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these lines can be observed 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 for 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 organ substances contain on an average about 50 of the of sound-waves, or any other form of energy which is promore elementary atoms, we may assume that the smallest pagated so as to pass wholly out of one portion of the 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 more than about a million organic molecules. Some It has been found, by means of the spectroscope, that exceedingly simple organism may be supposed 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 consists 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 appearthat 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 harmonic 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 inactive 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 molecules 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. are 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 another 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 molecule 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 disturbance of the luminiferous medium comcven 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 ich acts on the air, producing notes of * Sec F. Galton, " 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
of them faster than others, so that the sound contains fewer series of bright lines, whose wave-lengths are in simple and fewer notes, till at last it is reduced to the fundamental arithmetical ratios. note of the bell.? If we suppose that there are a great But if we suppose the molecule to be constituted accordmany bells precisely similar to each other, and that they ing to some different type, as, for instance, if it is an are struck, first one and then another, in a perfectly elastic sphere, or if it consists of a finite number of atoms irregular manner, yet so that, on an average, as many kept in their places by attractive and repulsive forces, the bells are struck in one second of time as in another, and roots of the equation will not be connected with each other also in such a way that, on an average, any one bell is not by any simple relations, but each may be made to vary again struck till it has ceased to vibrate, then the audible independently of the others by a suitable change of the result will appear a continuous sound, composed of the connections of the system. Hence, we have no right to sound emitted by bells in all states of vibration, from the expect any definite numerical relations among the waveclang of the actual stroke to the final hum of the dying lengths of the bright lines of a gas. fundamental tone.
The bright lines of the spectrum of an incandescent gas But now let the number of bells be reduced while the are therefore due to the harmonic vibrations of the molesame number of strokes are given in a second. Each bell
Each bell cules of the gas during their free paths. The only effect will now be struck before it has ceased to vibrate, so that of the motion of the centre of mass of the molecule is to in the resulting sound there will be less of the fundamental alter the time of vibration of the light as received by a tone and more of the original clang, till at last, when the stationary observer. When the molecule is coming towards peal is reduced to one bell, on which innumerable hammers the observer, each successive impulse will have a shorter are continually plying their strokes all out of time, the distance to travel before it reaches his eye, and therefore sound will become a mere noise, in which no musical note the impulses will appear to succeed each other more rapidly can be distinguished.
than if the molecule were at rest, and the contrary will be In the case of a gas we have an immense number of the case if the molecule is receding from the observer. molecules, each of which is set in vibration when it The bright line corresponding to the vibration will thereencounters another molecule, and continues to vibrate as fore be shifted in the spectrum towards the blue end when it describes its free path. The molecule is a material the molecule is approaching, and towards the red end when system, the parts of which are connected in some definite it is receding from the observer. By observations of the way, and from the fact that the bright lines of the displacement of certain lines in the spectrum, Dr Huggins emitted light have always the same wave-lengths, we learn and others have measured the rate of approach or of that the vibrations corresponding to these lines are always recession of certain stars with respect to the earth, and Mr executed in the same periodic time, and therefore the force Lockyer has determined the rate of motion of tornadoes in tending to restore any part of the molecule to its position the sun. But Lord Rayleigh has pointed out that accordof equilibrium in the molecule must be proportional to its ing to the dynamical theory of gases the molecules are displacement relative to that position.
moving hither and thither with so great velocity that, From the mathematical theory of the motion of such a however narrow and sharply-defined any bright line due to system, it appears that the whole motion may be analysed a single molecule may be, the displacement of the lino into the following parts, which may be considered each towards the blue by the approaching molecules, and independently of the others:- In the first place, the centre towards the red by the receding molecules, will produce a of mass of the system moves with uniform velocity in a certain amount of widening and blurring of the line in the straight line. This velocity may have any value. In the spectrum, so that there is a limit to the sharpness of desecond place, there may be a motion of rotation, the angular finition of the lines of a gas. The widening of the lines momentum of the system about its centre of mass remain due to this cause will be in proportion to the velocity of ing during the free path constant in magnitude and direc- agitation of the molecules. It will be greatest for the tion. This angular momentum may have any
value molecules of smallest mass, as those of hydrogen, and it will whatever, and its axis may have any direction. In the
increase with the temperature. Hence the measurement third place, the remainder of the motion is made up of a of the breadth of the hydrogen lines, such as C or F in number of component motions, each of which is an the spectrum of the solar prominences, may furnish harmonic vibration of a given type. In each type of evidence that the temperature of the sun cannot exceed a vibration the periodic time of vibration is determined by certain value. the nature of the system, and is invariable for the same system. The relative amount of motion in different parts
ON THE THEORY OF VORTEX ATOMS. of the system is also determinate for each type, but the absolute amount of motion and the phase of the vibration The equations which form the foundations of the of each type are determined by the particular circumstances mathematical theory of fluid motion were fully laid down of the last encounter, and may vary in any manner from by Lagrange and the great mathematicians of the end of one encounter to another.
