n experimentally
compared with the amount received from the sun. The results differ
rather widely, but in the case of Arcturus the ratio of the star's light
to sunlight may be taken as about one twenty-five-thousand-millionth--i.
e., 25,000,000,000 stars, each equal to Arcturus, would together shed
upon the earth as much light as the sun does. But we know that light
varies inversely as the square of the distance; for instance, if the sun
were twice as far away as it is, its light would be diminished for us to
a quarter of its present amount. Suppose, then, that we could remove the
earth to a point midway between the sun and Arcturus, we should then be
5,700,000 times as far from the sun as we now are. In order to estimate
how much light the sun would send us from that distance we must square
the number 5,700,000 and then take the result inversely, or as a
fraction. We thus get 1 / 32,490,000,000,000, representing the ratio of
the sun's light at half the distance of Arcturus to that at its real
distance. But while receding from the sun we should be approaching
Arcturus. We should get, in fact, twice as near to that star as we were
before, and therefore its light would be increased for us fourfold. Now,
if the amount of sunlight had not changed, it would exceed the light of
Arcturus only a quarter as much as it did before, or in the ratio of
25,000,000,000 / 4 = 6,250,000,000 to 1. But, as we have seen, the
sunlight would diminish through increase of distance to one
32,490,000,000,000th part of its original amount. Hence its altered
ratio to the light of Arcturus would become 6,250,000,000 to
32,490,000,000,000, or 1 to 5,198.

This means that if the earth were situated midway between the sun and
Arcturus, it would receive 5,198 times as much light from that star as
it would from the sun! It is quite probable, moreover, that the heat of
Arcturus exceeds the solar heat in the same ratio, for the spectroscope
shows that although Arcturus is surrounded with a cloak of metallic
vapors proportionately far more extensive than the sun's, yet, smothered
as the great star seems in some respects to be, it rivals Sirius itself
in the intensity of its radiant energy.

If we suppose the radiation of Arcturus to be the same per unit of
surface as the sun's, it follows that Arcturus exceeds the sun about
375,000 times in volume, and that its diameter is no less than
62,350,000 miles! Imagine the earth and the other planets constituting