VII. METHODS OF PERIODIC ANAYLSIS.
Need for such analysis.—During these modern times of rainfall and sunspot records we may compare such records with tree-growth and obtain the interesting correlations exhibited in the last two chapters; but the tree records extend centuries and even thousands of years back of the first systematic weather or sun records of any kind. Without being over-precise or exhaustive, it is interesting to note that California weather records began about 1851. Records on the Atlantic coast began largely in the half-century before that date. London has a rainfall record since 1726, Paris since 1690, and Padua since 1725. Good sunspot records began about 1750, but the number of maxima and minima is known between 1610 and 1750, although the exact dates are uncertain. All this does not carry us very far back, but it serves as an excellent basis for the correct interpretation of the record in the trees.
It would be possible to apply correlation formulas to the Arizona tree records and perhaps to the sequoias and construct a probable rainfall record for long periods of time, but apart from Huntington's study of the "Climatic Factor in History," the chief use of such a record would be in studying the laws which govern rainfall; and this is best done through cycles. We shall find that the sunspot cycle plays an important ro1e in rainfall. But we find traces of the solar cycle in nearly all of our tree groups, and evidently the way to read the trees is to study first of all their alphabet of cycles. Hence the best methods of identifying cycles must be used.
Proportional dividers. — If a short series of observations is to be tested for a single period, it can be done by mathematics, but it will take many hours and give a result in terms so precise as often to deceive. This, for example, has been the difficulty with the mathematical solution of the sunspot curve. It seems to the writer that the safer way to solve such a curve is by a graphic process, plotting the curve and applying equal intervals along it. An extremely good instrument for this purpose is the multiple-point proportional dividers. By a system of pivots and bars, 16 or more points are maintained in a straight line and at equal intervals, while the space between two successive points may be drawn out from one-eighth inch to one inch. The remarkable persistence of the half sunspot period in the early Flagstaff trees was detected in this way.
The projection of equal spacing on curves as long as 12 to 15 feet has been done by a 10-foot india-rubber band with small metal clips pinched on at regular intervals. As the band was stretched all the intervals were enlarged by equal amounts, and periodic phenomena were detected. Similar use could be made of the sharp shadows cast by the glowing carbon of an arc-light. The shadow of a transparent