194 BORTHWICK—THE DIAMETER- 
numbers attached to the trees are those of his lists. In many cases 
I was able to extract cylinders fully five inches long, and in no 
case less than two inches. The length of the cylinder is, how- 
ever, not necessarily an indication of the number of year-rings in 
it. A cylinder five inches long from a broad-ringed or fast- 
growing tree may contain no more or even fewer year-rings than 
a cylinder four inches long from a narrow-ringed or slow-growing 
tree. The greatest number of year-rings extracted was forty 
from a horse-chestnut, while fifteen to twenty-five was an easily 
obtained number. from other species. (See Table 1.) 
The breadth of the year-rings sometimes varies greatly on 
different sides of the same tree, especially in isolated trees which 
have not been grown in the company of others. This was 
well shown on many of the cylinders, so that cylinders of the 
same length from different sides of the tree do not necessarily 
have the same number of year-rings, and conversely cylinders 
with the same number of year-rings are not necessarily of equal 
lengths. This can be seen from the accompanying Table III. 
Having got the four borings I counted off the number of year- 
rings in each. It was generally found that one of the cylinders 
showed a smaller number than any of the others. I therefore 
marked off this number ( say 7) on each of the other cylinders, 
disregarding any that were left over, as they did not come into 
consideration in making out an average. Having done this, I 
next found the aggregate length of the cylinders for this number 
of year-rings, and by dividing this by two and subtracting the 
result from the present diameter (bark included) I obtained the 
diameter which the tree had as many years ago as there were 
marked off rings in the cylinders. I next subtracted in succes- 
sion twice the mean breadth of each annual ring from the 
diameter of the corresponding year, which gave the diameter of 
the preceding year. This operation gave the intermediate 
diameters and again the diameter 7 years ago. The first opera- 
tion was an excellent means of checking the second. 
It was then an easy matter to get the circumference for each 
year from the diameters. By subtracting the circumference for 
a certain year from that of the year following I got the circum- 
ference increment. 
On comparing the results obtained by both methods—tape and 
