on the application of the law of gravitation to the atomic theory-english-gustasv theodor fechner

7/30/2019 On the Application of the Law of Gravitation to the Atomic Theory-English-Gustasv Theodor Fechner.

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On the application of the law of gravitation to the atomic theory 1)

from

MG Fechner, acad. Lecturer in Leipzig.

. l If we want to defend the view that the body is a system of atoms ormolecules 2) are, by no other force than their mutual gravitational force can be

determined to balance or to move 3) , show that we have that the really make basic

phenomena of matter and explain appropriate discordant among themselves a way to

the law of that force. We will therefore try to solve the inferior and in a later paper the

following problems:

1) How can the existence of material points (the ponderable atoms) in stable 4) are

designed distances from each other5) , if these points are solicited by no other force

than that mutual Gravitattionskraft?

2) In what ways can explain without specific concurrence repulsive forces, the

contraction and expansion of the body and the transition between the various states of

aggregation in each other simply by their mutual gravitational ponds?

3) What relationship has the so-called imponderables to the ponderable parts are

attached and how can the simultaneous changes that mutually dependent in

Ponderabilien and imponderables explained by mere effect of the law of gravitation?

1)This paper follows on from the earlier in this archive (Vol. IX. H.3. p.257.) given, and is written withreference thereto. I will not repeat the rules here Vorerinnerungen that everything shared here so long must be

considered problematic until it succeeds an exact mathematical analysis, to take possession of the same, butthis seems to still be subject to insurmountable difficulties.

2)The most appropriate it seems to me, the body atoms off towards the analogy of the heavenly bodies (which

one might think as atoms of a larger body) not yet present as absolutely indivisible, but as indivisible inrelation to each other, insofar processes between them as between the whole and nothing Ponderables proceed

from one to the other passes. This analogy is here provisionally established, incidentally develop even more bythe following.

3)The fact that the atoms are subject to the laws of gravity, is actually a conclusion which, gravitational law is

itself justified as essential to the nature of the generally applicable to any size and smallness of material massesthat only certain, in the experience of reasoned evidence to the contrary Us likely to cause this Act to limit

material mass limits for certain. However, this would mean setting a conflict between experience and

mathematics, nowhere else instead finds, and how it would be possible, upon receipt of such a limitation, but tobe calculated by integration of the gravity effect of the smallest particles, the gravity effect of a whole body,

however, is always still open the possibility that, besides the gravity at the atoms still other forces can occur,

which surpassed the effect of that. However, the adoption of such vires occultae we might only be justified ifthere would be no way to explain the phenomena of matter by forces that are essential to it as such, what is to

be tried just here.

4)Or those distances where only the atoms oscillate to some extent to the principles of their mutual

equilibrium, because in fact we will be led to such.

5)Taking time to atoms, as does, in fact, the compressibility and expandability of the body and the ratio of the

different aggregate states to each other, an assumption of varying distances (but for the same condition of the

body are stable) is essential. The difficulty of explaining this by mere attraction forces, has been one of themain causes for the adoption of repulsive forces until now.


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. 2So much can see that a quiet distance of all the atoms of a body by mere

attraction forces would be inexplicable without extensive deduction. In fact, we

consider one of 5 identical, same distance in a straight line disponierter

atoms a, b, c, d, eAlthough existing row, then the average atomic cdoes not change

its place, because the attractions from both sides are equal: but to the lying by atomsmust move towards the ends of the middle and can not rather come to rest until they

are all come to the touch.

Understandably, such a shape must also be done in any other system of movement

of atoms, because the attraction than can compensate for some of the same in

opposite directions in the middle. But not necessary, that, when the atoms are other

than an initial rectilinear disposition which we set up by their mutual attraction to the

close contact, but this is merely to be the case for certain special cases. In general, if

three or more mutually attracting bodies are present, it will not even require a

deflecting pulse to keep this body of approximation to the touch, for it may always be

two of them strive therefore moving in a straight line one after the other: but at the

same time attracting third mass they constantly distract from this straight line and act

as each mass continuously disruptive to the approach of any two others. If now is not

the central forces of attractions and already attained speeds of movement of all

masses come together in some time on one point, which can only happen in some

cases initial motion circumstances, it is a continuous, though variable, or, as we may

call it, moving away the same may take up to infinity 6) .

6) It can be a thereto, if not fruitful, but making interesting remark. Two atoms are by itself not capable of

continuous movement and determine if they are held by a foreign power at a distance from each other only bytheir numbers always a straight line. Three or more atoms are sufficient to elicit an indefinitely lasting

movement by themselves and determine their number at any time by a curved line. Should this not in aUPHOLSTERY the binary composition of lifelessness and rectilinear form of inorganic bodies on the one hand

and on the other hand, are ternary or multiple composition, the internal automatic lively exchange and the

curvilinear shapes of the organic body?

