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Life and Works
| Order of Distance. |
Number of Stars there is Room for. |
Magnitude. | Number of Stars of that Magnitude. |
| 1........ | 26 | 1 | 17 |
| 2........ | 98 | 2 | 57 |
| 3........ | 218 | 3 | 206 |
| 4........ | 386 | 4 | 454 |
| 5........ | 602 | 5 | 1,161 |
| 6........ | 866 | 6 | 6,103 |
| 7........ | 1,178 | 7 | 6,146 |
| 8........ | 1,538 |
The result of this comparison is, that if the order of magnitudes could indicate the distance of the stars, it would denote at first a gradual and afterward a very abrupt condensation of them, at and beyond the region of the sixth-magnitude stars.
If we assume the brightness of any star to be inversely proportional to the square of its distance, it leads to a scale of distance different from that adopted by Herschel, so that a sixth-magnitude star on the common scale would be about of the eighth order of distance according to this scheme—that is, we must remove a star of the first magnitude to eight times its actual distance to
