It is always supposed, that the oscillations of the plane are so minute in comparison with the length _d_, that their extent may be neglected in this calculation: and this hypothesis is actually consistent with the fact, since there is every reason to suppose that the excursions of the incandescent particles are very small in comparison with the extent of an undulation, which, though an extremely minute space, is still an appreciable quantity, and may be actually measured. Besides, [p119] even if the amplitude of these oscillations were not in the first instance so wholly inconsiderable, it would be sufficient to consider an undulation at a greater distance from the centre of agitation, in order that their extent might be diminished in any required proportion.
In the second, or retrograde oscillation, the plane, returning through the same space, must communicate to the stratum of fluid in contact with it, and to the rest in succession, a motion in a direction contrary to that of the first oscillation; for when the plane recedes, the stratum in contact with it, urged against the plane by the elasticity or the expansive force of the fluid, necessarily follows it, and fills up the vacuum which its retrograde motion tends to produce. For the same reason, the second stratum is urged against the first, the third against the second, and so forth. It is thus that the retrograde motion is communicated, step by step, to the most distant strata: its propagation is effected according to the same law that governs the direct motion; the only difference is in the direction of the motions, or, in the language of mathematics, in the sign of the velocities which are imparted to the molecules of the fluid. We see then that the different velocities which have existed in the solid plane, during its second oscillation, must exist at the moment which we are considering, in the different strata comprehended in the other half of _d_, but with contrary signs. Thus the velocity, for example, which the plane had in the middle of the second oscillation, which is its maximum of retrograde velocity, must now be found in the fluid stratum situated at the distance 1/4 _d_ from the centre of agitation, while the maximum of direct velocity is found, at the same instant, in the stratum which is at the distance 3/4 _d_ from the centre of agitation.