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action of the atoms would have caused a repulsion between one of the intervals between the pieces ; to him, therefore, the two systems insuperable by any force which we can the gravel is by no means a homogeneous and continuous command. Thus, a number of soldiers with firearms may substance. occupy an extensive region to the exclusion of the enemy's In the same way, a theory that some particular substance, armies, though the space filled by their bodies is but small. say water, is homogeneous and continuous may be a good In this way Boscovich explained the apparent extension of working theory up to a certain point, but may fail when bodies consisting of atoms, each of which is devoid of we come to deal with quantities so minute or so attenuated extension. According to Boscovich's theory, all action that their heterogeneity of structure comes into prominence. between bodies is action at a distance. There is no such Whether this heterogeneity of structure is or is not conthing in nature as actual contact between two bodies. sistent with homogeneity and continuity of substance is When two bodies are said in ordinary language to be in another question. contact, all that is meant is that they are so near together The extreme form of the doctrine of continuity is that that the repulsion between the nearest pairs of atoms stated by Descartes, who maintains that the whole universe belonging to the two bodies is very great.

is equally full of matter, and that this matter is all of one Thus, in Boscovich's theory, the atom has continuity of kind, having no essential property besides that of extension. existence in time and space. At any instant of time it is all the properties which we perceive in matter he reduces to at some point of space, and it is never in more than one its parts being movable among one another, and so capable place at a time. It passes from one place to another along of all the varieties which we can perceive to follow from a continuous path. It has a definite mass which cannot be the motion of its parts (Principia, ii, 23). Descartes's own increased or diminished. Atoms are endowed with the attempts to deduce the different qualities and actions of power of acting on one another by attraction or repulsion, bodies in this way are not of much value. More than a the amount of the force depending on the distance between century was required to invent methods of investigating them. On the other hand, the atom itself has no parts or the conditions of the motion of systems of bodies such as dimensions. In its geometrical aspect it is a mere geo- Descartes imagined But the hydrodynamical discovery of metrical point. It has no extension in space. It has not Helmholtz that a vortex in a perfect liquid possesses certain the so-called property of Impenetrability, for two atoms may permanent characteristics, has been applied by Sir W. exist in the same place. This we may regard as ono Thomson to form a theory of vortex atoms in a homoextreme of the various opinions about the constitution of geneous, incompressible, and frictionless liquid, to which bodies.

we shall return at the proper time. The opposite extreme, that of Anaxagoras -the theory that bodies apparently homogeneous and continuous are so

OUTLINE OF MODERN MOLECULAR SCIENCE, AND IN PARin reality-is, in its extreme form, a theory incapable of

