bright in itself as some of our first-magnitude stars. The smallest telescope of the set showed a large number of stars; these must, then, be twice as far from us, on the average, as the stars just visible to the naked eye. But first-magnitude stars, like Sirius, Procyon, Arcturtus, etc., become just visible to the eye if removed to twelve times their present distance. Hence the stars seen in this first telescope of the set were between twelve and twenty-four times as far from us as Arcturus, for example.
"At least," as Herschel says, "we are certain that if stars of the size and lustre of Sirius, Arcturus, etc., were removed into the profundity of space I have mentioned, they would then appear like the stars which I saw." With the next telescope, which collected nine times more light than the eye, and brought into view objects three times more distant, other and new stars appeared, which were then (3 x 12) thirty-six times farther from us than Arcturus. In the same way, the seven-foot reflector showed stars 204 times, the ten-foot 344
