An essay upon force in nature and its effects upon matter

Introduction

MONG the chief principles received by, and as science, pertaining to the relations of force in nature to matter, is that laid down by Sir Isaac Newton, viz: that every particle of matter has the property of attraction for every other particle, and that the law is, that as between masses of matter, attraction is directly as the mass and inversely as the square of the distance. Is this a true statement? Has it ever been demonstrated so as to be beyond criticism? If it is not a trae statement, it may serve a mischievous end in obstructing inquiry in a broad field of nature, perhaps capable of making large returns.

Perhaps as good a way as any of testing this principle, as to its truth, is to make the inquiry whether the entirety of planetary movements can in fact be produced by it. If it can not be, the principle must be defective, because planetary movement is claimed to depend upon it. ;

The following essay embodies an attempt to show that planetary movement can not be perfected by the theory of gravitation as received. Beyond this, suggestions are offered in support of the idea that planetary movements are caused by the effect of force om matter, not inherent in matters and further, that the one primal force on which planetary movement depends, modified by special effects upon substances differing in kind, in arrangement, andgfh position, is that which, under the modified conditions, is e

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Ut Introduction. : called by the various names of force, as of attraction and repulsion, cold and beat, electricity, Magnetism, weight, etc,—in other words, it is thought that differences of forces 4y name should be taken as being expressions of differences in manifestation of a same force, but not of specific differences of forces 3—the differences as to manifestation arising from peculiarities of matter on which the one force acts. :

Without making any claim that this idea, or the suggestions made under it, have scientific value, it can be asserted that upon statement, observed facts in nature come in, and lend thema support such that the mind seems willing to ascribe to them a higher value than that of a happy concurrence between supposed agency and observed conditions, which may be taken as obedience to it.

SECTION SECTION SECTION SECTION SECTION SECTION SECTION SECTION SECTION SECTION SECTION SECTION SECTION SECTION

SECTION i, , III, Iv

Vi, vil, VII, Ix, x, xi, XII, XIII, XIV,

XV,

Conctusion,

Contents

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PAGE

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Section II

For the purposes of this investigation let us take as given: 1. A force, simply, by which, if not resisted, a planet would be moved toward the sun, in direction of a right line connecting their centers; and 2. A portion of the curve of the planet’s orbit in its approach toward the sun.

To find the relative value of the force, and its direction which, with the force given, will produce that curve.

This force, as to its value and direction, being ascertained, it will be attempted to show that it, codperative with the force given, will, among other effects, produce those on which the first and second laws of Kepler are founded, will not only give rise to the times and spaces of “ falling ” bodies agreeably to the Newtonian law, but will exhibit a reason why bodies must be accelerated in their

“fall? agreeably to that law, and finally will not conflict with the third law of Kepler.

Incidentally, among other things, it will appear from the condition of conflict of force arising,

1. That the path of a circle is impossible in planetary

motion.

2. That the argument, as to the third law of Kepler, gives rise to the curious result of a permitted libration in the eccentricities of planets, which (the forces in question remaining unchanged in their nature) can only arise from the interference of an extraneous Cause.

3. That the phenomenon of gravitation, or, of ‘‘ falling,” does not exist, except as the result of a conflict of forces. It can only be considered as an isolated force by way of mental analysis or separation.

And under this seems to reside a very important condition, viz: That under the operation of those natural forces causing planetary motion, bodies and particles of matter are not attracted toward each other in direction of right lines connecting their centers, but are forced toward each other in the curves of spirals closing upon the centers each of the other. Among other things it would seem to result from this, that the sidal wave is not the result of attraction.

4. A further result appears that, as one of the effects of the conflict of force, a planet, from its aphelion to its perihelion point, should revolve upon its axis with increased rapidity ; uniformity in times of revo-

lution, as, for instance, of the earth, being preserved by increasing and decreasing friction of the moon upon it in its approach to, and its departure from, the sun.

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4 Force in Nature, es

If these are right results, it serves to show that the ascertainment of the nature and value of centrifugal force is of importance, as opening new features as to the effects of natural forces. It shows that there is no simple force as of gravitation by which a body must be accelerated, but that acceleration is the result of the antagonism of forces always equal, each perhaps always of a constant value, but exerted within limits constantly narrowing or expanding. In fact, the discussion of this antagonism of force may lead us to new ideas as to the very nature of that of which we speak as productive of planetary motion, even to realizing it as in close and inseparable relationship with the vegetable and animal life around us.

