From this we see that the motions of the stars shew a real approach, and even a fairly close approach, to equipartition of energy. The question which naturally presents itself is whether this approximate equality of energy can be attributed to any other cause than long-continued gravitational interaction between the stars. This latter agency could undoubtedly produce it, but could anything else produce a similar result? The last column of the table provides the answer. It shews the temperatures to which a gas would have to be raised, in order that each of its molecules should have the same energy as the different types of stars. This may well seem an absurd calculation. A star weighing millions of millions of millions of tons goes hurtling through space at a speed of about 1,000,000 miles an hour; are we seriously setting out to inquire how hot a gas must be for every single one of its tiny molecules to have the same energy of motion, the same power of doing damage—for that is what energy of motion really amounts to—as the star? The calculation is undoubtedly absurd, and it is meant to be, because it is leading up to a _reductio ad absurdum_. If the observed equipartition of energy were brought about by any physical agency, such as pressure of radiation, bombardment by molecules, by atoms or by high speed electrons, this agency would have to be at a temperature, or in equilibrium with matter at a temperature, of the order of those given in the last column. These are temperatures of the order of 10⁶² degrees. We can be pretty sure no such temperature exists in nature, whence the argument runs that the observed equipartition of energy cannot have been brought about by physical means, and so must be the result of gravitational interaction between the stars. The age of the stars is, then, simply the length of time needed for gravitational forces to bring about as good an approximation to equipartition of energy as is observed. The calculation of this length of time presents a complicated but by no means intractable problem. All the necessary data are available, and as the method of calculation is well understood from previous experience in the theory of gases, the mathematician may be trusted to supply a reliable and reasonably exact answer when we ask him, but even without his help we can see that the time must be very long indeed.