CLIMATIC CYCLES AND TREE-GROWTH
A STUDY OF THE ANNUAL KINGS OF TREES IN
RELATION TO CLIMATE AND SOLAR ACTIVITY
BY
A. E. DOUGLASS
Director of Steward Observatory, University of Arizona
PUBLISHED BY THE CARNEGIE INSTITUTION OF WASHINGTON
WASHINGTON, 1919
CARNEGIE INSTITUTION OF WASHINGTON
PUBLICATION No. 289
PRESS OF GIBSON BROTHERS, INC.,
WASHINGTON, D. C.
CONTENTS.
PAGE.
I. INTRODUCTION 9
Trees suitable for climatic study 11
Introduction to special studies on the
yellow pine 12
Location 12
Climate and seasonal conditions. 13
II. PRELIMINARY STUDIES ON THE YELLOW
PINE 15
Yearly identity and the dating of rings 15
Cross-identification 16
Cross-identification and climate. 17
Month of beginning annual means. . . 17
The time of year of ring formation. . . 18
Significance of subdivisions in
rings 20
Number of trees necessary for reliable
results 21
Direction of maximum growth . . 22
Rate of growth and age 22
Growth and soil 22
III. COLLECTION OF SECTIONS 23
The first Flagstaff group of 25 sections 23
Subgroups 24
First suggestion of cross-identifi-
cation 24
The Flagstaff 500-year record. ... 24
The second Flagstaff group of 7 sec-
tions 27
The Prescott group 27
South of England group 29
Outer coast of Norway group 30
Inner coast of Norway group 32
Christiania group 35
Central Sweden group 35
South Sweden group 36
Eberswalde (Prussia) group 37
Pilsen (Austria) group 39
Southern Bavaria group 39
Old European trees 40
Windsor (Vermont) group 41
Oregon group 42
The Sequoia group 44
The Sequoia journey of 1918 49
IV. DETAILS OF CURVE PRODUCTION 54
Preparation of radial samples 54
Form of sample 54
Method of cutting 54
Preparation for measurement ... 55
Identification of rings 55
Fire-scars 56
Cross-identification between dis-
tant points 57
The difficult ring 1580 58
Measuring 58
Tabulating 59
Averaging 60
Smoothing 61
Standardizing 63
Plotting 64
Problems in plotting 64
V. CORRELATION WITH RAINFALL 65
Result of study of curves 65
Early tests of rainfall correla-
tion 65
The Prescott correlation 66
Accuracy 66
PAGE.
V. CORRELATION WITH RAINFALL — contd.
The Prescott correlation — continued.
Mathematical relation of rainfall
and growth 67
Character of the conservation
term 67
Summary 70
Sequoia correlation with rainfall. 70
Future work 72
Meteorological districts 72
Meteorological districts and
growth of trees 72
Arizona and California 73
Meteorological districts and solar
correlation 73
VI. CORRELATION WITH SUNSPOTS 74
Dry-climate tests 74
Wet-climate reaction 74
The European groups 76
Windsor (Vermont) correlation. . 79
The sunspots and their possible causes 81
Appearance 81
Suggested causes of sunspots. ... 82
Length of the sunspot period ... 84
Tree-growth and solar activity . . 84
VII. METHODS OF PERIODIC ANALYSIS . ... 85
Need for such analysis 85
Proportional dividers 85
The optical periodograph 86
Schuster's periodogram 86
The optical periodogram ....... 86
Application to length of sunspot
period 88
Production of differential pattern 89
Theory 90
The automatic optical periodograph. 92
The curve 92
Track and moving mechanism . . 92
Differential pattern mechanism . 93
The periodogram mechanism. ... 94
Periodograms 96
Resolving power of the periodo-
graph 96
VIII. CYCLES 98
Significance of cycles 98
Predominant cycles 98
Locality and solar cycles 99
Illustrations of cycles 101
The 11-year cycle 101
The 11-year cycle in sequoia.. . . 102
Correlation curves 103
Double and triple cycles 103
A 2-year cycle 106
Periodograph analyses 107
Differential patterns 107
The 11-year cycle 107
Changes in the 1 1-year tree-cycle
of Arizona 108
Sequoia pattern 109
Other solar cycles 109
The 100-year cycle 110
Illustration by the periodograph . 1 10
Summary Ill
Addendum 112
APPENDIX 113
Tables of mean tree-growth by groups 113
Bibliography 124
ILLUSTRATIONS.
PLATES.
PAGE.
PLATE 1.
A. Bottomless pits near Flagstaff, illus-
trating drainage through lime-
stone 12
B. Yellow pine forest of northern Ari-
zona 12
PLATE 2.
Cross-identification of rings of growth
in yellow pine (Pinus ponderosa) . 24
PLATE 3.
A. Section of Scotch pine from Southern
England 30
B. Section of Scotch pine from coast of
Norway 30
PLATE 4.
A. Section of Scotch pine from 6s, Nor-
way 36
B. Section of Scotch pine from Dalarne,
Sweden 36
PLATE 5.
A. Upland contours, above Camp 6 in
Sequoia Grove: D-19 46
B. Basin contours, Indian Basin, look-
ing S. E. : D-12 and 13 in center. 46
PLATE 6.
A. Cutting radial sample from end of
log, Converse Hoist, D-20, age
2800 years 50
B. Site of oldest tree, Converse Hoist,
D-21, age 3200 years 50
PLATE 7.
A. Cutting sample from stump, Enter-
prise: D-22, age 3000 years 52
B. Centennial stump, Enterprise; cut in
1874, D-23, age 3075 years 52
PLATE 8.
A. Section of Scotch pine from Ebers-
walde, Prussia, showing solar
rhythm 74
B. Another section from the same forest,
showing same rhythm 74
PLATE 9.
A. Periodogram of the sunspot numbers,
1755-1911. Corrugations show
periods. The numbers give length
of period in years. The white
line is the year 1830 and shows
Phase 88
PAQK.
PLATE 9 — continued.
B. Differential pattern used in making
the periodogram, consisting of
the sunspot curve mounted in
multiple 88
C. Same pattern photographed out of
focus to show discontinuities in
the vertical lines 88
D. Sweep of sunspot numbers, 1755-1911 88
E. Differential pattern of sunspot num-
bers made b5' the periodograph
process 88
PLATE 10.
A. The automatic optical periodbgraph. 94
B. Differential patterns of Sequoia rec-
ord, 3200 years at 11.4 94
PLATE 11.
A. Periodogram of standard 5-year
period 96
B. Periodogram of mixed periods 96
C. Periodogram of sunspot numbers
1610-1910 96
D. Periodogram of Flagstaff 500-year
record to show cycles between
4 and 15 years of length 96
E. Periodogram of same continued to
25 years 96
PLATE 12. Differential patterns:
a. Sunspot numbers, 1610-1910 at 11.4. 108
h. 57 European trees, 1830-1910 at 11.4. 108
c. 80 European trees, 1800-1910 at 11.4. 108
d. South Sweden, 1830-1910 at 12.0. . . 108
e. Vermont group, 1650-1910, at 11.3. 108
/. Flagstaff group, 500 years, at 11.4 ... 108
g. Flagstaff group at 23.5 years 108
h. Norway, 1740-1910, at 23.8 years.. . 108
i. Austria, 1830-1910, at 22.0 years. . . 108
j. Norway, N-2 400 years, at 33.0 .... 108
k. Vermont, 250 years, at 32.5 108
/. Sweden, 1740-1910, at 37.0 108
m. Sequoia, 1300-250 B. C., at 33.0 108
n. Flagstaff, 500 years, at 33.0 108
u. Sequoia, 3200 years at 101 108
p. Flagstaff, 500 years at 120 108
q. Standard 5-year period at 5.0 years. 108
r. 5 to 10 year logarithmic variable
period at 8.0 108
ILLUSTRATIONS.
TEXT-FIGURES.
PAGE.
1. Effect of monthly distribution of pre-
cipitation on thickness of rings of
growth; Prescott, Arizona 19
2. Monthly and yearly precipitation at
Prescott, and size and character of
rings 21
3. Annual growth of trees at Flagstaff
from 1385 to 1906, A. D 25
4. Comparison of two Flagstaff groups.
Variations in annual rainfall according
to month of beginning annual means . 26
5. Growth of individual trees compared
with precipitation at Flagstaff 27
6. Annual growth of trees near Prescott,
Arizona 28
7. Annual rainfall and growth of trees
(Group V) at Prescott. Dotted line
=rainfall. Solid line=growth 29
S. The nine European groups 31
9. Sunspots and growth of trees at Ebers-
walde, Germany 38
10. Growth of old European trees. A. Six
Norwegian trees, mostly from inner
fjords. B. Eight trees from Dalarne,
Sweden 40
11. Oregon group. Curve No. 1, actual
tree growth; No. 2, trees growth de-
partures, smoothed; No. 3, sunspot
numbers displaced 2 years to left .... 43
12. Cross-identification in first five sequoias
and gross rings in No. 1 48
13. Correlation between tree growth and
rainfall in smoothed curves; Flagstaff. 65
14. Early test of correlation between tree
growth and rainfall by years ; Flagstaff 66
15. Relation of tree growth and rainfall at
Prescott. Tree growth and rainfall
unconnected 68
16. Five-year smoothed curves of growth
and rainfall 68
17. Accumulated rain and smoothed tree
growth 68
18. Actual tree growth and growth calcu-
lated from rain 68
19. Actual rain and rain calculated from
tree growth 68
20. Huntington's early curves of sequoia
growth and rainfall compared with
growth calculated by a conservation
formula 71
21. Comparison of Fresno rainfall (after
Huntington) and sequoias D-l to 5. . 71
22. Sunspot numbers and annual rings in
spruce tree from south Sweden 75
PAGE.
23. Six European groups, standardized
and smoothed 75
24. Three European groups, standardized
and smoothed 77
25. Comparison between 57 north Europe
trees (smoothed) and sunspot num-
bers. The trees are from England,
Norway, Sweden, and north Germany 77
26. Dates of large rings in 80 European
trees compared with sunspot curves.
Ordinates give number of trees in
total of 80 showing maxima in re-
spective years 78
27. Tree growth at Windsor, Vermont,
showing measures unconnected: same
standardized and smoothed, and sun-
spot numbers displaced 3 years to left 78
28. Smoothed quarterly rainfall (upper
curve), sunspot numbers (center),
and tree growth (lower) at Windsor,
Vermont, 1835 to 1912 79
29. Correlation curves of solar cycle, rain-
fall, and tree growth at Windsor, Ver-
mont, 1835 to 1912 80
30. Schuster's periodogram of the sunspot
numbers 86
31. Diagram of theory of differential pat-
tern in periodograph analysis 91
32. Smoothed curve of Arizona pines show-
ing the half-sunspot period for 120
years 102
33. Changes in the 11-year period in 500
years. Solid line, Arizona pine;
dotted line, sequoia 103
34. Correlation curves in the 11-year cycle 104
35. Early curve of Arizona nines from 1700
to 1900 A. D. (No. 4) compared with
double and triple sunspot cycles com-
bined (No. 3) 105
36. Double sunspot period in tree growth
at inner fjords of Norway; lower curve
a 22.8-year cycle 105
37. Double sunspot rhythm in sequoia,
D-12 about 300 A. D 105
38. Triple sunspot cvcle in a single tree
from northern Norway. Lower curve,
a 34-year cycle 106
39. D-22 at 750 to 660 B. C., showing a
2-year period 106
40. Two differential patterns of Hunting-
ton s preliminary 2000 year sequoia
record. The most prominent cycle is
about 105 years in length, shown in
the upper diagram 109
CLIMATIC CYCLES AND TKEE-GKOWTH
A STUDY OF THE ANNUAL RINGS OF TREES IN RELATION
TO CLIMATE AND SOLAR ACTIVITY
BY A. E. DOUGLASS
Director of Steward Observatory, University of Arizona
CLIMATIC CYCLES AND TKEE-GKOWTH,
I. INTRODUCTION.
The investigation described in the subsequent pages bears close
relation to three sciences. It was approached by the author from the
standpoint of astronomy and a desire to understand the variations of
the sun. It was hoped that these variations could be more accurately
studied by correlation with climatic phenomena. But the science of
meteorology is still comparatively new and supplies us only with a
few decades of records on which to base our conclusions. So botanical
aid was sought in order to extend our knowledge of weather changes
over hundreds and even thousands of years by making use of the
dependence of the annual rings of trees in dry climates on the annual
rainfall. If the relationship sought proves to be real, the rings in the
trunks of trees give us not only a means of studying climatic changes
through long periods of years, but perhaps also of tracing changes in
solar activity during the same time. Thus astronomy, meteorology,
and botany join in a study to which each contributes essential parts
and from which, it is hoped, each may gain a small measure of benefit.
It is entirely natural that the yellow pine, Pinus ponderosa, common
on the western Rockies, should have been the first tree studied, since
it was an intimate and extensive acquaintance with the forest and with
the climate of northern Arizona that led the writer to the thought of
possible relation between the two. The climate had been sought for
astronomical reasons because its limited rainfall of about 22 inches
gave many clear nights and superb skies. The forest with its great
extent and stately trees proved wonderfully attractive and the absence
of undergrowth or of other species of trees was its most noticeable
feature to anyone accustomed to moist climates. Evidently the
absence of undergrowth was related to the dryness, and the critical
problem of the tree was to survive periods of drought rather than to
compete successfully with other species in the struggle to obtain food
supply. The following argument, therefore, was naturally suggested:
(1) the rings of trees measure the growth; (2) growth depends largely
upon the amount of moisture, especially in a climate where the quantity
of moisture is limited; (3) in such countries, therefore, the rings are
likely to form a measure of precipitation. Relationship to temperature
and other weather elements may be very important, but precipitation
was thought to be the controlling factor in this region and for the sake
of simplicity it is the element fundamentally considered throughout
the present study.
In the very beginning of the work it was expected that only in large
averages would a relationship be found between tree-growth and
climate. Accordingly, something like 10,000 measures had been made
9
<5V*S
10 INTRODUCTION.
on the pines of northern Arizona and the results all tabulated, when it
occurred to the writer to compare the annual growth of Flagstaff trees
directly with the 8 or 10 years of rainfall records taken at the United
States Weather Bureau station recently established there. It was
immediately seen that the accuracy with which tree-growth as shown
in the rings may represent annual rainfall was far greater than antici-
pated. In a considerable number of cases, but especially in the dry-
climate groups, this has been found to be in the neighborhood of 70
per cent, which is raised substantially by applying a formula to allow
for some degree of moisture conservation. At the present time, there-
fore, it is possible to lay a foundation for this study directly in the fact
that the rings of trees form an approximate measure of the rainfall.
When the studies were carried to northern Europe an equal exactness
in following the rainfall was not found, but a direct correlation was
discovered between tree-growth and solar activity. Subsequent
groups have been obtained from moist regions of the United States,
and one is led to believe that this altered reaction is a question of pre-
cipitation and that it must be kept well in mind in any application of
the methods hereafter described.
Since the beginning of this investigation, in 1901, assistance has been
received from several sources which it is a pleasure to acknowledge at
this time. Mr. T. A. Riordian, of Flagstaff, had 24 sections of the
early Flagstaff group cut from the ends of logs and shipped to me.
Mr. Willard P. Steel assisted in the measuring of the first 25 sections
and a number of friends helped in the tabulation. Mr. C. H. Hinderer,
of the United States Forest Service, at Prescott, Arizona, assisted in
procuring the Prescott groups. Mr. H. S. Graves, Chief of the United
States Forest Service, gave me several letters of introduction to foresters
in Europe, by which I was greatly assisted in procuring the 9 European
groups. I am glad to express my obligation to Dr. H. H. Jelstrup of
Christiania, Professor Gunnar Schotte of Stockholm, Professor Dr.
A. Schwappach of Eberswalde, and Professor A. Cieslar of Vienna, for
especial aid in this connection. Assistance in completing the Vermont
group was given by Mr. M. H. Douglass and others, and for aid in
procuring the Oregon group I am glad to mention the excellent work
of Mr. Robert H. Weitknecht, who was for a time connected with the
United States Forest Service at Portland, Oregon. I am indebted to
Mr. George A. Hume, of the Sanger Lumber Company, for important
help in connection with the sequoia groups. In 1914 a grant of $200
was received from the Elizabeth Thompson Science Fund for study
upon the correlation between tree-growth and solar variation. In 1918
a fund of $250 was placed at my disposal by the American Association
for the Advancement of Science. This was for the purpose of extend-
ing the sequoia ring-record from 2,200 years in length (the result of
preceding collection) to 3,000 years. This material was collected in
INTRODUCTION.
11
the summer of 1918 and the measurements and tabulation finished soon
after. I wish gratefully to acknowledge the courtesy of the editors of
the Astrophysical Journal and the Bulletin of the American Geograph-
ical Society for permission to use illustrations and extracts from articles
of mine which they have published. Plate 9 and figure 31 in the text
are from the former journal. Thanks are also extended to Professor
Ellsworth Huntington for the use of several text-figures which first
appeared in my chapter of his work (1914).
TREES SUITABLE FOR CLIMATIC STUDY.
During the course of this investigation the wood and growth of
numerous species of trees have been examined with reference to their
adaptability to the purposes herein described. The collections visited
include several in London, especially one in the South Kensington
Museum, fossils in the Jermyn Street Museum, the lumber-yards of
Messrs. W. W. Howard Bros. & Company, tree sections and fossils
in the geological museum at Berlin, fossils in the lignite beds of Grube
lisa near Dresden, and fossils chiefly in Munich and Vienna. In
TABLE 1. — List of trees in the Jessup collection whose rings were counted.
Scientific name.
Common name.
Locality.
Approx-
imate
center,
A. D.
Possible
periods.
Quality
of ring
sequence.
Pinus torreyana
Torrev pine
San Diego, Cal
1790
1 1 years ....
