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The limit of the velocity of gases has a special interest in general physics, because it is closely related to the limit of motive force in the universe. Apart from gravity, the agencies by which motion is produced in inorganic bodies are chiefly of an explosive nature in their origin or their application. A moving body, whatever its size may be, cannot cause another body to move faster than itself by direct collision. An airgun, for example, cannot discharge its shot with a speed greater than that of the gaseous molecules; and this must be the case in all explosions which are due to the compression of gases still retaining the gaseous form.

A moving body, however, may indirectly be the cause of much more rapid motion than its own. A blow near the pole of a sphere may set it spinning with an immensely greater velocity at the equator. Or a blow on the short end of a lever in any form may have this result. Nor is it clear that the maximum velocity of a gas is the greatest speed at which its molecules have moved in passing from a solid or liquid to a gaseous form. We cannot, therefore, learn by this method alone what is the highest speed attainable by explosive agencies.

If, however, the explosion of one pound of gunpowder will drive out a ball weighing six pounds with a speed of 1,600 feet per second, we must conclude generally that the blow delivered by the powder must have been given with a velocity at least seven times as great, even if it could be conceived of as given by the whole mass of the gunpowder. The velocity of the gaseous molecules would thus be more than 11,000 feet per second. Now, the mean molecular velocity of the gases of gunpowder cannot be greater than that of nitrogen, which is 1,600 feet per second at the freezing point, and to raise this to 11,000 feet would need a temperature of not less than 25,000° F., which is beyond the probable temperature of the explosion. But if at the instant of passing into a gaseous

state the elementary atoms are dissociated, and their relative weight thereby reduced to one-half, a mean velocity of 1,600 feet would be raised to 2,300 feet at the freezing point, and would become 11,000 feet at a temperature of about 12,000° F.

The explanation is scarcely sufficient, however. Part of the gaseous molecules may be supposed to strike the ball immediately, and the rest on their rebound from the side of the powder chamber so quickly afterwards as to be practically efficient; but the energy of the powder is, in fact, divided between the ball driven in one direction and the gun in another, and the whole mass of the powder cannot transfer its whole motion to the ball. Unless, therefore, the actual internal temperature of the gases at the instant of liberation is really much beyond 25,000° F., it seems necessary to suppose that the velocity with which the atoms of the gases fly apart at that instant is much greater than that which, as gases, they afterwards retain.

The case here considered is that of a projectile discharged with a speed of 1,600 feet per second. Far higher velocities, however, are possible, at least in theory. When the weight of the projectile is as great as that of the gases by which it is expelled, the mean velocity of those gases is the greatest that can be given to the projectile. But if portions of the gas are moving at a speed greater than the mean, they may give a higher velocity to a smaller body if they can be made to strike it effectively. In practical gunnery a higher velocity is not necessarily given by making the weight of the powder much greater than that of the shot; but there are mechanical reasons for this. If the maximum velocity of gaseous molecules may, as I have suggested, be taken as about seven times the mean velocity, then, in hydrogen for example, some of the molecules are moving at the freezing point with a velocity of not less than eight miles in a second, and this would become more than fifty miles at a temperature of 25,000° F. We might

give this velocity to a projectile of proportionate weight if we could use for our explosive, hydrogen, liberated at this temperature, and in such a form that the molecules having the maximum velocity were the effective ones; and this would again be doubled if the hydrogen atoms were dissociated. Whether this will ever be possible here may well be questioned, but it is not unlikely that we see the actual process operating in the sun when jets of hydrogen appear to rush at otherwise incredible speed beyond his visible atmosphere.

NOTE. It appears that in any atmosphere round an attracting sphere, the height at which the whole mass of air is divided into two halves of equal weight depends on the nature of the gas, the temperature, and the force of gravity, and is not affected sensibly by the total quantity. For suppose the quantity doubled; the weight of the upper half is doubled, and the lower half being also doubled in quantity, but under twice the pressure, will have its density doubled, but its volume unchanged.

It appears also that when gravity and temperature are the same, the height of the lower half atmosphere will be inversely proportional to the relative weight of the gas. For suppose hydrogen, with relative weight about, to be substituted for air, in such quantity that the total mass is the same, the pressure of the upper half atmosphere will be the same, and the volume of the lower half will therefore be fourteen times greater.

It appears, further, that the height of the lower half atmosphere will closely approximate to half the height to which the mean molecular velocity of the gas, considered as a

projectile force, would carry a projectile upwards from the surface of the sphere. For this is known by observation to be the case in the earth's atmosphere. The height of the lower half is about 3 miles, or more nearly 3.4 miles. The velocity which would carry a projectile to twice this height, in vacuo, from the surface, is 1,510 feet per second. The mean molecular velocity of the mixed nitrogen and oxygen of the air is 1,510 feet at -22° F.

The mean temperature of the first 6.8 miles of the atmosphere, as a whole, is probably not quite so low as 22o, but it cannot be very much higher. At the same time the molecular velocity of the air is somewhat less than that of its nitrogen and oxygen, from the presence of carbonic acid, which is heavier, and of aqueous vapour, which is an imperfect gas. Allowing for this, the approximation to the velocity of 1,510 feet is so close, that we can hardly doubt their practical identity.

The relation between these heights must also hold good, whatever the gas may be, and in the case of any attracting sphere.

For the height of the half atmosphere, the square of the molecular velocity at the same temperature, and therefore the projectile height, are all of them inversely as the relative weight of the gas composing the atmosphere. And if the force of gravity varies, the height of the half atmosphere is inversely as the pressure, and therefore as the force of gravity; and so is the projectile height near the surface. And if the temperature varies, the height of the half atmosphere and the square of the molecular velocity both vary directly as the absolute temperature.

The height of the upper half of the atmosphere is not subject to the same laws, but practically it must always be nearly the same multiple of the lower half. Whatever the height of the lower half may be, the density is reduced to

about one-billionth at about forty times this height, and an atmosphere of any density consistent with the constitution of a gas is practically at an end when reduced to this extent. The decrease of gravity in ascending need hardly be considered.

It seems possible, therefore, to state concisely a general law of atmospheres, depending on the relative weight of the gas, the force of gravity, and the temperature. The relative weight and the temperature determine the molecular velocity. The velocity and the force of gravity determine the projectile height. Half this height is the depth of the lower half atmosphere, and forty times this depth is the limit beyond which there can be no atmosphere of an appreciable kind.

Some curious results appear to follow. At ordinary temperatures, no atmosphere of oxygen or nitrogen can be so much as one hundred and forty miles high on any planet larger than the earth. On Jupiter, where gravity is 24 times as great, such an atmosphere could not be appreciable at a greater height above the surface than sixty miles.

An atmosphere of hydrogen on Jupiter might be appreciable at a height of nine hundred miles if in sufficient quantity. But if there is any gas whose relative weight is to hydrogen as that of hydrogen to air, Jupiter might have an atmosphere of it thirteen thousand miles deep; and he could hold a gas of this kind, for its mean molecular velocity at the freezing point would be about four miles per second, while thirty-three miles per second would be necessary to carry it away from him. Such a gas could not remain on the earth, and its absence here does not therefore entitle us to say that it has no existence. Many things connected with the physics of the larger bodies point to the probable presence in the universe of some materials far lighter than anything we are acquainted with. If they exist, it is on the larger bodies only that they can be found, since they could not be retained by the smaller ones.

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