76 CLIMATIC CYCLES AND TREE-GROWTH. 
best Eberswalde sections. In view of the as yet unsuccessful efforts 
to obtain a photograph of this section, its measures have been plotted 
and are found in figure 22 with the sunspot curve for comparison. In — 
the figure the upper curve gives the actual measures with the standard- 
izing line drawn through them. The middle curve shows the same 
measures reduced to percentage departures from the line and smoothed 
by Hann’s formula. The lowest curve shows the corresponding sun- 
spot numbers. It would be highly interesting to know the exact 
conditions under which a tree produced such a curve of growth as this. 
In the opinion of the writer, it would not be impossible to find other 
trees of this type, and even to identify them without real injury to the 
tree, so that surrounding conditions could be studied. 
The European groups.—For better comparison, the nine European 
groups have been corrected for change of growth-rate with age, reduced 
to percentages of their own means, smoothed by Hann’s formula, and 
plotted in figures 23 and 24 together with the sunspot curve. They do 
not all follow the sunspot numbers with equal accuracy, and the six 
groups showing best agreement are segregated in the first of the two 
figures. The north German and south Sweden groups around the 
Baltic Sea are the most satisfactory; the group from the west coast of 
Norway is almost as good. Then come the Dalarne, Christiania, and 
south of England groups. These six in figure 23 have the times of sun- 
spot maxima indicated by broken lines carried straight upward from the 
sunspot curve at the bottom. Of the other three groups, the trees from 
the inner coast of Norway as a whole appear to show a reversed cycle, 
probably because they were in deep inland valleys, while the southern 
groups, northwest Austria, and southern Bavaria close to the Alps 
have combined agreement and disagreement, so that they can not as 
yet be considered to give a definite result. They are shown by them- 
selves in figure 24. 
However, in the 6 groups representing the triangle between England, 
northern Germany, and the lower Scandinavian peninsula, a variation 
in growth since 1820 showing pronounced agreement with the sunspot 
curve is unmistakable. Every sunspot maximum and minimum since 
that date appears in the trees with an average variation of 20 per cent. 
This is shown in figure 25, which contains the mean of the 57 trees 
of the six groups, with the sunspot curve placed below for comparison. 
Theagreementis at once evident. The apparent increase of tree-growth 
with increase in the number of sunspots becomes still more striking 
when the means are summated in a period of 11.4 years, as shown in 
the lower part of the figure. 
A second important feature of figure 25 is that five of the eight min- 
ima show a small and brief increase in tree-growth. This suggestion of 
a second maximum is of interest, because in it we find agreement with 
Hann and Hellmann in their studies of European rainfall and sunspots, 
and it lends added weight to results which each author obtained but 