Pinus radiata
]Vlonterey pine
Monterey, Cal
1855
22 years . . .
Pinus monticola
^Vestern white pine
Oregon
1641
1 1 ye a rs ;
Pinus strobiformis
Mexican white pine.
Southern Ari-
1706
Bruckner.
22 years ....
Pinus strobus ....
White pine
zona.
Nova Scotia ....
1740?
22 years;
Fair.
Pinus tseda
Loblolly pine
Florida
1731
Bruckner.
Pinus echinata
Short-leaved pine
Missouri
1650
Xsuga hetero-
TVestern hemlock
Canada north-
1700
Uncertain. . .
phylla.
Tsuga caroliniana
Carolina hemlock.
west coast.
Carolina
1697
Poor, 22 yr. ;
Good.
Tsuga canadensis .
Pseudotsuga ma-
Canadian hemlock .
Bigcone fir
Nova Scotia. . . .
Southern Cali-
1525
1480?
Bruckner.
11 years;
Bruckner .
11 years. . . .
Good.
Good.
crocarpa.
Pseudotsuga mu-
Douglas fir.
fornia.
Oregon ....
1315
1 1 vears ....
Good.
cronata.
Picea sitchensis
Tideland spruce
Northwest coast
1798
Very good.
Picea rubens
Red spruce
Nova Scotia
1610
Sequoia gigantea
Bigtree
California
550
Bruckner. . .
Good.
Taxodium dis-
Bald cypress
Florida
1670?
tichum.
Cupressus mac-
Macnab cypress.
Northern Cali-
1760
Very good.
nabiana.
Toxylon pomifer-
Osage orange.
fornia.
Southern Arkan-
1765
Fair.
um.
Ulmus fulva
Slippery elm
sas.
Missouri
1770
20 years ....
12 INTRODUCTION.
America, collections were examined at the Smithsonian Institution in
Washington, the horticultural exhibit at the Panama-Pacific Exposition
in 1915, the museum at Chicago, but especially the Jessup collection
in the American Museum of Natural History in New York City.
Much careful counting of rings was done at the latter.1
Considering all the trees examined, the conclusion was reached that
the conifers, by the great regions they cover, the great variety of
climates they endure, and especially by the prominence of their rings,
seem best adapted to the purpose in hand. The chief trees, used with
approximate number of rings measured in each, are: the yellow pine
(Pinus ponderosd) about 14,000; Scotch pine (P. silvestris) about 9,000 ;
hemlock (Tsuga canadensis) 2,500; Douglas fir (Pseudotsuga mucronata)
2,500; sequoia (Sequoia gigantea) 47,000.
INTRODUCTION TO SPECIAL STUDIES ON THE YELLOW PINE.
Before taking up the details of collection and measurement it is
desirable to describe certain preliminary studies, such as those upon
the yearly identity of the rings, time of the year of ring formation, and
so forth. These studies were made chiefly upon the yellow pine of
northern Arizona, but from the similarity between the pine and the
other trees used it seems safe to say that the results apply equally to the
Scotch pine, sequoia, hemlock and other species employed.
Location. — The yellow pines upon which the studies were made
were obtained near Flagstaff, in the central part of northern Arizona,
at an elevation of about 6,800 feet above the sea. The northern part
of the State is largely a plateau forming the southern extension of the
great Colorado Plateau. This high area is intersected some 65 miles
north of Flagstaff by the Grand Canyon of the Colorado River. South
of the town the high elevation extends 50 to 75 miles, varying only a
few hundred feet from place to place, and then falls away abruptly at
the "Rim." Oak Creek Canyon begins some 10 miles south of Flag-
staff and flows to the south into the Verde River. The general drainage
nearer town is gently to the northeast into the Little Colorado River
some 40 miles away. Ten miles north of town the plateau culminates
in the San Francisco Peaks, which reach an elevation of 12,700 feet.
This mountain is a finely shaped volcanic mass with the old crater
breaking away into a canyon toward the northeast. The town is in
latitude 35° N. and longitude 113° W., and lies between two ancient
lava streams 200 to 400 feet in height. It has a ' ' wash ' ' flowing through
it from north to south, but this carries water only in time of severe
storm or of rapidly melting snow.
1 The 17-foot section of sequoia was reviewed with some care and the dates on it checked.
The dating is well done, as the errors are mostly under 15 years. The rings are large an do
not show marked variations in width. Much repair work has been done on it, and the pieces of
wood filling the drying cracks near the year 800 A. D. almost completely interrupt the continuity
of the rings.
DOUGLASS
PLATE 1
A. Bottomless pits near Flagstaff, illustrating drainage through limestone.
B. Yellow pine forest of northern Arizona.
INTRODUCTION. 13
The general country rock is Kaibab limestone in horizontal layers
forming the plateau, surmounted by lavas over extensive areas near
the mountain. The bedrock is covered by a thin soil, largely formed
in place. The soil over the limestones is porous, while that over the
lavas has much clay and holds water. There is no swampy ground and
therefore no conservation of moisture from year to year. Consequently
variations in moisture-supply are quickly felt by the trees. The pine
forest is remarkable for the absence of other kinds of vegetation. It
covers all parts of the plateau from about 5,000 feet in elevation to
about 9,000. At the lower edge of the pine forest a belt of cedars,
smaller than the pines and round in shape and with dark-green, thick
foliage, makes an attractive landscape.
Climate and seasonal conditions. — The climate follows naturally
from the latitude and altitude and the distance from the ocean. In
the winters there may be from 1 to 6 feet of snow on the ground at one
time. The storms are of the characteristic temperate-zone cyclonic
types, but on account of the altitude the preliminary south or east
winds are rarely observed. Storms come from the Pacific coast and
rain occurs about a day later than in southern California,. Spring and
autumn are the dry seasons, and the warmest time of year is usually
in June, just before the summer rains begin. The summer rains occur
in July and August and often come in "spells" that last a week or two,
with thunderstorms in the afternoons or at night, followed by clear
mornings. Unlike the winter storms, the summer rains are local and
apt to be torrential in character, with heavy run-off.
Meteorological records in northern Arizona are necessarily meager,
yet not so deficient as might be expected. The country was first
settled in the " fifties," when gold was discovered in Arizona as well
as in California, and lines of travel were established from Santa Fe
westward across the plateau. The "blazings" on the pine trees
marking the earlier roads are still to be distinguished. Soon after the
opening of the country the government located military camps at
various places, and from that time records of rainfall and temperature
were kept. The record at Whipple Barracks, near Prescott, begun in
1867, has been continued at Prescott to the present time. It is the
longest consecutive record in the pine forest and is therefore used below.
The extreme range in temperature observed in Flagstaff is from
about 20° F. below zero to about 100° F. above. But the town is in a
peculiarly sheltered position and exhibits much lower night extremes
than the "mesas" 200 to 400 feet above it. I have observed a differ-
ence of 26° F. between the top and bottom of the hill west of town at
sunrise on a winter morning. During the early years of the Lowell
Observatory, which is located on the mesa 350 feet above the town,
the lower minima were about 5° F. These figures show the conditions
to which the trees are subjected.
14 INTRODUCTION.
The unobstructed topography of the plateau where the trees were
collected is without doubt a very favorable feature. This leads to
very similar conditions for the trees over many miles of country and
doubtless greatly assisted in producing concordant tree-records. On
the other hand, the San Francisco Peaks, 10 miles north of town, illus-
trate how meteorological data may vary in rugged localities. The west
slopes of these mountains are exposed to the winter westerly storms
and have an immense snowfall. Springs abound and all favorable
localities are taken up as ranches. East of the mountain, however,
the land is dry and barren, and long distances intervene between
watering-places.
In a very rugged country like that about Prescott similar differences
between east and west mountain slopes must constantly occur. This
is the reason of an early difficulty with the Prescott groups. Nearly
60 trees from various localities were measured before a group was
found close enough to Prescott to be compared minutely with records
of precipitation at that place.
II. PRELIMINARY STUDIES ON THE YELLOW PINE.
YEARLY IDENTITY AND THE DATING OF RINGS.
In comparing the growth of trees with rainfall and other data, it is
essential that the date of formation of any individual ring shall be cer-
tain. This depends directly on the yearly identity of the rings or the
certainty with which one ring and only one is formed each year. The
fundamental starting-point in all identification is the ring partially
formed at the time of cutting the tree. This is usually found with ease
and has led to no uncertainty in the pine. In the sequoia this partial
ring is exceedingly soft and had been rubbed off in nearly all trees
examined. It was found unmistakably in a tree cut on the date of visit.
Superficial counting of rings is subject to errors due to omission and
doubling of rings. In the first investigation of trees at Flagstaff it was
supposed that the results were subject to an error of 2 per cent, most
of which arose from double rings near the center of the tree. But the
discovery and application of the method of cross-identification revolu-
tionized the process of ring identification, and it was proved that the
error of unchecked counting in the Arizona pines was 4 per cent and
lay almost entirely in the recent years. It was due to the omission of
rings or the fusion of several together.
Apart from cross-identification, confidence in the yearly identity
of rings comes from the following sources:
(1) Belief that the well-marked seasons of the year cause absolute
stoppage of growth in winter. The January mean temperature at
Flagstaff is 29° F. and that of July is 65° F.
(2) The known time of cutting of nearly 100 different trees dis-
tributed through perhaps a dozen different years successfully and
accurately checks cross-identification in the later years of the tree.
(3) The various identifications adopted for recent years check
exactly with the neighboring rainfall records in Prescott and other
places where such comparison can be made. This will have further
illustration in connection with the chapter on rainfall and tree-growth.
(4) A check on the accuracy of the accepted identification of the
Flagstaff trees was made by noting every statement of weather, freshets,
or crop-failures mentioned by the historian Bancroft in his accounts
of the settlements of Arizona and New Mexico. There were 14 cases
in which the noted feature of the year agrees with the tree-record to
one doubtful disagreement. The most striking correspondences occur
with reference to the flood on the Rio Grande in 1680, the famines
between 1680 and 1690, and the droughts in Arizona in 1748, 1780,
and 1820-23.
The effect of the undetected omission or the doubling of the rings
in individual trees is to lessen the intensity of the variations in the
curve of growth obtained by the averaging of many trees. T 1
16 CLIMATIC CYCLES AND TREE-GROWTH.
may be divided into two classes: first, local errors of identity in small
groups of rings in a few individual trees, which simply flatten the
curve without affecting the final count; second, cases in which a given
ring, in spite of attempts at cross-identification, is still in doubt,
showing clearly in perhaps half of the trees and not in the other half.
Such cases affect the final count, but do not flatten the curve. They
leave a question of one year in the dating of all the earlier portions of
the curve. Only two cases of this latter kind have been noted. One
was the year 1822 in the Flagstaff pines (of which there is very little
doubt) and the other is the ring 1580 in the sequoias, which was finally
decided by material gathered in the special trip of 1919.
CROSS-IDENTIFICATION.
Apart from care in measuring the rings, the details of which will be
given in Chapter IV, the most fundamental and essential feature of the
method of studying tree-growth is the cross-identification of rings
among a group of trees. The ease and accuracy with which this can
be done in a fairly homogeneous forest is remarkable. A group of 13
tree sections collected along a distance of a quarter of a mile in the
forest of Eberswalde, near Berlin, show almost identical records. Two
to ten rings in every decade have enough individuality to make them
recognizable in every tree. A group of 12 sections from Central
Sweden show such agreement that there is not a single questionable
ring in the last 100 years or more. Especially marked combinations
of rings can occasionally be traced across Europe between the groups
hereafter mentioned. In Arizona the identification across 70 miles
of country is unquestioned, and even at 200 miles the resemblance
is apparent.
The value and accuracy of cross-identification was first observed
in 1911 in connection with the Prescott trees. After measuring the first
18 sections, it became apparent that much the same succession of rings
was occurring in each; therefore the other sections were examined and
the appearance of some 60 or 70 rings memorized. All the sections
were then reviewed and pinpricks placed in each against certain rings
which had characteristics common to all. For example, the red ring
of 1896 was nearly always double, while the rings of 1884 and 1885 were
wider than their neighbors. In the 60 years investigated several
obvious details in each decade appeared in every tree. After this
Success it was evident that the process should be applied to the Flag-
staff trees which had been previously collected. Of the 25, however,
only 19 had been preserved. A minute comparison was made between
these with complete satisfaction. Since then this process has been
applied with great care to every group.
After the Flagstaff set was finished, it was compared with the Pres-
cott group. It was interesting to find that the Flagstaff ring records
PRELIMINARY STUDIES ON THE YELLOW PINE. 17
could be identified at once in terms of the rings at Prescott; the narrow
ring of 1851 was seen to correspond to one in the Prescott series. The
compressed series from 1879 to 1885 likewise had its counterpart at
Prescott and formed the portion of the sections which gave the most
difficulties in identification. On the whole, so far as can be judged
without minute study, the Prescott trees from relatively high eleva-
tions approximating the elevation at Flagstaff have a considerably
closer resemblance to the Flagstaff sections than do those growing
at lower altitudes.
Cross-identification and climate. — The process of cross-identification
appears to be applicable to areas far removed from one another,
but as the distances increase the resemblances between tree-growth
records decrease, due to climatic differences. The correspondence
between trees in different regions thus becomes a test of climate and
we note a possible field for the application of this process in the delinea-
tion of similar climatic areas or meteorological districts. It seems to
the author that in this way the growth of vegetation may easily be
made of fundamental value in practical meteorology.
MONTH OF BEGINNING ANNUAL MEANS.
It is evident that it must take some time for the transmutation of
rain into an important part of the organic tissue. There is evidence,
as will be shown later, that the summer rains often have a prompt
effect. The winter precipitation, however, is necessarily more remote in
its action. Much of the first growth in the spring must come from the
melting of the autumn and winter snows. It seems reasonable, there-
fore, to consider any snowfall as applying to the following yearly ring.
At Flagstaff the precipitation of November is almost always in the
form of snow, and therefore that month should certainly be considered
as falling after the arboreal New Year of tliat locality. In view of the
uncertainty as to the exact month when the precipitation begins to
have an influence upon the growth of the following season, and of
probable variations in different years, it seemed wise to test the matter
by a purely empirical method. The annual rainfall was ascertained
for yearly periods beginning (1) with July 1 of the preceding year,
(2) with August 1, and so on to (9) with March 1 of the current year.
Another method involved a separating of the summer rains, one-half
to apply on each adjacent winter, while a final method involved a
simiLar division of the winter rains. This was done for 12 years at
Flagstaff and 43 at Prescott. Part of the Flagstaff curves are given
in the lower portion of figure 4, where the rainfall can be compared
with the growth of the trees. The curves plotted from these tests were
found to have substantial disagreements, although of course the
smoothed curves of all of them would be practically identical. A
comparison of the growth of the tree with these various curves showed
18 CLIMATIC CYCLES AND TREE-GROWTH.
that the use of the year beginning November 1 at Flagstaff and
September 1 at Prescott gave the closest agreement between growth
and rainfall. At Flagstaff the majority of the trees came from a thin
clay soil derived in place from decomposed lava, and so there was little
depth for the storage of moisture. At Prescott the sections of group 5,
shown in the solid line of figure 7, came from trees growing in a porous
soil of decomposed granite in a rather flat depression with reaarded
drainage, so that conservation would have a greater influence. Perhaps
this explains why the year beginning September 1 gives the best results.
In the region of the great sequoias nearly all the precipitation in the
mountains (and quite all in the valleys where comparative rain records
are found) comes in the winter months. For these trees, therefore,
the winter precipitation is compared with the growth for the succeeding
year and the month of beginning annual means is in the autumn.
THE TIME OF YEAR OF RING FORMATION.
Among the problems connected with the relation of the growth of
trees and the amount of rainfall, one of the most interesting was sug-
gested by Director R. H. Forbes, formerly of the Arizona Experiment
Station. This was to determine the time of formation of the red or
autumn portion of the rings and the causes for the formation of double
rings, which were very numerous in the Prescott group. It seems
evident at once that the growth of red cells is related to the decreased
absorption of moisture as winter approaches. A number of tests were
made on the Prescott group. The first was designed to determine
the character of the rainfall in the years producing double rings. The
half-dozen most persistent cases were selected and in each of these the
red ring was found double in the following number of cases: 4 out of
10 in 1896; 5 out of 10 in 1891 ; 7 out of 10 in 1881 ; 4 out of 10 in 1878,
1872, and 1871. The average width of all the rings was 1.55 mm. The
mean rainfall by months for the years above selected was found and
is plotted in the solid line of the upper diagram of figure 1. Six other
rings showing one double in 10 trees in 1898, but no doubles in 1897,
1885, 1884, 1876, and 1874, and averaging 1.54 mm. in thickness, were
then selected and the curve of rainfall by months for the year during
which they grew has been plotted as the upper dotted line in figure 1.
In each curve the 6 months preceding and the 2 months following the
year are included. The curves seem to indicate clearly that the chief
cause of doubling is a deficiency of snowfall in the winter months,
December to March. This appears to mean that if the winter pre-
cipitation is sufficient to bridge over the usual spring drought, the
growth continues through the season, giving a large single ring which
ends only in the usual red growth as the severity of winter comes on.
If, however, the preceding winter precipitation has not been entirely
adequate, the spring drought taxes the resources of thetree and some red
tissue is formed because of deficient absorption in the early summer before
the rains begin. When these rains come the tree continues its growth.
PRELIMINARY STUDIES ON THE YELLOW PINE.
19
It appears further that if not only the winter snows are lacking, but
the spring rains are unusually scanty, then the tree may close up shop
for the year and produce its final red tissue in midsummer, gaining no
immediate benefit from the summer rains. This appears to be the
interpretation of the lower diagram of figure 1. Here the same 6 big
en
o
•g
c
c
o
o.
I
July Oct. Jan. Apr. July
> i i i
-Solid line=Rainfall producing;
big doubles, 1.55 mm.
\
Oct. Jan. Apr.