. 3Thus we see that although a permanent but constantly changing, removal of

atoms by virtue of mere attraction of the same is probably possible. However, we are

not entitled to introduce us, as for example a crystal as a kind of fermenting mass,where each atom moving to a ponderables all other atoms and each other they would

contribute to determine the movement, but rather we can all conclude that the

ponderable atoms with the same body condition in relatively fixed positions, most

with no noticeable oscillations are located at the positions of their balance with each

other, and so the experience seems even the way we think to contradict a sole

effective attraction, and it has, in fact, of this point of the matter until now always

considered. But it is still, until now ignored retarded, left case in which we can find

the solution to our problem. To him we now turn.

There can be masses of systems thinking in which to rest (little or oscillation) of a

part of these masses and continuous movement of the other part of these masses are


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mutually interdependent.

From this proposition from whose discussion will follow immediately, seems to me

the rest of the ponderable atoms in the bodies by a duly combined movement of the

imponderabeln atoms 7) in full compliance with both the nature of the law of

gravitation itself, than to explain the phenomena.

7) Only figuratively and because of the distinction, however they can still carry the name of imponderable

atoms, as their attraction as well as the coming of the other into account. We will in the following often thanplanetary atoms, in contrast to the ponderable or solar atoms which constitute, so to speak, the skeleton of the

ponderable mass, respectively.

. 4In fact, we want to show only that such an arrangement of matter for individual

rest masses is generally required for movement of the other, and then, as by the action

of attraction law itself such arrangements, the first sight after only a very special

hardly possible in reality, cases might appear to be caused most likely by themselves.

Suppose we have two more (solar or ponderable) atomsA ,B , in PL 111 fig. 1st

round which closed paths in an indefinite number of smaller (or so-called planetary

imponderable) atoms 8) a , b , c ..... moving in such a way that at any time a greater

number of them in the common scale ofA andB , as would run through their

clearance 9) , these planetary atoms, whileA andB are by virtue of their peculiar

attraction strive to approach this approximation counteracted by the

massesA andB attract to itself and it would balance forA andB can exist if the ratio

of the mass sizes and distances of all solar and planetary atoms would be measuredand would (through reciprocal compensation) during the movement that the sum of

the attractions which the masses a , b , c , d, e to the side where they are located

onA voice, always in balance would remain with the sum of attractions, which

according to the opposite direction off,g, h , i , k, l, m , n , and the other

resting 10) massB are expressed. Now, however, should such a strict balance of

massesA andB in order seldom or never take place during the whole revolution of

the planetary masses. Will be the further considerations that the movement of

planetary atoms to the solar so arranges to allow only small oscillations of the

approach and the same distance but most probably11)

, so it seems this to be almost anecessary consequence of the law of attraction. However thereof afterwards.

8) Hard light, heat, electricity.

9) This is, for example in Figure l after the nature of the tracks listed there instead, whereas in Fig 4 in general,

always a same amount imponderable atoms through the gap when moving the outer space.

10) , however, is the totality of the masses a , b , c , d, e in mass against the mass sizef,g, h ...B to thedisadvantage, but an advantage in terms of proximity and nothing prevents both circumstances be compensated

. thinking By the way, seems to me the possibility that there is a sufficient number of mutually mutuallyattracting bodies, two or more of them may be in silence or approximate rest, during movement of the other,

even to brighten up the fact that it taken thoretisch, any time the expression for the rate for a certainnumber of bodies set to zero and can be derived from the equations thus resulting conditions must, whichsubstituted in the formulas for the rest of the body, the movement must determine the same as it is really


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needed this rest that body to have to follow. This requires not that the forces of each of the rest of the body tobe zero are (in which case the problem would be impossible, since the rest mass of such shape even disappear)

because of differential expression for the velocity is dv = dt, where on means the total force acting body. In

order that dv = 0 will, is merely requires that also is equal to 0. This but may as well through opposition of

the individual forces which express the remaining masses than by the disappearance of the individual forcesthemselves, ie, the masses of which they are expressed, are zero. The execution of calculations of this type but

would like to, as far as I can see the current state of the analysis are as yet insurmountable difficulties.

11) This fact leads to a surprising analogy, by engaging in such shape of the visible pulse in all of nature, thealternation of expansion and contraction, even in the nuclear realm as would find something much Grounded

again.

