The other difficulty connected with yearly identity is the omission of rings. Missing rings occur in many trees without lessening the value of the tree unless there are extensive intervals over which the absence produces uncertainty. A missing ring here and there can be located with perfect exactness and causes no uncertainty of dating. In fact, so many missing rings have been found after careful search that they often increase the feeling of certainty in the dating of rings.

Missing rings occur when autumn rings merge together in the absence of any spring growth. This rarely if ever occurs about the entire circumference of the tree. There are a few cases in which, if the expression may be excused, I have traced a missing ring entirely around a tree without finding it. I have observed many cases in which the missing ring has been evident in less than 10 per cent. of the circumference. Some are absent in only a small part of their circuit. I have observed change in this respect at different heights in the tree, but have not followed that line of study further. It is beautifully shown in the longitudinally bisected tree.

One sees from this discussion what the probable errors may be in mere counting of rings. In the first work on the yellow pines the dating was done by simple counting. Accurate dating in the same trees (19 of them) later on showed that the average error in counting through the last 200 years was 4 per cent., due practically always to missing rings. A comparison in seven sequoias between very careful counting and accurate dating in 2,000 years shows an average counting error of 35 years, which is only 1.7 per cent.

Full confidence in yearly identity really comes from another source. The finding of similar distribution of large and small rings in practically all individuals of widely scattered groups of trees over great periods of time has been evidence enough to make us sure. This comparison process of groups of rings in different trees has received the rather clumsy name of "cross-identification.' Cross-identification was first successful in the 67 Prescott trees, then was carried across 70 miles to the big Flagstaff groups. Later it was found to extend 225 miles further to southwestern Colorado with extreme accuracy, 90 per cent. perhaps. This is over periods. of more than 250 years. Catalina pines from near Tucson have a 50 per cent. likeness to Flagstaff pines. There are many points of similarity in the last 200 years and many differences. Santa Rita pines are less like the Flagstaff pines than are the Catalinas. In comparison with the California sequoias, differences become more common. The superficial resemblance to Arizona pines is 5 or 10

per cent. only. That is, out of every 10 or 20 distinctive rings with marked individuality, one will be found alike in California. and Arizona. For example, A. D. 1407, 1500, 1580, 1632, 1670, 1729, 1782, 1822 and 1864 are small in Arizona pines and California sequoias. While only a few extreme individual years thus match, there are correspondences in climatic cycles to which attention will be called later.

Cross-identification is practically perfect amongst the sequoias stretching across 15 miles of country near General Grant National Park. Trees obtained near Springville, some 50 miles south, show 50 to 75 per cent. resemblance in details to the northern group. This was far more than enough to carry exact dating between these two localities. Cross-identification in some wet climate groups was extremely accurate. A group of 12 logs floating in the rivermouth at Geffle, Sweden, showed 90 to 95 per cent. resemblance to each other. The range was 100 to 200 years and there were no uncertain years at all. The same was true of some 10 tree sections on the Norwegian coast and of 13 sections cut in Eberswalde in Germany. A half dozen sections cut in a lumber yard in Munich did not cross-identify with each other. A group of 5 from a lumber yard in Christiania was not very satisfactory. The vast majority, however, have been absolutely satisfactory in the matter of crossidentification. Nothing more is needed to make the one ring a year ideal perfectly sure, but if there were, it would come in such tests as frequently occur in checking the known date of cutting or boring, with a set of rings previously dated. That has been done on many occasions in Arizona and California. To give final assurance, the record in the yellow pine was compared with statements of good and bad years, and years of famine, flood and cold, reported in Bancroft's "History of Arizona and New Mexico," and it was found that his report identified with the character of the growth in the corresponding years of the trees.

Three results may be noted before leaving this important subject. Deficient years extend their character across country with more certainty than favorable years. A deficient year makes an individual ring small compared to those beside it. Large rings, on the other hand, are more apt to come in groups and so do not have quite the same individuality. Nor are they as universal in a forest. If they occur at a certain period in one tree, the chances are about 50 per cent. that the corresponding years in the neighboring trees will be similarly enlarged. If, however, a very small ring occurs in a tree, the chances are over 90 per cent. that the neighboring trees will show the same year small.2

Second, with many groups of trees where the resemblance be

tween their rings is strikingly exact, a small number of individuals such as 5 will answer extremely well for a record, and even fewer will give valuable and reliable results. But the central part of a tree has larger growth and is less sensitive than the outer part. Its character is somewhat different. To get a satisfactory representation through several centuries, therefore, it is better to combine younger trees with older ones to get a more even and constant record of climatic conditions.

The third thought is this. The spreading of a certain character over many miles of country stamps it in almost every case as climatic in origin, because climate is the common environment over large areas.

III. NUMBER AND LOCATION OF TREES

The whole number of trees used is nearly 450 and includes cone-bearing trees from Oregon, California, Arizona, New Mexico, Colorado, Vermont, England, Norway, Sweden, Germany and Bohemia. The total number of rings dated and measured is well over 100,000. The average ages found in these various trees are very interesting. The European groups reach for the most part about 90 years, although one tree in Norway showed 400 years of age, and 15 were found beginning as early as 1740. The Oregon group of Douglas firs goes back to about 1710, the Vermont hemlocks. reach 1654, the Flagstaff yellow pines give a number of admirable records from about 1400.