last century, but the number of solutions of cases of fluid The values of the periodic times of the different types of motion which had been actually worked out remained very vibration are given by the roots of a certain equation, the small, and almost all of these belonged to a particular type form of which depends on the nature of the connections of of fluid motion, which has been since named the irrotathe system. In certain exceptionally simple cases, as, for tional type.
tional type. It had been shown, indeed, by Lagrange, instance, in that of a uniform string stretched between two that a perfect fluid, if its motion is at any time irrotational, fixed points, the roots of the equation are connected by will continue in all time coming to move in an irrotational simple arithmetical relations, and if the internal structure manner, so that, by assuming that the fluid was at one of a molecule had an analogous kind of simplicity, we time at rest, the calculation of its subsequent motion may might expect to find in the spectrum of the molecule a be very much simplified.
It was reserved for Helmholtz to point out the very 1 Part of the energy of motion is, in the case of the bell, dissipated remarkable properties of rotational motion in a homoin the substance of the bell in virtue of the viscosity of the metal, and assumes the form of heat, but it is not necessary, for the purpose
geneous incompressible fluid devoid of all viscosity. We of illustration, to take this cause of the decay of vibrations into
must first define the physical properties of such a fluid. In account.
the first place, it is a material substance. Its motion is
continuous in space and time, and if we follow any portion | when p is the density, which in the case of our homogeneof it as it moves, the mass of that portion remains invari ous incompressible fluid we may assume to be unity, the able. These properties it shares with all material sub
operator stances. In the next place, it is incompressible.
represents the rate of variation of the symbol to form of a given portion of the fluid may change, but its which it is prefixed at a point which is carried forward volume remains invariable; in other words, the density of with the fluid, so that the fluid remains the same during its motion. Besides this,
ou du du
du the fluid is homogeneous, or the density of all parts of the
+ v +w
öt dt dx dy Auid is the same. It is also continuous, so that the mass of the fluid contained within any closed surface is always p is the pressure, and V is the potential of external forces. exactly proportional to the volume contained within that There are two other equations of similar form in y and 2. surface. This is equivalent to asserting that the fluid is Differentiating the equation in y with respect to z, and not made up of molecules ; for, if it were, the mass would that in z with respect to y, and subtracting the second from vary in a discontinuous manner as the volume increases the first, we find
d do dow continuously, because first one and then another molecule
(5). would be included within the closed surface. Lastly, it is
dz êt a perfect fluid, or, in other words, the stress between one portion and a contiguous portion is always normal to the tions (1) and also the condition of incompressibility,
Performing the differentiations and remembering equasurface which separates these portions, and this whether the fluid is at rest or in motion.
du dv dw
(6), We have seen that in a molecular fluid the interdiffusion of the molecules causes an interdiffusion of motion of
δα different parts of the fluid, so that the action between
du + B
ot contiguous parts is no longer normal but in a direction
dz tending to diminish their relative motion. Hence the
Now, let us suppose a vortex line drawn in the fluid so perfect fluid cannot be molecular.
as always to begin at the same particle of the fluid. The All that is necessary in order to form a correct mathe
Let matical theory of a material system is that its properties components of the velocity of this point are u, v, w.
us find those of a point on the moving vortex line at a shall be clearly defined and shall be consistent with each
distance ds from this point where other. This is essential; but whether a substance having
ds = wdo such properties actually exists is a question which comes to
(8) be considered only when we propose to make some practi- | The co-ordinates of this point are cal application of the results of the mathematical theory.
x + ado , y+Bilo , z+ydo . (9), The properties of our perfect liquid are clearly defined and consistent with each other, and from the mathematical and the components of its velocity are theory we can deduce remarkable results, some of which
03 do , vt
W + may be illustrated in a rough way by means of fluids
öt which are by no means perfect in the sense of not being consider the first of these components. In virtue of viscous, such, for instance, as air and water.