SECTION III. Let a ba’ represent the path of

the earth in its orbit about the sun

8, between the point in its entire

orbit most remote from the sun at

@ and that nearest the sun at a’, or

3” between the higher and lower ver-

tices of the ellipse. In pursuing the

a path from @ toward a’, the earth constantly approaches the sun until it arrives at a’, where there is exhibited the greatest predominance, if any, of the force of gravitation over that of repulsion, or of centripetal over centrifugal force, obeyed by a velocity of the earth in direction of the sun, greater than at any other point through which it has passed. If it is true that the approximation of the earth to the sun is occasioned by the predominance a ee ee ee se

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And its Effects. Is of the power of gravitation over that of repulsion, then, the earth increasing in velocity from @ to a’, it is evident, that the predominance has been increasing from a to a’, and that the earth from the point a’ must be impelled toward the sun by a force greater than has affected its movement in any other point of its orbit from @ to a’.

Now, the path of the earth from a@ to a’ is that of a spiral closing upon 8, and if the nature of the forces acting upon the earth, resulting in that path, are supposed to be the same at a’ as at a, the continued path of the earth should be upon the prolongation of the spiral in the direction 0, in obedience to the constantly-increasing predominance of the power of gravitation, or the centripetal force. But at a’ the earth begins to depart from the sun upon the path a’ b’ a; which, having accomplished, its entire orbit has become an ellipse composed of two spirals, a a’ and a’ a, one closing and one expanding, relatively to s, symmetrical with each other; for the completion of which the power of repulsion, or the centrifugal force, from a’ to ay must exceed that of gravitation, by the same measure in which the power of gravitation exceeded that of repulsion to perfect the path a 6 a’, . It follows that the forces of gravitation and repulsion expended in forcing the earth to the completion of its entire orbit have been equal.

Since the power of gravitation is at its maximum at a’ where the earth has acquired its greatest velocity in the direction of the sun, the fact, that at this point the earth begins to recede from the sun, shows that the power of repulsion at this point is equal to that of gravitation. At a’, from whence might have been expected the most rapid approach to the sun, the opposing forces have become equal, and a’ has, in terms of mechanics, become a dead

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7 a ‘ Oe ate on : ij “a . : SPEED Distr eOreay ah. Lar wildcat a 6 Force in Nature, point as to motion, in direction of a right line passing through a’ and the sun’s center, and in direction of the sun generally as relates to that part of the orbit already accomplished. Bya like process of reasoning a becomes another dead point in the reverse.

It necessarily follows, that the opposed forces affecting the point a, or the earth, at @ and a! being equal, they must be equal at any and every intermediate point between a and a’; and as the peculiarity of the ellipse is, that as to its path it approaches to and departs from the sun, or the focus to which one of the opposed forces is always directed, the orbit, being the result of opposed forces always equal, can only result by reason of a constant change of position of those forces relatively to each other.

CoroLiary.—As two equal and directly-opposed forces can not be productive of motion, to result in any orbit whatever, these antagonistic forces must be exerted so as to form some angle greater or less with each other. From whence, since one of the forces is always directed toward an immovable point in space, the forces themselves can not be productive of a circle about such a point as a center; for, the circumference of a circle being for every point thereof perpendicular to the radius (which radius represents one of said forces) can only result from those forces when they form with each other an angle of 180°, which is impossible, for at that angle they become directly opposed.

Hence, it would seem that, on the conditions stated, the orbit of a circle is impossible in planetary motions.

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And its Effects.

“I

Section IV

Let the point @ be held in space by the two equal opposed forces as, a b, 5” of which @ s for any position of a b shall always act in direction of the immovable focus of force s. Now, for the moment, dropping the consideration of the force @ s, suppose the force a b to be suddenly deflected so as to hold the general direction a b’, The point @ will be moved to 0’, at a distance of d b! from a 4, considered as a position of reference. If the force a

6’ is obstructed from moving the point a@ in direction @ 6, but is still free to move it in direction d b/, then the point @ will be moved to d’,a distance a d' = d 6’, where it will be affected by the force d’ ’, unexpended remnant of a 0.

