THE STELLAR UNIVERSE. 



of the seventh magnitude are only visible under the most 

 favourable atmospheric conditions, and by the sharpest eyes ; 

 now, if we suppose these stars, or others similar to them, to be 

 placed at twice their distance, the light they transmit will be 

 diminished in a fourfold proportion ; and since at their actual 

 distance they were barely visible, they will be evidently invisible 

 at the augmented distance. Bu f if we suppose a telescope- 

 directed to them, which has the power of increasing the light 

 transmitted to the eye in a fourfold proportion, they will, when 

 seen through it, appear exactly as stars of the seventh magnitude ;. 

 and if the telescope be capable of increasing the light in a greater 

 proportion, they will appear as stars of a still greater magnitude. 



In like manner, if we suppose stars of the seventh magnitude 

 removed to three times their present distance, their light would be 

 diminished in a ninefold proportion. But a telescope which would 

 increase the light transmitted to the eye in a ninefold proportion, 

 would make such stars appear like those of the seventh magnitude. 



By following the same supposition, we may imagine stars of the 

 seventh magnitude to be removed successively to four, five, 

 six, &c. times their present distance, when their light would be 

 decreased in a sixteen-fold, twenty-five-fold, and thirty-six-fold, 

 &c. proportion, so that all would be removed far beyond the 

 limits of visibility by the naked eye. But if telescopes be suc- 

 cessively directed to such stars, which are capable of increasing 

 the light received from them in a sixteen-fold, twenty-five-fold, 

 thirty-six-fold, &c. proportion, they will be all seen as stars of 

 the seventh magnitude. 



Although it be highly probable, if not certain, that the innumer- 

 able suns, which appear to us as stars, have different real mag- 

 nitudes, we may, in taking them in large collections, assume that 

 their average magnitude is the same or nearly so, since it is in 

 the highest degree improbable, that the small suns would be all 

 placed at the greatest distances from the solar system, while the 

 large suns would be placed nearest to it. Assuming, then, that 

 the average magnitude of the stars taken in large collections is 

 uniform, it will follow, that their succession of distances will be 

 proportional to the square roots of the powers of the telescopes, 

 Avhich are capable of collecting sufficient light from them to- 

 give them the appearance of stars of a given magnitude, the 

 seventh, for example, as seen with the naked eye. 



39. Such was the principle which inspired Sir W. HerscheL 

 with the stupendous idea of gauging the universe. He contrived 

 to vary the power of his telescopes to collect the light of the stars 

 in such a manner as to bring into view, successively, those 

 which filled regions of space between given limits of distance. 

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