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=E2=86=90Par= t=20 I | On =
some=20
Dynamical Conditions applicable to Le Sage's Theory of=20
Gravitation by |
P= art=20 III=E2=86=92 |
Preston, Samuel Tolver (1877), = =E2=80=9COn some=20 Dynamical Conditions applicable to Le Sage's Theory of = Gravitation, No.=20 II=E2=80=9D, Philosophical Magazine 4: = 364-375 |
No. II[1]
1. THE explanation of gravitation has now risen to the rank of one of = the=20 foremost problems of modern science; indeed the day for the ascription = of occult=20 qualities to matter is now gone, and phenomena, demand an explanation by = the=20 reason. The ascription of an occult quality, so far from throwing light = upon a=20 phenomenon, only serves to darken it. The effects of gravity (like all = other=20 physical effects) being effects of motion, have, like other physical = effects, to=20 be explained. A rational explanation has to be given for the motion of = approach=20 of two masses. If we were to make an exception of this case, it might be = argued=20 that we might make an exception of other cases; and since all = physical=20 effects are effects of motion, we should thus in principle have nothing = to=20 explain at all.
2. The absolute necessity for giving an explanation of gravity being=20 admitted, we may inquire what has hitherto been done in this respect. = The=20 only theory worthy of serious consideration, or which has stood = any test=20 at all, is the theory put forward by Le Sage of Geneva. An immense = advance in=20 dynamics has been made since his day. It therefore behoves any one to = ask how=20 far the principles put forward by him admit of being improved and = modified=20 according to modern advances in dynamics.
3. To any one who has carefully read Le Sage's theory,[2]=20 it will be evident that the theory consists mainly in a series of = postulates or=20 conditions arbitrarily assumed so as to be adapted to produce the = results=20 required. Le Sage assumed (1) the movement of streams of particles = coming from=20 an indefinite distance in space and converging towards the visible = universe. He=20 even calculates (by a given velocity of motion) the distance those = particles=20 would require to have come which produce gravitation, at a remote epoch = of=20 10,000 years (page 22). He therefore calls the particles, from the = enormous=20 distance he supposes them to come, "ultramundane particles." Next = he=20 assumes, quite arbitrarily, that the particles move uniformly or = equally in=20 all directions, this being necessary in order that the action [365] = of=20 gravity may be equal in all directions. He computes (roughly at about = 3,000,000)=20 the number of different directions in which separate streams of = particles would=20 require to be moving in order to produce everywhere that sensible = uniformity of=20 pressure which is the characteristic of gravity (page 25). It will be = noted that=20 these are all assumptions in themselves entirely arbitrary. He next = assumes that=20 the mean velocity of the streams of particles is everywhere the = same, and=20 the density everywhere the same.
4. It will be observed that this theory gives no possible idea as to = how such=20 a motion of streams of particles among themselves could be kept up, or = naturally=20 maintained. Le Sage attempts to evade the difficulty of the particles=20 encountering each other by assuming them to be so small that "not more = than one=20 out of every hundred of the particles meets another during several = thousands of=20 years." This only removes the difficulty a step further on, without = avoiding it.=20 Indeed it may be observed that the theory, in the state in which Le Sage = left=20 it, is little more than a series of postulates, some of them almost as=20 unrealizable as gravity itself. This does not detract from a distinct = merit in=20 the origination of the theory; for it must be remembered how little = dynamical=20 principles were advanced at Le Sage's time, and how few resources he had = to draw=20 upon.