. 5Here we see already a way to return the repulsive effect of heat on mere

attractions. In fact, the more the Community perimeters of two solar or ponderable

atoms of the heat atmosphere, ie, increasing the mass of the moving planetary atoms,

the further they have to be pulled from each other, so that THEREFORE really this

attractive effect of heat, assimilate to the ponderable atoms, a repulsive effectbetween the ponderable atoms themselves could be 12) . By the way, it is easy to see

from the foregoing, as well as three or more masses thus can be kept at rest or lower

oscillation against each other, that in associated conditions, a greater number of

planetary masses in their area, as moved by their space, including we are a superficial

schema in Figures 2 and 3 have been 13) .

12)Here, however, have to immediately offer a variety of claims: if the imponderables to express an attractiveeffect on the ponderable atoms, they must also possess gravity, contributing to the severity of the body andmove at an accelerated rate after the earth, not all of which case appears. I believe, however, these objections in

. 15th enough to have lifted.13)

there are is used in this schemata wherever a respective, two, three atoms have common paths around, only

important to indicate the ratio of the movement in the periphery to the movement through the gap of the solar

mass, not the actual shape of the tracks, which still must include far more varied curves in it. One wouldincidentally while the inside is a an atomic system to ever, two, three or more ponderable atoms was called

jointly moving imponderable gebundne heat, which in the communal area of all, that may on the surface of the

system, call ongoing, natural electricity .

. 6In order to show but the way in which such arrangements may come to pass,

we will send forward the following observation. Imagine two solar atoms only in avery far away from each other, each of which then acts as a single center for himself

and all planetary atoms, depending on whether they come into the vicinity of one or

the other, so ellipses, parabolas or hyperbolas for describe the nature of their original

motion circumstances in such a way that when one thinks both solar atoms connected

by a straight line, generally at any time as much planetary atoms intersect the

intermediate lines, or run through the gap of the two atoms, as by its exterior, ,

though. you do not want to initially set equal to a particular distribution of the

imponderables.

Let us now imagine the same solar atoms approached infinity, then, is because they

represent a mass, no more planetary atom can cut their intermediate line, but all must


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move only in its scope.

From this it necessarily follows that if two initially very distant solar atoms

gradually approaching attraction by its own or through any cause, the planetary

atoms, which run to each of them in particular, their orbits must gradually change in

the way that they their motion, whereby they are guided between two atoms,

converted into those of which they are made merely by two atoms, or in other words,the mono central movement must with more approximation pass the attracting centers

for increasing planetary atoms in a bi-center until in total approximation, the same is

become bizentral for all, but where the two coincide centralization.

. 7 Consider now two solar or pondorable atomsA andB , which initially are in a

very great distance in a space through which a certain quantity of free flows of

imponderable indefinite directions, and assume that each of these ponderable atoms

from this free imponderable that came near him, a certain quantity of bound, ie have

determined to closed movements around. Assuming that all conditions for both atoms

were initially equal, we are the same arrangement with their imponderabeln

atmospheres by the FIG Scheme 4 can imagine.

It is easily seen that in this very large distance, where generally the same amount of

imponderable atoms, the intermediate line ofA andB must be cut as their outer space,

own imponderable atmosphere each atom without infiuence on the move because of

the attraction off,g, h , i , kofB is kept the balance toward the equal attracting the

planetary compositions a , b, c, d, e to the opposite side, thus isA definitely only by

the attraction ofB and the imponderable atmosphere to motion are determined, though

because of the huge distance with a weak force and inversely asB ofA . Both will

therefore begin to approach.

. 8 To the same extent, however, when this happens, the trajectories of the atoms

to be imponderabelnA andB in the manner indicated above must change by

modifying the schema of Figure 4 more and more into the scheme of Figure

1 converting, namely by imponderable atoms to only mono centrallyA orB could

only now beginning to be bizentral move both, and such shape is more and more

gone out of the space of the two atoms in its exterior, a part goes away in endless

lines, such as We this in our previous paper (. Vol IX, p 268) have discussed and thus

the phenomenon of convergence in each of antibody molecules released due to heator light, while at the same time some of the available free space of the imponderable,

through which the ponderable atoms move at their approach through, on the other

hand in relation to their approach an ever larger part of the two jointly, as shall be

bound by any particular.