Dotted line=Rainfall producing
big singles, 1.54 mm.
C^
Dotted line=Rainfall producing
small singles, 0.61 mm.
Solid line=Rainfall producing_
big doubles, 1.55 mm.
4.0
3.0
2.0
1.0
4.0
3.0
2.0
1.0
5.0
4.0
3.0
2.0
1.0
3.0
2.0
1.0
FIG. 1. — Effect of monthly distribution of precipitation on thickness of rings of
growth; Prescott, Arizona.
doubles mentioned above are plotted, together with a selected list of
6 small singles particularly deficient in red tissues. They are, 1904
double once in 10, 1902 double once in 10, 1899 single, 1895 single,
1894 single, and 1880 double once in 10. In these it is evident that
drought in the spring stops the growth of the tree. The double ring,
therefore, seems to be an intermediate form between the large normal
single ring, growing through the warm parts of the year, and the small,
deficient ring, ending its growth by midsummer. This occasional
failure to benefit by the summer rains probably explains why the
Prescott trees do not show an agreement of more than about 70 per
cent between growth and rainfall. It suggests also that the Flagstaff
trees, which grow under conditions of more rainfall and have very few
double rings, give a more accurate record than those of Prescott.
Consistent with this view of the doubling is the condition of the outer
ring in the Prescott sections collected by Mr. Hinderer. These trees
Monthly rainfall for 1909
Monthly rainfall for 1910
20
CLIMATIC CYCLES AND TREE-GROWTH.
were cut during various months from May to November. Naturally,
those cut in May are in the midst of their most rapid growth, while
those cut in summer may or may not show the double ring just forming.
The conditions are shown in table 2.
TABLE 2.
Group.
Altitude.
Date of cutting.
Cutting season.
Remarks.
feet.
1
6,125
1911
May, June. . . .
9 out of 10 show white tissue only.
2 and 4
6,420
1909
July to Sept. . .
30 out of 33 show red ring just form-
ing, probably a doubling.
5
5,800
1909
Summer
3 or 4 out of 10 show red ring just
forming, probably a doubling.
3
6,800
1910
Oct. and Nov.
All 12 show white without red, prob-
ably a large single.
By reference to figure 1, showing the curves of monthly rainfall for
1909 and 1910, it will be seen that 1910 would be likely to carry its
growth through the year and produce a single line, as in group 3 above.
The year 1909 is of intermediate character, having heavy winter
precipitation and a severe spring drought of 3 months. In the groups
cut at this time 33 out of 43 show a red ring forming in July, August,
or September, doubtless the preliminary ring of a double. This lesser
red ring is due to the spring drought, and its appearance at this time
indicates a lag of a couple of months, more or less, in the response of
the tree to rain. The whole matter of the relative thickness of the red
and white portions of the rings is illustrated in figure 2. The heavy
sinuous line shows the rainfall month by month at Prescott throughout
the 43 years under consideration. The total rainfall for the year is
indicated by the dotted rectangles while the size and character of the,
rings is shown in the solid rectangles. In these the white portion
indicates the white tissue and the shaded portion indicates red tissue.
Significance of subdivisions in rings. — The normal ring consists of a
soft, light-colored tissue which forms in the spring, merging into a
harder reddish portion which abruptly ends as the tree ceases growth
for the year. The present subject (namely, the time of year of ring
formation) indicates that the red tissue appears as the tree feels lack
of sufficient moisture. Therefore, the great diversity in relative size
of the red tissue and the occasional appearance of false rings undoubt-
edly has a real significance as to distribution of precipitation during the
growing-season. This subject is a very promising one, but has received
little attention in the present work. The trees of the Prescott group
offer a few interesting examples of two or three false red rings in one
year; they also have exceptionally many cases of omitted rings; both of
these peculiarities are explained by the fact that these trees are close
to the lowest elevation at which the climate permits them to live; they
are therefore greatly affected by rainfall distribution and probably
exaggerate its changes.
PRELIMINARY STUDIES ON THE YELLOW PINE.
21
588
ff
%
r
y
Annual precipitation in inches (dotted lines)
H- eo co ~ ro co — to co
ooo o £> o o <5 o
)
)-.
i>?T::
}:
h
\
Sf-
S 8 S
NUMBER OF TREES NECESSARY FOR RELIABLE RESULTS.
In seeking the best curve of tree-growth which a given locality
can supply, it might be thought at first that a very large number of
trees must be obtained in
order to get an average,
but experience has shown
that the number may be
very small. In order to
test the accuracy ob-
tained from a small num-
ber of trees, a comparison
was made between large
groups and small. Of the
original 25 trees in the
first Flagstaff group, 19
were subjected to very
careful cross-identifica-
tion. Averages were then
obtained of the oldest 5,
going back about 400
years, the oldest 10 (350
years), the oldest 15 (300
years), and the entire 19
reaching back only 200
years. Finally, the record
of the oldest 2 was carried
back fully 500 years. On
plotting the groups of 15,
10, and 5 with its exten-
sion of 2, it became im-
mediately evident that 5
trees gave almost the same
growth as 15, even to
small details. Between
these 5 and the oldest 2
taken by themselves the
agreement was not quite
so perfect, yet was so close
that errors thus intro-
duced would not affect
the curves. It must not
be taken for granted
without test that this re-
markable agreement be-
tween very small groups
of trees is true necessarily
for other trees or even for
\
l^
w
Monthly precipitation in inchest solid lines.)
FIG. 2. — Monthly and yearly precipitation at Prescott and
size and character of rings.
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 the rugged character of the region.
Direction of maximum growth. — The maximum trunk-growth was
observed to occur 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 snow and 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 changes of moisture on limestone than on volcanic rocks.
III. COLLECTION OF SECTIONS.
The material upon which the discussion of climatic cycles and tree-
growth is based has been derived from 230 trees collected in the 15
years from 1904 to 1918. The regions drawn upon comprise chiefly
Arizona with its yellow pine, the Baltic drainage area of north
Europe with its Scotch pine, and the high Sierras of California with
their great sequoia. Two small collections come respectively from
the northeast and northwest coast of the United States. The col-
lections have been made in small, convenient groups as opportunity
offered, to each of which a name has been given which will appear
below.
The relative dimensions of the various groups may be expressed hi
terms of the number of measures of rings. In the first Flagstaff group
there were about 10,000. In the second Flagstaff group of 1911 only a
few hundred. The Prescott groups included about 4,000; the 9
European groups about 9,000. The Vermont group had between
2,500 and 3,000, and the Oregon group about the same. The first
collection of sequoias in 1915 had about 25,000 measures and the col-
lection in 1918 embraced about 22,000.
Throughout the whole study it was desired to get as long records
as possible and old trees were therefore selected. In nearly every case
this meant large trees also. Apart from this no special selection of
trees was made at any tune, save only in the Christiania group, in which
so many of the logs showed a " complacent" habit, with long succes-
sions of equal rings rather large in size, that some effort was there made
to find the logs which showed variations in ring-size. A complacent
ring-record without doubt means that the environment of the trees was
well adapted for its best development.
THE FIRST FLAGSTAFF GROUP OF TWENTY-FIVE SECTIONS.
The plan of using tree-rings for the general purpose of a check on
astronomical and meteorological phenomena was first formulated in
1901. The first measurements were made in January 1904, on a huge
log in the yards of the Arizona Lumber and Timber Company at Flag-
staff. This method of measuring was extremely inconvenient and the
succeeding 5 sections were cut from logs and sent to town for more
careful examination. Hence the exact location of these first 6 was
never visited. The remaining 19 trees were selected in 1906 by myself
in the forest while the logs were yet lying near their stumps, and I was
able to mark on each section the points of the compass and otherwise
describe the location. The measurements were completed in 1907 and
published in the Monthly Weather Review of June 1909. They had
not been subjected to cross-identification and, when the value of this
23 /&
•
- , v
24 CLIMATIC CYCLES AND TREE-GROWTH.
process was recognized in 1911, the 19 sections of which samples had
been preserved were compared and a complete cross-identification
carried through. Thus the errors of identity in the former tabulation
were found (published in 19143) and a complete new set of tables and
averages made from the original measures. For a time it was thought
that an error of one year might exist in the period of the great drought
of 1820-23, but the various checks made upon identity lead easily to
the belief that there are no errors of identity in this 500-year series.
Subgroups. — The trees of this group were divided into three sub-
groups consisting of (1) 6 trees from 3 miles south of Flagstaff; (2) 9
trees from 11 miles southwest of Flagstaff; (3) 10 trees from a point
1 mile west of the last subgroup. A comparison of the 3 subgroups
clearly reveals the general character of the longer periods hereafter
to be discussed and shows lesser variations to be common to all.
Interesting differences, depending on the location in which the trees
grew, have been mentioned.
First suggestion of cross-identification. — Other interesting facts came
to light. It was especially noticeable that a given year of marked
peculiarity could be identified in different trees with surprising ease.
This is illustrated in plate 2, where shavings from 5 of the Flagstaff
trees have been photographed; the photographs have been enlarged
to such a scale that the distance from the large ring 1898 (indicated
by the upper line of black crosses) to the small ring 1851 at the lower
line of crosses is equal in all cases. The other lines of crosses indicate
the noticeably broad rings of 1868 and 1878. An examination of the
photographs shows that a very characteristic feature is a group of
narrow rings about the years 1879 to 1884. These can be identified in
practically every tree and an examination of many stumps which were
not measured showed that it was easy to pick them out wherever one
chose. Striking verification of this was found in the case of a stump
near town which had been cut about 20 years previously. By finding
this group of rings, the writer was able to name the year when the tree
was felled and the date was verified by the owner of the land. In the
more recent work this same group shows conspicuously among Prescott
trees, and in general 95 per cent of these trees have rings so charac-
teristically marked that the identification of the same series of rings
can be made with little doubt, whether at Flagstaff or at Prescott.
The Flagstaff 500-year record. — Figure 3 shows the Flagstaff tree
record from 1385 to 1906 A. D., a period of 522 years. The table of
measures from which the curve was plotted will be found on page
112. To give the record from 1503 to 1906, 5 trees are used, and com-
parisons showed that these 5 gave as accurate a record as a larger
number whose inclusion would have shortened the record or made
awkward breaks in it. The earlier part of the record is from 2 trees
DOUGLASS
PLATE 2
Cross-identification of rings of growth in yellow pine (I1 in UK
COLLECTION OF SECTIONS.
25
3.0mm-
2.5mm.
l.omm.
0.5mm.
180Q _ISSO 7900'
FIG. 3. — Annual growth of trees at Flagstaff from 1385 to 1906, A. D.
26
CLIMATIC CYCLES AND TREE-GROWTH.
only. A comparison between the 5 and these oldest 2 taken by them-
selves give an agreement not absolutely perfect, yet so close that
errors thus introduced will not materially affect the curves. However,
the oldest 2 were very slow-growing trees and they required on the
average an increase of about 30 per cent in order to make their curve
continuous with the whole 5. Thus the tree-record is made to begin
at 1385. In the recent years of the record also, between 1891 and 1896,
a slight correction was made for omitted rings, the complete omission
of a ring being an exaggeration that introduces error.
Year
1870
1880
1890
1900
1910
25 sections measured in 1904-6
h
Summer
May 1 to Nov. 1
1900
1910
Year
1900
1910
Year
FIG. 4. — Comparison of two Flagstaff groups. Variations in annual rainfall
according to month of beginning annual means.
COLLECTION OF SECTIONS.
27
1900
Year
1905
1910
THE SECOND FLAGSTAFF GROUP OF SEVEN SECTIONS.
In 1911 the writer visited Flagstaff again and made a trip into the
forest where cutting was going on, in order to procure a few additional
samples of the yellow pine which would check the recent part of the
tree-record previously obtained and bring it up to date for comparison
with rainfall values. The location was about 12 miles southeast of
town and from 6 to 12 miles east of the region from which the first
Flagstaff group was obtained. Seven cuttings
were procured from the edges of stumps, thus
bringing away a triangular pyramid of wood,
which included the outer 50 to 100 rings.
Figure 4 shows how well the second group
checks the first and indicates that even a small
group of trees, no more than 7 in number, is
sufficient to give results of considerable accu-
racy. Indeed, we may go further and say that
a single tree under favorable conditions may
give results of very great value. This is evident
in figure 5, where the 7 sections from the last
Flagstaff group are plotted separately, the most
rapid grower at the top, just below the rainfall
curve, and the slowest-growing tree at the
bottom. All rise alike because the conditions
of rainfall in 1900-10 were more favorable than
in the preceding decade, but all (especially the
curve of section 4) show a more or less close
relation to the rainfall at Flagstaff, even though
that town was some 12 miles away. The great
sinuosity which a quick-growing tree may show
is well illustrated in section 4 in the great dif-
ferences between successive years. A lack of
sinuosity is shown in section 5 at the bottom.
This difference supports the conclusion already
reached that slow-growing trees are of less value
than rapid ones in the determination of climatic
cycles. The results of the measures of this group serve as a check
on the preceding measures and are shown in the figures just referred to.
They are, therefore, not tabulated in this book.
THE PRESCOTT GROUP.
Prescott is located in the northerly part of the Bradshaw Mountains,
at an elevation of 5,200 feet. The rocky subsoil is largely granite
disintegrated at the surface and worn into steep hillsides, deep gorges,
and picturesque masses of rounded boulders. The ridges are sharp
and rugged, and the general contour is very irregular. There are very
— 30
$ 20
/ \J
^VxN
o.
*o 10
*..
Is
ov. 1 to
sJov. 1
s
-c n
c
Set
,4
£
o n
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XV
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1 <
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V
1 n
Sec
6.
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1 =.
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Sec
.7
/V
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i o E
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Sec
3
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Sec
2
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.0
0.0
Sec
1
/-
*"
'^V
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u.o
Sec
5
-^v
u.o
n ft
FIG. 5. — Growth of indi-
vidual trees compared
with precipitation at
Flagstaff.
28
CLIMATIC CYCLES AND TREE-GROWTH.
few isolated peaks. The mountains are covered with pines from their
crests to a little below the level of the city.
This Prescott group was obtained in 1911 for the purpose of testing
the conclusions derived from the Flagstaff trees some years earlier.
Year 1870
1880
1890
1900
2.0
1.0
0.0
2.0
1.0
I o.o
E
£ 2.0
E
c
s
bo
lo.o
< 2.0
1.0
0.0
2.0
1.0
0.0
/\A
A
/\
1910
Group I
Trees 1-10
Group II
Trees 11-35
Group III
Trees 36-50
Group IV
Trees 51-60
Mean of
all trees
1-70
1870 1880 1890 1900 191Q-
FIG. 6. — Annual growth of trees near Prescott, Arizona.
It consists of 67 trees selected in 5 subgroups depending on their
nearness to town. The farthest was 10 miles southeast and the
nearest was 1 mile south. It was apparent that the agreement between
growth and precipitation increased as the location of the actual rain-
fall station was approached. The nearest subgroup, containing 10
COLLECTION OF SECTIONS.
29
trees, shows so much greater agreement than the others that it has been
used alone in drawing final conclusions. Its site was a small, poorly
drained level space near the bottom of the valley.
In this group there was no necessity of duplicating the Flagstaff
records, and therefore small V-shaped cuttings were made at the edges
of the stumps, only triangular pieces of wood giving the outer half cen-
tury of ring-growth being brought away. These were the samples on
which the value of the cross-identification was discovered, as already
described. Identical series of rings were observed in nearly every tree
of the group.
o
c
30
25
20
1870
1880
Year
1890
1900
1910
= 15
10
0
V
V
:••
3.0
2.0 £
1.0
o
0.0
FIG. 7. — Annual rainfall and growth of trees (Group V) at Prescott. Dotted line: rainfall.
Solid line: growth.
I
Out of 67 sections averaging 50 rings each, only 6 gave any identifica-
tion trouble. In 2 of these, 2 rings were lacking, but when allowance
was made for this defect the identification was satisfactory. Another
section had 2 extra rings, and another had 2 extra and 3 lacking. The
other 2 sections proved especially puzzling and were finally omitted
from the means. Of these 6 troublesome sections, the first 5 were very
slow growers. Hence it would seem advisable not to use extremely
slow-growing trees any more than is necessary. It may be urged that
trees do not grow continuously at the slow or fast rate and that we can
not tell how much of the change is due to rainfall. On the whole, how-
ever, it seems advisable to exclude trees or parts of trees whose identi-
fication is extremely difficult. The inner rings if well identified may be
extremely useful in carrying back early records, as the slow-growing
trees are likely to be among the oldest.
The averages of 4 subgroups and the means of all the Prescott trees
will be found plotted in figure 6. The curve of the fifth subgroup is
given in figure 7, where it may be compared with the rainfall of Prescott.
SOUTH OF ENGLAND GROUP.
This group of 11 sections was obtained in January 1913 at Fleet,
near Aldershot, some 30 miles west-southwest of London. The trees
were the common pine, Pmws si7yes£m, and averaged about a foot
in diameter. The growth was very rapid and the wood was full of
30 CLIMATIC CYCLES AND TREE-GROWTH.
moisture. The trees had formed a border to a little plot of cultivated
land with a southwesterly exposure. The average age was 54 years.
The rings were all extremely plain, averaging 2 to 4 mm. in size, and
cross-identification was everywhere perfect. Of the 50 or 60 rings,
about 10 had marked characteristics and were easily recognized in
nearly every section. It was noted that a few sections had numerous
rings more sharply defined on the summer side of the dense red portion
than on the usual winter edge. One of the 11 sections is shown in
plate 3, A.
The appendix contains a table of mean tree-growths of the 1 1 British
sections; the years 1859 to 1863 inclusive show means of 6 trees only,
as some did not extend back that far ; of these, 2 had their centers about
1858, 2 in 1857, and 2 in 1855. The owner 'of the land informed me
that the trees had all been planted at the same time, and therefore this
apparent discrepancy may be due to sections cut at different heights
above the ground. These means are plotted in figure 8.