5. I have pointed out (Phil. Mag. Sept. 1877) what (whether already = observed=20 by others or not) cannot but be regarded as a somewhat startling fact, = viz. that=20 no postulates whatever are required for a dynamical theory of = gravitation, but=20 that it may be shown that particles of matter in free motion in space = must=20 inevitably of themselves arrange their motions so as to produce the = effects of=20 gravity =E2=80=94 or the special effects of gravity (variation as the = square of the=20 distance &c.) must be produced from pure dynamics in the case of a = system of=20 particles in free motion in space, without any necessity for postulates = as to=20 the character of the motion at all. This follows from the principles = which have=20 been investigated in connexion with the modern kinetic theory of gases, = of which=20 Le Sage was ignorant. For it has been demonstrated by Professor Maxwell, = in=20 connexion with the kinetic theory of gases, that particles of matter in = free=20 collision among each other in space will automatically arrange = their=20 motions so as to move uniformly in all directions, i. e. so that = an equal=20 number of particles are moving in any two opposite directions (this = being the=20 necessary condition for equilibrium of pressure in a gaseous medium[3]).=20 This character [366] of motion, it may be observed, is the first = important=20 condition required by Le Sage's theory =E2=80=94 which condition = therefore follows as a=20 rigid dynamical fact, not as an arbitrary postulate, as he made it. This = motion=20 of the particles uniformly or equally towards all directions is = not a=20 mere chance fact, but a rigid adjustment, of such a character that when = by any=20 artificial means this mode of motion of the particles is disturbed they = will=20 automatically, of themselves, return back to this regular form of = motion=20 (i. e. so that an equal number of particles are moving in all = directions'). The=20 other conditions put forward as postulates by Le Sage, viz. that the = density of=20 the streams of particles should be the same in all parts, and the = mean=20 velocity the same in all parts, are equally necessary results following = from the=20 kinetic theory of gases =E2=80=94 not, therefore, postulates at all.
6. The only further condition required is that the mean length of = path of the=20 particle, before being intercepted by collision with each other, should = be great=20 enough to produce the effects of gravity =E2=80=94 i. e. so that the = particles of the=20 medium may act as streams upon masses immersed in the medium, or may = stream past=20 two opposed masses, which by their mutual screening or sheltering action = produce=20 the observed effects of gravity. The mean length of path of a particle = depends=20 (as is known) upon its size. One size of particle is not =C3=A0 = priori more=20 likely than another. By simply, therefore, making the particles small = enough,=20 any mean path, however great, may be attained. We thus observe that all = the=20 arbitrary postulates of Le Sage's theory, together with all the effects = of=20 gravity, naturally and inevitably follow from the simple admission of = the=20 existence of matter in space whose normal state is a state of motion, or = the=20 existence of a medium in space constituted according to the kinetic = theory of=20 gases. In this way the mode in which the motion of the streams of = particles=20 through each other is naturally kept up in a state of dynamical = equilibrium, is=20 quite easily explained.
7. Here we do not want an indefinite waste of matter, or an = indefinite supply=20 of matter from ultramundane space (as Le Sage imagined) to produce = gravity, but=20 gravity is produced by matter or a medium which as a whole is = stationary,=20 and whose internal motion is kept up and perfectly naturally maintained = by the=20 rigid laws of dynamics. The difficulty of the collisions is here = completely got=20 over; for the collisions of the particles among each other, so far (as = Le Sage=20 supposed) [367] from interfering with the uniformity of their motions, = is the=20 very condition which corrects and maintains the uniformity of = motion in=20 opposition to external disturbing causes. This is the main point which = was=20 utterly inexplicable in Le Sage's theory; for it was impossible to see, = in the=20 way he put it, how such a motion of streams of particles should be kept = up=20 uniformly in all directions, under continual collisions with themselves = and with=20 mundane matter. By the application of the principles of the modern = kinetic=20 theory of gases to the case, this point is completely solved. As before=20 remarked, it is almost startling that the particular form of motion = which the=20 particles themselves automatically keep up should be precisely that one = which is=20 required to produce gravity (or an effect varying as the square of the = distance=20 &c.), =E2=80=94 also that it should make the density and = mean velocity=20 equal in all parts, which is necessary for the effects of gravity.[4]
