per unit of surface will be four times as great, or will vary as the square of the density. The elasticity at equal temperatures being proportional to the density, it follows that, were the temperature the same in the two masses, the elasticity would be double in the case of mass B; whereas, to balance the hydrostatic pressure, it should be quadrupled. The temperature of B must, therefore, be twice as great as that of A. It follows that in the case of stars of equal volume, but of different masses, the temperature must be proportional to the mass or density.

But how will it be if we suppose the density of the two bodies to be the same, and, therefore, the mass to be proportional to the volume? In this case the attraction at a given point will be proportional to the diameter of the body. If, then, we suppose one body to have twice the diameter of the other, but to be of the same density, it follows that at corresponding points of the interior, the hydrostatic pressure will be twice as great in the larger body. The density being the same, it follows that the temperature must be twice as high in order that equilibrium may be maintained. It follows that the stars of the greatest mass will be at the highest temperature, unless their volume is so great that their density is less than that of the smaller stars.

IT

CHAPTER XIII

STELLAR EVOLUTION

As yet this world was not, and Chaos wild

Reigned where these heavens now roll, where earth now rests.

T follows from the theory set forth in the last chapter that the stars are not of fixed constitution, but are all going through a progressive change -cooling off and contracting into a smaller volume. If we accept this result, we find ourselves face to face with an unsolvable enigma,-How did the evolution of the stars begin? To show the principle involved in the question, I shall make use of an illustration drawn from another work. An inquiring person, wandering around in what he supposes to be a deserted building, finds a clock running. If he knows nothing about the construction of the clock, or the force necessary to keep it in motion, he may fancy that it has been running for an indefinite time just as he sees it, and that it will continue to run until the material of which

it is made shall wear out. But if he is acquainted with the laws of mechanics, he will know that this is impossible, because the continued movement of the pendulum involves a constant expenditure of energy. If he studies the construction of the clock, he will find the source of this energy in the slow falling of a weight suspended by a cord which acts upon a train of wheels. Watching the motions, he will see that the scape-wheel acting on the pendulum moves very perceptibly every second, while he must watch the next wheel for several seconds to see any motion. If the time at his disposal is limited, he will not be able to see any motion at all in the weight. But an examination of the machinery will show him that the weight must be falling at a certain rate, and he can compute that at the end of a certain time the weight will reach the bottom, and the clock will stop. He can also see that there must have been a point from above which the weight could never have fallen. Knowing the rate of fall, he can compute how long the weight occupied in falling from this point. His final conclusion will be that the clock must in some way have been wound up and set in motion by an external force a certain number of hours or days before his inspection, and must be again wound up by such a force unless it is to stop.

If we accept the theory that the heat of the stars is kept up by their slow contraction we must think of the universe of stars as of a clock which is running down. As we can see by the eye of reason that the weight of the clock was higher yesterday than it is to-day, so we

can compute that the stars must have been larger in former times, and that there must have been some finite and computable period when they were all nebulæ. Not even a nebula can give light without a progressive change of some sort. Hence, within a certain finite period the nebulæ themselves must have begun to shine. How did they begin? This is the un

solvable question.

The process of stellar evolution may be discussed without considering this question. Accepting as a fact, or at least as a working hypothesis, that the stars are contracting, we find a remarkable consistency in the results. Year by year laws are established and more definite conclusions reached. It is now possible to speak of the respective ages of stars as they go through their progressive course of changes. This subject has been so profoundly studied and so fully developed by Sir William and Lady Huggins that I shall depend largely on their work in briefly setting it forth. At the same time, in an attempt to condense the substance of many folio pages into so short a space, one can hardly hope to be entirely successful in giving merely the views of the original author. The following may, therefore, be regarded as partly the views of Sir William Huggins, condensed and arranged in the order in which they present themselves to the writer's mind, and partly those of the writer himself.

There is an infinite diversity among the spectra of the stars; scarcely two are exactly alike in all their details. But the larger number of these spectra, when

1 Publications of Sir William Huggins's Observatory, vol. i., London, 1899.

carefully compared, may be made to fall in line, thus forming a series in which the passage of one spectrum into the next in order is so gradual as to indicate that the actual differences represent, in the main, successive epochs of star life rather than so many fundamental differences of chemical constitution. Each star may be considered to go through a series of changes analogous to those of a human being from birth to old age. In its infancy a star is simply a nebulous mass; it gradually condenses into a smaller volume, growing hotter, as set forth in the last chapter, until a stage of maximum temperature is reached, when it begins to cool off. Of the duration of its life we cannot form an accurate estimate. We can only say that it is certainly to be reckoned by millions and probably by tens of millions or even hundreds of millions of years. We thus have in the heavens stars ranging through the whole series from the earliest infancy to old age. How shall we distinguish the order of development? Mainly by their colours and their spectra. In its first stage the star is of a bluish white. It gradually passes through white into yellow and red. Sir William gives the following series of stars as an example of the successive stages of development:

Sirius; a Lyræ.

a Ursa Majoris.

a Virginis.

a Aquilæe.

Rigel.

a Cygni.

Capella; the sun.