Limiting Density.—Such a process of contraction and rise in temperature obviously must have a limit. Sooner or later the atoms of the gas must get so close together that there is little room for further compression. Under such conditions the rise of internal temperature would slow up and then cease and the star would ultimately cool down, behaving more like a liquid than a gaseous mass. Until within a few years it was supposed that this change would begin to happen when the mean density of the star was less than that of water; and a theory of stellar evolution, pro posed originally by Sir Norman Lockyer and reconstructed by H. N. Russell, held the field for some time. But in 1924 A. S. Eddington pointed out that the ionized atoms throughout the main mass of a star, being stripped of all their outer electrons, must occupy far less space than under ordinary conditions, so that seri ous departures from the simple gas-laws should not be anticipated till their density had become many thousands of times greater than that of water. The range of possible contraction of a star must theref ore be very great.
This conclusion of theory is fully confirmed by observation. It is now possible to calculate the diameters of hundreds of stars, and the densities of a great number. The latter range from less than a thousandth part that of ordinary air in the case of great red stars like Antares to more than a thousand times that of platinum in the case of the companion of Sirius and the other "white dwarfs." Stars of the former sort appear to be "young"—in the sense that they have most of their visible life still before them— and those of the latter class to be "old." The sun, whose mean density is 1.4 times that of water, comes not far from the middle of the sequence.
Age of a Stan—When the length of a star's life comes to be considered, the contraction theory meets with grave difficulties. The amount of gravitational energy which would have been released by the contraction of the sun, for example, from an indefinitely great size to its present dimensions is readily cal culable, and is found to amount to as much as would supply the present rate of radiation from the surface for 46,000,000 years. More than half this must still be stored inside the sun and twenty million years' supply at most can be counted available for radiation. This was pointed out long ago by Lord Kelvin.
But there is now abundant evidence from radioactive data that the oldest sedimentary rocks recognized by geologists are of the order of a thousand million years old (probably some what more), and that, during all this interval, the temperature of the earth's surface has been closely the same as at present. The sun has therefore, during geological time, dissipated in radiation more than 5o times as much energy as it could have derived from gravitational sources, and yet has remained of about the same brightness all the time. For the giant red stars of low density the
case is even stronger. The gravitational energy available for a star's past radiation is proportional to (M being the star's mass and R its radius). For Antares, for example, for which R is 480 times as great as for the sun, and M probably only 30 or 40 times as great, the available energy is some three times as great as for the sun. Antares radiates heat at io,000 times the sun's rate, so that its whole past history, if gravitational energy only were available, would occupy only 6,000 years.
Sub-Atomic Energy.—Such arguments, have convinced prac tically all workers in the field that the sun, and the stars in general, must draw to maintain their radiation upon some vast supply of energy whose very existence was previously unsuspected. The problem of stellar evolution thus enters upon a new and difficult stage, for, since this "unknown source" of energy has never been tapped in our laboratories, it is hard to find out about it. Atomic theory, in its present state of development, is not able to tell us very much, but, what it does tell is striking. The only storehouses in the known universe small enough to hold so much energy are the tiny nuclei of the atoms, or perhaps the still smaller protons and electrons of which they are composed. For particles at greater distances, such as those at the periphery of an atom, the forces are not great enough to do so much work. The main source of stellar energy appears therefore to be of "sub-atomic" nature. In this conclusion, again, all workers agree.
Loss of Mass.—A second conclusion follows from the theory of relativity. According to this all energy possesses mass, and mass and energy are, to some degree at least, interconvertible, in a definitely known ratio. To m grams of matter correspond me' ergs of energy (where c is the velocity of light). Translated into more familiar units, this means that it is as legitimate to speak of a pound of heat as of a pound of iron. But a pound of heat is a very large amount, measured by ordinary standards; it would suffice to raise 20 million tons of rock to a temperature of 1,50o° C. and melt it into incandescent lava. The amounts of heat in volved in all ordinary thermal changes are therefore of such small mass that it is still usually permissible to treat heat as "im ponderable"; but when it comes to the radiation of the stars the case is different. The sun radiates energy into space at the rate of 3.8X ergs per second—a number too great to be directly appreciable even by the physicist. Expressed as mass, this means that the sun is getting rid of 4,200,000 tons of heat every second. No other mode of statement comes so near to conveying to human apprehension the tremendous activity of a star.