Fbr ready comparison it seemed desirable to standardize this British
curve as well as each of the other European curves. Each curve is
therefore corrected for changing rate of growth with age and also very
slightly smoothed to get rid of the confusing effect of the 2-year "see-
saw " described later. In the present group, after careful consideration,
the standardizing line follows the tree-growth through a uniform curve
in the earlier years and becomes straight in the later years. Percentage
departures from this mean standard line give the standardized curve.
These percentage departures smoothed by Hann's formula will be
found plotted in figure 23, together with similar curves from the other
European groups.
•
OUTER COAST OF NORWAY GROUP.
On the advice of Dr. H. H. Jelstrup of Christiania, I visited the
Forest School of Sopteland, a small place located about 18 miles south
of Bergen, near latitude 60°. The elevation is but little above sea-
level, and irregular intervening hills give slight protection from the
North Sea storms. This group of 10 Pinus silvestris sections was
collected on January 3, 1913, from logs in the yard of the Forest School.
The logs had been cut within a week or two in Os, 12 miles to the
south, on an exposed part of the coast and probably close to sea-level.
Os is on the north shore of one of the larger inlets entering on the north
side of Hardanger Fjord.
The average diameter was 6 to 8 inches and the average date of the
center was about 1840, but one extended back to about 1800 and
another to 1700. The average size of rings was about 1.25 mm. The
group cross-identified extremely well and on a preliminary inspection
seemed to show somewhat rhythmic variations in growth. In these
DOUGLASS
PLATE 3
B
A. Section of Scotch pine from southern England.
B. Section of Scotch pine from coast of Norway.
COLLECTION OF SECTIONS.
31
I85O
2.0
1.0
1.0
0.5
1.5
1.0
1.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
1.0
1.5
1.0
I.
.Nor way, Inner Fjords
VH. tlsersvv<9la<2 Prussia
.VII. N.W. Austria
K. 5.
Mm.
a.o
1.0
1.0
0.9
1.5
1.0
1.5
1.0
1.0
0.5
1.0
0.5
1.0
0.5
I.S
1.0
1.5
1.0
FIG. 8. — The nine European groups.
32 CLIMATIC CYCLES AND TREE-GROWTH.
sections there is more than usual variation in different radii, an excess
of growth starting in one direction and then slanting off in some other
direction. Here it was found also that maxima were not always the
same in different radii. It was suspected that some radii tried to follow
a single cycle and others a double cycle. A photograph of one of these
sections is shown in plate 4, A.
The appendix presents a table of mean growth of this group from
1845 to 1912. No. 2 had its center in 1865, and between that date and
1845 extrapolated values have been used in forming the means. These
extrapolated or artificial values preserve the average shown by the
individual tree during its years of growth, but are made to vary from
that average in accordance with the variations of the rest of the trees
in the group. From 1828 to 1844 the mean of 3 sections only is given.
The actual mean has in this latter case been multiplied by 1.25 to bring
the average into accord with the group, for the mean of these 3 for the
11 years from 1845 to 1855 inclusive is only 80 per cent of the mean
of the group. In this group one center was in 1865, three in 1844, one
in 1842, one in 1840, one in 1836, one in 1827, one in 1800, and one in
1693.
These means are plotted in figure 8. The same corrected to a
standard mean and smoothed by Hann's formula will be found in
figure 23. No real correction for age has been made in this case, for
there seems little change in rate of growth that can certainly be
identified as such. The whole, therefore, has been simply reduced to
scale for comparison with other groups by dividing every year by 1.25,
which is very nearly the average growth in millimeters.
INNER COAST OF NORWAY GROUP.
It is a great help to visit the exact locality in which the trees grew,
or to get very near it, as in the groups already described, and especially
to obtain personal information in a mountainous country like Norway,
where meteorological conditions may vary enormously within a few
miles. But it was impossible in the present group, whose sections had
mostly been collected some years before for use in the forest service
and schools. By courtesy of various officials I was permitted to
examine and measure these sections in their offices, and whenever it
was possible thin sections were cut off for me to add to my collection.
In measuring sections of which samples were not retained, for example
B 15, B 16, and N 2, there was no opportunity of cross-identifying
rings, and hence unusual precautions were observed in numbering the
rings. If at any spot they seemed to be very close together with any
chance whatever of mistake by omission or doubling, the numbering
was carried to as many other radii as were necessary for a check, and
worked over very carefully until the best possible result was obtained
COLLECTION OF SECTIONS. 33
and all doubt seemed to be overcome. Nevertheless, judging by past
experience, unchecked counting leaves a doubt wherever the rings are
reduced to 0.1 to 0.2 mm. in thickness.
Another disadvantage of this group ie that the trees came from
very diverse localities, and hence do not represent homogeneous con-
ditions. Therefore, each section in the group will have special men-
tion. The first number in the group, B 11, was cut from a log of
Pinus silvestris lying on the woodpile in the yard of the forest school
at Sopteland. The tree had been brought in for firewood late in 1912,
but was undoubtedly dead at that tune, for the outermost ring checked
with the Os group unmistakably as 1911. This view was supported
by the decayed bark and moldy trunk. This section was 9 by 14
inches in size and had the center (date 1734) some 3 inches from one
end, producing one of the most uniform cases of eccentric growth which
I have seen.
Nos. B 12, 13, and 14 cross-identify most satisfactorily with the Os
group. From one to six individual characters or a most convincing
sequence of characters were obvious in every decade. Section 12, a
foot across, was cut in 1909, and the last complete ring was unmis-
takably of 1908 by comparison with the previous group. A section
was cut for me at the school in Sopteland. The original was marked
"No. 1, 1909, Knagenkjelm, Kaupanger," a location on Sogne Fjord,
some 80 miles northeast of Bergen. My section shows the bark and
. very dense, handsome wood with strongly marked rings. Its center is
at 1682. No. B 13, center at 1807, is of about the same size and from
the same place, and was marked "No. Ill, 1909." Its outer ring also
identified as 1908. A portion of this section also was cut for me.
No. B 14, center 1779, was marked "No. 1, 1909, Lyster Sana-
torium," on Sogne Fjord. As in the other two cases, its outer ring was
plainly 1908. A thin section was cut for me. Its size was 12 by 14
inches. B 16 was marked "No. 3, 1909," from the same place. This
huge section was 28 inches in diameter and 7 inches thick, and its
center was about 1724. There was a series of very small rings from
1787 to 1794 and another from 1806 to 1813. I have no section of it
and so no cross-identification could be attempted, but the measures of
the recent years agree with No. 14 from the same place.
No. B 15, center at 1633, was also measured at the school and no
section retained for comparison with the others. It is the only one from
its locality. It was marked "No. 1, 1909, Nestaas, Granvin," on
Hardanger Fjord. It was cut in October and the first ring was con-
sidered to be of that same year. The rings were very clear back to
1680 and in fact to the center, but between the center and 1680 they
were very small.
34 CLIMATIC CYCLES AND TREE-GROWTH.
All the sections so far in this group came from the west side of
Norway near latitude 60°. The remaining two came from farther
north and were first examined in the office of Dr. Jelstrup. No. N 1
was a small tree some 6 inches in diameter with its center in 1848. It
grew in Mo i Ranen in latitude 66° 15', a 2 days' trip by boat from
Trondjem. The rings show a rhythmic character, and a photograph
of the thin section presented to me is given in plate 3, B. As in the
other similar photographs, the years of sunspot maxima are marked
with arrows. It was cut in 1907 and the outer incomplete ring was
taken as of that year. The identification with trees from near Bergen
is poor, as would be expected.
No. N 2 was an interesting cross-shaped section from beyond the
Arctic Circle, latitude 68° 45'. It had been damaged by forest fires at
various times to such an extent that the injured parts of the trunk
ceased growing while the rest kept on; hence it was of this extraordi-
nary shape. It was cut in the winter of 1905-6, and the outer ring was
taken as of 1905. As a rule the rings were very easy to follow until
before the year 1600, and even then by carrying the ring to other arms
the identification seemed practically certain. The rings reached a
suspiciously small size between the center at 1497 and 1512.
The measuring of this 400-year section was done on December 31,
1912. By noting ring after ring with care, tracing all rings a short
distance and following the one case of suspected double across into
another arm, there seemed to be no errors, certainly none of doubling,
and none suspected of disappearance. Letters B, BB, indicating
maximum growth, were placed at the center of groups of large rings as
the measuring progressed, without knowledge of any relation between
them. That same day, on looking over the measures, a Bruckner
period seemed indicated. The maxima were marked as the measuring
progressed. See table 3, on page 35.
This series of maxima, 270 years long, from 1561 to 1830, shown in
figure 38, permits the application of a 34-year period with an average
error of less than 3 years. If that case were alone, I would not include
it here, but I believe I shall be able to show it in a number of very old
trees in widely separated localities.
From the above description it is evident that we have in this group
some very interesting trees, even though they grew far apart. They
are probably worth more as individuals than as a group, but until
more trees can be added from their various localities the usual method
of presenting them here is used. So the group means are tabulated in
the appendix, using an extrapolated value of N 1 from its center in
1848 back to 1821. These means will be found plotted in figure 8.
They have been corrected for age and reduced to standard size in the
COLLECTION OF SECTIONS.
35
usual way by a straight sloping line reading 1.90 mm. in 1820 and 1.15
mm. in 1910. The corrected means smoothed by Hann's formula will
be found plotted in figure 24.
TABLE 3.
Date of maxima
as marked.
Differences
in years.
Suggested maxima
on 34-year period.
Residuals.
1830
1831
— 1
1797
33
1797
0
1754
43
1763
9
1696
/ 29
\ 29
1729 \
1695 /
1
1657
39
1661
—4
1528
29
1627
1
1561
/ 33
\ 34
1593 \
1559 /
2
1535
26?
1525
10?
CHRISTIANIA GROUP.
This group of 5 Pinus silvestris sections was secured from logs at a
little sawmill in the outskirts of Christiania. The logs cut in the
neighborhood were in a large pile at the mill, and after the snow was
brushed from them suitable ones were selected. Usually in such cases
the largest and oldest were taken, but in this group the growth was
exceptionally complacent. Accordingly, preference was given to those
which showed variability in size of rings.
These sections were measured a' month or two later. Cross-identi-
fication proved very unsatisfactory. Large variations were found in
the 5 specimens. On this account it was felt that there might be
several errors in this group which could perhaps have been removed
by a larger number of trees for intercomparison. The centers of the
5 were respectively at 1848, 1824, 1797, 1807, and 1790. The average
diameter was about 1 foot. On page 1 14 will be found the mean growth
of these sections and the plot of the same will be found in figure 8.
There seems no special change in growth with age, and the whole series
was merely reduced to percentages by dividing each yearly value by
1.50 mm. These values, smoothed by Hann's formula, will be found
plotted in figure 23.
CENTRAL SWEDEN GROUP.
These 12 sections, showing an average diameter of about 11 inches
and an average age, of 190 years, were obtained from the sawmill near
Gefle, on the coast, 60 miles north of Stockholm. The mill, one of the
largest in Sweden, was some 4 miles from the town, on the river coming
36 CLIMATIC CYCLES AND TREE-GROWTH.
from the interior. The logs came from the vicinity of Dalarne in
central Sweden, a large district. The bark is taken off as required by
law and the logs are floated down to the mill. I visited the mill on
Saturday, December 28, 1912. Twelve sections had been cut, but they
were too thick and the whole 12 were cut a second time. These logs
had been in the water a year and the last ring would therefore be of
1911 or possibly 1910. Of the 12, I think that all but 2 or 3 show the
1911 ring. Though these sections must have come from a considerable
area (unless in the water and mid-afternoon darkness they accidentally
secured original neighbors from thousands of logs), they identify
among themselves extremely well. Cycles or pulsations were noticed
and marked on all the sections of this group before identification.
No. S 8 seems the most regular; a photograph of it is reproduced in
plate 4, B. The cross-identification for the last 100 years hardly needs
review, as it is entirely reliable and practically nowhere are there
doubtful rings.
The means of the years 1820 to 1910 are given in the appendix and
a plot of the same will be found in figure 8. The tree-growth in this
group and others before 1820 will be taken up separately. There seems
to be here no real change of growth with age, and the values were
changed to standard by dividing by 0.8 mm. These results were then
smoothed by Hann's formula and plotted in figure 23.
SOUTH SWEDEN GROUP.
This group of 6 sections was measured at Stockholm on December
27, 1912, in the office of Professor Gunnar Schotte, chief of the Swedish
Forest Service. In my lists they are numbered from S 13 upward.
They are all Pinus silvestris save S 14 and S 17, which are spruce,
Picea excelsa. No. S 14 is noted particularly because it showed as
perfect a sun-spot rhythm as G 8 from Eberswalde, whose photograph
is given in plate 8, A. An entirely satisfactory cross-identification was
made at the time of measurement.
The individual trees came from different localities and are therefore
mentioned separately. No. S 13 was marked "4105-6" and was cut
in May 1909. It grew about 100 miles southwest of Stockholm, in
latitude 58° 40'. About 1833 it has a doubtful ring which was settled
by comparison with other measures. Its center was in 1763. No.
S 14, a Picea excelsa, marked "4105-14," was cut in July 1910 on the
east side of Vetter Lake, less than 100 miles .south west of the preceding.
Its center was in 1816. No. S 15, marked "4105-2," was cut in August
1909, about latitude 64° 30', near Lycksele, Lapland. It showed clear
and well-sized rings to its center in 1701. No. S 16, marked "4131-al, "
was cut in August 1910, in Elf dais, in latitude 61° 24'. Its center was
about 1838, but its inner 10 rings were uncertain and therefore not
DOUGLASS
PLATE A
A. Section of Scotch pine from Os, Norway.
B. Section of Scotch pine from Dalarnc, Sweden.
COLLECTION OF SECTIONS. 37
used. No. S 17, Picea excelsa, marked " 4105-5," was cut in May
1909, in the same locality as S 14 and shows a similar rhythm. Its
center was in 1777. No. S 18 was a small section marked "4131-a-12."
It was cut in October 1910, in latitude 58°, well to the west of the
others. Its radius measured only 2 inches. The average diameter of
the other sections was about 12 inches.
On page 115 will be found the means of these sections, with two
extrapolations, one from 1820 to 1848 and the other from 1820 to 1878.
This curve will be found plotted in figure 8. It has been corrected for
age and reduced to percentages by dividing by the readings of a
straight line extending from 1.90 mm. in 1820 to 0.70 mm. in 1910.
This corrected set has been smoothed by Hann's formula and will be
found plotted in figure 23.
EBERSWALDE (PRUSSIA) GROUP.
These 13 trees were cut and sections prepared for me by the kindness
of Professor A. Schwappach of Eberswalde. They were all Pinus sil-
vestris planted about 1820 to 1830, exactly alike in height and size,
with tall, straight, clear trunks about 10 inches in diameter and bushy
tops. The land is a gently rolling country with a slight northerly slope,
leaf-covered ground, a sandy soil with loam on top, and an elevation
above the sea of 200 to 300 meters. The height above the city level
was 200 feet or so; the locality was south and west of Eberswalde
station. The trees cut were scattered along a quarter of a mile and so
did not represent any close grouping. Their rings show almost identical
records; 2 to 10 in every decade have enough individuality to make
them recognizable in every tree.
On the first examination of these sections in November 1912, it was
evident that their growth follows with fidelity the sunspot curve since
1830. This may be traced in the curves below and in the accompanying
photographs of two of the sections in plate 8. It will be seen at once
that there is a rhythmic sway in the growth, groups of large rings
alternating with small ones. The arrows plateed in the photographs
mark the years of maximum sunspots. Taking the group as a whole,
the maximum growth comes within 0.6 year of the sunspot maximum.
To one maximum alone they fail to respond, namely, 1894; instead of
rising, the curve drops in 1892, 1893, and 1894. I have tried to find
cause for this, but was informed by Professor Schwappach that there were
no fires, pests, or other known causes for it except climatic conditions.1
1 Schwappach. Zeitschrift Forst- und Jagdwesen, September, 1904. A recent bulletin of
the Mellon Institute, by J. F. Clavenger, entitled, "Effect of the soot in smoke on vegetation,"
suggests at least a possibility. Clavenger shows photographs of tree sections in the neighborhood
of iron mills, in which the growth is normal until the smoke from the mills pours over the forest,
and then the rings rapidly decrease in size. It would solve the puzzle if it could be shown that
smoke from the iron and brass works in the neighboring city came over the forest of Eberswalde
more abundantly at about this time. Dr. Schwappach writes that the manufactories and repair
shops are 3 km. distant and in his opinion the decrease in growth can not be due to smoke from them.
38
CLIMATIC CYCLES AND TREE-GROWTH.
On page 114 will be found the Eberswalde means from 1830 to 1912.
Only one center occurs later than that date of beginning, namely,
1833. The others were mostly between 1821 and 1827. The means
of this group are plotted in figure 8 and also shown more in detail in
figure 9. These means have been corrected for age and reduced to
1820 30 40 1850 60 70 80 90 190& 1910
Mms.
Nos. 1-6
Nos 7-13
Nos. 1-13
Nos. 1-13
corrected
for age
Nos. 1-13
smoothed
Sun spot
curve
100
0 . 0
A
\
FIG. 9. — Sunspots and growth of trees at Eberswalde, Germany.
percentages of a mean line reading 2.57 mm. in 1830 and 0.54 mm. in
1910. These in turn have been smoothed and plotted in figure 23.
In considering the significance of the agreement above noted, one
should, in my opinion, keep in mind first the unusually homogeneous
environment of these particular trees and the great care they have
received, and second, the suggestion they contain of eventually defining
distinct meteorological districts in which homogeneous effects are noted.
A small pine of 60 rings from the Hartz Mountains was examined in the
COLLECTION OF SECTIONS. 39
Geological Museum at Berlin, in which the same cycle was prominent.