8. It is an interesting fact to observe that the distance through = which=20 gravity will act will depend on the range through which the streams of = particles=20 are comparatively unimpeded, i. e. on the mean length of path of the = particles.=20 By making, therefore, the mean length of path of the particles loss than = the=20 average distance of the stars, it would follow that the stars do not = gravitate=20 towards each other, which satisfies the condition for the stability of = the,=20 universe. It is evident (as has been already pointed out by others) that = the=20 assumption of all the bodies of the universe gravitating towards each = other is=20 quite inconsistent with stability; and to the truly philosophical mind = any=20 theory which rendered such an assumption of instability necessary would = be in=20 itself improbable. It is only necessary that the mean length of path of = the=20 particles be great enough to produce effects of gravity throughout [368] = the=20 greatest range in which we have observed them, which is but an = infinitesimal=20 fraction of the distance of the stars.[5]
9. It may perhaps be well just to sketch here the mode of action of = the=20 medium in producing gravity, the manner in which the intensity is made = to vary=20 as the square of the distance, &c. Let A (in the annexed = diagram)=20 represent a molecule or mass; let C represent the bounding surface of an = imaginary hollow sphere described about A. Then, since the particles of = the=20 medium are moving uniformly in all directions, a number of them will be = passing=20 in all directions through the imaginary spherical surface C. Only those=20 particles which are passing (sensibly) along the radii of the spherical = surface=20 will strike A; and therefore we need only regard those special particles = which=20 radiate towards A. The molecule A being therefore struck equally on all = sides,=20 will accordingly remain at rest. But if now we suppose a second molecule = to be=20 placed at B, then out of the whole number of particles which are = directed=20 towards A, the molecule B will intercept a number which is proportional = to the=20 area which B cuts off from the whole spherical area C. The molecule A = will=20 therefore now, owing to the sheltering power of B, be struck with a = fewer number=20 of particles in the direction B A. The balance of the pressure being = thus upset,=20 A will be propelled towards B. The same holds true of B relatively to A = (on=20 drawing the imaginary spherical surface C'). The two molecules A and B = are=20 therefore propelled towards each other mutually. It now remains to = illustrate=20 how the impulsive action varies as the square of the distance. It = will be=20 at once evident that since the area of a spherical surface is as the = square of=20 the radius, therefore, if B [369] were removed to a double distance, the = imaginary spherical surface described through B with A as a centre, = would have=20 four times the area; but the area of the molecule B remaining constant, = B would=20 therefore only shelter A one fourth the amount it did before; and = accordingly A=20 would be impelled towards B with one fourth the force, =E2=80=94 the = same being true of=20 B relatively to A.
10. It is found that gravity is proportional to mass. It must = therefore be=20 assumed that, owing to the porosity of bodies, or open structure of the=20 molecules, the gravific medium ( whose particles are extremely minute) = can=20 penetrate freely into the interior of bodies, and thus act upon the = internal=20 molecules, so that the total effect is proportional (sensibly) to the = number of=20 molecules, or gravity is proportional to mass. Of course this could not = hold=20 true with an infinite mass; but it is rigidly demonstrable (by a given = degree of=20 porosity) that it could hold true with as near a degree of approximation = as=20 experience has shown, and even nearer if necessary. Independent physical = reasons=20 tor inferring this extreme porosity or permeability of matter will be = given=20 further on.
11. My main object in this paper is to meet all possible objections = which=20 have been or might be urged against this theory, as, if it be true, it = ought to=20 stand against all criticism; and if, on the other hand, it be erroneous, = the=20 sooner it is demonstrated so the better. It may just be remarked, in the = first=20 place, that in principle there appears to be no other theory = conceivable=20 which at all would satisfy the conditions of gravity. Gravity can be = referred to=20 two conceivable causes : =E2=80=94 (1) to a motion possessed by the = molecules of=20 matter themselves, disturbing the equilibrium of pressure of the = surrounding=20 medium; (2) to an independent motion of the medium itself acting upon = the=20 molecules. The first of these two conditions appears to be inadmissible; = for if=20 gravity were due to a motion of the molecules of matter, then since we = can=20 readily modify or interfere with the motion of the molecules of matter = (as by=20 heat), we could thereby interfere with gravity. The fact, therefore, = that it has=20 been found impossible to interfere with gravity, points to a motion in = the=20 external medium (which is beyond our control) as the cause. It would be = well to=20 keep this fact in view before lightly regarding Le Sage's theory as a = mere=20 hypothesis. To the careful observer it will appear to contain = rather the=20 essence of a necessary fact, from the absence of (in principle) = any other=20 conceivable cause; and if the theory can be shown to be a practical one, = consistent with admitted mechanical principles, it will have every = condition for=20 acceptance. To us it seems that a closer study of the theory only serves = to show=20 its [370] many mechanical beauties and extreme simplicity as a means to = an end,=20 satisfactory, not only in the absence of any other conceivable cause, = but as=20 affording a perfectly rational conception to the mind of the processes = by which=20 the effects are brought about.