TICULAR OF THE MOLECULAR THEORY OF GASES. development. To explain the properties of any substance by this theory is impossible. We can only admit the We begin by assuming that bodies are made up of parts, observed properties of such substance as ultimate facts. each of which is capable of motion, and that these parts There is a certain stage, however, of scientific progress in act on each other in a manner consistent with the principle which a method corresponding to this theory is of service. of the conservation of energy. In making these assumpIn hydrostatics, for instance, we define a fuid by means of tions, we are justified by the facts that bodies may be one of its known properties, and from this definition we divided into smaller parts, and that all bodies with which make the system of deductions which constitutes the science we are acquainted are conservative systems, which would of hydrostatics. In this way the science of hydrostatics not be the case unless their parts were also conservative may be built upon an experimental basis, without any con systems, sideration of the constitution of a fluid as to whether it is We may also assume that these small parts are in motion. molecular or continuous. In like manner, after the French This is the most general assumption we can make, for it mathematicians had attempted, with more or less ingenuity, includes, as a particular case, the theory that the small to construct a theory of elastic solids from the hypothesis parts are at rest. The phenomena of the diffusion of gases that they consist of atoms in equilibrium under the action and liquids through each other show that there may be a of their mutual forces, Stokes and others showed that all motion of the small parts of a body which is not perceptible the results of this hypothesis, so far at least as they agreed to us. with facts, might be deduced from the postulate that elastic We make no assumption with respect to the nature of bodies exist, and from the hypothesis that the smallest the small parts—whether they are all of one magnitude. portions into which we can divide them are sensibly homo We do not even assume them to have extension and figure. geneous. In this way the principle of continuity, which Each of them must be measured by its mass, and any two is the basis of the method of Fluxions and the whole of of them must, like visible bodies, have the power of acting modern mathematics, may be applied to the analysis of on one another when they come near enough to do so. Tho problems connected with material bodies by assuming them, properties of the body, or medium, are determined by tho for the purpose of this analysis, to be homogeneous All configuration and motion of its small parts. that is required to make the results applicable to the real The first step in the investigation is to determine the case is that the smallest portions of the substance of which amount of motion which exists among the small parts, we take any notice shall be sensibly of the same kind. independent of the visible motion of the medium as a Thus, if a railway contractor has to make a tunnel through whole. For this purpose it is convenient to make use of a a hill of gravel, and if one cubic yard of the gravel is 80 general theorem in dynamics due to Clausius. like another cubie yard that for the purposes of the contract When the motion of a material system is such that the they may be taken as equivalent, then, in estimating the time-average of the quantity (mxa) remains constant, the work required to remove the gravel from the tunnel, he state of the system is said to be that of stationary motion. may, without fear of error, make his calculations as if the When the motion of a material system is such that the gravel were a continuous substance. But if a worm has to sum of the moments of inertia of the system, about three make his way through the gravel, it makes the greatest axes at right angles through its centre of mass, never varies possible difference to him whether he tries to push right by more than small quantities from a constant value, against a piece of gravel, or directs his course through the system is said to be in a state of stationary motion.

The kinetic energy of a particle is half the product of where A is the temperature reckoned from absolute zero, its mass into the square of its velocity, and the kinetic and R is a constant. The fact that this equation expresses energy of a system is the sum of the kinetic energy of all with considerable accuracy the relation between the volume, its parts.

pressure, and temperature of a gas when in an extremely When an attraction or repulsion exists between two rarified state, and that as the gas is more and more compoints, half the product of this stress into the distance pressed the deviation from this equation becomes more between the two points is called the virial of the stress, apparent, shows that the pressure of a gas is due almost and is reckoned positive when the stress is an attraction, entirely to the motion of its molecules when the gas is rare, and negative when it is a repulsion. The virial of a system and that it is only when the density of the gas is consideris the sum of the virials of the stresses which exist in it. ably increased that the effect of direct action between the If the system is subjected to the external stress of the molecules becomes apparent. pressure of the sides of a vessel in which it is contained, | The effect of the direct action of the molecules on each this stress will introduce an amount of virial p V, where other depends on the number of pairs of molecules which p is the pressure on unit of area and V is the volume of at a given instant are near enough to act on one another. the vessel

The number of such pairs is proportional to the square of The theorem of Clausius may now be stated as follows : the number of molecules in unit of volume, that is, to the In a material system in a state of stationary motion the square of the density of the gas. Hence, as long as the time-average of the kinetic energy is equal to the time- medium is so rare that the encounter between two molecules average of the virial. In the case of a fluid enclosed in a | is not affected by the presence of others, the deviation from vessel

Boyle's law will be proportional to the 'square of the (mu) = {pV+ }&3(Rr),

density. If the action between the molecules is on the where the first term denotes the kinetic energy, and is half

whole repulsive, the pressure will be greater than that given the sum of the product of each mass into the mean square

by Boyle's law. If it is, on the whole, attractive, the of its velocity. In the second term, p is the pressure on

pressure will be less than that given by Boyle's law. It unit of surface of the vessel, whose volume is V, and the

appears, by the experiments of Regnault and others, that third term expresses the virial due to the internal actions

the pressure does deviate from Boyle's law when the between the parts of the system. A double symbol of

density of the gas is increased. In the case of carbonic summation is used, because every pair of parts between

acid and other gases which are easily liquefied, this deviawhich any action exists must be taken into account. We

tion is very great. In all cases, however, except that of have next to show that in gases the principal part of the

hydrogen, the pressure is less than that given by Boyle's pressure arises from the motion of the small parts of the

law, showing that the virial is on the whole due to medium, and not from a repulsion between them.

