3 § Variable Stars. [January, 
The same reasoning, of course, applies to the statement 
under the second head. Unless the two bodies are differently 
constituted, how are we to suppose that one managed to 
retain its internal heat long after the other had become cold 
and without brilliancy ? All our knowledge goes to show 
that heated bodies of similar constituent elements — be they 
planets, rocks, or anything whatever — pass through their 
stages of cooling under a settled law and at a settled rate. 
We will, by way of example, illustrate this law by comparing 
the Earth and Moon. The Earth contains 81*5 more gra- 
vitating matter than the Moon ; but its surface is greater 
than the moon’s in the ratio of 13^ to 1. Therefore, as- 
suming them to have started upon their separate existences 
at the same time and at the same temperature, the Earth 
would part with its heat 8i|- times slower in virtue of its 
mass, but 135- times faster by reason of its greater extent of 
heat-radiating surface. By combining this proportion we 
shall see that the Moon would take scarcely one-sixth of 
the time to pass through its respective stages as would the 
Earth. This rule must obviously be modified somewhat 
when we compare bodies such as the Earth and Sun, because 
the greater power of the Sun would gather more external 
matter from the outer space to feed his decaying energies 
than could be possible for the Earth, so that the Sun would 
take, proportionately, far longer to cool than the much 
smaller Earth, in consequence. But Algol and its theoretical 
satellite are, as we have seen, so nearly of a size that they 
ought practically to pass through their respective stages of 
cooling in an equal time. 
The faCt, however, above stated, that bodies cool, gene- 
rally speaking, under a settled law, is fatal to statement (3) 
also. So long as the heat of the larger orb is greater than 
than that of the lesser, so long will it be impossible that the 
mean density of the larger should be greater than the density 
of the smaller, unless — unless we re-admit some such sub- 
sidiary hypotheses as those which we have just shown to be 
unsound. We may, in faCt, take it as a general rule that 
between any two orbs of equal size the density of one would 
be greater or less according as its internal heat was less or 
greater than its neighbour’s. 
In applying the above considerations to Algol and its the- 
oretical planet, we shall not fail to be struck with the faCt 
that the opaque orb must have parted with its heat at a 
much more rapid rate than the brighter, unless some acci- 
dental collision on a vast scale vapourised Algol without 
affeCting its planet, which contingency must be regarded as 
