THE CURVE OF THE BIG TREES. 147 



sides, but the lost portions between the twenty-third and twenty-seventh years would 

 never have been replaced. Should such a tree reach the age of 3,000 years, it might 

 well appear 500 years younger on one side than the other. In a case hke that of Plate 6 

 it is an easy matter to perceive the loss of the rings, but when a tree becomes large and 

 the rings are not only very thin, but have a length of from 20 to 100 feet, as seen on the 

 stump, it is extremely difficult to follow an individual ring and see whether it dies out or is 

 continuous. Occasionally one can perceive ring after ring dying out, as is illustrated at 

 A in Plate 6. At other times this can not be seen, but as the stump is counted farther 

 and farther toward a given side the number of rings keeps increasing. In stiU other cases 

 the loss of rings is manifest enough and makes no difficulty. This is true in cases of injury, 

 such as burning. It is illustrated in Plate 7, where the rings are seen to tend to grow out 

 from either side over the injured portion until finally they coalesce and the scar is no longer 

 visible on the surface, although it still shows when the tree is cut. Where such scars 

 exist it is always possible to avoid them in measuring, but in trees which have been sub- 

 jected to many injuries, in order to avoid them, the measuring must be done upon lines which 

 zigzag. In such cases the rings vary in width more than would be the case if only climatic 

 causes were active. Such trees were in general avoided in our measurements, although a 

 few were included, because they were of unusual age. Trees which have lost rings in the 

 other, less noticeable fashion can not so easily be detected or avoided, inasmuch as two 

 counts are necessary before their character becomes evident. Even then one can not 

 be sure that the error is reaUy in the tree and not in the observer until a third count has 

 been made. Cases where three or more counts proved highly divergent were rejected in 

 our final computations. Usually, however, a fair degree of agreement was found. In the 

 majority of cases the first two readings were in such close agreement that both could be used. 

 Nevertheless, differences of 1 or 2 per cent are common. In such cases we have assumed 

 that the larger value comes nearer to representing the true age. 



From what has just been said, it is evident that while many trees have the full number 

 of rings on all sides, many others show deficiencies. Hence it is impossible to be sure of 

 the exact age of any tree unless measurements are made on all sides. With trees having a 

 diameter of 10 to 20 feet or more, and numbering their rings by the thousand, this is 

 practically an impossibihty because of the expense and time involved. If a small number 

 of measurements, one, two, or tliree, are made upon each tree at places determined by 

 the accidents of cutting and of smooth, clean, easily read radii, there is bound to be a 

 deficiency in the apparent as compared with the real age of the trees. In individual cases 

 the radii having the maximum number of rings will happen to be counted and the true 

 age will be obtained. In the best trees, those which do not have the habit of dropping any 

 rings, this will happen continually. With the other trees it will happen only rarely, and 

 thus in any large group there is sure to be an error. This error can not be calculated 

 exactly, since there is no known rule as to how much of a given ring is lost and how much 

 retained. If we make an assumption as to tliis matter, however, the rest can readily be 

 calculated. Let us assume that conditions are hke those in figure 34. Here the age of 

 the tree is supposed to be 100 years. In the half of the trunk indicated by the letters 

 A^, A-, and A' all the rings are complete. In the other half they die out at regular intervals, 

 until the minimum is reached at B, half-way between A' and A', the two points where the 

 maximum comes to an end. This will be readily seen from the diagram, where the number 

 of rings at the minimum is assumed to be 76. Suppose, now, that only one radius were 

 measured in an infinite series of trees of this kind. This radius would fall at all possible 

 positions, as chance might dictate. Half of the time it would have the maximum value 

 of 100 rings. During the rest of the time it would vary from 100 to 76, with an average 

 value of 88. Hence the average of all the readings would be the mean of 88 and 100, 

 or 94, which is less than the true maximum by 6, or by one-fourth of the difference between 



