Let us now turn our thoughts for a moment to the propagation of the rarefaction. Supposing, as before, the middle row _a x_ to represent the particles of air in equilibrium under the pressure of the atmosphere, and suppose the particle _a_ to be suddenly drawn to the right, so as to occupy the position _a″_ in the highest line of dots: _a″_ is immediately followed by _b″_, _b″_ by _c″_, _c″_ by _d″_, _d″_ by _e″_; and thus the rarefaction is propagated backward toward _x″_, reaching a point _o″_ in the line of particles by the time _a_ has completed its motion to the right. Now, why does _b″_ follow _a″_ when _a″_ is drawn away from it? Manifestly because the elastic force exerted between _b″_ and _a″_ is less than that between _b″_ and _c″_. In fact, _b″_ will be driven after _a″_ by a force equal to the difference of the two elasticities between _a″_ and _b″_ and between _b″_ and _c″_. The same remark applies to the motion of _c″_ after _b″_, to that of _d″_ after _c″_, in fact, to the motion of each succeeding particle when it follows its predecessor. The greater the difference of elasticity on the two sides of any particle the more promptly will it follow its predecessor. And here observe what the _cold_ of rarefaction accomplishes. In addition to the diminution of the elastic force between _a″_ and _b″_ by the withdrawal of _a″_ to a greater distance, there is a further diminution due to the lowering of the temperature. _The cold developed augments the difference of elastic force on which the propagation of the rarefaction depends._ Thus we see that because the heat developed in the condensation augments the rapidity of the condensation, and because the cold developed in the rarefaction augments the rapidity of the rarefaction, the sonorous wave, which consists of a condensation and a rarefaction, must have its velocity augmented by the heat _and the cold_ which it develops during its own progress. It is worth while fixing your attention here upon the fact that the distance _a′ o′_, to which the motion has been propagated while _a_ is moving to the position _a′_, may be vastly greater than that passed over in the same time by the particle itself. The excursion of _a′_ may not be more than a small fraction of an inch, while the distance to which the motion is transferred during the time required by _a′_ to perform this small excursion may be many feet, or even many yards. If this point should not appear altogether plain to you now, it will appear so by and by. § 10. _Ratio of Specific Heats of Air deduced from Velocity of Sound_