With regal' to the extent of the atmosphere, we may consider it under two points of view : first, the extreme limits to which it is possible for it to extend, considered mathematically as a masa rotating round the terrestrial axis in the same time; secondly, the much narrower physical limits founded on its nature as an elastic fluid, and having regard to the great diminution of temperature at high altitudes Any particle of the revolving atmosphere is acted on by two forces, namely, gravity, which is directed nearly to the centre of the earth, and the centrifugal force produced by rotation, which is directed according to the line by which that point is orthographically projected on the earth's axis, and tends directly from that axis. The former force varies 'aversely as the square of the distance from the earth's centre ; the latter, directly as its perpendicular distance from the earth. axis. At any point taken in the external surface of the atmoe phere, thy resultant ariaing from both forces must be nurtnal to that surface, in order that its form may be permanent.. At the terreatiial e plater the ratio of these two forces is known ; as we ascend in the atmosphere (dung an equatorial radius produced, gravity diminishes and centrifugal force increases, both in this instance being directly opposite : hence it is vary to calculate the distance of a point in that radius where the two forces are exactly wind. Beyond that point the centrifugal forca predominates, and no particle there situ,sted could remain attached to our atmosphere, revolving with the earth both in its diurnal and orbital motions.
The above point therefore defines the extreme limit to which it is possible for 'our atmosphere to extend, and which is at a distance of about 30,000 miles from the centre, or 26,000 from the earth's equatorial surface, though it by no means follows that it must extend so far. Other data would be necessary to give the actual extent ; for instance, the height of the barometer nt the surface of the sea, and the law of the diminution of temperature in the upper strata of the air. The figure of the extreme surface can however be determined from these considerations, which is that of an oblate spheroid flattened at the Doles, and in which the pular axis is to the equatorial in the ratio of 2 to 3.
As the phenomenon of twilight indicates an extreme degree of rarefaction in the atmosphere at an inconsiderable altitude above the earth's surface, we shall now consider some of the physical causes which demonstrate that the actual limits of that fluid are much more contracted than the extreme possible limits given above.
Representing by p, 8, and t respectively, the pressure, density, and temperature of the sir at the surface of the earth, and by p', 8', and t', like quantities for a portion of air at a certain elevation, it follows front ee Mr where /3 pre the general laws of gaseous bodies that p _(1 + p (1+/3 Bents the fraction Now the pressure measures the elastic force of the Oriel particles : this elasticity cannot become negative, and ceases to exist when which may happen either because (1 +041=0, or S'=0. This last supposition would bring us to the consideration of
the mathematical limits above treated on ; the former, to the physical limits depending on the decrease of temperature at high altitudes, hence the air ceases to be an elastic fluid, according to this reasoning, 1 BOO when e = 3 — —2G6,' centigrade. Now the law of the decre- went of heat in the atmosphere proceeds in a progression quicker than an arithmetical, and as the plane of perpetual snow is at a compara tively small altitude in climates of mean temperature, it is easy to see that front 100 to 200 miles altitude would be sufficient to diminish the tempe rature to the above number of 266 below zero. Even if the simple law p=(1+$ t) a was not strictly rigorous at such low temperatures as-206' centigrade, still a diminution of temperature fur a given density would produce a diminution of elasticity, and scarcely interfere with the general conclusion arrived at from that law.
But even limits thus obtained would, in all probability, be still too extensive, for it is not neceastry that the elasticity should be totally destroyed : it .is sufficient that the repulsive power of two con tiguous particles of air at that altitude shall be less than the force of gravity, and if theme two forces are equal, it will be the extreme extent at which the air can remain attached to the globe, leaving out of con sideration the centrifugal force, which at that altitude is inconsiderable, and which would itself tend to remove those particles. Hence the limits become still more contracted by this consideration, and it will not be necessary that the temperature should bo as low as-260% Some have imagined that planetary atmospheres are due to the attraction of the masses of the planets on a rare elastic fluid dissemi nated through space, but this supposition will not bear investigation ; fur putting aside the consideration of the extreme cold of the planetary spaces, tine hypothesis is not corroborated by the dimensions of the atmospheres of the sun and planets, which would then depend on their masses, and the present total disappearance of the satellites of Jupiter behind their primary would be converted into an annular appearance round his body at the time of the eclipse of n satellite.
We have seen that the unequal distribution of heat in the atmos phere is a maiu source of the velocities and directions of winds, and consequently of the distribution of climate ; but on the other hand, the earth itself, having its own distribution and radiation of heat, reacts) on the atmosphere and produces dew, hoar-frost, &c. In like manner the sea and the Polar fields of ice materially affect the general distribution of heat.