22 CLIMATIC CYCLES AND TREE-GROWTH. 
this yellow pine under all conditions. Without doubt it is here due to 
homogeneous climatic conditions in a uniform topography and a tree 
sensitive to varying moisture-supply. 
In a good many cases where the number of trees in a group has 
decreased in earlier years, it has been found (by carrying overlapping 
curves through a considerable period) that a few trees give essentially 
the same curves as a large number. From the entire experience I have 
been led to assign a minimum preferably of 5 trees in any one group, 
while in some groups (notably the yellow pine of Arizona and the 
sequoias of California, together with the Scotch pine in central Sweden 
and in north Germany), 2 trees would give a very excellent record. In 
only one group have 5 failed to give a satisfactory record, and that was 
the set of Scotch pines from the outskirts of Christiania. The cross- 
identification of this group was not felt to be satisfactory, and a double 
number of trees from that locality would have been an advantage. This 
failure was thought to be due in part to therugged character of theregion. 
Direction of maximum growth.—The maximum trunk-growth was 
observed to ovcur a little east of north. The average difference between 
the radii was 12 per cent. An explanation of this increased growth to 
the north is to be found in the increased amount of moisture on that 
side, due to the slower melting of snowand decreased evaporation in the 
shade. For nearly all these trees the ground had a gentle slope toward 
the south, so that moisture working down hill reaches the north side 
of the root system first. 
Rate of growth and age.—The relation of average ring-width to 
radius was found to be intermediate between an inverse proportion to 
the radius and an inverse proportion to the square of the radius. If 
the tree merely increased in diameter without growing upward, the 
width should be roughly inversely proportional to the radius. If the 
tree is increasing in height at the same time, we should expect an 
inverse proportion to the square of the radius. We find the relation to 
be between these. 
Growth and soil.—In early studies of 25 yellow pines at Flagstaff 
it was noticed that a certain subgroup of 6 trees dropped to its strong 
minima in 1780 and 1880 more promptly than the others. This 
appears to be connected with the soil upon which the trees grew. This 
subgroup stood on a limestone formation where the soil is porous and 
the rock below full of cracks. The other two subgroups grew on 
recent lavas, very compact and unbroken, covered with a rather thin 
layer of clayey soil. With the former, therefore, the rain passed 
quickly through the soil and away, and we do not find so much con- 
servation of moisture as in the latter, where the water could find no 
convenient outlet. On the whole, the growth seems to be more rapidly 
influenced by changesof moisture on limestone than on volcanic rocks. 