| attractive forces between the molecules. In the first place, if the pressure of a gas arises from the

Another kind of evidence as to the nature of the action repulsion of its parts, the law of repulsion must be inversely

| between the molecules is furnished by an experiment made as the distance. For, consider a cube filled with the gas

by Dr Joule. Of two vessels, one was exhausted and the at pressure p, and let the cube expand till each side is n

other filled with a gas at a pressure of 20 atmospheres; times its former langth. The pressure on unit of surface

and both were placed side by side in a vessel of water,

which was constantly stirred. The temperature of the according to Boyle's law is now , and since the area whole was observed. Then a communication was opened of a face of the cube is në times what it was, the whole

between the vessels, the compressed gas expanded to

twice its volume, and the work of expansion, which at pressure on the face of the cube is - of its original value. | | first produced a strong current in the gas, was soon conBut since everything has been expanded symmetrically, the

verted into heat by the internal friction of the gas. When distance between corresponding parts of the air is nown

all was again at rest, and the temperature uniform, the times what it was, and the force is n times less than it was.

temperature was again observed. In Dr Joule's original Hence the force must vary inversely as the distance.

experiments the observed temperature was the same as But Newton has shown (Principia, bk. i prop. 93) that

before. In a series of experiments, conducted by Dr Joule this law is inadmissible, as it makes the effect of the dis

and Sir W. Thomson on a different plan, by which the tant parts of the medium on a particle greater than that of

thermal effect of free expansion can be more accurately the neighbouring parts. Indeed, we should arrive at the

measured, a slight cooling effect was observed in all the conclusion that the pressure depends not only on the density

gases examined except hydrogen. Since the temperature of the air but on the form and dimensions of the vessel

depends on the velocity of agitation of the molecules, it which contains it, which we know not to be the case.

appears that when a gas expands without doing external If, on the other hand, we suppose the pressure to arise

work the velocity of agitation is not much affected, but entirely from the motion of the molecules of the gas, the

that in most cases it is slightly diminished. Now, if the interpretation of Boyle's law becomes very simple. For,

molecules during their mutual separation act on each other, in this case

their velocity will increase or diminish according as the PV = {(mv2).

force is repulsive or attractive. It appears, therefore, from

the experiments on the free expansion of gases, that the The first term is the product of the pressure and the volume, force between the molecules is small but, on the whole, which according to Boyle's law is constant for the same attractive. quantity of gas at the same temperature. The second term Having thus justified the hypothesis that a gas consists is two-thirds of the kinetic energy of the system, and we l of molecules in motion, which act on each other only have every reason to believe that in gases when the when they come very close together during an encounter, temperature is constant the kinetic energy of unit of mass hiut which, during the intervals between their encounters is also constant. If we admit that the kinetic energy of

which constitute the greater part of their existence, are anit of mass is in a given gas proportional to the absolute

describing free paths, and are not acted on by any molotemperature, this equation is the expression of the law of cular

cular force, we proceed to investigate the motion of such a Charles as well as of that of Boyle, and may be. written

system. PV =RO,

The mathematical investigation of the properties of such

& system of molecules in motion is the foundation of mole , cogency. But it is purely chemical reasoning; it is not cular science. Clausius was the first to express the dynamical reasoning. It is founded on chemical experirelation between the density of the gas, the length of the ence, not on the laws of motion. free paths of its molecules, and the distance at which Our definition of a nolecule is purely dynamical A they encounter each other. He assumed, however, at least molecule is that minute portion of a substance whicla moves in his earlier investigations, that the velocities of all the about as a whole, so that its parts, if it has any, do not part molecules are equal The mode in which the velocities are company during the motion of agitation of the gas. "The distributed was first investigated by the present writer, result of the kinetic theory, therefore, is to give us informawho showed that in the moving system the velocities of tion about the relative masses of molecules considered as the molecules range from zero to infinity, but that the moving bodies. The consistency of this information with number of molecules whose velocities lie within given the deductions of chemists from the phenomena of comlimits can be expressed by a formula identical with that bination. greatly strengthens the evidence in favour of the which expresses in the theory of errors the number of actual existence and motion of gaseous molecules. errors of observation lying within corresponding limits. Another confirmation of the theory of molecules is The proof of this theorem has been carefully investigated derived from the experiments of Dulong and Petit on the by Boltzmann, who has strengthened it where it appeared specific heat of gases, from which they deduced the law weak, and to whom the method of taking into account the which bears their name, and which zaserts that the specific action of external forces is entirely due.

