VII. METHODS OF PERIODIC ANALYSIS. 
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 rdéle 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 mathe- 
matical 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 in- 
strument 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 
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