. 9 Since these shape the ratio of the imponderable's outdoor space both

ponderable atoms with their approach increases more and more in its clearance

against, it must in a corresponding degree of return, they learn to the side facing away

from each side, always more to grow, and although the attraction of the systemA to

systemB with its approximation always growing, so can but this increase experiencedin part by the loss, both systems virtue by the release of a portion of their

imponderabeln mass whose vacant, partially compensated, but partly, and this is the


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main thing that can always be originally such a number of planetary atoms around

each of the solar atoms assume that the ratio of entering into the outer space planetary

masses is so great in the approximation to by his return, in some moments the further

approximation to prevent both;, in a word, it can cause the whole assembly, which we

. 4 as to effect stable distances of the solar atoms, by virtue of the law of gravitation

required declared. . 10 There are hereafter two ponderable atoms, they provided only a sufficient

number of planetary masses to have, which prevents the representation of phenomena

to take as anything to be able to mutual attraction not approach indefinitely, but in

some, by their own masses and the mass ratios of their planetary atmospheres certain

degree of approximation is the return of running in their common peripheral

planetary atoms keep this part of the balance and the solar or ponderable atoms are

then not closer together. But it is then no real fixes Stationary same can accept, but

the ponderable atoms are still in relation to their and their atmospheres common

center of gravity, depending on the changing situation of planetary atoms (in which,however steadily accumulating in the outer space remains mostly) back and oscillate

again within certain limits. However, these oscillations can of achievement that

GIeichgewichtspunkts to not be great, and because upon further approximation the

same once more planetary atoms occur in the outer space and thus the pondorabeln

atoms have to call back when removing the same but more atoms in the gap and

thereby re-approximation of the ponderable atoms cause.

. 11 It is clear that the boundaries where the ponderable atoms cease to approach

each other, so must occur rather, the more each atom planetary matter has to be,

because so several planetary atoms then, when approaching the ponderable or solaratoms, turn to the outside and thus express a stronger return, therefore, be, and it's

certainly not a circumstance which prevented in cases where such consistent

distances express themselves, this really attach a sufficient number of planetary

mass. On the other hand could also really nderen cases as little planetary mass to be

present, that a limit approximation of the never occurring by increasing the

approximation attraction of ponderable atoms would receive the excess weight on the

influence of altered nuclear distribution. In this case, they would generally not

approach though to touch, because they would have to be always more or less

deflected from their straight attraction through their planetary mass, but probably toeach other or their common center of gravity to move, so to speak, by would also

performed always mutually to each other.

. 12th From the above mentioned, from now until now can be a very simple

explanation of the propagation of the movement through the body and elasticity give

the same and show how they depend only on the same principle.

The fact that two pondorable atoms attract each other, but remain at a certain

degree of approximation, in case they have sufficient planetary atmospheres, requires

that in this case the influence which related with the approximation different

arrangement of the planetary atmospheres to remove both atoms manifests, increases

in a greater ratio than the influence which the approximation of the atom itself


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expresses to enhance their attraction, therefore, conversely, that upon removal of two

ponderable atoms of each other from any cause - the first influence decreases in a

greater ratio than the other14) .

14) Always presumed here that originally such a mass of planetary atoms was found that the solar atoms had to

remain stationary at a certain distance from each other.

So put two ponderable atomsAandBare by virtue of the arrangement of theirCommunity planetary atmospheres in equilibrium, but now goingAtoBapproached

by force by any force, it is in virtue of the correspondingly increasing accumulation

of planetary atmospheres, in outer space striving to rejection betweenAandBcan be

increased through. Now two cases are possible. Can eitherBevade, then it is in virtue

of the above-mentioned repulsion as much ofARemove it comes back to the

previous one, the balance required between two distance, and so, consequently, the

whole system is ofAandBby merely onAalone acting force to be moved away. The

same will be the case if pond in a system of three or more. AtomsA,B, C... a force

only onAacts that allow theBstrives to approach by herebyBto the equilibriumdistance ofAto come to the Capproaches and this is the same reason

whyBofAremote, turn the original to the distance fromBremoved, so that the shape

of such motion by the entire atom number must reproduce.

The other case is that in whichB is prevented by a resistance upon application of a

forceA to avoid. Then it is so long the force obtained in a forced state of

approximation; must now only when the forceA to the same reason in its original

distance fromB to snap back (which is done by a certain number of oscillations), out

of which in the previous case, whereB was not prevented from escaping, the same

ofA distant to the original distance.

How can we explain the course of the same principle took way made the reproduction

of motion and elasticity, no discussion will hereafter require.

. 13 A fact that should help to give weight to this theory is that each

communication of motion requires time: as it is, in fact, it is evident that the change

in atmosphere arrangement, ie, the change in the course of planetary masses which

these atmospheres composed, can not be done in one indivisible moments.

