is 2,500 times the weight below, and the latter, therefore, must move with a velocity which will increase its force 2,500 times. That is, it must move 50 times as fast; for the square of 50 is 2,500. 50 times 32 feet in a second is 1,600 feet in a second; which is about the mean velocity of the molecules of air. It would be the exact velocity at a given temperature if exact figures had been used instead of round numbers. The difference is not great.

These proportions, it will be seen, hold good whatever the length of the tube may be. Suppose it to be one foot instead of 32 feet. The weight of the resisting column of air is only nd of the former weight. But it will all strike the piston innd of the former time, and gravity in that time, therefore, will only have exerted and of its former force upon the weight above the piston.

Now, in observations of the moon, no evidence of an atmosphere there has been discovered, either directly or by its effect upon light. The total absence of any gaseous covering is not positively demonstrated, for it might exist without being detected if it were extremely thin and shallow and permanently transparent. But there are no good grounds for supposing that perfect transparency could be maintained. Any atmosphere on the moon's surface would be subject to very rapid movement, from the great difference in temperature between the light and dark sides of the satellite. If there were any water, there would certainly be clouds, and if there were none, it is probable that finely powdered dust would be abundant, and would be often carried into the air.

Assuming that there is in fact no atmosphere on the moon, an inquiry into the cause of this condition is at once suggested. If planetary bodies with cool surfaces have atmospheres round them, these must consist of the gases or vapours that are permanent at low temperatures, and the

number is not large. But some of them are so abundant on the earth, and there are so many proofs of their existence in other bodies, that their presence may naturally be expected anywhere. There are distinct evidences of atmospheres in the principal bodies of the solar system, and that the moon should be without one requires explanation.

The Kinetic theory of gases gives a probable reason for this exceptional state. A gas being a substance in which the individual molecules are moving rapidly in all directions, the atmosphere of any of the bodies in space is a layer of gas so situated that there is nothing to prevent its molecules from flying off and leaving it, except the force of gravity. This force depends on the planetary mass, and in a small body like the moon, it is so feeble that anything leaving its surface with a velocity of about 7,500 feet in a second will never return.*

Now, 7,500 feet per second is the mean velocity of the molecules of hydrogen at a temperature of about 300° F., and is therefore a speed within the reach of gaseous molecules generally. If it is actually reached by the molecules of gases at the moon's surface, they cannot remain there.

The speed of gaseous molecules as deduced from their pressure is only the average speed, and this is doubtless less than the highest.

As the molecules of a gas are all equal in size and weight, we might infer that when in any definite portion of it they are subject to the same conditions, the velocities, which are the result of those conditions, would be uniform. But if this

* The velocity required is the square root of 2RG, where R is the moon's radius, and G the acceleration due to gravity at her surface.

The moon's diameter is 2,153 miles. Taking the moon's mass and radius as unity, and the earth's mass and radius as 88 and 3-68--

x 32.2 = 4.9 feet G at moon's surface.

3.682

88

were the case at any instant, this uniformity of speed would be immediately destroyed by their mutual encounters. When two moving bodies come into collision, the speed of both of them is necessarily changed. If they are equal, and move with equal speed in opposite directions when they meet, there is an instant when both of them stop, absolutely, and if we suppose their elasticity to be perfect, so that they rebound with the same velocity as before, the force of elasticity, like all other forces, requires an interval of time to produce its final effect, and during that interval all the velocities between the final one and actual rest are passed through. And molecules moving in all directions must meet each other at all angles, and during the periods of all their velocities, and therefore with all varieties of effect on each other's momentary motions, the general result being that there is a speed which is never exceeded, but that at every instant there are molecules moving at every intermediate speed between this and the state of rest. We assume, therefore, that some molecules are necessarily moving faster than the average in all gaseous masses, and the question, What is the greatest speed attained by any of them? becomes one of considerable interest.

It is the greatest speed, and not the average speed, that will determine whether an atmosphere of gas can remain on the surface of an attracting body; for if only a small proportion of the gaseous molecules move fast enough to fly away, and if this condition is permanent, the whole will gradually drain off, and the departure of the whole atmosphere is only a question of time.

I propose to consider what inference concerning this maximum velocity might be drawn from the hypothesis that the moon possesses no atmosphere, because the molecular velocity of gases at her surface is too great to allow them to remain there.

There are good grounds for the hypothesis itself. The moon's appearance suggests the action of volcanic and explosive forces as among its causes, and these forces, as known to us, require the agency of gaseous matter. If such a surface as the moon presents could be produced merely by the cooling of a melted mass, which is not probable, the heat of fusion would certainly liberate many substances in a gaseous form, and that all of these should condense into solids is again unlikely. And the analogy of the earth, to which she is so near, and of other bodies in the solar system, leads us to expect that gases would be found on the moon if they could be retained there.

If Mr. G. H. Darwin's theory of the effect of tidal action is accepted, and if we suppose, in consequence, that the moon at some former period was almost in contact with the earth, or was perhaps a piece broken off her, the presence of gases on the moon, if it were possible for them to remain there, might be assumed with increased certainty. Admitting that our knowledge on the subject is not positive, we may at least adopt the hypothesis as a probable one. It is the only one which satisfactorily accounts for the want of any atmosphere on the moon.

The mean velocity of gaseous molecules is in inverse proportion to the square root of the molecular weight, and in direct proportion to the square root of their absolute temperature; the freezing point of water being 492° F. above absolute zero. Taking the molecular weight of hydrogen as unity, that of oxygen is 16. The square root of 16 is 4, and the mean velocity of oxygen, therefore, is to that of hydrogen inversely as 4 to 1 at the same temperature. The mean velocity of hydrogen at the freezing point is about 6,000 feet per second That of oxygen, therefore, is 1,500 feet per second. The molecular weight of nitrogen being 14, of which the square root is 3.74, the mean velocity of nitrogen at the

freezing point is 1,600 feet per second. These velocities are increased by nearly one-half at twice the absolute temperature, which is 524° F.; are doubled at four times the temperature, or 1,508° F.; are trebled at 3,968° F., and quadrupled at 7,412° F.

On the other hand, they are reduced to one-half at 337° below zero F., and to one-fourth at 430° below zero F., or 30° above absolute zero.

The temperature of the moon's surface when exposed to sunshine, which is continuous for fourteen days, cannot be very low. Various experiments have made it probable that it rises above the boiling point of our thermometers. If it rises at any time to 300° F., this temperature is sufficient to drive away an atmosphere of hydrogen, even if the mean velocity of its molecules were also their highest. We may say at once, therefore, that hydrogen could not remain in a gaseous form on the surface of the moon. But oxygen and nitrogen, or gases of still greater weight, are what may be expected, and they would as certainly remain at any temperature possible at the moon's surface, unless their highest velocities greatly exceeded the mean. Assuming that the temperature reaches 300° F., the mean velocity of oxygen at that temperature is 1,900 feet, and of nitrogen 2,000 feet per second. To carry these away from the moon, the maximum velocity cannot be less than four times as great as the mean.

If we take heavier gases, such as chlorine and carbonic acid, with relative weights 35 and 22, their mean velocities at 300° F. will be respectively about 1,250 and 1,600 feet per second, and to carry these away the maximum velocity must be six or seven times as great as the mean.

It is not probable, however, that the whole atmosphere of the moon, if there were one, would acquire the temperature of the heated surface.

The temperature of our own atmosphere, at considerable