averaging near the larger figure. It should more properly be called a "broken" period perhaps, since it is made up of different periods for different intervals, first one and then another predominating. The methods used in the search for this 2-year period have revealed frequently a solar cycle also, and there seems to be some obscure connection between the two.
Differential patterns. — The periodograms, as already shown, indicate the different cycles operating within a certain range. Any one cycle together with others close to it may be studied more minutely on the differential pattern produced when the instrument is set at the desired period. Plates 12 and 10, b, are arranged to illustrate this and at the same time show the solar cycles in several of the groups. A periodic effect equal in length to the setting of the instrument is indicated by a vertical row of light crests or dark spaces. These rows may be seen in any of the patterns. If the row of crests points downward to the right, its period is greater than the setting of the instrument; if to the left, the period is less. The straightness of the row indicates the regularity of the period. Plate 12, q, is made from the standard 5-year period with a setting at 5.0 years. The first pattern in plate 12 shows the regularity of the sunspot period since 1610 A. D. The interval in the latter part of the eighteenth century, when the cycle was reduced to less than 10 years, is distinguished by a bending of the row toward the left. This is followed by a deflection toward the right during the interval of readjustment from 1790 to 1830. The direction of any row becomes an exact measure of its period.
If a period is constant, the row of crests is straight. A zigzag row made up of short, straight parts means that one period after another becomes predominant. A curved row means a constantly changing period. Some examples of apparent curved rows may be picked out in the sequoia pattern. A curved row may indicate some other function than a simple period. Pattern R in plate 12 is made to illustrate a logarithmic variable, beginning at the top as a 5-year period and changing by a constant percentage increase to a 10-year period at the bottom. The instrument is set at 8.0 years.
The 11-year cycle. — The first 6 patterns in plate l2 illustrate this cycle. The first gives the sunspot numbers from 1610 to 1910, including the uncertain ones from 1610 to 1750. Pattern B gives the fine vertical row shown by the 6 groups of trees from north Europe. This was shown as a curve in figure 25, page 77. The qualitative test of the entire 80 European trees is shown in pattern C. This may be seen as a curve in figure 26. The small secondary maxima at several of the minima show as light crests between the main rows. Pattern D shows a 12-year period in south Sweden during the past 50 years, preceded by