heats of equal weights of gases are inversely as their comThe mean kinetic energy of a molecule, however, has a bining weights, or, in other words, that the capacities for deånito value, which is easily expressed in terms of the heat of the chemical equivalents of different gases are quantities which enter into the expression for the distribu equal. We have seen that the temperature is determined tion of velocities. The most important result of this investi by the kinetic energy of agitation of each molecule. The gation is that when several kinds of molecules are in motion molecule has also a certain amount of energy of internal moand acting on one another, the mean kinetic energy of a mole- tion, whether of rotation or of vibration, but the hypothesis cule is the game whatever be its mass, the molecules of of Clausius, that the mean value of the internal energy greater mass having smaller mean velocities. Now, when I always bears a proportion fixed for each gas to the enerov gases are mixed their temperatures become equal. Hence of agitation, seems highly probable and consistent with we conclude that the physical condition which determines experiment. The whole kinetic energy is therefore equal that the temperature of two gases shall be the one is that to the energy of agitation multiplied by a certain factor. the mean kinetic energies of agitation of the individual mole. Thus the energy communicated to a gas by heating it is cules of the two gases are equal. This result is of great divided in a certain proportion between the energy of agitaiinportance in the theory of heat, though we are not yet tion and that of the internal motion of each molecule. For able to establish any similar result for bodies in the liquid a given rise of temperature the energy of agitation, say of a or solid state,

million molecules, is increased by the same amount what In the next place, we know that in the case in which the ever be the gas. The heat spent in raising the temperature whole pressure of the medium is due to the motion of its is measured by the increase of the whole kinetic energy. molecules, the pressure on unit of area is numerically The thermal capacities, therefore, of equal numbers of equal to two-thirds of the kinetic energy in unit of volume. molecules of different gases are in the ratio of the factors Hence, if equal volumes of two gases are at equal pressures by which the energy of agitation must be multiplied to the kinetic energy is the same in each. If they are also obtain the whole energy. “As this factor appears to be at equal temperatures the mean kinetic energy of each nearly the same for all gases of the same degree of atomicity, molecule is the same in each. If, therefore, equal volumes Dulong and Petit's law is true for such gases. of two gases are at equal temperatures and pressures, the Another result of this investigation is of considerable number of molecules in each is the same, and therefore, importanco in relation to certain theories, which assume the the masses of the two kinds of molecules are in the same existence of æthers or rare media consisting of molecules ratio as the densities of the gases to which they belong. very much smaller than those of ordinary gases. According

This statement has been believed by chemists since the to our result, such a medium would be neither more nor tine of Gay-Lussac, who first established that the weights less than a gas. Supposing its molecules so small that of the chemical equivalents of different substances are they can penetrate between the molecules of solid substances proportional to the densities of these substances when in such as glass, a so-called vacuum would be full of this rare the form of ga3. The definition of the word molecule, gas at the observed temperature, and at the pressure, whathowever, as employed in the statement of Gay-Lussac's law ever it may be, of the ætherial medium in space. The is by no means identical with the definition of the same specific heat, therefore, of the medium in the so-called word as in the kinetic theory of gases. The chemists vacuum will be equal to that of the same volume of any ascertain by experiment the ratios of the masses of the other gas at the same temperature and pressure. Now, the different substazces in & compound. From these they purpose for which this inolecular æther is assumed in these deduce the chemical equivalents of the different substances, theories is to act on bodies by its pressure, and for this that of a particular substance, say hydrogen, being taken purpose the pressure is generally assumed to be very great. as unity. The only evidence made use of is that furnished Hence, according to these theories, we should find the by chemical combinations. It is also assumed, in order to specific heat of a so-called vacuum very considerable comscount for the facts of coinbination, that the reason why pared with that of a quantity of air filling the same space. substances combine in definite ratios is that the molecules We have now made a certain definite amount of progress of the substances are in the ratio of their chemical equiva towards a complete molecular theory of gases. We know lents, and that what we call combination is an action the mean velocity of the molecules of each gas in metres which takes place by a union of a molecule of one substance per second, and we know the relative masses of the molecules to & molecule of the other.