The motion of a fluid is said to be irrotational when ite equation (7) we may write it is such that if a spherical portion of the fluid were sud
Bio + denly solidified, the solid sphere so formed would not be
ydo . (11), dx
dz rotating about any axis. When the motion of the fluid is rotational the axis and angular velocity of the rotation of
du dz ut
do (12), any small part of the fluid are those of a small spherical
dz do portion suddenly solidified. The mathematical expression of these definitions is as
do follows:-Let u, v, w be the components of the velocity of
do the fluid at the point (x, y, z), and let
But this represents the value of the component u of the dv dw dw du du dv B
velocity of the fluid itself at the same point, and the same
thing may be proved of the other components. then a, ß, y are the components of the velocity of rotation Hence the velocity of the second point on the vortex line of the fluid at the point (x, y, z). The axis of rotation is identical with that of the fluid at that point. In other is in the direction of the resultant of a, b, and y, and words, the vortex line swims along with the fluid, and is the velocity of rotation, w, is measured by this resultant. always formed of the same row of fluid particles. The
A line drawn in the fluid, so that at every point of the vortex line is therefore no mere mathematical symbol, but line
has a physical existence continuous in time and space. 1 dx i dy 1 dz
By differentiating equations (1) with respect to x, y, and Bds ds
2 respectively, and adding the results, we obtain the equawhere s is the length of the line up to the point x, y, z, is tioncalled a vortex line. Its direction coincides at every point
da dß dg
(14). with that of the axis of rotation of the fluid.
dx dy da We may now prove the theorem of Helmholtz, that the
This is an equation of the same form with (6), which points of the fluid which at any instant lie in the same
expresses the condition of flow of a fluid of invariable vortex line continue to lie in the same vortex line during density. Hence, if we imagine a fluid, quite independent the whole motion of the fluid.
of the original fluid, whose components of velocity are a, The equations of motion of a fluid are of the forin
B, y, this imaginary fluid will flow without altering its du dV
Now, consider a closed curve in space, and let vortex
du dy dot
lines be drawn in both directions from every point of this Besides, it is in questionable scientific taste, after using curve. These vortex lines will form a tubular surface, atoms so freely to get rid of forces acting at sensible diswhich is called a vortex tube or a vortex filament. Since tances, to make the whole function of the atoms an action the imaginary fluid flows along the vortex lines without at insensible distances. change of density, the quantity which in unit of time On the other hand, the vortex ring of Helmholtz, flows through any section of the same vortex tube must be imagined as the true form of the atom by Thomson, satisfies the same.
Hence, at any section of a vortex tube the more of the conditions than any atom hitherto imagined. product of the area of the section into the mean velocity of In the first place, it is quantitatively permanent, as regards rotation is the same. This quantity is called the strength its volume and its strength,—two independent quantities. of the vortex tube.
It is also qualitatively permanent as regards its degree of A vortex tube cannot begin or end within the fluid ; for, implication, whether “knottedness” on itself or “ linked if it did, the imaginary Auid, whose velocity components ness" with other vortex rings. At the same time, it is are a, b, y, would be generated from nothing at the begin- capable of infinite changes of form, and may execute ning of the tube, and reduced to nothing at the end of it. vibrations of different periods, as we know that molecules Hence, if the tube has a beginning and an end, they must do. And the number of essentially different implications lie on the surface of the fluid mass. If the fluid is infinite of vortex rings may be very great without supposing the the vortex tube must be infinite, or else it must return degree of implication of any of them very high. into itself.
But the greatest recommendation of this theory, from a We have thus arrived at the following remarkable philosophical point of view, is that its success in explaining theorems relating to a finite vortex tube in an infinite phenomena does not depend on the ingenuity with which fluid :-(1.) It returns into itself, forming a closed ring. its contrivers “ save appearances,” by introducing first one We may therefore describe it as a vortex ring. (2.) It hypothetical force and then another. When the vortex always consists of the same portion of the fluid. Hence atom is once set in motion, all its properties are absolutely its volume is invariable. (3.) Its strength remains always fixed and determined by the laws of motion of the primitive the same. Hence the velocity of rotation at any section fluid, which are fully expressed in the fundamental equations. varies inversely as the area of that section, and that of any The disciple of Lucretius may cut and carve his solid segment varies directly as the length of that segment. (4.) atoms in the hope of getting them to combine into worlds ; No part of the fluid which is not originally in a state of the follower of Boscovich may imagine new laws of force to rotational motion can ever enter into that state, and no part meet the requirements of each new phenomenon ; but he of the fluid whose motion is rotational can ever cease to move who dares to plant his feet in the path opened up by rotationally. (5.) No vortex tube can ever pass through Helmholtz and Thomson has no such resources. His any other vortex tube, or through any of its own convolu- primitive fluid has no other properties than inertia, invaritions. Hence, if two vortex tubes are linked together, able density, and perfect mobility, and the method by which they can never be separated, and if a single vortex tube is the motion of this fluid is to be traced is mathematical knotted on itself, it can never become untied. (6.) The analysis. The difficulties of this method are enormous, but motion at any instant of every part of the fluid, including the glory of surmounting them would be unique. the vortex rings themselves, may be accurately represented There seems to be little doubt that an encounter between by conceiving an electric current to occupy the place of two vortex atoms would be in its general character similar each vortex ring, the strength of the current being pro- to those which we have already described. Indeed, the portional to that of the ring. The magnetic force at any encounter between two smoke rings in air gives a very point of space will then represent in direction and magni- lively illustration of the elasticity of vortex rings. tude the velocity of the fluid at the corresponding point of But one of the first, if not the very first desideratum in the fluid.