It was not measured, as the date of cutting was not known.
PILSEN (AUSTRIA) GROUP.
This group of 7 Pinus silvestris sections was measured in the office
of Dr. A. Cieslar, in the Hochschule der Bodenkultur at Vienna. I
have no samples of them in my collection, but they were carefully
cross-identified before measuring. Two sections had the ring for 1849
very doubtful, but its identity was verified by comparison with the
others. The average date of the center was 1821 and the average size
11 inches in diameter. They all came from a forest station near Pilsen,
in northwestern Austria. I have not seen the locality, but judging by
the appearance of the country a little farther south the mountains are
not rugged.
The mean measures upon this group from 1830 to 1912 are given
on page 114; their plot is in figure 8. The curve is very peculiaf,
and it is hard to say how it should be corrected for age. It descends
sharply from 3.62 mm. in 1830 to 1.25 mm. in 1851, and from that
point on it remains 1.25. This bent line has been applied, and the
resulting percentages have been smoothed and plotted in figure 24.
SOUTHERN BAVARIA GROUP.
This group of 7 Pinus silvestris and 1 Picea excelsa sections was cut
for me by the kindness of Messrs. Klopfer and Konigen in Munich
from logs in their yards. The trees had been cut in the winter of
1911-12 at Altotlinz, Ober Bayern, some 50 miles south, at a con-
siderable altitude, in the northern valleys of the Alps. The rings in
all these were clear and distinct and no doubtful case's were found
except a very few near the center of two sections, which were omitted
in the means; yet the cross-identification was not fully satisfactory.
Sections numbered M 2, M 6, and M 8 in this group showed 1 to 2
entire discordances out of about 10 features in the last 60 years. The
others agree fairly well. Possibly this condition results from the rugged
and non-homogeneous region where they grew.
On page 116 will be found the means from 1848 to 1911. In these,
M 6 and M 7 are extrapolated for about 12 years, and M 8 for 2.
These means will be found plotted in figure 8. The curve shows
apparently a very rapid decrease of growth with age. The correction
line assumed is a line reading about 3.15 mm. in 1850, 2.10 mm. in
1860, then with decreasing slope reaching a nearly level line at 0.90
mm. between 1895 and 1911. The means have been reduced to per-
centages of this line and smoothed by Hann's formula and plotted in
figure 24.
40
CLIMATIC CYCLES AND TREE-GROWTH.
OLD EUROPEAN TREES.
It is of course most desirable to carry the tree-records back as far as
possible for verification of any feature observed in recent years and for
additional information. But one is met by the rapidly diminishing
number of specimens and the liability of obtaining records which are
not representative of the regions on account of the increasing effect of
individual and accidental variations. It is true that in the very homo-
geneous region about Flagstaff, Arizona, an average of 5 trees and even
of 2 gave a valuable record corroborated by comparisons with larger
numbers; but in these European groups the oldest trees are all from
the Scandinavian peninsula, and probably the individual trees of
which I have samples are representative of widely different localities
in a rugged and mountainous country. Even though not homogeneous,
the 15 oldest trees have been segregated in 2 groups covering the inter-
val from 1740 to 1835.
Group A represents the inner coast of Norway and includes the
following trees: No. B 3, 6s, south of Bergen; No. B 11, Sopteland,
south of Bergen; No. B 12, Sogne Fjord; No. B 15, Hardanger Fjord;
No. B 16, Sogne Fjord; No. N 2, latitude 68° 45'.
1750.
1800
FIG. 10. — Growth of old European trees. A, six Norwegian trees, mostly from
inner fjords. B, eight trees from Dalarne, Sweden.
Group B is made up of 8 trees from Dalarne, central Sweden, and
1 from Lapland, latitude 64° 30'. This group, therefore, represents
somewhat more homogeneous conditions, but yet it can not be well
summarized in its larger fluctuations. When plotted with Group A,
as in figure 10, it shows the latter to have a considerable tendency to
reversal, a characteristic already observed in this region. But there
are discrepancies in Group B consisting of sudden depressions in growth
COLLECTION OF SECTIONS. 41
which suggest injury, as in 1756 and 1769 and 1770. A very regular
recovery from these depressions sustains this idea of their cause. The
means of the 2 groups are given on page 116.
A few trees are perhaps available for periods antedating 1740. The
centers of 5 are as follows: B 12 in 1682, B 15 in 1641, N 2 in 1497,
S 4 in 1510, S 9 in 1660. But the first 3 are from separate localities in
Norway and the other 2 are from central Sweden, so it seems hardly
profitable to include them here in a group on account of the tendency
to reversal between those localities. The section N 2, 400 years old,
from high latitude on the Norwegian coast, presents a feature of interest
as noted in connection with the Norwegian group, namely, a pronounced
fluctuation very nearly 34 years in length. The measures on this tree
have been plotted, a mean sinuous line drawn through them, and then
this mean line transferred to a different scale, smoothed graphically,
and photographed to form figure 38 on page 106. The more formal
analysis of this interesting tree-record with the periodograph confirms
this periodic fluctuation.
WINDSOR (VERMONT) GROUP.
On return from Europe it seemed desirable to learn how American
trees react in similarly moist climates. But it was not easy to secure
sections. There are very few large pines near the Eastern cities. One
"pitch" pine from 50 miles south of Boston, with more than 100
rings, was secured, but there were no others in that immediate vicinity.
Five white-pine sections from near Middleboro, Massachusetts, were
obtained, but their rings were too few in number, being only 50 to 60.
Finally a satisfactory series of hemlock, Tsuga canadensis, from
Windsor, was collected. Six sections came from the northwest slopes
of Mount Ascutney at the lower and very steep end of the Brownsville
trail. Five of these I cut from the stumps myself and preserved, and
one was measured on the stump itself with full cross-identification.
The remaining 5 of the 11 were cut from logs in a lumber-yard in Wind-
sor; they came from across the river on a farm about 3 miles from
town. Thus 7 or 8 miles separated these two subgroups. But the
whole are here retained in one group, for the cross-identification,
though difficult, was perfectly satisfactory. In order to be quite sure
on this point, the subgroups were left separate until their curves could
be compared. The Ascutney subgroup, with one extrapolation,
extends back to 1695, and from that date 2 trees were carried back to
1650. A comparison between the 2 and the whole 6 showed har-
monious curves in their overlapping parts. This curve shows an aver-
age growth of considerably less than 1 mm. in all its earlier years and
up to the year 1808, when its yearly growth doubled. This sudden
42 CLIMATIC CYCLES AND TKEE-GROWTH.
increase was interpreted to mean that at that time these hemlocks
emerged from the shade of surrounding trees. The change was so
rapid and great that it seemed likely to be due to the cutting down of
the surrounding forest. In this subgroup, also, the years 1770 and
1821 were so extremely small that injury on those dates seemed
likely.1 The other subgroup from east of Windsor extends easily to
1650, with one extrapolation of 20 years and another of 3. It shows no
effects in 1770 or 1821, but does show a temporary slight rise in 1807,
and then a gradual increase to well over 2 mm. by 1870 or 1880, as
would be expected when light-loving trees gradually push their way
out into preeminence above their neighbors. A comparison between
these two curves in their minor details confirms the view that all 11
may be included in one group.
The means of the Windsor hemlock sections from 1651 to 1912 are
given on page 116. In 1651 the figures give an average derived from
only 6 sections. This increases to 9 sections in 1694, and from 1695 the
whole 11 sections are used. These numbers have been smoothed and
plotted, and their resulting curves will be found in figure 27, together
with the sunspot curve.
OREGON GROUP.
Following the New England group, a set of Douglas firs was obtained
from a logging area about 25 miles northwest of Portland, Oregon.
Several points of interest appe'ar in connection with -this group. In the
first place, the samples were not radial specimens of the wood itself as
heretofore, but were pieces of blotting-paper of suitable size which had
been rubbed into the tops of the weathered tree stumps. These were
made in 1912 by Mr. Robert H. Weinknecht, who writes as follows:
"The prevailing age on the tract is about 210 years on the stump. The
trees selected were average with neither suppressed nor abnormally large
growth. An average typical radius was selected on each stump. Twenty-
three impressions from this one locality were obtained and sent. Twenty-one
came from stumps cut in the summer of 1908, one from a stump cut in 1909,
and one from a stump cut in 1912. The method of taking the impressions
was one devised by Mr. Higgs and described by him in the Forest Quarterly
for March, 1912. It was found that fresh stumps gave very poor results
and especially poor for the last 50 years. This was attributed to pitch form-
ing near the outer parts of the stump and to the fact that the weathering of
the stump had not been sufficient to bring the rings out in relief. Some of
the impressions were gone over with a pencil to bring out the rings where
they were faint or broken. This was done carefully and checked by the
number of rings counted on the stump."
During the course of identification and measurement, it was observed
that only a small proportion of the ring impressions show distinctly
1 A letter was published in the local newspaper, asking if anyone had any information regard-
ing forest fires in 1770 or 1821 or of lumbering in that locality in 1807 or 1808, but no reply has
been received.
COLLECTION OF SECTIONS.
43
the ending of each year's growth, which is usually the best measuring-
point. In good reproductions the measures are satisfactory, different
observers agreeing within 0.1 to 0.2 mm. In others, however, there is
much chance for judgment in selecting the measuring-point, and
observers differ 0.3 to 0.5 mm. Nevertheless it is easy to judge of the
relative sizes of rings and the only injurious effect is to reduce variations.
The cross-identification was very satisfactory, with practically no
doubtful cases and only a few which required careful study. It is not
likely that there is a single error in identity throughout the 17 sections
in this group. Two other trees, one cut in 1909 and the other of
No.l
No.Z
No. 3
17/0
No.l
No. 2
No.3
s
-
'
HA
f\/\
V
1810
1850
Z
I
0
I.Z
1.0
0.8
Years
1300
FIG. 11. — Oregon group. Curve No. 1, actual tree-growth; No. 2, tree-growth
departures, smoothed; No. 3, sunspot numbers displaced 2 years to left.
unknown date, but probably cut in 1902, were not included. They
showed special characteristics, such as an evident injury in 1861-62,
affecting the 1862 ring and several others following it. They show
also small growth in 1886, and even in 1887 and 1888 following the
minimum growth of 1884 and 1885 prominent in the large group. The
tree (cut probably in 1902) shows a minute growth in the years 1779
to 1783 inclusive, evidently the result of injury. These two sections
are full of character and may prove valuable.
Five other rubbings similar to the group of 17 were discarded
because defective in some parts. The attempt to trace the lost lines
with a pencil-mark gave no help. One of the 17 was defective since
44 CLIMATIC CYCLES AND TREE-GROWTH.
1835, and only the earlier part, ending in 1834, was used. Extra-
polated values for the missing part were derived in the usual way.
A few short, apparently doubtful, regions of rings required careful
study and it was found that well-adjusted illumination of the rubbings
was very necessary to their correct reading. When the ring impres-
sions were deep in the paper, the end of the rubbing showing the tree
center was held toward the source of light in order that the elevation
corresponding to the beginning of the spring growth might be brightly
illuminated. When the impressions were shallow and faint, it was
noted that the rings became very distinct if the rubbing was held
between the eyes and the light, thus giving a very faint and perfectly
even illumination. If this did not bring out the individual rings, the
rubbing was not used.
The location in which these trees grew was visited in 1918 and
general contours were noted. The hills are low and comparatively
flat-topped, with disintegrated rocks showing in railroad cuttings.
The sides of the hills are steep, and the valley bottom is narrow and
usually has a wash near its center. In general the drainage is toward
the east, but there is no high and sharp ridge between this region and
the ocean on the west. The situation is far enough north to have a
good snowfall in winter. It is about 800 feet above sea-level.
The tabular matter giving the results of the measures on the 17
Douglas firs of Oregon will be found on page 117. The plotted values
appear in figure 11.
THE SEQUOIA GROUP.
In 1911, after examining the writer's results obtained on the yellow
pines, Huntington made an extensive series of measurements on the
big tree, Sequoia gigantea. He did this work on the stumps themselves
by direct counting from the outside. This introduced errors of begin-
ning due to removal or injury of outer rings, and errors of omission
which of course could not be checked. In order to correct for large
errors of omission, he worked out an approximate correction on the
grounds of probability which depended upon a comparison between
two or more radii of the tree, and in that way many errors were com-
pensated. In the vast majority of cases, his measures were not of
individual rings but of successive groups of ten. I have collected seven
of his trees, and after complete cross-identification verify his centers
as shown in table 4.
But Huntington's method of working directly on the stump enabled
him to get data from a very large number of trees, some 450, in a way
that served his purpose very admirably. He was searching for general
effects, and accuracy to a year or two was less essential. He wished to
approximate absolute values of rainfall in past climates, in contrast
with which my chief aim is to get relative and periodic values. These
COLLECTION OF SECTIONS.
45
two different purposes supplement each other in a highly valuable
manner. Therefore, for him, the determination of the general curve,
with an allowance for larger growth near the center, was most important.
For that purpose he used both young and old trees. Necessarily he
visited places where the trees had been cut. The two chief regions of
his measurement were in the King's River Canyon district close to the
General Grant National Park, and in an old lumber region near
Springville, which is south of the Sequoia National Park.
Following Huntington's route, I visited the former region in August
1915. The town of Hume, the mill-site of the Sanger Lumber Com-
pany, is reached from Sanger by daily auto stage and formed, therefore,
an excellent base of operations. Hume is at an elevation of about
5,500 feet, on the shore of a large artificial pond, into which the logs
are dumped as they are brought down from the camps. A narrow-
TABLE 4.
Sequoia
No.
Huntington's
No.
Huntington's
first year
of tree.
Identified
first ring.
Distance
from center
in inches.
Probable
date of
center.
12
92
17 A. D.
Not ident.
8(?)
13
91
585 A. D.
588 A. D.
0
14
96
387 A. D.
389 A. D.
0
15
59
121 B. C.
159 B. C.
o
21
22
23
74
195
116
1318 B. C.
1141 B. C.
1191 B. C.
1304 B. C.
1086 B. C.
1121 B. C.
1
7
10
1316 B. C.
1160 B. C.
1200 B. C.
gage logging road extends in an easterly direction from Hume, high up
on the southern side of King's River Canyon. It winds in and out of
the various small canyons or basins that empty into the large ravine.
The elevation of the log road increases gradually from Hume until it
reaches 7,000 feet at Camp 6 and Camp 7, which are about 7 and 9
miles distant respectively.
Camp 6 and Camp 7 are the names of the two recent logging sta-
tions. Camp 6 was occupied in 1915 and was located on the east-
ern side of Redwood Basin. The camp sites are usually chosen in
such localities, for in each basin there is an enormous collection of
accessible timber. In general the tops of the mountains are very
rugged and the slopes exceedingly steep. The upper ridges are apt to
be very sharp, but in the higher altitudes there is a tendency for the
weathering of the mountain to produce this basin type of contour.
From the accumulation of soil and the enormous snowfall in winter
these become exceedingly swampy. Below the basin the w'ater is
carried by sharp, narrow canyons down very steep grades to the river
far below. These groves of sequoias are between 6,000 and 7,000 feet
above the sea. The climate at this elevation presents a contrast
between an intensely cold winter season with 10 to 15 feet of snow and
46 CLIMATIC CYCLES AND TREE-GROWTH.
delightfully mild summers. The latter have occasional thunder-storms
whose waters quickly run down the mountain slope. Thus conserva-
tion plays an important part in the growth of these trees by rendering
the winter precipitation more important than the summer and by per-
mitting the moisture to remain long in the swampy places.
Three groups were obtained from this general region in 1915. The
first of these came from the uplands above Camp 6 close to the west
line of section 17, township 13 south, range 29 east. This region
may be found on the Tehipite Quadrangle of the United States Geo-
logical Survey. The group includes Nos. 1 to 5. No. 1 was a splen-
did tree, about 19 feet in its greatest diameter, growing at the upper-
most limit of the logging area. Its growth was rapid, and yet it
was an extremely sensitive tree, showing beautiful variations from
year to year. No. 2 was obtained a little lower down and is mentioned
here because it has been used as the standard of the whole sequoia
group, having probably a more perfect record than any other tree
measured. Its center was about 300 B. C. No. 5 was a small tree
which was cut just at the time I came within hearing distance. I
thought that two blasts of dynamite were set off and found afterwards
that only one charge of dynamite had been used to break through the
last support of the mighty tree; the other report was the tree itself
crashing to the ground. Yet this was a small tree, only some 12 feet
in diameter, and its age was about 700 years. It proved of particular
value to the whole sequoia group, because it was the only tree on which
was obtained the ring of the current year, thus permitting a very
important correction to be made in the dating of rings. This had an
important bearing on the relationship of rings to rainfall.
The second group included Nos. 6 to 11, and was made about a
mile to the north and 700 feet lower altitude in the swampy basin whose
outlet was similarly toward the northeast. No. 6 grew at the edge
of the little brook running through the basin and its rings proved later
very uncertain in identity, because its habit was complacent, i. e., the
rings were nearly all alike in size.1 No. 7 was an improvement on it,
and No. 8, which was still farther from the creek, was perhaps the best
of this group of 6. It gave a very fine cross-identification with the first
group. No. 11 was also very close to the creek near the outlet of the
basin and, as with No. 6, it was impossible to be sure of the identifica-
tion, owing to its complacent character.
- The third group consisted of 4 trees from Indian Basin, about 10
miles northwest of the Redwood Basin and 3 miles north of Hume.