of different gases. We also know that the molecules of This kind of reasoning, when presented in a proper form one and the same gas are all equal in mass. For if they and sustained by proper evidence, has a high degree of

See Gustav Hansemann, Die Aline und ihre Bewegungen. 1871. Sitzungsberichte der K. K. Akad., Wien, 8th Oct. 1868. 1 (H. G. Mayer.)

are not, the method of dialysis, az employed by Graham, I temperature of different parts of the medium, and constitutos would enable us to separate the molecules of smaller mass | the phenomenon of the conduction of heat in gases. from those of greater, as they would stream through porous These three phenomena—the diffusion of matter, of substances with greater velocity. We should thus be able motion, and of heat in gases-have been experimentally to separate a gas, say hydrogen, into two portions, having investigated,—the diffusion of matter by Graham and different densities and other physical properties, different Loschmidt, the diffusion of motion by Oscar Meyer ana combining weights, and probably different chemical pro Clerk Maxwell, and that of heat by Stefan. perties of other kinds. As no chemist has yet obtained These three kinds of experiments give results which in specimens of hydrogen differing in this way from other the present imperfect state of the theory and the extreme specimens, we conclude that all the molecules of hydrogen difficulty of the experiments, especially those on the conare of sensibly the same mass, and not merely that their duction of heat, may be regarded as tolerably consistent mean mass is a statistical constant of great stability. with each other. At the pressure of our atmosphere, and