a complete theory of matter is to explain—first, mass, and These properties of vortex rings suggested to Sir William second, gravitation. To explain mass may seem an absurd Thomsoni the possibility of founding on them a new form achievement. We generally suppose that it is of the of the atomic theory. The conditions which must be essence of matter to be the receptacle of momentum and satisfied by an atom are permanence in magnitude, capa- energy, and even Thomson, in his definition of his primibility of internal motion or vibration, and a sufficient tive fluid, attributes to it the possession of mass. But amount of possible characteristics to account for the differ- according to Thomson, though the primitive fluid is the ence between atoms of different kinds.
only true matter, yet that which we call matter is not the The small hard body imagined by Lucretius, and adopted primitive fluid itself, but a mode of motion of that primiby Newton, was invented for the express purpose of ac
tive fluid. It is the mode of motion which constitutes the counting for the permanence of the properties of bodies. vortex rings, and which furnishes us with examples of that But it fails to account for the vibrations of a molecule as permanence and continuity of existence which we are revealed by the spectroscope. We may indeed suppose accustomed to attribute to matter itself. The primitive the atom elastic, but this is to endow it with the very pro- fluid, the only true matter, entirely eludes our perceptions perty for the explanation of which, as exhibited in aggre- when it is not endued with the mode of motion which gate bodies, the atomic constitution was originally assumed. converts certain portions of it into vortex rings, and thus The massive centres of force imagined by Boscovich may renders it molecular. have more to recommend them to the mathematician, who In Thomson's theory, therefore, the mass of bodies has no scruple in supposing them to be invested with the requires explanation. We have to explain the inertia of power of attracting and repelling according to any law of what is only a mode of motion, and inertia is a property of the distance which it may please him to assign. Such matter, not of modes of motion. It is true that a vortex centres of force are no doubt in their own nature indivisible, ring at any given instant has a definite momentum and a but then they are also, singly, incapable of vibration. To definite energy, but to show that bodies built up of vortex obtain vibrations we must imagine molecules consisting of rings would have such momentum and energy as we know many such centres, but, in so doing, the possibility of these them to have is, in the present state of the theory, a very centres being separated altogether is again introduced difficult task.
It may seem hard to say of an infant theory that it is I "On Vortex Atoms,” Prog Roy. Soc. Edin., 18th February 1867. bound to explain gravitation. Since the time of Newton,
the doctrine of gravitation has been admitted and ex- | them, so that a very small proportion of the corpuscules pounded, till it has gradually acquired the character rather are stopped even by the densest and largest bodies. We of an ultimate fact than of a fact to be explained.
may picture to ourselves the streams of corpuscules coming It seems doubtful whether Lucretius considers gravita- | in every direction, like light from a uniformly illuminated tion to be an essential property of matter, as he seems to sky. We may imagine a material body to consist of a conassert in the very remarkable lines
geries of atoms at considerable distances from each other, “ Nam si tantundem est in lanæ glomere, quantum
and we may represent this by a swarm of insects flying in Corporis in plumbo est, tantundem pendere par est :
the air. To an observer at a distance this swarm will be Corporis officium est quoniam premere omnia deorsum." visible as a slight darkening of the sky in a certain quarter. - De Rerum Natura, i. 361.