. 14 In order not to exceed the limits of the extent of matching for this journal,

memoir, I go on the continued application of, I hope now clearly present, theprinciple to other phenomena of matter to some objections which we compared

different circumstances the admissibility thereof may be found to be considered. In a

subsequent paper I think these applications, particularly in relation to

thermodynamics, the chemical phenomena and the physical states to come back, here

it is enough for me to have shown the fruitfulness of the principle for the present

purpose in general.

. 15 Our whole theory assumes that the so-called imponderables with attraction

gifted matter are the same all ponderable matter itself, merely by the relative size of

their atoms different from what makes that the ponderable atoms they decide to movearound and not vice versa. Just seems the experience of a severity of imponderables


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to contradict at all, because on the one hand an increase or decrease of which is

accompanied in a ponderable body with no bemerklichen weight change, on the other

hand seems to be displaced the light through the attraction of the earth in any

accelerated motion, as yet under would be a prerequisite for his severity of the

case. However, considering that it requires already sensitive scales to measure the

increase and decrease of the air in a solid body, but that the free imponderables inrelation to air are undoubtedly far thinner than the air at the solid bodies, so it is

easily recognize the inaccessibility of our mechanical aids to measurements of this

kind at all, more so probably because every escape of light or heat the escaping only a

small fraction of the remaining imponderable's is, as well as the mass of the comet as

it approaches the sun through the Escape the Schweifteilchen not seem to be

significantly reduced. But As for the fact that the light do not show accelerated

motion, no case motion to the earth, so the perception of such, though they in all

strictness instead would find, but with the tremendous initial velocity, which one is

compelled to assume in the light, so would the knitted impossibilities are, as I have inmy treatise on the light (XII a 2 ff this Arch.) shown by calculation.

. 16 We now turn to another objection which can be lifted only by one after the

first sight paradoxical, adoption, but which, on closer inspection by a striking analogy

to this, PERFORMING, our theory can be used to support rather because they This

analogy calls up to her existence.

Should our theory can ever find instead, they must, as we will show now, the

ponderable atoms possess many billions of times greater density and the

corresponding distances are together, as the ponderable bodies whose basis they

make, or the density of an atom will the tightness of the body in which it is received,approximately level must remain as the tightness of the sun or of Planets for leaks in

the system of a thousand and more solar systems, worein it is receivedso that such

shaping the atoms in miniature the conditions of the world body in large, with which

they are already animated by the same forces, imitate, and every body as it can be,

consider a system of numerous small, in relatively large distances from each floating

suns that are each individually or collectively several orbits of planetary atoms. It

needs no discussion that this view is much beauty, so poetic, has decreased by seems

to make life in the seemingly most steadfast and determined by the existence of all

the body by balancing the fine balance allwaltender forces. The natural philosopherwho takes possession of this view, is it a big step to press forward and perhaps

believe already justified by the beauty of so attractive inferences and by the

subsequent from all sides analogies their way; physicist abstracted but cheap of such

reasons .

. 17 Consider the fact itself, which compels us to set out the assumption of such

enormous density of atoms in relation to bodies composed of them.

It is certainly to the law of gravity that attract all bodies, two stones on earth,

therefore, to be just as good as she herself from the ground, except that the size of the

attraction of the stones with each other against the world disappears, because excess

weight of the mass of the latter. If now, you will have to close, this circumstance does


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already with two relatively even large stones that their mutual attraction can be

considered as zero, how much more this will have to be the case with the almost

infinitely small atoms, and if a stone the other, which falls next to him from a height,

precisely because of this fact can not determine to move, how much less is an atom

for others to determine the movement because their mutual attraction must be

outweighed by the common attraction to the earth body as infinite. Now, however,experience shows us that the cohesion, which we did by attraction of atoms depends

on the law of gravity is a force that even significantly outweigh the seriousness by

any body else, for example, we handle at its upper end , with its lower end should fall

in ruins. Therefore seems the cohesion (and just as the chemical attraction) by the law

of gravity can not be explained at all.

Several physicists have therefore found also persuaded to accept a growing force

for cohesion, for a price higher than the ratios of the square nearby. However, this

seems to us to not be absolutely necessary, if we consider the following.

Go to the law of gravitation two elements, the mass, but also the proximity of the

attracted body. Now, in relatively closer proximity of two bodies can, however, their

magnetic effect almost disappear on each other when a third, though distant attractive

center has a disproportionate mass superiority over both, as in the above case of two

stones and the phenomena of planetary attraction toward the sun. But however as

here the element of mass has the upper hand over the element of proximity and

thereby determines the attraction, as can also be reversed cases think where the

element of proximity to such a degree outweighs the element of earth, that the

attraction of a body (earth or Erdmittelpunkts) although of greater mass but against

the mutual attraction of two bodies of smaller mass (atoms), which disproportionatelybut closer than this body (the center of the earth) are disappearing. So pull two balls

already on the surface, which have each only one millionth of the mass of the Earth,

each other more strongly than they are attracted to the earth's center, wofern their

centers closer to each other than to the thousandth part of the earth's radius are.