But as yet we have not considered the phenomena which at the temperature of melting ice, the mean path of a enable us to form an estimate of the actual mass and molecule of hydrogen is about the 10,000th of a milli. dimensions of a molecule. It is to Clausius that we owe metro, or about the fifth part of a wave-length of green light. the first definite conception of the free path of a molecule The mean path of the molecules of other gases is shorter and of the mean distance travelled by a molecule between than that of hydrogen. successive encounters. He showed that the number of The determination of the molecular volume of a gas is encounters of a molecule in a given time is proportional to subject as yet to considerable uncertainty. The most the velocity, to the number of molecules in unit of volume, obvious method is that of compressing the gas till it and to the square of the distance between the centres of | assumes the liquid form. It seems probable, from the great two molecules when they act on one another so as to have resistance of liquids to compression, that their molecules an encounter. From this it appears that if we call this are at about the same distance from each other as that at distance of the centres the diameter of a molecule, and the which two molecules of the same substance in the gaseous volume of a sphere having this diameter the volume of a form act on each other during an encounter. If this is the molecule, and the sum of the volumes of all the molecules case, the molecular volume of a gas is somewhat less than the molecular volume of the gas, then the diameter of a the volume of the liquid into which it would be condensed molecule is a certain multiple of the quantity obtained by by pressure, or, in other words, the density of the molecules diminishing the free path in the ratio of the molecular is somewhat greater than that of the liquid. volume of the gas to the whole volume of the gas. The Now, we know the relative weights of different molecules numerical value of this multiple differs slightly, according with great accuracy, and, from a knowledge of the mean to the hypothesis we assume about the law of distribution path, we can calculate their relative diameters approxiof velocities. It also depends on the definition of an mately. From these we can deduce the relative densities encounter. When the molecules are regarded as elastic of different kinds of molecules. The relative densities 80 spheres we know what is meant by an encounter, but if calculated have been compared by Lorenz Meyer with the they act on each other at a distance by attractive or repul-observed densities of the liquids into which the gases may sive forces of finite magnitude, the distance of their be condensed, and he finds a remarkable correspondence centres varies during an encounter, and is not a definite between them. There is considerable doubt, however, as quantity. Nevertheless, the above statement of Clausius to the relation between the molecules of a liquid and thoro enables us, if we know the length of the mean path and of its vapour, so that till a larger number of comparisons the molecular volume of a gas, to form a toleravly near have been made, we must not place too much reliance on estimate of the diameter of the sphere of the intense action the calculated densities of molecules. Another, and perhaps of a molecule, and thence of the number of molecules in a more refined, method is that adopted by M. Van der unit of volume and the actual mass of each' molecule. To Waals, who deduces the molecular volume from the deviacomplete the investigation we have, therefore, to determine tions of the pressure from Boyle's law as the gas is comthe mean path and the molecular volume. The first numerical estimate of the mean path of a gaseous molecule The first numerical estimate of the diameter of a moleculo was made by the present writer from data derived from the was that made by Loschmidt in 1865 from the mean path internal friction of air. There are three phenomena which and the molecular volume. Independently of him and of depend on the length of the free path of the molecules of a each other, Mr Stoney, in 1668, and Sir W. Thomson, in gas. It is evident that the greater the free path the more 1870, published results of a similar kind-those of Thomson rapidly will the molecules travel from one part of the being deduced not only in this way, but from considerations medium to another, because their direction will not be so derived from the thickness of soap bubbles, and from the often altered by encounters with other molecules. If the electric action between zinc and copper. molecules in different parts of the medium are of different The diameter and the mass of a molecule, as estimated kinds, their progress from one part of the medium to by these methods, are, of course, very small, but by no another can be easily traced by analysing portions of the means infinitely so. About two millions of molecules of medium taken from different places. The rate of diffu-hydrogen in a row would occupy a millimetre, and about sion thus found furnishes one method of estimating the two hundred million million million of them would weigh length of the free path of a molecule. This kind of a milligramme. These numbers must be considered as diffusion goes on not only between the molecules of exceedingly rough guesses ; they must be corrected by more different gases, but among the molecules of the same gas, extensive and accurate experiments as science advances ; only in the latter case the results of the diffusion cannot but the main result, which appears to be well established, be traced by analysis. But the diffusing molecules carry is that the determination of the mass of a molecule is a with them in their free paths the momentum and the energy legitimate ebject of scientific research, and that this mass which they happen at a given instant to have. The is by no means immeasurably small. diffusion of momentum tends to equalise the apparent Loschmidt illustrates these molecular measurements by motion of different parts of the medium, and constitutes a comparison with the smallest magnitudes visible by means the phenomenon called the internal friction or viscosity of of a microscope. Nobert, he tells us, can draw 4000 lines eases. The diffusion of energy tends to oqualise the in the breadth of a millimetre. The intervals between

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these lines can be opserved with a good microscope. A air, this motion is of a certain definite type, and if left to
cube, whose side is the 4000th of a millimetre, may be taken itself the whole motion is passed on to other masses of air,
as the minimum visibile für observers of the present day. and the sound-wave passes on, leaving the air behind it
Such a cube would contain from 60 to 100 million molecules at rest. Heat, on the other hand, never passes out of a
of oxygen or of nitrogen ; but since the molecules of hot body except to enter a colder body, so that the energy
organised substances contain on an average about 50 of the of sound-waves, or any other form of energy which is pro-
more elementary atoms, we may assume that the smallest pagated so as to pass wholly out of one portion of tho
organised particle visible under the microscope contains / medium and into another, cannot be called heat.
about two million molecules of organic matter. At least! We have now to turn our attention to a class of molecular
half of every living organism consists of water, so that the motions, which are as remarkable for their regularity as the
smallest living being visible under the microscope does not motion of agitation is for its irregularity.
contain mure than about a million organic molecules. Some It has been found, by means of the spectroecope, that
exceedingly simple organism may be cupposed built up of the light emitted by incandescent substances is different
not more than a million similar molecules. It is impossible, according to their state of condensation. When they are
however, to conceive so small a number sufficient to form in an extremely rarefied condition the spectrum of their
a being furnished with a whole system of specialised light cousists of a set of sharply-defined bright lines. As
organs.

the substance approaches a denser condition the spectrum
Thus molecular science sets us face to face with physiolo- tends to become continuous, either by the lines becoming
gical theories. It forbids the physiologist from imagining broader and less defined, or by new lines and bands appear
that structural details of infinitely small dimensions can ing between them, till the spectrum at length loses all its
furnish an explanation of the infinite variety which exists characteristics and becomes identical with that of solid
in the properties and functions of the most minute organ- bodies when raised to the same temperature.
isms.