12. The most difficult thing perhaps at first sight is to = conceive the=20 great permeability or porosity of matter necessary to this theory. It = may be=20 perhaps just noted in passing, that most truths are strange at = first=20 sight, or else it would be competent for any one to arrive at them. = I think=20 it may be shown that this open structure of matter is a thing in itself=20 probable, and also distinctly warranted on independent grounds. In = architectural=20 and engineering structure generally we do not observe a solid block = formation,=20 if I may so express it, but that open structure which is essential to = elasticity=20 and strength. So in molecular architecture, we may not expect to find a = mass a=20 solid block, but of open structure, though we naturally cannot = see the=20 interstices. Again, the perfectly free passage of light or the waves of = aether=20 through a piece of glass, or a wave of obscure heat through a block of=20 rock-salt, also of the magnetic disturbance through all matter, would by = itself=20 prove the extremely open structure of matter. There is therefore no = difficulty=20 in admitting the openness of structure of matter essential to the = dynamical=20 theory of gravitation, as this is in itself a natural thing, pointed to = by other=20 facts.[6]
13. The next difficulty is one pointed out by Professor Maxwell in a = notice=20 of Le Sage's theory (Encycl. Brit. 1875, page 46, under the word "ATOM").=20 The argument there is that, in view of the demonstrated fact that = particles of=20 matter in collision with each other tend to acquire the same = kinetic=20 energy, therefore the kinetic energy of a molecule of ordinary matter = would=20 ultimately tend to become equal to that of a gravific particle, and that = therefore it would appear that the continual impacts of the particles of = the=20 gravific medium would necessarily raise matter to an enormous = temperature, as=20 the velocity of the gravific particles must of necessity be assumed = extremely=20 high. This objection would seem to have considerable weight; but I think = it=20 admits of being surmounted on taking certain facts into consideration. = It will=20 be admitted that, in order to produce gravity, it is only necessary = [371] that=20 not less than a certain total of energy should be contained in a = given=20 volume of the gravific medium, not that thereby the energy of = each=20 particle should necessarily be great. The energy of each particle (whose = sum=20 produces a given total of energy) would evidently depend on the number = of=20 particles in unit volume. Professor Maxwell assumes that it is = "tolerably=20 certain that N, the number of (gravific) corpuscles which are at any one = time=20 within unit of volume, is small compared with the value of N for the = molecules=20 of ordinary bodies." Now we may ask, is this certain or = necessary?=20 for the whole hinges upon this. If, on the contrary, the number of = gravific=20 particles in unit volume were not restricted, then by adding to the = number of=20 particles, and thus subdividing the total energy among them, the energy = of each=20 particle might be made indefinitely small. It might possibly be thought = that=20 such a number of particles would be inconsistent with a long free path. = But if=20 the subject be considered, it will be observed that a free path of given = adequate length may be obtained with an indefinite number of particles, = provided=20 the particles be minute =E2=80=94 or that, no consequence how numerous = the particles=20 (and therefore how small the energy of each), an adequate mean path can = be got=20 by reducing their size, their velocity being augmented so as to keep the = energy=20 in unit of volume constant. This high velocity of the particles may be . = shown=20 on other grounds to be a likely condition; for by this means the whole = medium is=20 rendered completely impalpable, or its presence vanishes from the senses = =E2=80=94 the=20 medium opposing no measurable resistance to the passage of bodies = through it.=20 Accordingly, as by a given amount of energy in unit volume the energy of = each=20 particle is inversely as their number, so by multiplying the particles = the=20 energy of each may be made indefinitely small; and therefore the energy=20 transferred to the molecules of matter would be made indefinitely small, = or=20 there would be no measurable rise of temperature at all. This, I submit, = removes=20 the difficulty in question.