This basin is a broad, flat, fertile area with an outlet toward the
northeast. Four trees were obtained there which Huntington had
already counted. Nos. 12 and 13 came from the flat middle area of the
basin. No. 12 was not included in the final averaging because its rings
1 Since the trip of 1919 the identification of No. 6 has been fully established.
DOUGLASS
PLATE 5
*• 4&- /*• « V * ' * " v1- 1IL<
•» -« . . j. •** «/» ' _ V *-w • . '••>-
»:
£33& $ . -
A. Upland contours, above Camp 6 in Sequoia Grove: D-19.
B. Basin contours, Indian Basin, looking S. E.: D-12 and D-13 in center.
COLLECTION OF SECTIONS. 47
could not be identified at all, chiefly owing to large numbers of com-
pressed rings in the last 500 years or more, and to several heavy fire-
scars and its generally complacent character. In 1919 a short radial
sample was cut from another part of the stump and a complete and
satisfactory identification obtained. It shows very fine rhythmic growth
in places. No. 13 was not included in the final averages, because its
rings were very complacent and perfect identification was not obtained.
Nos. 14 and 15 were obtained from the northern side of the valley and
their identification was entirely satisfactory. The agreement which
they give with Huntington's ' 'first year of tree ' ' has already been quoted.
The three groups whose collection has been described above showed
on examination certain interesting relationships to the location in
which they were found. The first group was obtained high up on a
hillside, where the slope of the ground was 15° to 25°. It was not very
far from the top of a sharp ridge and there was no opportunity for
moisture to collect and remain for long periods on the soil. Therefore
one would expect these trees to show variation related to the amount
of snowfall each winter, if any did. The growth of some of these trees
was large but full of constant variation, and they were therefore of the
type which I have called "sensitive." They do in fact show best of
any the relationship to precipitation which will be described in a later
chapter. The second group came from a characteristic feature of the
country, namely, a basin with thoroughly water-soaked soil.
The luxuriance of vegetation in these basins before lumbering was
wonderful. The sequoias grew often within a few feet of each other,
and even between them were pines, firs, and cedars. Lumbermen
often point out the bottom of a basin and say that such a place ran
over 1,000,000 board feet to the acre. To-day nearly all the trees are
gone and debris and rubbish are scattered about everywhere. The
constant supply of water in the basin made the trees less dependent
upon the annual precipitation and they show, in fact, large rings with
very slight variation from year to year. They are typical examples
of the "complacent" habit. Complacent trees contribute much less
to a knowledge of climatic variations, and some of them have to be
discarded because of uncertainty in the dating of their rings.
The third group, Nos. 12 to 15, came from Indian Basin, where
logging had been done about 1903. Its outlet, like the others, was
toward the northeast. It had, however, a much larger flat area, now
covered by extensive fields of hay and by forage. The characteristics
of the trees found here were the same as in the groups already described.
No. 1 (with a 7-foot radius) was first counted and marked with
provisional dates. The 'rings were coarse and the numbering seemed
promising, but proved later to have 6 to 8 errors in the last 700 years.
No. 5, which was the tree cut down during my visit, was then dated
48
CLIMATIC CYCLES AND TREE-GROWTH.
provisionally. It was 700 years old, with coarse, sensitive rings, and was
the only one of the group showing the ring for 1915. In comparing
these two for larger variations no accordance was recognized and in
details cross-identification failed also, due (as afterwards found) to
accumulated errors in No. 1.
No. 2 was then counted and compared with No. 5 with apparent
certainty and satisfaction. The former was nearly 6 feet in radius,
with small rings, 2,200 years old, and with all but 3 years represented.
The last 700 years were thus compared minutely with No. 5 and the
earlier parts with No. 1, and one ring (later identified as 699 A. D.) was
found to have been overlooked. The earlier parts were later all checked
D+
%
m
^/V^^-A/^
V
<w>
3.5
3.0
2.5
2.0
1.5
1.0
0.5
1.0
.5
0.5
0 <
1.0
0.5
0
1.0
0.5
1850
60
70
80
90
1900
10
FIG. 12. — Cross-identification in first five sequoias and gross rings in No. 1.
against No. 3 and no suspicion of error was discovered. This number
was, therefore, taken as the best type of specimen of this group.
Large fluctuations of size rarely occur in it.
No. 3 was next counted by comparison with No. 2. No. 3 has few
large fluctuations and large portions of it match No. 2 with the greatest
accuracy. Nevertheless, as a standard with which to compare others,
it would be misleading, for it frequently omitted rings; in one place
7 rings and in another 6 rings are entirely missing, and half a dozen
more in singles and in pairs. Yet cross-identification with No. 2 was
easy and perfectly convincing as to the location of the missing rings.
COLLECTION OF SECTIONS. 49
No. 4 proved to have fairly large rings with 3 to 4 single ones missing
and some hard to find, but the identification was easy and entirely
satisfactory. No. 1, which was by this time recognized as the most
difficult of the group, was reexamined in detail by comparison with
No. 5, which proved difficult, with No. 2, which was somewhat better,
but especially with No. 4, which proved to have the closest similarity,
and all apparent errors were removed. It was very apt to drop out
completely rings which were a little below the average. No. 5 seemed
to have no tendency to subdue or drop rings. This, with its disclosures
of the ring for 1915, showed the necessity of including younger trees in
any new group to avoid mistakes in the outer slow-growing parts of the
older trees. A comparison of the last 70 years' growth of sections 1 to
5 is given in figure 12. An illustration of "gross" rings is seen in the
upper curve.
When the second subgroup was compared with the first, two com-
plete omissions from No. 2 and the others of that first subgroup were
discovered. This necessitated the complete renumbering of the first
five sections.
The sections were measured at this stage of the dating process. The
final renumbering was made after the 1919 trip, the purpose of which
was settling the identity of a doubtful ring occasionally found between
1580 and 1581. The existence of this ring was established and the
necessary corrections on the sections and in the tabular matter in this
book have been made. All subsequent comparisons have verified this
identification.
THE SEQUOIA JOURNEY OF 1918.
The visit to the Big Trees in 1918 was for the purpose of procuring
material so that the tree-record from the 2,200 years already secured
could be extended to 3,000 years. It was expected to do this without
great difficulty, for Huntington had enumerated 3 trees over 3,000
years of age, and he had placed numbers on the tops of stumps so that
these could be readily identified. Nevertheless, in consequence of the
occasional absence of a number on the top of a large stump which had
been counted by him, a little more care proved to be necessary than
was anticipated.
After procuring an outfit in San Francisco, I selected Hume as a
base and immediately went out on the log road to Camp 6, the old
location of the groups obtained in 1915. All the stumps from which
samples had been taken (including Nos. 1 to 15) were visited and each
was marked with its respective number preceded by the letter D. This
marking was done by a chisel, and. the figures were usually about 4
inches in height. Placing the capital D before each number made it
certain that no number would be accidentally read upside-down.
Naturally the stumps from which samples have been taken show the
large cut from center to outside, and there is no doubt about their
50 CLIMATIC CYCLES AND TREE-GROWTH.
belonging to the group. But if other samples are taken in future years,
this numbering will prevent confusion. All the 23 stumps are thus
identified by a number in this series.
I had hoped on this trip to find other trees as old as Huntington's
three, and therefore searched carefully for the largest stumps. All
those over 20 feet in diameter and a number of less size were estimated
for age. This was done by measuring the average width of rings here
and there along a radius and multiplying by the length of the radius.
About 50 were thus tested. In many cases the result has proved to be
within 50 years and sometimes much closer, but these estimations
were not very reliable, there being several large mistakes in them. In
attempting to pick out the oldest stumps among several thousand
without spending much time or getting very far from camp, it is impos-
sible to make these estimates with very great care. It was felt that
much help would have been obtained from a small range-finder and
telescope, the former to give the distance of the stump and the latter
its diameter. In the course of a few days this would have saved many
miles of tramping and the oldest trees would have been found more
readily.
On the steep upland slopes above Camp 6, two trees were estimated
at about 2,500 years in age. These were afterwards numbered D 18
and D 19. D 18 was an immense tree which was cut down in 1914 at
the time a motion-picture company was operating in the sequoia forest.
It is referred to by the lumbermen as the "Moving Picture Tree."
It had to be blasted from the stump before it fell, and the stump was so
completely shattered that no sample could be cut from it. In falling,
the trunk of the tree split in halves through a large part of its length,
and most of it remains where it fell. About 40 feet of logs were cut
away between the ruins of the stump and the rest of the tree. Accord-
ingly my sample was cut from the lower end of the broken top and at a
point which had been about 50 feet above the ground.
Close by the location of No. 18, and on the steep upper hillside just
below the track which extends on to Camp 7, is No. 19. A log from it
rests uphill with its upper end at the railroad embankment. The
section was taken from the stump nearly 60 feet below (see plate 5).
Camp 7 was visited and used as a base for two days. It is 2 miles
beyond Camp 6 on the ridge at the farther side of Windy Gulch. There
are some very fine stumps close to the road that goes down from the
camp into the basin, which were estimated to be 2,300 or 2, 400 years old.
No. 16 was found high up in the gulch that extends toward the top
of the mountain just south of the camp. The gulch faces toward the
east and at the location of the tree has a slope of 15°. No. 17 comes
from the basin some hundreds of feet below the camp. It was a wind-
fall and the lumberman thought it might have been lying there a great
many years. As it was a very large tree and of slow growth, it was
DOUGLASS
PLATE 6
mm
V ••
A. Cutting radial sample from end of log, Converse Hoist: D-20, age 2SOO years.
B. Site of oldest tree, Converse Hoist: D-21, age 3200 years.
COLLECTION OF SECTIONS. 51
hoped that its center would prove of very great age. But the results
were disappointing, for it turned out that it had fallen only a few years
before the logging began and that its age was only 2,200 years. It had
so many compressed rings in its outer parts that the last 800 years
were not considered worth measuring.
On leaving the vicinity of Hume several days were spent at the
General Grant National Park. It formed an ideal center for a con-
siderable region. Horseback trips were made to the area which
Huntington calls the " World's Fair District," "Converse Hoist," and
by other names. No. 20 was a fallen tree with a northerly exposure,
on the west side of the upper basin, not far from the old hoist at the
top of the ridge. It was on the west side of the abandoned railroad.
It was found that the tree fell only 6 years before the logging was
done. A log had been taken out and the sample was cut from the top
of the fallen stump. No. 21 is the most interesting of all, because it
gives the oldest record by nearly 200 years. It is on the east side of the
railroad and brook in the lower part of the upper basin, and some 30
feet above the level of the brook. It is not at all impossible that during
its long life the topographic character of the ground about it has
altered materially. It is somewhat complacent in its later growth, but
this does not persist throughout its record. The top of the stump had
carbonized, become extremely brittle and very hard to cut. Though
bits of wood broke off and clogged the saw, every piece was marked and
preserved. The radial sample has been glued together in the labora-
tory and is now 9 feet long. The original center of the stump was
badly cracked through contraction in drying, but there were lacking
only about 2 inches at the center. The central portion, perhaps a foot
in diameter, was not firm enough to be cut out with the saw. It was
therefore removed very carefully and is now mounted in a special box
in the laboratory. The oldest complete ring in good condition was
identified as 1305 B. C. Possibly two more rings may be added. A
hundred yards to the south and slightly higher up the hillside is the
"World's Fair Stump." This was cut in 1892 at a height of more than
20 feet above the ground, and to-day the stump is very difficult to
climb, as the scaffold built around it has broken away.
A trip was made from the General Grant National Park to the
upper part of the Comstock millsite, known also as Wigger's. The
stage road goes near it and the point is known as "Big Stump." The
stump, easily seen from the road, is some 25 feet in diameter with a
raised square in the center. The location is in a side basin close to a
small brook. An examination of the rings showed that the tree had
grown with the greatest rapidity, as the rings were of enormous size.
It was estimated to be 1,500 years old. No sample was taken of it.
A trip was also made from the park to visit the General Grant Tree
and if possible estimate its age. There is an extensive burnt area on
52
CLIMATIC CYCLES AND TREE-GROWTH.
the upper side of the tree in which the rings may be observed. These
rings are large, and various estimations of the age of the tree obtained
in two different visits gave an average of 2,500 years. Near the General
Grant Tree is the stump of what was known as the Centennial Tree.
It was said that a section of this tree was exhibited in 1876. Since
then the stump has been badly burned and is in poor condition for
cutting a sample. Some estimate of the rings showed their size to be
large, and the age of the tree, therefore, was not very great, perhaps
1,800 years. This confirms the estimate of the General Grant Tree
near by.
TABLE 5. — Sequoia list.
6
X
CS
I
o
w
Huntington's No.
Huntington's
first year
of tree.
Identified
central com-
plete ring.
First
complete ring
not central.
Estimated loss in
center.
Estimated years
lost.
Probable
center of
tree.
"Sid
as
03 '-'
JH-2
— 1 O
c3 V
,Q *•*
r
1
o .
£2
•82
3.S
M
a
<o
i-3
Location.
Dl
592 A. D.
cm.
yrs.
1323
yrs.
1323
Camp 6, Uplands.
2
274 B. C.
4 5
15
289 B. C.
2204
2189
Do.
.3
310 B. C
2225
2225
Do.
4
425 A. D.
1490
1490
Do.
5
1202 A. D.
713
713
Do.
61
1125 A. D.2
7902
7902
Camp 6, Basin.
7
594 A. D.
13 5
75
519 A. D.
1396
1321
Do.
8
294 B. C.
2209
2209
Do.
9
311 A. D.
1604
1604
Do.
10
362 A. D.
1553
1553
Do.
II1
697 A. D.
7 5
46
651 A. D.
1264
1218
Do.
121
9?
17 A. D.
135 A. D.
14
65
70 A. D.
1845
1780
Indian Basin.
131
91
585 A. D.
588 A. D.2
13272
13272
Do.
14
96
387 A. D.
388 A. D.
1527
1527
Do.
15
59
121 A. D.
160 B. C.
2075
2075
Do.
16
506 B. C.
2421
2421
Camp 7, Uplands.
17
308 B. C.
2223
14383
Camp 7, Basin.
18
294 B. C.
2209
2209
Camp 6, Uplands.
19
242 B. C.
8
35
277 B. C.
2192
2157
Do.
20
902 B. C.
2817
2817
Converse Hoist.
21
74
1318 B. C.
1305 B. C.
2 3
12
1317 B. C.
3232
3220
Do.
22
195
1141 B. C.
1087 B. C.
12 0
75
1162 B. C.
3077
3002
Enterprise.
23
116
1191 B. C.
1122 B. C.
14
80
1202 B. C.
3117
3037
Do.
1 Omitted from the means on account of some deficiency in identification.
2 Identification very nearly right.
3 Not identified after 1130 A. D.
Leaving the vicinity of the General Grant National Park and going
south to Porterville, thence by rail to Springville, a 3 days' trip was
arranged to the old Enterprise millsite. Camp was made at the cabins,
about 10 minutes' walk below the millsite. On going up from the
camp, No. 23, known as the Centennial Stump, was found at once,
as it is of enormous size, high in the center, and covered with names of
visitors. It is located close beside the road and near the wash, about
100 yards from the clear space once occupied by the Enterprise Mill.
The oldest tree which Huntington found at this locality had been
DOUGLASS
PLATE 7
^^3t — o-w •".- »
».-/•«._ *^— ". — , . V.-.
A. Cutting sample from stump, Enterprise: D-22, age 3000 years.
B. Centennial stump, Enterprise, Cut in 1874: D-23, age 3075 years.
COLLECTION OF SECTIONS. 53
numbered 116 in his lists. This stump had no number on it, but from
the date of its cutting and its age of nearly 3,100 years, it is without
doubt the one he refers to. The tree was cut in the winter of 1874-75
for exhibition at the Centennial. The trunk was hollowed out and
prepared for transportation in pieces to Philadelphia, where it was
said to have been erected, making a sort of hut. In consequence of
the uneven surface left, it was very difficult to cut a sample from this
stump. However, one was at last secured, which is 12 feet long as it
lies on the table in the laboratory.
No. 22 was Huntington's No. 195 and grew near the center of the
millsite. Its cutting was extremely easy and its cross-identification
with No. 23 and the other trees farther north proved entirely reliable.
The location from which these two interesting trees were obtained
is at the very top of a ridge with a steep descent on the east to the
North Fork of the Middle Fork of the Tule River and a similar descent
on the west to the Tule Valley. The top of the ridge is several hundred
yards wide, with opportunity for considerable snow to collect there in
winter. It receives little drainage from any source. Just north of it
is Mount Moses, high and rugged, and to the south are high ridges
extending toward Bear Valley.
All the sections obtained in these various trips were shipped to
Tucson, and four weeks of continuous work were spent in cross-
identification. All the identifications were satisfactory except the
year 1580, which was finally determined by the special trip in 1919.
The general method of measuring and marking these sections will be
found in the next chapter and the tabulation of averages at the back of
the book. Owing to the interest in these trees of remarkable size and
age, a list of the 23 collected in these two trips is given in table 5.
IV. DETAILS OF CURVE PRODUCTION.
PREPARATION OF RADIAL SAMPLES.
Form of sample. — Nearly all of the 230 trees used in this investiga-
tion are represented by portions preserved in my collection. Wherever
possible the entire section, 1 to 3 inches or more in thickness, was
brought to the laboratory for examination. Unless the section was
light and easily handled, it was found convenient to cut from it a radial
piece showing the complete series of rings from center to bark. Natur-
ally the enormous trees of the sequoia groups could be obtained only
in radial form. The paper rubbings from Oregon and the small cuttings
of the Prescott and second Flagstaff groups were also of this type.
Hence the radial sample is regarded as the usual or type form in which
the material appears in the laboratory. If the original section was
small the radial piece appears as a bit of wood cut across the grain,
square or triangular in cross-section and a foot, more or less, in length.
Method of Cutting. — The partial radials, such as used in the Prescott
group, were secured from the stumps in place by making saw cuts at
the edge of the stump in two directions, meeting a few inches below the
surface. In this manner a piece of wood in the form of a triangular
pyramid was secured and was sent to the laboratory. The radials of
the sequoias were cut altogether from the tops of stumps or from the
ends of logs that lay on the ground. From the manner in which the
trees were cut down it was usually possible to get a clear surface of
stump or log from the bark on one side to somewhat past the center
where the under-cut had been made. After a minute examination of
the surface exposed, a radius was selected which would give the greatest
freedom from fire-scars and other irregularities of ring distribution.