We see that a path revealed in such manner, regardless of against the ground so

disproportionate smallness of atoms with the law of gravity to reconcile the existence

of cohesion, by namely the proximity of the atoms in proportion to their mass, the

mass of the earth and the distance from the center of the earth, in which the Earth's

mass must be thought united, so assume that the influence of this proximity providesabout the influence of the mass of the Earth to such a degree as to make it the

phenomena of cohesion necessary. - By itself, it may have nothing improbable, and

some a priori philosophy might conclude that the nature of two cases, both of which

are feasible in the formula of its laws as may, will have not only realized the one, and

that therefore while it has carried out a case in the phenomena of gravity and the

movements of the planets, where the mass is the decisive factor for the attraction,

even another realm'll find instead, where it depends on the area.

. 18 This general observation, however, seems closer but when taking into account

all circumstances thereby lead to contradictions. One finds that if two small atoms

themselves (with their attractive centers to which the removal is to apply the law of


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gravitation, in any case remain to the sum of their radii away from each other) to

attract more in contact or close contact of their surfaces, as they are attracted by the

vast mass of the Earth, its tightness for many billions of times must be greater than

that of the Earth 15) , therefore, of course, much greater, if they are to attract more and

from a distance, which in any case actually see the atoms instead . But if we were to

assume that the body stocks really so dense atoms and then calculated, in whichdistances, these atoms would have found for the mean density of the composite from

their bodies as we watch those came out, so we would see each other again, that these

distances were so great that the attractions of the atoms could be a very small fraction

of the attraction they learn through the earth only, so we seem to accept very dense

atoms that we yet introduced only to explain the cohesion again lead to nothing by, us

both required in order not to come with the observed mean density degrees of body in

opposition, by increasing the distance to lose the profit again, we were looking to

acquire the atoms by increasing their resistance; or in a word, Our adoption by to

explain the phenomenon A, thus seems to fall into inevitable conflict with oneanother.

15), namely the removal of its attracting centers would otherwise still remain too large to allow for their small

mass, a preponderance or just DC coming up with the earth force, if not precisely this circumstance would beoffset by the adoption of a large leak for them by this way a relatively large mass is compressed into a small

space. It must, as one can easily calculate a spherical atom of Rhine. Foot radius has a 2 trillion 3371

million times have greater density than the mean density of the earth is to express only on its surface a severityequal attraction, or to be of the nature that a material point directly to befnde on its surface, just as much of

him as would be attracted to the Earth. But it is foot radius apparently still too large accepted by far for

the size of an atom and in turn it can be shown that the smaller one assumes the atoms, even more so its density

must be placed growing, if they are still in contact of their surfaces one of the Earthpower to express the sameforce because of reduction of its radius, although the proximity of their centers and therefore the square ratio ofthis approximation, the attraction of atoms grows, alone at the same time the mass of the atoms, and the

attractive force decreases according to the cubic relationship, so that So definitely decreases the attraction ofatoms in constant contact with their surfaces by the simple ratio of its stages, which is now to compensate

decrease by a corresponding increase in the density.

. 19This objection, however, can raise when we, in accordance with all previous,

the cohesion and generally make attraction phenomena of the atomic world not

merely of the solar relatively fixed atoms dependent but gebundnen also and mainlyby the attraction of the planetary, or so-called , moving imponderabeln atoms. The

solar atomAis characterized in the distance and relative equilibrium against

atomBobtained in that a larger amount of planetary mass, on the outside of the

system ofAandB,as moved by its interspace. Now we canAandBvery well in such

distances from each other move that their mutual attraction would be far outweighed

itself from the earth, because the observed tightness of the body, in fact, this requires,

we provided only the one attraction put much stronger, found between each of the

two atoms and its first planetary mass surrounding it instead. Because:

1) Can we then without getting a huge leak for the whole system of atoms, thetightness of all the individual both as solar planetary Atoms very large, because the

density of the bare mass in the solar neighborhood of each atom must then be


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enormous, but even these can be removed accordingly.

2) Is it possible to see how the gravity can not produce disturbance in the

movements of planetary atoms to solar when the mutual attraction of the same in

their area actually much stronger than Earth's, because the planetary masses then

solar of the atoms such velocity must obtain informed that even if they come in larger

distances from their solar atoms, the attraction of the earth, their direction can notchange noticeably (as we see one such example in the light).

