9. BUT now the chord having recovered its rectilinear situation I k L, the following motion will be changed, for the point K, which before advanced with a motion more and more accelerated, though by the force it has acquired it will go on to move the same way as before, till it has advanced near as far forwards, as it was at first drawn backwards; yet the motion of it will henceforth be gradually lessened. The effect of which upon the particles _a, b, c, d, e, f, g_ will be, that by the time the chord has made its utmost advance, and is upon the return, these particles will be put into a contrary rangement; so that _f_ shall be nearer to _g_, than _e_ to _f_, and _e_ nearer to _f_ than _d_ to _e_; and the like of the rest, till you come to the first particles _a_, _b_, whose distance will then be nearly or quite what it was at first. All which will appear as follows. The present distance between _a_ and _b_ is such, that the elastic power, by which _a_ repels _b_, is strong enough to maintain that distance, though a advance with the velocity, with which the string resumes its rectilinear figure; and the motion of the particle _a_ being afterwards slower, the present elasticity between _a_ and _b_ will be more than sufficient to preserve the distance between them. Therefore while it accelerates _b_ it will retard _a_. The distance _b c_ will still diminish, till _b_ come about as near to _c_, as it is from a at present; for after the distances _a b_ and _b c_ are become equal, the particle _b_ will continue its velocity superior to that of _c_ by its own power of inactivity, till such time as the increase of elasticity between _b_ and _c_ more than shall be between _a_ and _b_ shall suppress its motion: for as the power of inactivity in _b_ made a greater elasticity necessary on the side of a than on the side of _c_ to push _b_ forward, so what motion _b_ has acquired it will retain by the same power of inactivity, till it be suppressed by a greater elasticity on the side of _c_, than on the side of _a_. But as soon as _b_ begins to slacken its pace the distance of _b_ from c will widen as the distance _a b_ has already done. Now as _a_ acts on _b_, so will _b_ on _c_, _c_ on _d_, &c. so that the distances between all the particles _b, c, d, e, f, g_ will be successively contracted into the distance of _a_ from _b_, and then dilated again. Now because the time, in which the chord describes this present half of its vibration, is about equal to that it took up in describing the former; the particles _a_, _b_ will be as long in dilating their distance, as before in contracting it, and will return nearly to their original distance. And farther, the particles _b_, _c_, which did not begin to approach so soon as _a_, _b_, are now about as much longer, before they begin to recede; and likewise the particles _c_, _d_, which began to approach after _b_, _c_, begin to separate later. Whence it appears that the particles, whose distance began to be lessened, when that of _a_, _b_ was first enlarged, viz. the particles _f_, _g,_ should be about their nearest distance, when _a_ and _b_ have recovered their prime interval. Thus will the particles _a, b, c, d, e, f, g_ have changed their situation in the manner asserted. But farther, as the particles _f_, _g_ or F, G gradually approach each other, they will move by degrees the succeeding particles to as great a length, as the particles A, B did by a like approach. So that, when the chord has made its greatest advance, being arrived into the situation I ϰ L, the particles moved by it will have the rangement noted by the points α, β, γ, δ, ε, ζ, η, θ, λ, μ, ν, χ. Where α, β are at the original distance of the particles in the line A H; ζ, η are the nearest of all, and the distance ν χ is equal to that between α and β.