July ^, 1878]^ 



NATURE 



253 



rattlesnake does not, however, prevent the entrance of 

 the dog ; the rattlesnake is never wanton, and only 

 defends itself and takes necessary food. The dog will 

 pass by it to enter its burrow without being molested. 



Cleistogamous Flowers in Grasses.— Mr. C. G. 

 Pringle has discovered in Western Vermont cleisto- 

 gamous flowers in several grasses, especially Datithonia 

 spicata. The latter has many flowers totally concealed 

 in the sheaths, the glumes and pales being much simpli- 

 fied, but the sexual parts being perfect and producing 

 seeds. This plant is spreading rapidly in Vermont. 

 The seeds borne on the top of the culm fall mostly at 

 midsummer and lodge close to the parent plant, but the 

 concealed seeds stored around the culm remain till these 

 are disjointed and driven about by the autumn and 

 winter winds ; consequently, a wide means of dissemina- 

 tion is provided. 



ON THE VIEW OF THE PROPAGATION OF 

 SOUND DEMANDED BY THE ACCEPT- 

 ANCE OF THE KINETIC THEORY OF 

 GASES 



I. T T is an accepted fact that the molecules of a gas are 

 •*■ in motion among themselves in their normal state, 

 and incapable of acting on each other at a distance ; so 

 that a theory of the propagation of sound, based upon the 

 contrary suppositions that the molecules of a gas are at 

 rest in their normal state and capable of acting on each 

 other at a distance, cannot possibly be tenable. It there- 

 by becomes necessary to inquire what view of the propa- 

 gation of sound is demanded by the acceptance of the 

 kinetic theory of gases ; and this inquiry would appear to 

 be all the more important in view of the fact that the 

 mechanism of the propagation of sound in gases forms the 

 physical basis of a great part of acoustics, or the ground- 

 work upon which a number of its problems depend — the 

 physical basis that underlies a system being admittedly 

 the most important of the whole. 



2. The molecules of a gas being in motion among 

 themselves, it becomes evident after a very brief con- 

 sideration of the question, that the only way in which a 

 small impulse (or variation of velocity) termed a " wave " 

 can be propagated through a gas, is by the exchange of 

 motion normally going on among the molecules of the 

 gas. For the molecules have no other mode of acting upon 

 each other, excepting by exchange of motion. The rate 

 at which this "wave" (or small variation of velocity) is 

 propagated through the gas, will therefore depend on the 

 rate at which the molecules exchange motio7t, i.e. on the 

 normal velocity of the molecules of the gas. The sole 

 condition determining the velocity of propagation of sound 

 in a gas is therefore the velocity of the molecules of the 

 gas. Here, therefore, we have a very simple condition for 

 the velocity of sound (on the basis of the kinetic' theory), 

 or the velocity of sound becomes thus dependent only on 

 one condition. This simplicity is characteristic of the 

 rest of the kinetic theory, and is (it may be added) the 

 recognised quality of scientific truth. In gases of the 

 most diverse densities, specific gravities, pressures, and 

 temperatures, the velocity of sound is only dependent on 

 one condition, viz., the velocity of the molecules, of the gas. 



3. That the velocity of sound is independent of density, 

 will be evident from the consideration that the molecules 

 of gas are almost indefinitely small compared with their 

 length of free path, and also the time of a collision is 

 indefinitely small compared with the time taken to 

 traverse the free path, so that it does not matter how many 

 collisions (or exchanges of motion) occur along the line of 

 passage of the impulse (or " wave "), but simply on the 

 rate of motion of the molecules conveying the impulse. 

 So (to take a simple analogy by way of illustration), it 



I 



does not matter how many couriers are along the line of 

 route conveying a message, but on the rate of motion of 

 the couriers. Adding to the number of molecules in unit 

 of volume of a gas (or adding to the density) does not, 

 therefore, alter the velocity of sound in a gas, because it 

 does not alter the velocity of the molecules which (by 

 their exchange of motion) propagate the wave. The old 

 theory supposes that the velocity of sound is here un- 

 altered, because increased density diminishes the velocity 

 of propagation of the wave, and increased pressure 

 (attendant on the increased density) augments the velocity 

 of the wave, and thus the two conditions counteract each 

 other. On the kinetic theory, neither of these conditions 

 can have any effect, and therefore the explanation of the 

 unaltered velocity of the wave is perfectly simple, being 

 the cosequence of the unaltered velocity of the molecules 

 which propagate it. It is unnecessary to comment on the 

 contrasted simplicity of the view on the kinetic theory ; 

 which is, moreover, the true view, if the kinetic theory be 

 accepted. 



4. That the velocity of sound on the kinetic theory is 

 independent oi pressure, is sufficiently clear at first sight ; 

 for pressure evidently could not influence the rate at which 

 the molecules exchange motion among each other, 

 through which means alone the impulseis conveyed. 



5. That change of specific gravity (or molecular 

 weight) can by itself have no effect on the velocity of 

 the sound-wave, is evident from the fact that it cannot 

 matter whether the molecules exchanging motion among 

 each other (and propagating the impulse) be heavy or 

 light, provided their' velocity be the same. It has been 

 (as is known) demonstrated, generally from dynamical 

 principles, that a system of bodies in free collision all 

 tend to acquire the satne absolute energy. Hence the 

 velocity of each body depends on its mass (or varies 

 inversely as the square root of its mass). So the mass 

 of the molecules of hydrogen being (as is known) one 

 sixteenth that of the molecules of oxygen, the velocity of 

 the molecules of hydrogen is four times greater than that 

 of the molecules of oxygen ; and accordingly for this 

 reason the velocity of sound in hydrogen is exactly four 

 times greater than its velocity in oxygen — not, however, 

 because the molecules propagating the wave are heavy or 

 light. The molecules of hydrogen in their normal 

 exchange of motion, move at four times the speed (com- 

 pared with those of oxygen), and therefore propagate by 

 this exchange of motion the sound-wave at four times the 

 speed. The specific gravity (or molecular weight) of the 

 gas has evidently nothing whatever to do with the rate of 

 propagation of sound. The reason why the velocity of 

 propagation of sound appears to depend on the molecular 

 weight of the gas is because the velocity of the molecules 

 of the gas depends on the molecular weight. 



6. So also the velocity of sound is independent of the 

 temperature, provided the molecular velocity remains the 

 same. Of course this could only be true of different 

 gases {i.e., of gases of different molecular weights), 

 which — as is known — may be at different temperatures 

 and yet possess the same molecular velocities. In one 

 and the same gas of course the temperature could not be 

 altered without altering the molecular velocity, for the 

 " heat ^ itself consists in the motion of the molecules of 

 the gas. This is therefore evidently the cause why the 

 application of heat to a gas increases the velocity of 

 sound. The addition of " heat " simply represents (as is 

 known) the addition of velocity to the molecules of the 

 gas, which consequently, by their exchange of motion, 

 propagate the wave at a greater rate. The explanation 

 of the increased velocity of sound in a heated gas is thus 

 simple and direct. On the old theory the increased velocity 

 of the sound-wave in a heated gas is referred to the dimi- 

 nished density of the heated gas (attendant on its 

 expansion) ; and when the gas is confined, to its increased 

 pressure. Surely this is at best a somewhat laboured and 



