In order to exhibit this law in the plainest possible manner the dates of maxima and minima should be laid down on ruled paper in proper mathematical form, the _abscissæ_ of the curve representing the years, and the _ordinates_ the number of spots observed. An examination of a curve thus plotted shows two things:—(1) That the period is clearly an eleven-year one, as has been already stated; (2) that it is not however quite as simple in its form as it was at first thought to be; for in reality there are two periods superposed, the one rather more than half a century long, and the other extending over the 11 years already spoken of. We do not possess early observations sufficiently numerous and sufficiently good to enable us to draw any unimpeachable conclusions as to the nature of the long period; we can only be certain that it exists. The later labours of Wolf, however, fixed that period at 55½ years. It is a result of this that, according to Loomis, a period of comparative calm on the Sun existed between 1810 and 1825. Each maximum lies nearer to the minimum which precedes it than to the minimum which follows it, for the spots increase during 3.7 years, and then diminish during 7.4 years. According to De La Rue the increase occupies 3.52 years, and diminution 7.55 years. This concurrence between De La Rue and Wolf is surprising considering the diversity of the methods which led to results almost identical, the one set being based on the number of the spots, and the other on the superficial extent of the spots. The different periods in succession are not absolutely identical: but it has been remarked that if during any one period the decrease is retarded or accelerated, then the increase next following will be lengthened or contracted to a corresponding extent. In consequence of this we are sometimes able to predict with fair accuracy when the next ensuing maximum or minimum will take place. The most striking feature of such a curve as that just alluded to is the very sensible secondary augmentation which happens very soon after the principal maximum. A very curious circumstance has come to light in connection with the epochs of maxima and minima. In arranging the spots according to their latitude and longitude on a diagram sufficiently contracted, Carrington found that their latitude decreases gradually as the period of minimum draws near; then when their number begins to increase they begin to appear again at a higher latitude. This seems to be a definite law. At any rate Carrington’s conclusion has been found to hold good by the observations of Spörer and Secchi.