The method adopted by HERSCHEL was perfectly simple in principle, though most laborious in practice. Suppose any number of stars, A, B, C, D, E, . . . etc., near enough to each other to be well compared. The process consists simply in writing down the names of the stars, A, B, C, etc., in the order of their relative brightness. Thus if for a group of eight stars we have found at one epoch A, B, C, D, E, F, G, H, and if at another time the order was A, B, C, D, F, E, G, H, symptoms of variability are pointed out. Repeated observations, where the same star is found in different sequences, will decide the question. Thus, for the stars visible to the naked eye, we know exactly the state of the sky in HERSCHEL'S day, now nearly a century ago. Any material change cannot escape us. These catalogues have been singularly overlooked by the observers of our generation who have followed this branch of observation, and it was not till 1876 that they received proper attention and a suitable reduction (at the hands of Mr. C. S. PIERCE).
We owe to HERSCHEL the first trustworthy account of the stars visible to the naked eye, and since the date of his labors (about 1800) we have similar views published by ARGELANDER (1839), HEIS (1848), ARGELANDER and SCHÖNFELD (1857), GOULD (1860 and 1872), and HOUZEAU (1875). Thus his labors have been well followed up.
In the prosecution of this work HERSCHEL found stars whose light was progressively diminishing, others which regularly increased, one star whose light periodically varies (_[alpha] Herculis_), and at least one star (55 _Herculis_) which has utterly disappeared. On October 10, 1781, and April 11, 1782, he observed this latter star, but in May, 1791, it had totally vanished. There was no trace remaining.
The discovery of the variability of _[alpha] Herculis_ was a more important one than would at first sight appear. Up to that time the only variable stars known were seven in number. Their periods were four hundred and ninety-four, four hundred and four, three hundred and thirty-four, seven, six, five, and three days. These periods seemed to fall into two groups, one of from three hundred to five hundred days, the other comparatively much shorter, of three to seven days. _[alpha] Herculis_ came to occupy the middle place between these groups, its period being about sixty days.