Other more exact researches on the relative light of stars were made by HERSCHEL. These were only one more attempt to obtain a scale of celestial distances, according to which some notion of the limits and of the interior dimensions of the universe could be gained. Two telescopes, _exactly equal_ in every respect, were chosen and placed side by side. Pairs of stars which were _exactly equal_, were selected by means of them. By diminishing the aperture of one telescope directed to a bright star, and keeping the other telescope unchanged and directed to a fainter star, the two stars could be equalized in light, and, from the relative size of the apertures, the relative light of this pair of stars could be accurately computed, and so on for other pairs. This was the first use of the method of _limiting apertures_. His general results were that the stars of the first magnitude would still remain visible to the naked eye, even if they were at a distance from us _twelve_ times their actual distance.
This method received a still further development at his hands. He did not leave it until he had gained all the information it was capable of giving. He prepared a set of telescopes collecting 4, 9, 16, etc. (2 × 2, 3 × 3, 4 × 4, etc.), times as much light as the naked eye. These were to extend the determinations of distance to the telescopic stars. For example, a certain portion of the heavens which he examined contained no star visible to the naked eye, but many telescopic stars. We cannot say that no one of these is as 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_, _Arcturus_, 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 × 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 times, the twenty-foot 900 times farther from us than the average first-magnitude star. As the light from such a star requires three years to reach us, the light from the faintest stars seen by the twenty-foot would require 2,700 years (3 × 900).