It needs scarcely be said that these universally co-existent forces ofattraction and repulsion, must not be taken as realities, but as our symbolsof the reality. They are the forms under which the workings of the Unknowableare cognizable by us -- modes of the Unconditioned as presented under theconditions of our consciousness. How these ideas st and related to the absolutetruth we cannot know, but we may unreservedly surrender ourselves to themas relatively true, and may proceed to evolve a series of deductions havinga like relative truth. §75. Universally co-existent forces of attraction and repulsion,imply certain laws of direction of all movement. Where attractive forcesalone are concerned, or rather are alone appreciable, movement takes placein the direction of their resultant; which may, in a sense, be called theline of greatest traction. Where repulsive forces alone are concerned, orrather are alone appreciable, movement takes place along their resultant;which is usually known as the line of least resistance. And where both attractiveand repulsive forces are concerned, and are appreciable, movement takes placealong the resultant of the tractions and resistances. Strictly speaking thislast is the sole law; since, by the hypothesis, both forces are everywherein action. But very frequently the one kind of force is so immensely in excess,that the effect of the other kind may be left out of consideration. Practically,we may say that a body falling to the Earth follows the line of greatesttraction; since, though the resistance of the air must, if the body be irregular,cause some divergence from this line (quite perceptible with feathers andleaves), yet, ordinarily the divergence is so slight that we may disregardit. In the same manner though the courses taken by steam from an explodingboiler, differ somewhat from those which it would take were gravitation outof the question; yet, as gravitation affects its courses only infinitesimally,we are justified in saying that the escaping steam goes along lines of leastresistance. Motion, then, always follows the line of greatest traction, orthe line of least resistance, or the resultant of the two; and though thelast is alone strictly true, the others are in many cases sufficiently nearthe truth for practical purposes.
Motion set up in any direction is itself a cause of further motion inthat direction, since it is the manifestation of a surplus force in thatdirection. This holds equally with the transit of matter through space, thetransit of matter through matter, and the transit through matter of any kindof vibration. In the case of matter moving through space, this principleis expressed in the law of inertia -- a law which all the calculations ofphysical astronomy assume. In the case of matter moving through matter, wetrace the same truth under the familiar experience that any breach made byone solid through another, or any channel formed by a fluid through a solid,becomes a route along which, other things equal, subsequent movements oflike nature most readily take place. And in the case of motion passing throughmatter under the form of an impulse communicated from part to part, the factsof magnetization appear to imply that the establishment of undulations alongcertain lines, determines their continuance along those lines.
It further follows from the conditions, that the direction of movementcan rarely if ever be perfectly straight. For matter in motion to pursuecontinuously the exact line in which it sets out, the forces of attractionand repulsion must be symmetrically disposed around its path; and the chancesagainst this are infinitely great. It may be added that in proportion asthe forces at work are numerous and varied, the line a moving body describesis necessarily complex: witness the contrast between the flight of an arrowand the gyrations of a stick tossed about by breakers.
As a step towards unification of knowledge, we have now to trace thesegeneral laws throughout the various orders of changes which the Cosmos exhibits. §76. In the Solar System the principles thus briefly summarized areevery instant exemplified. Each planet aid satellite has a momentum whichwould, if acting alone, carry it forward in the direction it is at any instantpursuing -- a momentum which would make a straight line its line of leastresistance. Each planet and satellite, however, is drawn by a force which,if it acted alone, would take it in a straight line towards its primary.
And the resultant of these two forces is that curve which it describes --a curve consequent on the unsymmetrical distribution of the forces around.
When more closely examined, its path supplies further illustrations. Forit is not an exact circle or ellipse; which it would be were the tangentialand centripetal forces the only ones concerned. Adjacent members of the SolarSystem, ever varying in their relative positions, cause perturbations; thatis, slight divergences from that circle or ellipse which the two chief forceswould produce. These perturbations severally show us in minor degrees, howthe line of movement is the resultant of all the forces engaged; and howthis line becomes more complicated in proportion as the forces are multiplied.
If instead of the motions of the planets and satellites as wholes, weconsider the motions of their parts, we meet with comparatively complex illustrations.