14. It was pointed out by Le Sage that, in order to explain gravity, = it is=20 necessary to assume that the gravific particles rebound from the = molecules of=20 matter at a less velocity than they strike. Since, after the average = kinetic=20 energy of a molecule of matter has become at least equal to that of a = gravific=20 particle, no further transference of energy can take place from the = gravific=20 medium to matter (i. e. of course in the case of matter at rest), it is=20 necessary therefore to explain the diminished velocity of rebound of the = gravific particles. Sir William Thomson (Phil. Mag. May 1873) has = pointed out=20 that this may be a natural consequence of a difference of elastic = rigidity [371]=20 between the gravific particles and the molecules of matter. There may = possibly=20 be some who may be inclined to think that this explanation was somewhat = forced,=20 or was warranted only as explaining that special case, without being=20 independently likely. I think that, on considering the subject, it will = be found=20 that the explanation is in itself highly probable on independent = grounds. Where=20 do we find substances in nature whose elastic rigidity is the = same. It=20 would be in the highest degree unlikely that portions of matter = differing so=20 vastly from each other in dimensions as a molecule and a gravific = particle=20 should have the same elastic rigidity. If the elastic rigidity be = not the=20 same, it is a strict dynamical fact, not a supposition, that the energy = of the=20 particle after its rebound from a molecule, though the same in air omit, = will=20 not be the same in kind as before; but if the elastic rigidity of the = large=20 molecule be greater than that of the minute particle, a part of the = translatory=20 motion of the particle will be shivered into vibratory motion at the = encounter;=20 and therefore the particle will rebound with a less translatory motion, = the=20 deficiency of translatory motion representing the amount converted into=20 vibratory motion at the encounter. It is just as if a tuning-fork, a = flexible=20 ring, or any pliable elastic object whatever, were thrown against a hard = body=20 (say the hard surface of an anvil), when the body will rebound at a less = translatory motion than it struck, the deficiency of translatory motion = being=20 compensated for by an accession of vibratory motion. So with a gravific = particle=20 striking a molecule of matter; for mere size makes no difference in the=20 principle. It is therefore not an unnatural thing (but highly probable = on=20 independent grounds) that the gravific particles should have their = velocities=20 changed at impact against the molecules of matter. The energy of the = particle=20 remains unaltered by the impact; only the distribution of the energy in = the=20 particle is changed.
15. The next question is, Do the particles which have thus lost = translatory=20 motion and acquired an accession of vibratory motion, recover their = normal=20 proportion of translatory motion to vibratory motion again? It has been = pointed=20 out by Sir William Thomson that this must be the case. For it has been=20 demonstrated by Professor Clausius, in connexion with the kinetic theory = of=20 gases, that, in the case of a system of particles in free collision = among=20 themselves, the relation of the translatory motion to the vibratory = motion tends=20 to assume a constant value, so that when this relation is disturbed in = any way=20 it is again restored. 80, therefore, when the relation of the = translatory motion=20 to the vibratory motion of the gravific particles is disturbed by = collision with=20 the molecules of matter, this relation [372] is again restored to its = normal=20 value by the collisions of the particles among themselves. This, it may = be=20 observed, is therefore a rigid dynamical fact, not an hypothesis.
16. There is therefore no expenditure of energy or work whatever in = the=20 maintenance of gravity, since the; total amount of energy in the = particle is=20 unaltered by collision. Also no supply of energy to the gravific = particles is=20 required, since a state of motion is as natural as a state of rest. = Further, no=20 supply or waste of matter is required for the maintenance of gravity. Le = Sage=20 imagined that a continual supply of matter from ultramundane space was=20 necessary. He endeavours to get over this incongruous idea by making the = excuse=20 "that nature makes frequently such waste" (page 108). This is evidently = no=20 satisfactory excuse at all; in fact Le Sage, with the limited knowledge = of his=20 day, naturally could not get over the difficulty of the collisions, or = could not=20 form an idea of the conditions of equilibrium of streams of particles of = matter=20 moving in the way he assigned. With our modern knowledge we may deduce = that the=20 conditions of equilibrium of such streams of particles are of a = perfectly=20 definite character, so as to produce gravity as an inevitable fact. The = gravitic=20 medium, therefore, within the bounds of the visible universe is as a = whole at=20 rest; and no supply of matter whatever is required. The medium producing = gravity=20 is simply a medium constituted as a gas according to the kinetic theory = =E2=80=94 but=20 quite exceptional in character as regards the extreme minuteness of its=20 particles, their extremely high velocity, and long mean path, the high = velocity=20 rendering the medium completely impalpable, or its presence = imperceptible to the=20 senses. It is evident that the presence of such a medium could be only = rendered=20 directly palpable to the senses by the resistance attendant on = the motion=20 of bodies in it. Now it is a known dynamical fact that this resistance=20 diminishes as the velocity of the particles of the medium increases; = hence with=20 a given velocity no resistance whatever will be felt, and therefore the = presence=20 of the medium must elude detection. These deductions are therefore in = perfect=20 harmony with the facts. The mean length of path of the particles of the = medium,=20 though great compared with that in the case of ordinary gases, may be = considered=20 small in proportion for a gaseous medium that pervades the area of the = visible=20 universe.
