vibrations to the air, each communicated its vibrations to the other, we should have just the same alternation of concurrent and conflicting pulses. And if each of the two strings was combined with an aggregate of others like itself, in such way that it communicated to its neighbours both its normal and its abnormal vibrations, it is clear that through each aggregate of strings there would be propagated one of these compound waves of oscillation, in addition to their simple rapid oscillations. This illustration will, I think, make it manifest that when a mass of molecules which have a certain period of vibration, is placed in contact with a mass of molecules which have another period of vibration, there must result an alternation of coincidences and antagonisms in the molecular motions, such as will make the molecules alternately increase and decrease one another’s motions. There will be instants at which they are moving in the same direction, and intervening instants at which they are moving in opposite directions; whence will arise periods of greatest and least deviations from their ordinary motions. And these greatest and least deviations, being communicated to neighbouring molecules, and passed on by them {171} to the next, will result in waves of perturbation propagated throughout each mass. Let us now ask what will be the mutual relations of these waves. Action and reaction being equal and opposite, it must happen that whatever effect a molecule of the mass A produces upon an adjacent molecule of the mass B, must be accompanied by an equivalent reverse effect upon itself. If a molecule of the mass A is at any instant moving in such way as to impress on a molecule of the mass B an additional momentum in any given direction, then the momentum of the molecule of A, in that direction, will be diminished to an equal amount. That is to say, to any wave of increased motion propagated through the molecules of B, there must be a reactive wave of decreased motion propagated in the opposite direction through the molecules of A. See, then, the two significant facts. Any _addition_ of motion, which at one of these alternate periods is given by the molecules of A to the molecules of B, must be propagated through the molecules of B in a direction _away from_ A; and simultaneously there must be a _subtraction_ from the motion of the molecules of A, which will be propagated through them in a direction _away from_ B. To every wave of _excess_ sent through the one mass, there will be a corresponding wave of _defect_ sent through the other; and these _positive_ and _negative_ waves will be exactly coincident in their times, and exactly equal in their amounts. Whence it follows that if these waves, proceeding from the surface of contact through the two masses in contrary directions, are brought into relation, they will neutralize each other. Action and reaction being equal and opposite, these _plus_ and _minus_ molecular motions will