But resuming the consideration of the effect of the force a s we find that the expenditure of the force d 6, in removing the point @ to d’, has liberated an equal force ae to move the point @ toward the immovable center of force 8, and the point at which the forces to produce motion will cease to be effective for that purpose, will be where a will be held in equilibrium by two equal and directly opposed forces, remnants of a b and as, and also, where the line of those forces shall be parallel with @ 0’, the general direction in which the deflected force is made to act.

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8 Force in Nature, ; eee Wherefore, that point will be found in a line representing two directly opposed forces, drawn from 8, parallel to a 0’. But by Prop. 1, Theor. 1, of Newton’s Principia, if the point @, which otherwise would be moved in direction @ d’, be moved by some centripetal force toward the immovable center of force s, the resulting direction and distance will be such that equal areas will be swept over by a line connecting the point @ with the center of force, whether the point a@ be moved to d’ or to the new point sought. Now ad’ is given in position, and a s is common to both conditions, wherefore, for an area equal toad’ s, the point @ must be found at a distance from the line a s, and perpendicular to it, equal to a ad’, and nearer to s than is the point d’, and by construction ¢ is the only point which, in filling this condition, will be found in a line drawn from sg parallel to a b’.

But a d’ is perpendicular to a 8, taken as a radius, and, considered as a point, becomes a portion of the circumference of a circle of which s is the center ; therefore, in the same time that the point @ would describe the arc a d’ of a circle by the exertion of the force d 6, it will, by the co-operative exertion of the liberated force a e’, in direction s, describe the curve of a spiral, closing upon s in direction a e, equal to a e’; and this is as it should be by the terms of Sir Isaac Newton’s Proposition, because the areas a ds and a é’ 8 are equal, and the times of their description are equal.

Passing from the foregoing considerations, since the deflected force is always co-operative with that always in direction of the immovable center of force 8, the resultant described must always be descriptive of a curve, with respect to the point s of a spiral; and, since the straight pee ee line @ é’ is a portion of the curve of a spiral 3 it must be infinitely short, or, of itself, a3’

point. The very inception of movement of

the point a by two equal but opposing forces,

forming with each other any angle, must

bisect that angle, and the diagram s a 0!

must represent the ultimate effect of the . deflective force a 6’ in co-operation with the force @ 8, by which we have the two equal but opposed forces a 8, a 8’, productive of a d, and the point @ removed to d affected by the two equal and directly opposed forces d s, d 6’, remnants of as, a 0’. :

Section V

The force @ 8, or that of gravitation, has, since the time of Sir Isaac Newton, been recognized as one of the forces affecting a planet, compelling it to the completion of the path of its orbit. The path of the orbit, then, necessarily results from the action of this with some other force, and this latter force, from the consideration in Section III, must, at every point of that path, be equal to the force of gravitation; from whence it results that the continuing pathway of the orbit of the planet can result only from a continuing and relative change of position of these equal and opposed forces, one toward the other. Now, the diagram of the ultimate effect of the exertion of these forces for any one point of the path of the planet’s orbit, Section IV, must be that for every other point, at least, for that portion of the orbit between the higher and lower vertices of the ellipse; from whence it follows, that for every point, at least between those vertices, the planet is subjected to the action of remnant and directly opposed forces exerted in direction of right line connecting the center of the planet with the immovable center of force. One effect of the exertion of such remnant forces may be mechanical, forcibly holding the planet in position; another effect, also mechanical, may be that of pressure.

A very interesting consideration grows out of the peculiar features of. this diagram of force with reference to the continued path of the orbit. Relatively to the point s the continuation of @ d must become more inclined, or with a $ form an angle constantly becoming less than d as; the angle 6’ a s of the forces, resulting in the continuation of a d, must necessarily become constantly more acute, which shows that the opposed forces are constantly approximating to exertion in one and the same direction, or to one and the same force.

Section VI

Differing forces impressed in differing directions will result in one force in one “4 direction to create motion, and to the extent to which , they directly oppose each

e other will create pressure, or its equivalent. Let a force a 6 be impressed upon the point a in direction @ 6, and a force a 0’ be impressed on the same point in direction a ’, at one and the same time, od s v re

—

And its Effects. II then will the forces a b, a 6’ result in one force @ é in direction @ é from the point of origin of force a.