. 20 As a direct proof of the immense attraction strength of the atoms in their

vicinity can be incidentally mention the fact that the light, which can not be

appreciably deflected from its straight-line path from the total mass of the earth

considering his speed, but when it goes close to the masses of so much smaller atoms,

a well-known distraction after experiencing these atoms.

. 21 So we are now out there, the bodies have as systems of one hand relatively

fixed larger, on the other hand, to look at these moving smaller atoms, all of whichpossess atoms tremendous tightness and the arrangement is that the fixed centers in

relatively very are widely spaced from each other, but to urge the most mobile atoms

in the vicinity of this fixed center points together.

It will not be inappropriate, as the track from self-presenting analogy with the

arrangement of the heavenly bodies from the other side of something, not as if we

wanted to conclude, but because we can make some interesting comparisons here.

So we look at the world body as so many atoms in a larger size system or giant

body (or several such) and see what relationship does the tightness of such a single

world atom to intermediaries tightness of the system in which it is included, such asthe tightness of the sun or earth (the mass of the individual solar systems thinking to

the space occupied by their total system, distributed to the density of a system of any

quantity of solar systems16) . In order to do this accurately, we would certainly

actually the mutual distances of the solar system, and the mass that contains each one

of them, to know what is not so: but for our purpose it is enough out of the same mass

of our solar system and the distance to lay the nearest star as something general to

reason. Now we do not even know the distance of the nearest fixed star is certainly

one of us, but know that it is enormous. Would by its light intensity calculated the

star of the first magnitude, in case they were with our sun the same nature,320000mal be as far from us as the earth from the sun, and this relationship we will

assume as a least likely, anyway, another important factor where only the size of the

numbers to be shown in general, to thousands, even millions, more or less not.

16) Because it is understood that we are to retain the analogy, not only must the density of the earth or sun with

the intermediaries tightness of their own individual system, which just so imagine a solar atom with its

planetary atmosphere compare.

After Laplace provisions, the entire mass of our solar system was to be equal to asphere of 71.03 times the diameter of Earth from the mean density of the earth. We


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distribute this material to a diameter which is as much as the distance of the earth

from the sun 320000mal, then the tightness, this ball is filling, the mass density of the

earth inversely as the cube of 71.03 Earth radii to the cube by 320000 Erdweiten, or

(since 1 = 12130 Erdweite diameter of Earth) as the cube of 71.03, which we prefer

to put 72 17) , the cube of 12130mal 320000, di (7 digit guest by means of logarithms

calculated) as 1 to 1 trillion 156634 trillion. This is the ratio of the density of an atomin the large space, if we want to consider this in relation to a world body as such, to

the density of a system of several such world atoms.

17) The Uranus may still be behind the planet.

. 22Should really be the body systems present us with analogous ratios of atoms,

then offers the following represents Throw: It seems as if we are then the most

ponderable bodies appear to be somewhat thin, so the atoms in the void, what

separates , would have to lose a certain extent. But it is to take care that the gaps of

the higher atomic layers are always filled by the atoms of the lower part in the bodies

by putting them see through them, and that since the absolute distance of the atoms in

any case, as the ratio of the same may be designed to their own atoms, imperceptibly

can against all of us to be measurable distances, the space in which this gradually

thinking of the spaces completed for our eyes to an apparent continuity (considering

the distance from which we body the always need to look with our eyes, if at all

seeing the same should take place), can be so low to still appear to us as a layer of

thickness imperceptible. Quite a similar way we can see the Milky Way almost as a

coherent mass, regardless of their solar systems probably immense distance fromeach other.Moreover, we must always remember that the same ratios of atoms held in

our sense organs, as in the bodies that we perceive by and beings stocks whose hands

itself from solar systems in the corresponding distances would also feel the Milky

Way as a dense mass can how to nuclear systems, is a measure which, of course,

when we come to other levels of nature, not to throw away, for tightness and thinness

are merely relations, where we apply ourselves as a benchmark when we talk of big

or small. What is even more natural than that size, their relationship seems mediated

by an Act to other levels change, the transition to a corresponding degree. Maybe is

the density of atoms, the density of the composite from them world body and thetightness of the giant body that emerge again only by a combination of many celestial

bodies in a geometric progression, the exponent should be set but physically infinite.

. 23 It is not unlikely that even the sun equal to our atoms are able to organize

themselves to different states, but from what we can observe only a kind. The

isolation in which we see our sun seems to point to a gas state analog constitution of

the body to which it belongs, which I mention merely to counter the objection that

could be hernehmen of the newly implemented analogy that arrangements as we have

it set up to represent the cohesion, the sky will not (but perhaps hinted in the double

stars) sees.