This darkening will represent the action of the material If this is the true opinion of Lucretius, and if the down-body in stopping the flight of the corpuscules. Now, if the ward flight of the atoms arises, in his view, from their own proportion of light stopped by the swarm is very small, two gravity, it seems very doubtful whether he attributed the such swarms will stop nearly the same amount of light, weight of sensible bodies to the impact of the atoms. whether they are in a line with the eye or not, but if one The latter opinion is that of Le Sage, of Geneva, pro- of them stops an appreciable proportion of light, there will pounded in his Lucrèce Newtonien, and in his Traité not be so much left to be stopped by the other, and the de Physique Mécanique, published, along with a second effect of two swarms in a line with the eye will be less treatise of his own, by Pierre Prevost, of Geneva, in than the sum of the two effects separately. 1818.1 The theory of Le Sage is that the gravitation Now, we know that the effect of the attraction of the sun of bodies towards each other is caused by the impact of and earth on the moon is not appreciably different when streams of atoms flying in all directions through space. the moon is eclipsed than on other occasions when full These atoms he calls ultramundane corpuscules, because he occurs without an eclipse. This shows that the conceives them to come in all directions from regions far number of the corpuscules which are stopped by bodies of beyond that part of the system of the world which is in the size and mass of the earth, and even the sun, is very any way known to us. He supposes each of them to be so small compared with the number which pass straight small that a collision with another ultramundane corpus-through the earth or the sun without striking a single cule is an event of very rare occurrence. It is by striking molecule. To the streams of corpuscules the earth and the against the molecules of gross matter that they discharge sun are mere systems of atoms scattered in space, which their function of drawing bodies towards each other. A present far more openings than obstacles to their rectilinear body placed by itself in free space and exposed to the flight. impacts of these corpuscules would be bandied about by Such is the ingenious doctrine of Le Sage, by which he them in all directions, but because, on the whole, it endeavours to explain universal gravitation. Let us try to receives as many blows on one side as on another, it cannot form some estimate of this continual bombardment of thereby acquire any sensible velocity. But if there are ultramundane corpuscules which is being kept up on all two bodies in space, each of them will screen the other sides of us. from a certain proportion of the corpuscular bombardment, We have seen that the sun stops but a very small fracso that a smaller number of corpuscules will strike either tion of the corpuscules which enter it. The earth, being a body on that side which is next the other body, while the smaller body, stops a still smaller proportion of them. number of corpuscules which strike it in other directions The proportion of those which are stopped by a small remains the same.
body, say a 1 fb shot, must be smaller still in an enormous Each body will therefore be urged towards the other by degree, because its thickness is exceedingly small compared the effect of the excess of the impacts it receives on the with that of the earth. side furthest from the other. If we take account of the Now, the weight of the ball, or its tendency towards the impacts of those corpuscules only which come directly from earth, is produced, according to this theory, by the excess infinite space, and leave out of consideration those which of the impacts of the corpuscules which come from above have already struck mundane bodies, it is easy to calculate over the impacts of those which come from below, and the result on the two bodies, supposing their dimensions have passed through the earth. Either of these quantities small compared with the distance between them.
is an exceedingly small fraction of the momentum of the The force of attraction would vary directly as the product whole number of corpuscules which pass through the ball of the areas of the sections of the bodies taken normal to in a second, and their difference is a small fraction of the distance and inversely as the square of the distance either, and yet it is equivalent to the weight of a pound. between them.
The velocity of the corpuscules must be enormously greater Now, the attraction of gravitation varies as the product than that of any of the heavenly bodies, otherwise, as may of the masses of the bodies between which it acts, and easily be shown, they would act as a resisting medium inversely as the square of the distance between them. opposing the motion of the planets. Now, the energy of a If, then, we can imagine a constitution of bodies such that moving system is half the product of its momentum into its the effective areas of the bodies are proportional to their velocity. Hence the energy of the corpuscules, which by masses, we shall make the two laws coincide.
Here, then, their impacts on the ball during one second urge it towards seems to be a path leading towards an explanation of the the earth, must be a number of foot-pounds equal to the law of gravitation, which, if it can be shown to be in other number of feet over which a corpuscule travels in a second, respects consistent with facts, may turn out to be a royal that is to say, not less than thousands of millions. But road into the very arcana of science.
this is only a small fraction of the energy of all the impacts Le Sage himself shows that, in order to make the effec- which the atoms of the ball receive from the innumerable tive area of a body, in virtue of which it acts as a screen streams of corpuscules which fall upon it in all directions. to the streams of ultramundane corpuscules, proportional to Hence the rate at which the energy of the corpuscules the mass of the body, whether the body be large or small, is spent in order to maintain the gravitating property of a we must admit that the size of the solid atoms of the body single pound, is at least millions of millions of foot-pounds is exceedingly small compared with the distances between per second. See also Constitution de la Motière, &c., par le P. Leray, Paris,
What becomes of this enormous quantity of energy? If 1869.
the corpuscules, after striking the atoms, fly off with a