Draw a h intersecting the angle 5 a 6’ as a line of reference. At q@erect ac, ac’ perpendicular to a h, and connect. ¢ 6, c’ b’ by lines parallel with a h. The force a b may be considered made up of two forces, a ¢ to move the point @ to ¢, a distance a ¢ equal to b f from the line a h, and perpendicular to it, and ¢ 6, or af, to move the same point to f a distance a f, equal to ¢ 6 from the line ae, and perpendicular thereto. The force ab! may likewise be considered as the result of the two forces a ¢’, equal to 0’ jf’, and ¢ 0! equal to a f’.

But the forces @ ¢, a c/ are found as unequal forces opposing each other in the same right line, and therefore must be obeyed by motion in the direction of the greater force to the limit of its excess over the lesser; that is, a c—ac’=a d, The two remaining forces c 6, ¢ D equal to a f, af’ are positive to each other, being exerted in the same direction, and their ultimate effect to produce motion will be equal to ¢ 6+’ b’, or to a af". :

Now, since the force a d acts in general direction a d perpendicular to @ A, it will not at all alter the effect generated by the other forces ¢ }, ¢’ 5! acting in general direction a h, perpendicular to a d. The point a will therefore arrive at a distance @ d, perpendicular to the line a A, whether the force c b+ ¢ B/ acts or not. The same, may be said of the force ¢ b+ ¢ 8’, resulting in a distance equal toaf-+af" from the line ad. But, since the point can not occupy two positions at one and the same time, it must occupy one which will satisfy the effect of both forces, a dandaf+taf', at the same time; and this condition will oe 12 Force in Nature, OT be satisfied at the point ¢, which is at once at a distance @ f+a/f' from the line a d, and perpendicular to it, and at a distance h e, equal to a d, from the line a h, and perpendicular thereto.

By joining the points 6 e, 6’ e, it will be seen that the resultant force a e takes the direction of, and becomes equal to, the diagonal of the parallelogram made upon the lines a 6, a OU! given in position.

It will also be seen that the point @ arriving at ¢ will still be affected by the equal and opposed forces ac’, dc, as @ g, €g', though power to produce motion has ceased and given place to pressure, or its equivalent.

CoroLtary.—Since the production of @ d@ does not affect that of af+a/f’, nor is affected by it, and since, to produce it requires the combined exertion of the forces a b, a, ad may be said to be one, or the result of the full combination af the opposed forces a b, a 6’; so, likewise, af, af’ may be said to be the result of the same; and, since things equal to the same thing are equal to each other, a d may be said to be equal to aftaf'. This, though true, can only be true as to time, that is, that the point a would arrive at é within a time equal to that within which it would arrive at d or A. From this it would necessarily follow that the greater length of a f+a f’ over a d implies, in analysis, excess of velocity in its production.

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Section VII

(1.) ad produced by the co-operative forces a$ and ae, or a 6 deflected to a e, may be resolved into the two forces a f, d foraf,af'. Now, by corollary Section VI, df ora f’ and a f, considered as measures of time, are each the result of the combination of the forces a 8, a € to produce motion, and therefore equal to each other, both as to the forces employed and as measures of time. But @ d is equal to the same: wherefore, considered as to the forces employed to produce them, and as measures of time, af is equal to a d, \ that is, the point @ would be moved by the operation of the same forces in direction of a f to fin the same time that it would be moved in direction a@ d to d.

Now, the same forces operated through the same time must be productive of equal effects; but here is the accomplishment of a greater space in the same time, implying excess of velocity, which shows that some element is wanting to make up the equivalency. This element is supplied when the areas swept over by the radius vector @ $ are taken into account, for they are equal to each other, having a common base and altitude. This element discovered shows that the only equality of af with a d, resultants of equal forces in equal times, where the three elements of time, space, and velocity are considered, is where the forces

Ee ag ie 5 ee 14 Force in Nature,

Secth cet 5 tie eo are to be considered as accomplishing the production of equal areas about some common point, as 8, of which areas they are to be taken as parts of the contours. In other words, they must always be taken for the entire areas described about s.