. 24 We believe finally have an infinitely repeated objection to a philosophical


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school of the possibility that refer to the mere matter illimitierte attractions instead,

has made the need to take into consideration. Kant says: If one were to those without

a limiting repulsive force assume that all particles of matter would have to approach

to infinity and flow together in a point, so it could not really limited body take place,

as it shows us the experience.

Kant's proof would be all right if you spread the through space initially conceived

matter18) all attraction resistant and solely against a particular point addressed might

think, because there the motion of all particles in this direction then nothing

counteracted, so all the particles could are in fact only in this center to rest. But how

could probably head over to see 1) that in the infinite space in itself a point can be set

as the center, and therefore could in no points preferably be such a confluence, and 2)

what is the main thing that the limitation, which requires Kant to not coalesce into a

single point takes place, already it is that the inflowing to the same body also attract

each other reciprocally, and therefore distracted constantly with their directions to

this point, and must determine to movements to each other, such as we actuallyperceive the celestial bodies.

18) Kant, however, leaves the mat only caused by the attraction and repulsion, they would be at a prius the

matter, but basically they fall for him so that together, because he finds no other features in it, than of those

forces and the space in which they act, itself

Incidentally, the important fact remains undiscussed in Kant's view, where as the

reciprocal certain limitation of the attractive and repulsive force lie at different points

of the space, which makes it possible for him the emergence of different and mutuallylimiting body because, like setting the attraction and repulsive force par excellence in

the world about an arbitrariness that a certain amount of each distributed on certain

points, both must mutually cancel in general, or only the excess of one over the other

may not be effective. Now the philosophy is in their language although answer: A

arbitrariness in certain distribution of attraction and repulsion to certain conditions

need to single points of space not to be accepted, if you imagine that in space any

quantitative relations between attraction and repulsive force are realized, almost to

exhaustion of their term, and considering that basically a place only by a certain is

that we some observing any one arrangement of matter, ie, such a relation to it,however in relation to the infinite space of each place itself has an indifferent place,

which is not even a specific matter before creation of the place is, therefore, no

arbitrariness can find in terms of a choice of certain places instead.

This rejection of arbitrariness seems to me to be very good indeed given by you can

say it would be rather arbitrary, everywhere nemliche ratio thereof to want to put on

all points with par set of general attraction and repulsion, since in their phrase the

possibility of all conditions and there all is to find space in the room. Alone the same

circumstance would just as well come to the adoption of a sole attraction to equip by

here, rather than imagining an initial uniform distribution of the attractive force ormatter (philosophy will make between two no difference) across the room, but the

could make most general idea of their distribution, which would then cause the kind


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of self-assemblies as we really observe. It must be then that the more attractive parts

of the to determine from weaker attraction to the movement and the system thus

created either himself again by a mass of even stronger attraction to move or to those

discussed sentences against certain masses, by virtue of occurring in their

approximation peculiar arrangement of the moving masses around them are kept in

relative silence, and then the emergence of the solid body is based. In general,however, would hereafter in the infinity of space all possible under the general law of

attraction cases of motion occur because the matter hypothesi ex to start was at all

possible imaginable conditions and arrangements to each other, of which the nature

of their movement depends on which very well agrees with the idea that the world is

infinite, the exhaustive or to exhaust themselves aspiring realization of a concept or

an idea, which themselves are infinite things in themselves.

Suppose the latter notion, then the matter would also be represented as follows: The

general concept of matter as an attraction with talented area, involved in his

community at the same time all different degrees of attraction and all the differentparts of the room. Therefore, the realization of this concept in the world to the infinite

variety and different distribution of matter itself appears to be 19) .

19) The still remaining space of this page, I think not being able to use more than by the message that is

published by the ingenious author of the above essay just now, in L. Voss in Leipzig: the (with Biot's portraitspruce) first band the second edition of the German editor of Biot's textbook of experimental physics or natural

science experience. Compared with the 1 Bd of the first edition, this newly published first volume, amongother features, also characterized in that demonstrable inaccuracies in the previous edition corrected here and

incomplete representations appear completed here in a way that as much of the diligence of the translator, all of

whose thorough study the newer and latest discoveries testify. The other additions are either connected directlyto the text, or if the size of the circumference made it necessary to have turned on the special circuit chapter

proper place partly in the form of comments and additions. - With regard to the view developed in the aboveAbh reason, I ask the same way, the authors compare m. Introduction to the newer chemistry Bem.4 p 263-264. Kastner

on the application of the law of gravitation to the atomic theory-english-gustasv theodor fechner

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