THE CURVE OF THE BIG TREES. 



149 



true maximum — that is, of the actual age of the tree. By comparison of the first and 

 second readings of the trees actually measured, it is easy in any given group to compute 

 this difference between the average maximum and the average ininimum. Its value for 

 all our sequoias is shown in table 5. There it will be seen that for trees under 1,000 years 

 old it amounts to about 0.73 per cent. As the trees grow older it increases, until with 

 trees more than 2,000 years old it becomes 1.62 per cent. Thus it appears that as a tree 

 grows older the liability to loss of rings increases, so that a tree 2,000 years old is not only 

 likely to have lost twice as many rings as a tree 1,000 years old, because it is twice as old, 

 but this loss is likely to have been doubled. This greater proportion of loss among the old 

 trees is due, apparently, to the fact already discussed, that the trees which live to a great 

 age grow slowly in their youth. They are hard, knotty trees, able to resist drought, and per- 

 haps not suffering by the loss of a year's growth so much as do trees which grow rapidly. 



Table 5. — The difference between the first and second measurements of sequoias. 



The percentages given in table .5 enable us to form an estimate of the degree of accuracy 

 which we have probably obtained in determining the age of our trees. If we assume that 

 half of each tree, on an average, shows the correct number of rings, the ratio of the per- 

 centage of rings missing to the average difference between the maxmum and minimum 

 measurements will be 24 to 9. In group A of the table, the average age of the trees is 640 

 years. The average difference between the first and second readings amounts to 0.73 per 

 cent. From this we can deduce the equation, 24 : 9 : : X : 0.73. In this case. A' is the 

 percentage of difference between the absolute maximum and absolute minimum of the 

 trees in group A. Its value is 1.94 per cent, and this percentage of 640 equals approxi- 

 mately 12 years. This means that, according to the assumption made above, the average 

 tree under 1,000 years old misses 12 rings at some point in its circumference. 



In order to find how nearly the supposed maximum approximates the actual maximum, 

 another equation is necessary. In the assumed case of figure 34, the average maximum 

 amounts to 99.4 per cent of the absolute maximum, and is less than it by 0.6 per cent. 

 The difference between absolute maximum and absolute minimum is 24. The ratio of 

 24 to 0.6 equals that of 12 to Y, in which Y is the number of years by which the average 

 measured maximum in trees under 1,000 years of age is less than the average absolute 

 maximum. F, it will be seen, amounts to 0.3, or less than half a year. 



In the same way it is possible to calculate the number of years by which the maximum 

 reading of trees of any age will be less than its true value. Even in the case of the oldest 

 group of trees this amounts to only about 4 years, or 0.160 per cent of the age. This is 

 so small a number that it can be neglected, and in cases where two or more readings are 

 available we can assume that the error arising from the loss of rings is no greater than 

 the error due to mistakes in counting. 



Where only one reading is available, however, the case is quite different. In the ideal 

 case of figure 34, an average reading is 6 per cent less than the true maximum; 6 per cent 

 is two-thirds of the 9 per cent which we have seen to be the average amount by which 

 the maximum and minimum readings differ from one another if the two lines of measure- 

 ment be 135° apart. If we apply this ratio to the percentages of table 5, we find that in 

 trees under 1,000 years of age the average reading is less than the ti-ue maximum by 0.48 

 per cent, while in the oldest group of trees it is less by 1.08 per cent. 