Two lines about 8 inches apart were drawn with blue chalk along this
radius. Then two men with a saw 8 to 14 feet in length made a slanting
cut on one of the lines of sufficient depth and in the right direction to
meet a similar slanting cut from the other chalk line. In this way a
long piece of wood of V-shape in cross-section was obtained, extending
from the center to the outside and giving the full ring record.
In sequoias recently felled this cutting of the radials was extremely
easy, but many of the sections obtained were from stumps which had
been standing and weathering for 25 years and in one case 43 years.
The exposure carbonizes the top of the stump and makes it extremely
brittle and difficult to cut; small pieces break off and wedge the saw.
Thus it often becomes a very difficult task to extract the radial section.
The pieces into which the radial section breaks are marked for identi-
fication immediately, photographed and listed in notebook, and then
carefully packed for shipment. On arriving at the laboratory, they
are pieced together with the greatest care and then glued together in
groups, making the entire radial section a series of convenient pieces
about 2 to 3 feet in length.
54
DETAILS OF CURVE PRODUCTION. 55
Preparation for measurement. — These pieces were then examined to
find the longest sequences of clear and large rings, and guide-lines for
the subsequent identification and measurement were selected as nearly
as possible perpendicular to the rings. Such lines having been decided
on, two straight pencil lines, half an inch apart, were drawn and the
surface between these was " shaved." For this purpose, after the trial
of many other methods, a common safety-razor blade was clamped
to a short brass handle. With this very sharp blade the rough surface
of the wood is removed and the rings stand out very clear and distinct.
Besides the space between the lines, the region close outside is usually
shaved also for a preliminary trial at cross-identification, the final
marks being the only ones permitted between the guide-lines.
The best light for observing the rings is a somewhat diffused light
coming sharply from the side. A light falling on the wood perpendicu-
larly is apt to be very poor, either for visual work or photography.
Light from each side must be tried, for there is often a great difference
between the two directions, due probably to the way hi which the
knife passed over the wood and bent the ragged edges of the cells.
In photographing, the colors involved and the result sought (%. e., to
show the red rings as black) require an ordinary plate and a blue color-
screen.
When the surface is well prepared it is placed in a suitable light and
wet with kerosene applied by means of a bit of cotton on the end of a
small stick. This deadens the undesired details of the surface, and
brings the rings into greater prominence. The identified section is
now supported over the unknown and with watchmaker's glass in
eye and long needle in hand, the observer can make rapid comparison
and quickly put on the required marks.
IDENTIFICATION OF RINGS.
In the early Flagstaff work the rings were first numbered, beginning
at the outside without regard to the year in which they grew. But this
was found to add complexity and involve 'the use of a separate reduc-
tion from the provisional numbers to the true dates of the rings.
Accordingly the rings are dated at once as well as possible on some
selected section that gives promise of an accurate record. The identi-
fication mark is a pin-prick or very small hole placed on the last ring
of each decade. The middle year of each century has 2 pin-pricks and
the centuries are marked with 3; the 1,000-year mark is 4. Marks
found in error are "erased" by a scratch through them.
After the selected section is dated with the greatest care not to over-
look or mistake any rings, others are dated by direct comparison with
it. The common practical test in such comparison is the relation of
width of a ring to its half-dozen near neighbors. For some unknown
reason, rings of diminished size seem to carry more individuality than
enlarged rings, and so they are usually picked out for cross-comparison.
56 CLIMATIC CYCLES AND TREE-GROWTH.
In nearly every decade some are thus distinguished, and in each century
there are usually 3 to 4 conspicuously small rings which give very
important aid.
In the first work on the 2,200-year sequoia record, the identification
was a laborious task involving all the writer's spare time for a year.
The only real difficulty was with the ring for the year 1580. This was
temporarily called 1580A, but the material collected in 1919 showed it
to represent a year and a final and complete renumbering included it as
such. In the end the comparisons gave entire confidence as to the
identity of every ring. Section No. 2 gave the most nearly perfect
long record, beginning at 274 B. C., and is used as a standard with
which to compare all new ones.
The most difficult parts to identify are the compressed rings. Over
long periods, varying from 5 or 10 up to 100 years, the rings are some-
times so crowded together that large numbers of them seem to be
merged into one and their identification becomes extremely difficult
and in a few cases impossible. The great variations in sizes so produced
also exaggerate effects. These groups of compressed rings are con-
sidered as of little value, and in fact in many trees their measurement
is omitted altogether. Tree No. 12 of the sequoias obtained from the
Indian Basin had such bad groups of compressed rings that it proved
practically impossible to identify them without a large expenditure of
time not then available. Tree No. 17, also, from Camp 7, was found so
full of compressed rings in the last few hundred years that all measure-
ments were omitted after the year 1130 A. D.
Fire-scars. — Most of the big trees show fire-scars at some time in
their history, and the process of the tree's regeneration is very inter-
esting to observe. If the scar is small the woody growth quickly
comes in from each side and covers it. If the scar is very large, occupy-
ing perhaps one-quarter or one-third of the circumference, the tree
is likely never to recover and the burnt place remains permanently
on its side. In cases of less extensive burns, the wood from each side
year by year grows toward and over the injured spot, and if the injury
has not been too great the approaching sides may meet and imprison
their own bark within the tree. Thus one often sees the tops of the
stumps marked here and there by a hole as large as a foot in diameter,
filled with bark in perfectly good condition.
No. 12 had several fire-scars that interfered with the identification
of rings. No. 18 also had one or two fire-scars and in particular showed
a fire in the year 1781. The latter evidently stopped the growth at
that point completely, yet was not large enough to interfere with
recovery. In the sample in the laboratory the usual reddish-colored
heartwood changes about the year 1700 to the white sap wood, which
ends with the ring 1781 and shows a surface that was once covered with
bark. However, immediately outside of that surface, the red heart-
DETAILS OF CURVE PRODUCTION. 57
wood begins again with the year 1791 in a thick, rapid growth. The
heartwood continues for some 20 years before changing again into the
white sapwood, which persists to the outside. In order to make sure
that this gap would not prevent satisfactory identification, a small
portion was cut from another part of the outside of the tree, showing
some 300 rings without interruption; but this additional piece I found
in that case to be unnecessary.
In sections numbered 22 and 23, from the old Enterprise millsite,
there are injuries which do not greatly alter the appearance of the
rings, yet are sufficiently great to weaken the wood and cause it to
break at several points. If the break in such case is across the rings,
it is easy to carry the identity of rings past the injured point. But
when the break in any wood sample is all in one ring there may be a
doubt as to whether the break is between two rings or in the middle of
one. In the latter case there will apparently be an extra ring at that
point. If the break is obviously between two complete rings, then an
unknown number of rings may be lost at the broken point. The only
way to carry the correct dating of the rings past such broken places is
to secure samples from other parts of the same tree or from other trees,
which show 100 to 200 rings on each side of the uncertain place without
serious interruption. A simple cross-identification will show whether
any rings are lost. However, in Nos. 22 and 23 just referred to, nearly
all lines of breakage crossed the rings in a way that left no uncertainty.
But No. 22 had an injury and a break between complete rings at about
1020 B. C. and a pronounced injury at about 1060 B. C. No. 23 had
an extensive decayed place with the loss of about 35 rings at 1060
B. C. An extra piece cut from the stump of No. 23 carried the dating
across these gaps with perfect satisfaction and in complete accord with
No. 21 which had been secured 50 miles to the north.
Cross-identification between distant points. — The sequoias collected
in 1915 had come from the immediate vicinity of Camp 6, about 7
miles east of Hume, and from Indian Basin, which is 3 to 4 miles north
of Hume. The total extent of country covered was about 10 miles.
All these were identified and found to be very similar in their charac-
teristics. In 1918 the country represented was extended by sections
from the new Camp 7, some 2 miles east of Camp 6. Nos. 20 and 21
were then obtained from the old Converse Hoist, 4 miles from Indian
Basin and 15 miles from the Camp 7 district. Finally, 2 trees were
obtained from the old Enterprise millsite, 50 miles from the other
localities. It was realized at the time that there might be difficulties
of cross-identification between these 2 trees at Enterprise and the
other well-known and well-identified groups near Hume and the General
Grant National Park. However, it was very gratifying to observe
on close examination of these sections that no uncertainty was intro-
duced in the identity of the rings. One realizes from this that, so far
58 CLIMATIC CYCLES AND TREE-GROWTH.
as sequoias are concerned, a distance of 50 miles between groups is
likely to be no particular obstacle in cross-identification.
The difficult ring 1580.— The small ring 699 A. D. and several other
difficult ones were absent in comparatively few trees and any uncer-
tainty regarding them was removed in the early part of the work, but
it was not so with the ring of the year 1580. The best of the tree
records were from the uplands and usually omitted it, while many of the
basin trees which showed it were at first very uncertain in identifica-
tion. The ring was therefore provisionally called 1580A and held in
doubt for several years. The question of its reality was finally settled
in the affirmative by a special trip to the sequoias in 1919 and the
collection of a dozen carefully selected radial samples. The final
review of all the tree-records has resulted in satisfactory identification
of some previously doubtful cases and in complete conviction regarding
the ring for 1580 A. D. No other uncertain cases were discovered.
Considering the 35 sequoia records now (1919) made use of, it seems
possible that all errors of dating have been removed.
MEASURING.
Having prepared and identified the wood samples, the first method
of measuring was to lay a steel rule on edge across the series of rings
in a radial direction and to read off from the rule the position of the
outside of every red ring. These were either recorded at once by the
person measuring or were noted by a clerical assistant. This method
applied to the Flagstaff and Prescott trees and to the European and
Vermont groups. In nearly all of them the steel rule used was a meter
in length. It was ascertained by tests that the errors in readings of
this kind were less than 0.1 mm. on the average for a single reading.
For the Oregon group a microscope slide was used with a vernier which
gave at once readings to 0.01 mm. The readings obtained by either
of these methods were recorded in two columns on a page, and the
subtractions were performed afterwards, giving the actual width of the
ring in millimeters and fractions. Thus any error in the original
reading would affect two rings only. Very great numbers of readings
have been done a second time and vast numbers have been checked
over approximately; hence it is believed that errors of this kind are
extremely rare; out of 20,000 measures, perhaps 4 or 5 have been
discovered. Errors of subtraction may have occurred, but it is thought
that these also are extremely rare indeed, since practically all of the
work has been checked over a second time.
In the case of the sequoias, however, the method of measuring was
much more highly developed. It required a cathetometer with a
thread micrometer and adding machine. The cathetometer is placed
horizontally on the table and the wood to be measured is also put
DETAILS OF CURVE PRODUCTION. 59
horizontally on the table at a distance of about 33 inches. The cathe-
tometer telescope has a lens of such a focus that 1 mm. on the wood
section becomes 0.25 mm. in the focus. The micrometer has a screw-
thread with a pitch of 0.25 mm., so that one revolution of the microm-
eter head moves the thread through exactly 1 mm. as seen on the wood.
The individual measures of rings are made on the micrometer screw by
reading the graduation of the head to revolutions and hundredths,
giving directly millimeters and hundredths. On commencing a set of
readings the stationary thread of the micrometer is first placed on the
zero-year ring of each decade, and the reading of the cathetometer is
made and this is entered on the adding machine. A space is then
inserted on the adding machine and thereafter the micrometer reading
of each ring in the decade is added in column as fast as made. Then
another space is made on the adding machine and the total is entered
without clearing the machine. Immediately below this total the
reading of the cathetometer in the new position 10 years advanced is
made and inserted on the machine without addition. Then another
space on the machine is given, followed by the individual readings of
the next decade. In this way all the years are read individually by
the micrometer and every 10 years the sum of these readings is checked
against the cathetometer reading, which should come to the same
amount.
The reading of the micrometer screw to 0.01 mm. is closer than the
average setting can be obtained. The rule has been generally observed
that in every decade the agreement between the sum of the readings
obtained and the cathetometer reading should check within 0.20 mm.
In the earlier measures, where the rings were irregular or the surface
of the wood uneven, this accuracy of check was not obtained in a few
cases. Yet even there the error in checking was not much larger than
the figure mentioned, and it is expected that the results are sufficiently
close for all purposes desired. The 25,000 measures on the first group
of sequoias were begun by the writer, but after 2,000 had been done
they were continued by Mr. Edward H. Estill, who did them with
great care. In the second group, with 22,000 rings, the measuring had
been done by Mr. J. F. Freeman, who has made some slight alterations
in the method above described by which an increased accuracy is
obtained. As a result, the check between the decades by measure and
by cathetometer is nearly always within 0.10 mm.
TABULATING.
The paper used for the tables throughout has been a cross-ruled
paper with squares about three-eighths of an inch in size. This paper
is 8 by 10 inches in size and suffices admirably for small tables. Usually
20 numbers are placed on a horizontal line with the beginning year at
the left and with numbers from 1 to 20 at the top. Thus 1820, 1840,
etc., will be placed at the left, and 1821 will be the first date given in
60 CLIMATIC CYCLES AND TREE-GROWTH.
that line. When it is desired to make longer tables, the pages are
pasted together side by side or end to end, and then given a zigzag
fold, so that two pages are open at once. In the case of the sequoias,
with their 2,000 to 3,000 rings, no attempt has been made to paste
the pages together, but enough loose sheets are used to cover the entire
series at the rate of 20 years to a page. This gives sufficient vertical
space to include all the necessary trees in a group and to use subgroups
which may be summarized and averaged by themselves. An attempt
has been made to check the addition of these numbers throughout.
AVERAGING.
In simple averaging the sums are placed in ink on the table and
divided by the number of trees, using the slide rule for the process.
There are several questions in connection with this subject. The first
is whether straight averages of trees of widely different size give the
best report of the evidence of the trees. It is evident that in taking
averages of trees of mixed sizes the larger trees will carry more weight
and their variations will be more pronounced in the result. But it is
often the case that the smaller trees are the ones which show the
greatest relative variations in the rings. This can be so much the case
that the omission of a ring becomes a gross exaggeration. It is possible
to use the relative values by taking the logarithm of each ring measure,
averaging the logarithms, and then coming back to the number. This
could be called a geometrical averaging, since it would be the equivalent
of multiplying all the values together and then extracting the root
equal to the number of values. In this way the small trees of the
series would receive more importance. However, this plan is so long
that it has not been used in practice.
One of the most common and puzzling problems is the proper
method of handling the decrease in the number of trees in a group as
the center is approached. A group of 5 may be selected, for example,
and perhaps a century from the average center of the trees some one
tree whose rings differ from the average may come to its end. It means
that for 100 years near the center only 4 trees supply the data and at
the point where the 5 change to 4 there is a discontinuity in the curve.
In actual practice this lacking tree has usually been supplied by an
extrapolation from its subsequent curve. That is, the variations
assumed in the non-existent part of the tree follow precisely the
variations in the remaining trees, altered to the average size of the
missing tree by means of a constant factor, determined by overlapping
periods. Thus, if 5 trees carried easily back to 1820, but only 4 of
them extended to 1720, and it was desired to carry the full group to
1720, the period from 1820 to 1840 would be taken both for the 4 and
for the 1 alone and the ratio between them determined. Now, aver-
ages for the 4 are carried back to 1720, and then the factor found in
DETAILS OF CURVE PRODUCTION. 61
overlapping periods is applied to the mean of the 4, producing a prob-
able value of the fifth between the years 1720 and 1820. This probable
value is inserted in parenthesis in the table and all 5 values added up
for an average. As a rule, groups are carried back only far enough to
make assumed values of this kind a minimum in number.
There is one other problem in this immediate connection, namely,
that of " gross rings." By gross rings I mean certain regions in a section
where the average size of the rings becomes 2 to 5 times as great as
normal. This is a problem by itself, both as to cause and as to method
of treatment. Some study of its prevalence in different trees has been
made, and it is usually safe to say that where an epoch is shown to have
gross rings in one tree, the chances are at least even that the same
years will have gross rings in the next tree. Since gross rings may not
come oftener than once in several hundred years and last only 10 to
15 years, it is evident that we are dealing with something more than
mere accident. The phenomenon probably has a climatic character.
Yet, gross rings are not universal at any one time, and while one epoch
may show gross rings in half the trees of a group it does not show it in
the other half, judging by the groups examined. It is considered best
to allow the ring values to enter the curves just as they are found, for
while the gross rings disturb very greatly the size of a series of 10 to
20 rings, they do not seriously disturb the relation in size between a
ring and its immediate neighbors. They therefore, as a rule, do not
render the rings unidentifiable. It is likely, therefore, that they should
be included in the means, and if some better way of handling them is
discovered later it will not be difficult to apply it.
SMOOTHING.
In general the smoothing of a curve means removing some of the
minor variations, so that the larger variations may be perceived. In
the early part of the work the use of overlapping means was adopted.
At the very start, overlapping means of a considerable number, such
as 11 or 9, were used. This was quickly changed to overlapping means
of 3. These overlapping means were done by the calculating machine
(Brunswiga). On this machine three were added and then contin-
uously the one next in sequence was added, while one at the other end
of the three was dropped. However, this was changed to Hann's
formula, because his formula is normally easier to apply and it gives a
little more individuality to each observation. The method of applying
Hann's formula consisted in adding to a table two columns consisting
of, respectively, first and second intermediate values. This can be done
rapidly and without taking too much space. To express the differences
between overlapping means and Hann's formula graphically, we only
need to say that if we take successive groups of three in any curve,
forming a triangle, the center of gravity of the triangle is the value
62 CLIMATIC CYCLES AND TREE-GROWTH.
from overlapping means, but the point midway between the vertex
and the middle of the base is the point from Hann's formula. In the
present work Hann's formula has been used frequently, and in order to
shorten description of processes the word "Hann" has been used as a
verb.