(2.) If the arc a d of the spiral closing upon s, be more than a point, it can not be the result of a@ 8, a e; for the resultant of all antagonistic forces not in the same right line must be in one direction, or in one right line, and if a d be more than a point, it is susceptible of division until the number of right lines into which it may be divided will be equal to the number of points into which the arc @ d is divisible: therefore, the production of a d, if more than a point, must be by as many (relatively to each other) new and antagonistic forces as the arc has points.

Also, the diagram of the ultimate effect of the forces in Section IV shows an exhaustion of them by conversion into their resultant: wherefore, the production of every subsequent point of the arc must be by new force or forces. In other words, the earth, or a planet, is constantly obedient, relatively to antecedent ones, to new forces, and does not assist in the formation of its own orbit by impulse antecedently given.

(3.) Taking the arc @ d as more than a point, the earth, or £, arriving at d, is found to be nearer to S, or the arc a d is the curve of a spiral closing upon s, which can only be by a greater deflection of some new force with @ 8, or a!’ s,as a’ e’ than that of a @, or, the angle made by the new force to compel F to d, as e’’ a’’ s must be less than eas. Now, the value of the forces being unchanged, greater acuteness of the angle e’ as must result in a greater amount of force to produce motion upon Hat d ids vec it wad TRG ete pens

*

REPRE

ET wy than at a, or at any point intermediate between a and d. Therefore, the curve a b a’, Section ITI, showing a continuous approach to s, can only be accomplished by a continuously increasing acuteness of angle made by the opposed forces, always supposed to be equal. But continuously increasing acuteness of this angle must necessarily be productive of continuously increasing resulting force upon £, to produce motion: wherefore, the approach of EH toward $ in the path of the spiral must be with continuously increasing rapidity, and H must acquire a motion, uniformly accelerated, from zero at @, until its arrival at a’. The law of gravitation accords with, and is the same with, the law of uniformly accelerated motion, viz: that the distances passed over by a body starting from a state of rest with a uniformly accelerated motion are proportional to the squares of the times employed. The distance is equal to the time into the rate of motion, and the rate of motion must be for the same time as the force exerted. The approach of F toward s can be measured upon a right line connecting the centers of H and s, and it is evident that the same principle of uniformly accelerated motion will be applicable to its approach in this right line, as in the line of the real resultant of the forces, which is the path of the earth’s orbit.

Section VIII

It is thought to have been demonstrated, Section III, that for every point of the earth’s orbit the centripetal force and that of repulsion, or the centrifugal, must be equal, and that the production of successive points of that orbit can only be by change of position of those forces relatively to

Ne cate My, a 16 Force in Nature, a each other. Having found the diagram of the ultimate effect of the co-operation of these two forces for any point of the orbit, it is shown:

1. That relatively to a center of force to which one ts always directed, the resultant path must be that of a spiral closing upon that center, or a portion of the curve of an ellipse.

2. That by the very nature of their co-operation equal areas must, by the radius vector, be swept over in equal times.

3. That as these forces, by their co-operation, produce the curve of a spiral closing upon the sun, it must be by uniformly increased power to produce motion, resulting in uniformly increased velocity, which accords with the known obediences to that which is called the law of gravitation.

Now, as to the relation and dependency of these forces, the one to and upon the other: the very fact that they are always equal, both in detail and in the whole, and always co-operative, is of itself so strongly suggestive of relationship and dependency, the one with and upon the other, as almost to satisfy the mind without further investigation. But how can things in opposition be one and the same thing? Or, considered as one and the same, how can increased velocity be effected through the medium of one force? ae

If a force be impressed continuously upon a point in direction of a right line, in a space void of resistance, we can see that for equal times, or spaces, the force—or its equivalent, velocity—must increase, on the ground that impulse imparted will be added to force applied. But when the resultant direction is a given curve, there can be no increased force to effect motion by way of antecedent impulse, unless there comes with it a correspondingly opposed force to keep the body in the path of the given curve. Admitting the increase of the one, as by impulse antecedently given, whence comes the increase of the other, or negative?

In this connection Section V contains a statement of interest, viz: that the nature of the spiral closing upon the center of force requires that, by the changes of position of the opposed forces, they must necessarily form with each other increasing acuteness of angle as the path of the spiral approximates the center of force. This of itself demonstrates a constantly-increasing power impressed to produce motion, which, by taking the center of force as a point of reference, and measuring on a line connecting it with the body impressed, will necessarily become exhibited in the same way that the effect of the power of gravitation now is.