The oldest trees, of course, were the great sequoias from the Sierra Nevada Mountains in California. They were found to have ages that formed natural groups, showing probably a climatic effect. There are very few under 700 years old (except the young ones which have started since the cutting of the Big Trees). A number had about that age. The majority of the trees scatter along in age from 1,200 up to about 2,200 years, at which age a large number were found, one or two were found of 2,500 years, one of 2,800, one of 3,000, one at just under 3,100, and the oldest of all just over 3,200. The determination of this age of the older sequoias in the present instance is not merely a matter of ring counting, but depends upon the inter-comparison of some 55,000 rings in thirtyfive trees. In 1919 a special trip was made to the Big Trees and samples from a dozen extra trees obtained in order to decide the case of a single ring, 1580 A. D., about which there was some doubt, and it was apparent that the ring in question stood for an extra year. This was corrected and it now seems likely that there is no 2 This success in cross-identification applies to the groups examined. A recent group of coast redwoods from Santa Cruz, California, present a multitude of difficulties.

mistake in dating through the entire sequence of years, but if not correct the error is certainly very small.

IV. TOPOGRAPHY

The late Professor W. R. Dudley of Stanford University in his charming essay on the "Vitality of the Sequoia" refers to the fact that the growth of the Big Trees depends in a measure on the presence of a brook near by. This agrees with my own observations. Size is far from a final indication of age. The General Grant tree which has no running water near it and is the largest in the Park of that name, has a burnt area on one side in which the outer rings are exposed, allowing an estimate of its average rate of recent growth. From much experience with the way the sequoia growth is influenced by age, it was possible to assign 2,500 years as the approximate time it took this giant to reach its present immense diameter of close to 30 feet. But about three miles west near a running brook is a stump which is over twenty-five feet in diameter, but is only about 1,500 years old. That is the effect of contact with an unfailing source of water.

Perhaps the most general characteristic which stands out in the different groups of dry-climate trees is a close relationship of this kind between the topography and the growth produced. For that reason, I have visited the site of every dry-climate group and indeed have examined the stumps of almost every tree in my collection.

It was found that dry-climate trees which grew in basins with a large and constant water supply, and this refers especially to the sequoias, usually produced rings without much change in size from year to year. This character of ring is called "complacent." The opposite character is the "sensitive" ring where a decided variation is shown from year to year. Sensitive trees grow on the higher elevations where the water supply is not reliable and the tree must depend almost entirely on the precipitation during each year. Such trees grow near the tops of ridges or are otherwise separated from any collection of water in the ground. In case of the basin trees, one could be sure that a ring was produced every year, but owing to the lack of individuality in the rings for certain years, it was difficult to compare trees together and produce reliable data. In case of the sensitive tree growing in the uplands there was so much individuality in the rings that nearly all of the trees could be dated with perfect reliability, but in extreme cases the omission of rings in a number of trees required special study. Of course, these cases were easily settled by comparison with other trees growing in intermediate localities.

Trees growing in the dry climate of Arizona at an altitude where they have the utmost difficulty in getting water to prolong life become extraordinarily sensitive. In the same tree one finds some rings several millimeters across and others microscopic in size or even absent.

In order to express this different quality in the trees a criterion called mean sensitivity is now under investigation. It may be defined as the difference between two successive rings divided by their mean. Such quotients are averaged over each decade or other period desired and are believed to depend in part on the relative response of the trees to climatic influences. The great sensitiveness of the yellow pines as compared with the best sequoias is evident in any brief comparison of dated specimens.

V. INSTRUMENTS

In the course of this long attention to the rings of trees and in studying such a vast number of them, special tools to secure material and to improve and hasten the results have very naturally been adopted or developed. One goes into the field well-armed, carrying a flooring saw with its curved edge for sawing half across the tops of stumps, a chisel for making numbers, numerous paper bags for holding fragments cut from individual trees, a recording note book, crayon, a shoulder bag, camera and especially a kindly, strong-armed friend to help in the sawing. In the last eighteen months the Swedish increment borer has been used extensively to get records from living pine trees. Hard woods and juniper are too tough. It has previously been considered that the little slender cores, smaller than a pencil, so obtained, would hardly be worth working on. But the method of mounting them has been raised to such a degree of efficiency, and the collection of material becomes so rapid that the deficient length and the occasional worthless specimen are counterbalanced. Besides, it is often easy to supplement a group of increment cores by some other form of specimen extending back to greater age. The Mount Lemmon group, near Tucson, has eight cores giving a good record from about 1725 to the present time; a saw cutting from a large stump in Summerhaven carries the record back 150 years earlier. It should, however, be supported by at least one more long record and this can be done by the tubular borer described next.

The tubular borer was designed especially for the dried and sometimes very hard logs in the prehistoric ruins. It works well on pine trees and junipers. It gives a core an inch in diameter, which means a far better chance of locating difficult rings than in the increment borer cores which are only one fifth of that diameter. The borer is a one-inch steel tube with small saw-teeth on one