17. It would be a wrong idea to imagine that, because the particles = of the=20 gravitic medium are relatively very close compared with the molecules of = ordinary substances, therefore the quantity of matter forming the = gravific=20 medium must be relatively great. It is a mathematical fact that the = [374] total=20 quantity of matter contained in (say a cubic mile) of the medium might = be=20 indefinitely small, and yet the particles indefinitely close together, = provided=20 the particles are very minute. By a given velocity of the particles of a = medium,=20 the uniformity or steadiness of the pressure exerted against matter = evidently=20 does not depend on the size of the particles, but on their closeness = (which=20 determines the rapidity of succession of the collisions against matter). = By a=20 given proximity of particles, therefore, no consequence how minute they = may be (=20 and therefore how small the quantity of matter composing the medium), = the=20 pressure will remain equally steady. It follows, therefore, that a = medium may=20 produce all the uniformity of pressure due to the flow of a continuous = fluid,=20 and yet the quantity of matter composing the medium may be indefinitely = small.=20 Owing to the frequency of the collisions against matter, due to the = close=20 proximity of the particles of the gravific medium and their high = velocity, the=20 pressure exerted by the medium is so even and regular as to be = imperceptible to=20 the senses, excepting in the effect "gravity." The pressure termed = "gravity" due=20 to the motion of the particles of the gravific medium is no more = difficult of=20 realization than the pressure of the air due to the motion of its = molecules. To=20 get a true idea of the nature of the gravific medium, the conception of = extreme=20 closeness of arrangement of the particles, combined with extreme rarity = of the=20 medium, must be kept in view. It la easily conceivable, for example, = that the=20 particles of a cubic foot of the medium may be in very much closer = proximity=20 than the molecules of a cubic foot of lead (from centre to centre), and = yet the=20 total quantity of matter contained in a cubic foot of the medium may be = less=20 than that contained in a single molecule of lead.
18. The agent producing gravity must therefore not in any way be = looked at=20 (as one might possibly be liable to do at first sight) as representing a = prodigious quantity of streams of gross matter flying about, but simply = as the=20 quiet imperceptible motion of a relatively very small quantity of = excessively=20 finely subdivided matter which produces a perfectly uniform pressure, = the energy=20 of each particle by itself being totally imperceptible; or only the = resultant=20 effect or pressure is noticed, the inexorable motion of the particles = (and the=20 resultant effect "gravity") being as incapable of being interfered with = as the=20 conservation of energy itself. Surely no more rigid, constant and = unalterable=20 cause could be conceived of than that of the normal motion of the = particles of a=20 medium among themselves, which, by an inevitable automatic adjustment = arrange=20 their motions so as to produce the effects of gravity. "Gravity" [375] = is=20 distinguished by its unalterability under the influence of heat, and = general=20 constancy under all conditions. Could a more constant cause be imagined = than the=20 above? and could a more simple one be desired? or could any other means = of=20 satisfying all the conditions of the problem be conceived of? If = simplicity be a=20 mechanical recommendation, the simplicity of the above conditions will = recommend=20 themselves. We say simplicity; for surely we have the ne plus = ultra of=20 simplicity, when no postulates at all are required, but the total sum of = effects=20 may be said simply to evolve themselves out of pure dynamics.
London, October 1877.
This=20
work is in the public =
domain in=20
the United States because it was published before January =
1, 1923.=20
The author died in 1917, so this work is also in the public=20 domain in countries and areas where the copyright=20 term is the author's life plus 80 years or less. This = work may=20 also be in the public domain in countries and areas with = longer=20 native copyright terms that apply the rule of = the=20 shorter term to foreign = works. |