes and a Translation, by H. A. J. Munro, M.A. Second Edit. 1866. 2 vola. Cambridge : Deighton, Bell, & Co.
- Afterwards, I. 360, the quantity of body Is assumed as proportional to weight
- A homogeneous plenum may also be conceived as compressible.
- Sir William Thomson and Professor Tait find no difficulty in this conception.