Hence the vibrating systems, which are the source of the A microscopic germ is, we know, capable of development emitted light, must be vibrating in a different manner in into a highly organised animal. Another germ, equally these two cases. When the spectrum consists of a number microscopic, becomes, when developed, an animal of a of bright lines, the motion of the system must be comtotally different kind. Do all the differences, infinite in pounded of a corresponding number of types of harmonia number, which distinguish the one animal from the other, vibration. arise each from some difference in the structure of the In order that a bright line may be sharply defined, the respective germs? Even if we admit this as possible, we vibratory motion which produces it must be kept up in a shall be called upon by the advocates of Pangenesis to perfectly regular manner for some hundreds or thousands admit still greater marvels. For the microscopic germ, of vibrations. If the motion of each of the vibrating according to this theory, is no mere individual, but a repre-bodies is kept up only during a small number of vibrations, sentative body, containing members collected from every then, however regular may be the vibrations of each body rank of the long-drawn ramification of the ancestral tree, while it lasts, the resultant disturbance of the luminiferous the number of these members being amply sufficient not medium, when analysed by the prism, will be found to only to furnish the hereditary characteristics of every organ contain, besides the part due to the regular vibrations, of the body and every habit of the animal from birth to other motions, depending on the starting and stopping of death, but also to afford a stock of latent gemmules to be each particular vibrating body, which will become manifest passed on in an inactiv state from germ to germ, till at as a diffused luminosity scattered over the whole length of last the ancestral peculiarity which it represents is revived the spectrum. A spectrum of bright lines, therefore, in some remote descendant.

indicates that the vibrating bodies when set in motion are Some of the exponents of this theory of heredity have allowed to vibrate in accordance with the conditions of attempted to elude the difficulty of placing a whole world their internal structure for some time before they are again of wonders within a body so small and so devoid of visible interfered with by external forces. structure as a germ, by using the phrase structureless It appears, therefore, from spectroscopic evidence that germs. Now, one material system can differ from another each molecule of a rarefied gas is, during the greater part only in the configuration and motion which it has at a of its existence, at such a distance from all other moleculas given instant. To explain differences of function and that it executes its vibrations in an undisturbed and regular development of a germ without assuming differences of manner. This is the same conclusion to which we were structure is, therefore, to admit that the properties of a germ led by considerations of another kind at p. 39. aro not those of a purely material system.

We may therefore regard the bright lines in the spectrum The evidence as to the nature and motion of molecules, of a gas as the result of the vibrations executed by the with which we have hitherto been occupied, has been molecules while describing their free paths. When two derived from experiments upon gaseous media, the smallest molecules separate from one anothe; after an encounter, sensible portion of which contains millions of millions of each of them is in a state of vibration, arising from the molecules. The constancy and uniformity of the properties unequal action on different parts of the same moleculo of the gaseous medium is the direct result of the incon- during the encounter. Hence, though the centre of mass ceivable irregularity of the motion of agitation of its of the molecule describing its free path moves with uniform molecules. Any cause which could introduce regularity velocity, the parts of the molecule have a vibratory motion into the motion of agitation, and marshal the molecules with respect to the centre of mass of the whole molecule, into order and method in their evolutions, might check or and it is the dis urbance of the luminiferous medium comeven reverse that tendency to diffusion of matter, motion, municated to it by the vibrating molecules which constitutes and energy, which is one of the most invariable phenomena the emitted light. of nature, and to which Thomson has given the name of We may compare the vibrating molecule to a bell the dissipation of energy.

When struck, the bell is set in motion. This motion is Thus, when a sound-wave is passing through a mass of compounded of harmonic vibrations of many different

periods, each of which acts on the air, producing notes of * See F. Calton, “ On Blood Relationship,” Proc. Roy. Soc., June

as many different pitches. As the bell communicates its 13, 1872.

| motion to the air, these vibrations necessarily decay, some

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