Grave discrepancies were early perceived to exist between determinations of the sun's rotation by different observers. Galileo, with "comfortable generality," estimated the period at "about a lunar month";[416] Scheiner, at twenty-seven days.[417] Cassini, in 1678, made it 25·58; Delambre, in 1775, no more than twenty-five days. Later inquiries brought these divergences within no more tolerable limits. Laugier's result of 25·34 days--obtained in 1841--enjoyed the highest credit, yet it differed widely in one direction from that of Böhm (1852), giving 25·52 days, and in the other from that of Kysæus (1846), giving 25·09 days. Now the cause of these variations was really obvious from the first, although for a long time strangely overlooked. Scheiner pointed out in 1630 that different spots gave different periods, adding the significant remark that one at a distance from the solar equator revolved more slowly than those nearer to it.[418] But the hint was wasted. For upwards of two centuries ideas on the subject were either retrograde or stationary. What were called the "proper motions" of spots were, however, recognised by Schröter,[419] and utterly baffled Laugier,[420] who despaired of obtaining any concordant result as to the sun's rotation except by taking the mean of a number of discordant ones. At last, in 1855, a valuable course of observations made at Capo di Monte, Naples, in 1845-6, enabled C. H. F. Peters[421] to set in the clearest light the insecurity of determinations based on the assumption of fixity in objects plainly affected by movements uncertain both in amount and direction. Such was the state of affairs when Carrington entered upon his task. Everything was in confusion; the most that could be said was that the confusion had come to be distinctly admitted and referred to its true source. What he discovered was this: that the sun, or at least the outer shell of the sun visible to us, has _no single period of rotation_, but drifts round, carrying the spots with it, at a rate continually accelerated from the poles to the equator. In other words, the time of axial revolution is shortest at the equator and lengthens with increase of latitude. Carrington devised a mathematical formula by which the rate or "law" of this lengthening was conveniently expressed; but it was a purely empirical one. It was a concise statement, but implied no physical interpretation. It summarised, but did not explain the facts. An assumed "mean period" for the solar rotation of 25·38 days (twenty-five days nine hours, very nearly), was thus found to be _actually_ conformed to only in two parallels of solar latitude (14° north and south), while the equatorial period was slightly less than twenty-five, and that of latitude 50° rose to twenty-seven days and a half.[422] These curious results gave quite a new direction to ideas on solar physics.