tion, or the line of least resistance, or the resultant of the two, is a necessary deduction from that primordial truth which transcends proof.

Reduce the proposition to its simplest form, and it becomes still more obviously consequent on the persistence of force. Suppose two weights suspended over a pulley or from the ends of an equal-armed lever; or better still-suppose two men pulling against each other. In such cases we say that the heavier weight will descend, and that the stronger man will draw the weaker towards him. But now, if we are asked how we know which is the heavier weight or the stronger man; we can only reply that it is the one producing motion in the direction of its pull. Our only evidence of excess of force is the movement it produces. But if of two opposing tractions we can know one as greater than the other only by the motion it generates in its own direction, then the assertion that motion occurs in the direction of greatest traction is a truism. When, going a step further back, we seek a warrant for the assumption that of the two conflicting forces, that is the greater which produces motion in its own direction, we find no other than the consciousness that such part of the greater force as is unneutralized by the lesser, must produce its effect-the consciousness that this residuary force cannot disappear, but must manifest itself in some equivalent change the consciousness that force is persistent. Here too, as before, it may be remarked that no amount of varied illustrations, like those of which this chapter mainly consists, can give greater certainty to the conclusion thus immediately drawn from the ultimate datum of consciousness. For in all cases, as in the simpler ones just given, we can identify the greatest force only by the resulting motion. It is impossible for us ever to get evidence of the occurrence of motion in any other direction than that of the greatest force; since our measure of relative greatness among forces is their relative power of generating motion. And clearly, while the com

parative greatness of forces is thus determined, no multiplication of instances can add certainty to a law of direction of movement which follows immediately from the persistence of force.

From this same primordial truth, too, may be deduced the principle that motion once set up along any line, becomes itself a cause of subsequent motion along that line. The mechanical axiom that, if left to itself, matter moving in any direction will continue in that direction with undiminished velocity, is but an indirect assertion of the persistence of force; since it is an assertion that the force manifested in the transfer of a body along a certain length of a certain line in a certain time, cannot disappear without producing some equal manifestation—a manifestation which, in the absence of conflicting forces, must be a further transfer in the same direction at the same velocity. In the case of matter traversing matter the like inference is necessitated. Here indeed the actions are much more complicated. A liquid that follows a certain channel through or over a solid, as water along the Earth's surface, loses part of its motion in the shape of heat, through friction and collision with the matters forming its bed. A further amount of its motion may be absorbed in overcoming forces which it liberates; as when it loosens a mass which falls into, and blocks up, its channel. But after these deductions by transformation into other modes of force, any further deduction from the motion of the water is at the expense of a reaction on the channel, which by so much diminishes its obstructive power: such reaction being shown in the motion acquired by the detached portions which are carried away. The cutting out of river-courses is a perpetual illustration of this truth. Still more involved is the case of motion passing through matter by impulse from part to part; as a nervous discharge through animal tissue. Some chemical change may be wrought along the route traversed, which may render it less fit than before for conveying a current.

Or the motion may itself be in part metamorphosed into some obstructive form of force; as in metals, the conducting power of which is, for the time, decreased by the heat which the passage of electricity itself generates. The real question is, however, what structural modification, if any, is produced throughout the matter traversed, apart from incidental disturbing forces-apart from everything but the necessary resistance of the matter: that, namely, which results from the inertia of its units. If we confine our attention to that part of the motion which, escaping transformation, continues its course, then it is a corollary from the persistence of force that as much of this remaining motion as is taken up in changing the positions of the units, must leave these by so much less able to obstruct subsequent motion in the same direction.

Thus in all the changes heretofore and at present displayed by the Solar System; in all those that have gone on and are still going on in the Earth's crust; in all processes of organic development and function; in all mental actions and the effects they work on the body; and in all modifications of structure and activity in societies; the implied movements are of necessity determined in the manner above set forth. Wherever we see motion, its direction must be that of the greatest force. Wherever we see the greatest force to be acting in a given direction, in that direction motion must ensue. These are not truths holding only of one class, or of some classes, of phenomena; but they are among those universal truths by which our knowledge of phenomena in general is unified.

CHAPTER X.

THE RHYTHM OF MOTION.

§ 82. WHEN the pennant of a vessel lying becalmed first shows the coming breeze, it does so by gentle undulations that travel from its fixed to its free end. Presently the sails begin to flap; and their blows against the mast increase in rapidity as the breeze rises. Even when, being fully bellied out, they are in great part steadied by the strain of the yards and cordage, their free edges tremble with each stronger gust. And should there come a gale, the jar that is felt on laying hold of the shrouds shows that the rigging vibrates; while the rush and whistle of the wind prove that in it, also, rapid undulations are generated. Ashore the conflict between the current of air and the things it meets results in a like rhythmical action. The leaves all shiver in the blast; each branch oscillates; and every exposed tree sways to and fro. The blades of grass and dried bents in the meadows, and still better the stalks in the neighbouring corn-fields, exhibit the same rising and falling movement. Nor do the more stable objects fail to do the like, though in a less manifest fashion; as witness the shudder that may be felt throughout a house during the paroxysms of a violent storm. Streams of water produce in opposing objects the same general effects as do streams of air. Submerged weeds growing in the middle of a brook, undulate from end to end. Branches brought down by the last flood, and left entangled at the bottom where the current is rapid,

are thrown into a state of up and down movement that is slow or quick in proportion as they are large or small; and where, as in great rivers like the Mississippi, whole trees are thus held, the name "sawyers," by which they are locally known, sufficiently describes the rhythm produced in them. Note again the effect of the antagonism between the current and its channel. In shallow places, where the action of the bottom on the water flowing over it is visible, we see a ripple produced—a series of undulations. And if we study the action and re-action going on between the moving fluid and its banks, we still find the principle illustrated, though in a different way. For in every rivulet, as in the mapped-out course of every great river, the bends of the stream from side to side throughout its tortuous course constitute a lateral undulation—an undulation so inevitable that even an artificially straightened channel is eventually changed into a serpentine one. Analogous phenomena may be observed. where the water is stationary and the solid matter moving. A stick drawn laterally through the water with much force, proves by the throb which it communicates to the hand that it is in a state of vibration. Even where the moving body is massive, it only requires that great force should be applied to get a sensible effect of like kind: instance the screw of a screw-steamer, which instead of a smooth rotation falls into a rapid rhythm that sends a tremor through the whole vessel. The sound which results when a bow is drawn over a violin-string, shows us vibrations produced by the movement of a solid over a solid. In lathes and planing machines, the attempt to take off a thick shaving causes a violent jar of the whole apparatus, and the production of a series of waves on the iron or wood that is cut. Every boy in scraping his slate-pencil finds it scarcely possible to help making a ridged surface. If you roll a ball along the ground or over the ice, there is always more or less up and down movement—a movement that is visible while the velocity is considerable, but becomes too small and rapid to