Page:Popular Science Monthly Volume 58.djvu/148

140 must, for its application, require data impossible to obtain. We shall, therefore, confine ourselves to a brief outline of the main points of the subject. A fundamental proposition of the whole theory is Lane's law of gaseous attraction, which is as follows:

When a spherical mass of incandescent gas contracts through the loss of its heat by radiation into space, its temperature continually becomes higher as long as the gaseous condition is retained.

The demonstration of this law is simple enough to be understood by any one well acquainted with elementary mechanics and physics, and it will also furnish the basis for our consideration of the subject.

We begin by some considerations on the condition of a mass of gas held together by the mutual attraction of its parts. This attraction results in a certain hydrostatic pressure, capable of being expressed as so many pounds or tons per unit of surface, say a square inch. This pressure at any point is equal to the weight of a column of the gas, having a section of one square inch and extending from the point in

question to the surface. It is a law of attraction in a sphere of which the density is the same at equal distances from its center, that if we suppose an interior sphere concentric with the body, the attraction of all the matter outside that interior sphere, on any point within it, is equal in every direction, and, therefore, is completely neutralized. A point is, therefore, drawn towards the center only by the attraction of the sphere on the surface of which it lies.

At every point in the interior the hydrostatic pressure must be balanced by the elastic force of the gas. In the case of any one gas this force is proportional to the product of the density into the absolute temperature. This condition of equilibrium must be satisfied at every point throughout the mass.

Let the two circles in the figure represent gaseous globes, of the kind supposed. The larger one represents the globe in a certain condition of its evolution; the second its condition after its volume has contracted to one half. The temperature in each case will necessarily