In the analysis of curves already performed by the periodograph, the
curves have sometimes been smoothed by Hann's formula before
plotting and photographing. But a trifling error in the focus imme-
diately smooths the curve, and therefore it is evident that the pre-
liminary smoothing of a curve before plotting need not be done.1
Such preliminary smoothing helps the eye to judge variations in the
curve. The effect of out-of -focus position in a photograph may be
called optical smoothing. It is evident that optical smoothing may
be done in two directions, vertically and horizontally. In plotting a
curve it is evident that the desired smoothing must be in a horizontal
direction, but in the differential photographs made with the periodo-
graph', the directions of optical smoothing may have a very important
bearing on the judgment of the significance of the photograph. Of
course, in the differential pattern, long interference fringes are sought
and these are emphasized by optical smoothing parallel to them. Some
illustrations of this will be given under the subject of the periodograph.
Perhaps no feature of this subject of tree-growth and climatic and
solar variation has received more adverse comment than the matter of
smoothing curves. The author is entirely open to conviction as to the
advantage and disadvantage of such process, but it seems well to
remember that our views as to this are likely to be a matter of con-
vention rather than of actual thought ill relation to the subject in
hand. For instance, a monthly mean is a smoothed result. The
rainfall, instead of being taken as it came, mostly in a few days, espe-
cially in the summer, is treated as if it were the same for every day in
the month. Yearly means are smoothed values. The ordinary
method of plotting yearly means is a smoothed representation of those
quantities. The unsmoothed representation consists of what one may
call a columnar plot. Examples of plots of that type may be found in
connection with some rainfall records published by the United States
Weather Bureau and in a representation of the London rainfall for more
than 100 years published by the British Rainfall Association, and else-
where. In this kind of plot the rain for a year is not represented by a
dot, but by a block column which extends from the base-line up to the
required amount and it has a width equal to the interval of one year
according to the scale of the plot. Now, the ordinary way of represent-
ing rainfall places a dot at the middle of the top of this column, and
these dots are connected together by straight lines. It is immediately
1 The three-score of curves which are now specially prepared for examination with the periodo-
graph carry the mean values without smoothing.
DETAILS OF CURVE PRODUCTION. 63
seen that this cuts off each corner of the high column of any maximum
year and contributes those corners to the adjacent lower column, so
that the ordinary bent line of the rainfall record has thus been twice
smoothed — once in the yearly sum and once in the method of plotting.
In speaking of the above records, I have in mind the smoothing in
time intervals, but I would like to note also that whenever a district
is averaged as a whole the average thereof is a smoothing in space.
The temperature at any one time in a city station is a single definite
record; but if the mean temperature in a valley or a State, for example,
is tabulated, there is at once a spacial smoothing. In the minds of
many students of solar variation and weather, the reason why a large
group of meteorologists fail to get evidence of the relationship is because
they take the average of the whole earth at once in their test of tem-
perature changes or of rainfall. It is evident, therefore, that the rea-
son they do not get results is because they do too much smoothing of
the curves. Studies in connection with the present investigation have
given some indication that small districts balance each other in their
reaction to solar stimuli.
STANDARDIZING.
The fundamental data tabulated in the appendix are the means of
the actual measures of the various groups. They, therefore, contain
the effects of the two chief arboreal constants, which are (1) the nearly
universal big growth at the center of the tree and (2) the increased
size in some entire trees due to specially favorable environment. In
producing a perfectly normal record of tree-growth over long periods,
one desires to have it expressed throughout in terms of the normal
adult growth of an average tree. This is the kind of record most
suitable for analytical study. In the present study, in which so much
time has been spent in finding how the work should be done, on account
of the great labor involved no attempt has been made to apply these
corrections to individual trees; but in comparing groups with one
another it has seemed worth while to apply both corrections in a
simple manner. Each group supplies an approximate curve of its
decreasing growth with age. So, after plotting the means, a long
average line as nearly straight as possible is drawn through them.
This gives the factor by which individual rings may be reduced to the
standard adult growth ; at the same time this line enables us to reduce
the different groups to a common standard of size. Both corrections
are done at once by calculating for each year the percentage departure
of the plotted mean from this line. In actual tabulation this works
out very easily, for under each mean is placed the reading of this line,
and below that the quotient obtained by dividing the former by the
latter. The line of quotients then becomes the desired group curve
corrected for age and for mixed sizes. This process is the standard-
izing process referred to in previous descriptions.
64 CLIMATIC CYCLES AND TREE-GROWTH.
PLOTTING.
So many curves have been made in connection with this study that a
practically uniform system throughout has been adopted. The paper
used is a cross-section paper with the smallest divisions 2 mm. in extent
and with heavy lines at every centimeter. The smallest divisions are
uniformly used for one year unless in some special study. For the
illustrations, these plots are traced and drawings made from which
the engravings are reproduced. For use in the periodograph, the plot
is made on the same scale and continued in length to any amount up
to about 40 inches. The space between the base-line and the curve has
then been cut through with a sharp knife, usually a razor blade, and
the curves have been mounted in long strips some 4 inches wide and
50 inches long, and the backs painted with opaque paint. In this way
they are mounted for analysis. A mirror behind reflects light of the
sky overhead through the curve and supplies the necessary illumi-
nation for photography.
Problems in plotting. — In connection with the plotting of the curves
used in this study, certain problems have arisen which seem worthy of
consideration. The ordinary plot and the ordinary averaging seem
extremely good and appropriate when the variations are small in com-
parison with the mean values, but when the variations are large in
comparison with the mean values it does not seem to the writer certain
that the usual plotting conveys an accurate idea or gives a suitable
basis for further work. This may be illustrated by the plotting of
rainfall. If the rainfall doubles in some unusual year, it produces an
immensely greater change in the area of the curve than when it goes to
one-half of the mean. Doubling the mean produces the same changes as
going down to zero, though in proportion the latter is infinitely greater.
The enormous exaggeration, therefore, of excessive rain values was
felt to introduce misleading material in the ordinary form of a plot. In
order to overcome this at least one experiment has been made with
what is called a bilateral plot. In this the quantities from 0 to 100 per
cent of the mean are plotted as before, but the quantities over 100 per
cent of the mean are inverted in percentage and plotted above the
mean line on an inverted scale. It is recognized that this is not the
perfect way of making a plot of this sort, for by this plan the mean
value of the new curve will not be at the same point as before, but will
be somewhat below it. However, the matter is only in the experi-
mental stage and it has not been thought necessary to work out a
correct procedure.
V. CORRELATION WITH RAINFALL.
Result of study of curves. — On completing numerous curves of tree-
growth in the manner already described, three characteristics were
observed: (1) in arid-climate groups the annual rings are approximately
proportional to rainfall; (2) in moist-climate groups they vary with
the changes of solar activity; (3) in each they are subject to certain
cycles or periodic variation. The first of these is the subject of the
present chapter.
Early tests of rainfall correlation. — The earliest comparison with
rainfall hi this investigation was made between the first Flagstaff
subgroup of 6 trees and 43 years of precipitation records at Prescott,
67 miles distant. It was not expected that agreement in individual
years would be found; accordingly smoothed curves were used, con-
sisting of overlapping means of 9-year groups. This produced curves
of gentle variation, but similarity in the curves was evident. These
early curves are presented in figure 13. The best agreement was found
1870 I860 1830
Years
Fio. 13. — Correlation between tree-growth and rainfall in smoothed curves; Flagstaff.
by placing each mean of 9 years of rainfall at the end of the 9 years
as in this figure instead of in its center. This lag of four years seemed
inconsistent with the later results of yearly agreement without lag, and
in fact for years it has been accepted with some hesitation by the
writer. Yet in the present consideration of the subject it appears to
have a special significance. This existence of the lag in long periods
agrees in principle with the "accumulated moisture" effects observed
in the Prescott trees and with the idea of a tree exhibiting a reserve
power or vitality which may run low or be built up by varying environ-
ment. The principle will be referred to again below; it is sufficient now
to state that it seems quite reasonable to find no lag in yearly correla-
tion with rainfall and at the same time a very considerable lag in the
slower variations.
The comparison in figure 13 was made with Prescott records because
there were not at that time enough Flagstaff records to be of service.
But later, when a Weather Bureau station had been established in
Flagstaff for several years, the striking comparison shown in figure 14
65
66
CLIMATIC CYCLES AND TREE-GROWTH.
1900
1905
FIG. 14. — Early test of correlation
between tree-growth and rainfall
by years ; Flagstaff.
was made. In this the lower curve represents the average annual
growth of 25 trees and the upper curve is the precipitation 12 miles
distant. The latter is taken from November 1 to November 1 in order
to carry the snowfall into the following season of growth. This study
suggested the investigation of the time of
year to begin annual means of rainfall,
which has already been presented in
Chapter II. Figure 4 gives a comparison
between Flagstaff rain and the two Flag-
staff groups, and also shows how the best
time of beginning the year was deter-
mined. It proved to be November 1 at
Flagstaff and September 1 at Prescott,
where the nature of the ground gives
more chance of conserving moisture. The
great difference between individual trees in response to rain is also
shown in figure 5. It is evident that quick-growing trees serve as
better indicators.
THE PRESCOTT CORRELATION.
Five subgroups, numbering in all 67 trees, were obtained from
different points in the vicinity of Prescott. These all cross-identified
among themselves with entire success, both as individuals and as
groups. The group curves are shown in figures 6 and 7, but in com-
parison with the Prescott rainfall they differed greatly, the group
nearest the city showing much the best accordance. Accordingly this
group is plotted by itself in figures 7 and 15 with the rainfall curve.
On the whole there is much agreement, as may be seen by comparing
the crests and troughs of one with those of the other. The most con-
spicuous discrepancy is in 1886, where the rainfall decreases and the
growth of the trees increases. In 1873 the growth seems to have
responded to the decrease in rainfall, but to a greatly diminished
degree. The tree maximum of 1875, one year behind the extreme
maximum of 1874 in the rainfall, is entirely reasonable, since the
ground may become so saturated that the effects last until the following
year. On the whole, the curves shown in figure 7 support the idea of a
proportional relation between annual rainfall and annual growth.
Accuracy. — The accuracy with which the pine trees near Prescott
represent the rainfall recorded in that city for 43 years is, without
correction, about 70 per cent. By a provisional correction for con-
servation of moisture by the soil this accuracy rises to about 82 per
cent. The nature of this conservation correction is very simple; it
makes use of the "accumulated moisture" of the meteorologist. It
signifies that the rings in these dry-climate trees vary not merely in
proportion to the rainfall of the year, but also in proportion to the sum
CORRELATION WITH RAINFALL. 67
of the profits and losses of the preceding years. The " credit balance"
in their books at the beginning of the year has only somewhat less
importance than the income during the current year.
Mathematical relation of rainfall and growth. — In order to formulate
the relation between rainfall and tree-growth, an effort was made to
construct a mathematical formula for calculating the annual growth of
trees when the rainfall is known. Any such formula must perform
three principal functions: (1) reduce the mean rainfall to the mean
tree-growth; (2) provide a correction to offset the decreasing growth
with increasing age of the tree; and (3) express the degree of conserva-
tion by which the rain of any one year has an influence for several
years. In a formula of universal application other factors will play
a part, but for a limited group of trees in one locality they can be
neglected.
The first process, namely, the reduction of the mean rainfall to the
mean tree-growth, is a division by 250. This is the general factor K
in the formula below. The second part, namely, the correction for the
age of the tree, was practically omitted in forming the curves shown,
since judging by the Flagstaff curves its effect would be very slight in
the interval under discussion. In long periods it is an immensely
important correction and its effect should always be investigated.
Over the short periods used in this rainfall discussion the decrease of
annual growth with age may be regarded as linear and an approximate
formula is
Where Gn represents growth in any year n; Gv is growth in middle
year of series y, and c is the rate of change per year, a constant which
was 0.0043 in the last half century of the Flagstaff series. Over the
whole interval from 1700 to 1900, in the first Flagstaff curve, the
growth was approximately an inverse proportion to the square root of
the time elapsed since the year 1690 and may be closely expressed in
millimeters by the formula
10
T =
J. n
Vn - 1690
Tn is here the mean tree-growth for the year n. If G be the mean size
of rings, then the factor to be introduced in a general formula becomes
10
GVn-1690
Character of the conservation term. — This factor has two important
features: (1) in this arid climate it applies better as a coefficient than
as an additive term, and (2) it gives a prominent place to "accumulated
moisture" as commonly used in meteorology.
68
CLIMATIC CYCLES AND TREE-GROWTH.
The first assumption in regard to conservation was that the ring-
growth in any one year was built up by contributions from the current
year and previous years in diminishing proportion. For example,
it would be proportional to
Rn+$Rn-i+lRn-Z etc.
in which Rn is the rainfall for the current year, Rn-\ that for the year
preceding, etc. This may be called an additive correction. It did not
20.
10.
to.
0
10.
Potfec/ fine =
So//£/ /rrje = free
20.
10.
r'ne* ra/n/a// smoothed by Syr means
So/id ' /me * growth s/nooMiecJ &y S-yr means
ne = acctf/nu/afec/ /•»//»/&//
So//e/ //'f)e =
Ported '//hf - acfi/0/
groiv+h ca/cu/atrc/ from
2.0
1.0
0.0
2.0
1.0
0.0
o.o*
2.0 \
1.0
0.0
1810
1830
1830
l.tco
1910
FIQ. 15. — Relation of tree-growth and rainfall at Prescott, Arizona.
Tree-growth and rainfall uncorrected.
FIG. 16. — Five-year smoothed curves of growth and rainfall.
FIG. 17. — Accumulated rain and smoothed tree-growth.
FIG. 18. — Actual tree-growth and growth calculated from rain.
FIG. 19. — Actual rain and rain calculated from tree-growth.
give satisfactory results for the Prescott trees, although a formula of
this general type has been applied with some success to the sequoia,
which grows in more moist soil.
The variations in the Prescott trees were seen to be proportional
both to the rainfall of the year and to the average growth or activity
CORRELATION WITH RAINFALL. 69
which the trees had exhibited in the preceding few years. But this
average growth bore the same relation to the average or smoothed
rainfall that the accumulated moisture bore to the smoothed rainfall.
Hence the ratio between accumulated moisture and smoothed rainfall
gave at once the required ratio between smoothed tree-growth and
smoothed rainfall. These relations are shown in figures 16 and 17.
Accumulated moisture is simply the algebraic sum of the amounts
by which all the years in a series from the start to and including the
year desired depart from the mean. It may be expressed by a formula,
thus
An=(Rl-M) + (Rz-M)+. . ..(Rn-M)=Rl+Rz+Rs+.. .Rn-nM
and conversely
In this formula An is the accumluated moisture for the nth year of a
series of consecutive years whose mean rainfall is M.
The simple empirical formula for the tree-growth Tn for the nth
year of this series thus was found to be:
T „ cM+dAn p
•* « = A • - o - • Kn
On
in which c and d are small constants found advantageous in reducing
the accumulated moisture curve to proper scale. Sn is the reading
of the smoothed rainfall curve and the term cM+d An is the accumu-
lated moisture expressed in values above a base-line instead of depar-
tures from a mean. In actual numbers this becomes
m /• • i x 1 0.90 M + l An D ,. - , x
Tn(m inches) = — . - —^ — - . Rn(m inches)
on
The mean value of the rainfall M is 17.1 inches. The application of
this formula in calculating tree-growth at Prescott from the rainfall is
shown in figure 18.
The reversal of the process in order to ascertain rainfall from tree-
growth seems to be fully as accurate over this limited period, and its
result is shown in figure 19, where the curve has an average accuracy
of 82 per cent for individual years. In producing this reversal the
following operations were performed :
1. A 5-year smoothed curve was made of the tree-growth. This
,, 0.90M+ \An . , ,
gives us the term - — — - in the reversed tormula
•p _ _ &n _ m
n~-
250
2. This term is multiplied by 1,000 and 3.6M subtracted, leaving
An in inches.
70 CLIMATIC CYCLES AND TREE-GROWTH.
\
3. From An an approximate Rn is found by the formula
Rn = M+An-An_l
4. This series of approximate rainfall Rn is smoothed and becomes
the Sn of the formula.
5. Final values are then found by the proportion
0.90M +M, . q ,T 1P
• ' ' . O« • • J. n . -fin
250
It should be emphasized that the above formula for conservation
is the one found to apply under dry climatic conditions. In moist
climates the trees, so far as observed, seem to depend on other meteoro-
logical elements or combinations of elements.
The Prescott trees, as we have seen, even without correction give a
record of rainfall with an accuracy of about 70 per cent. It is possible
that the Flagstaff trees with their higher elevation, more certain rain-
fall, and more central location in the zone occupied by this species give
somewhat more accurate records. They are probably much less often
subjected to extremes of dryness, which throw the tree out of its
equilibrium and cause it to produce an abnormally small set of rings.
It seems likely, also, that the less compact soil, combined with a more
abundant precipitation, produces a yearly growth more nearly pro-
portional to the rainfall than at Prescott.
Summary. — In considering this reduction it seems fairly clear that
(1) there is a strong correlation between rainfall and tree-growth;
(2) the accuracy may be increased by introducing a conservation cor-
rection; (3) in dry soils this factor enters as a coefficient; (4) this co-
efficient depends on the state of activity of the tree ; (5) in the Prescott
trees this state of activity follows the curve of accumulated moisture.
Although the moisture-content of apparently dry ground may be a
most important item, it is by no means certain that the observed ac-
cumulated moisture effects consist in actual moisture in the ground.
It may be that they represent some vital condition of the tree. The
matter is a very interesting one for future study.
Sequoia correlation with rainfall. — On his return from the big trees
in 1912, Professor Huntington supplied me with a curve of sequoia
growth obtained from many comparatively young trees which had been
cut in the lower edge of Redwood Basin near Camp 6. On comparing
these with his curve of rainfall in the San Joaquin Valley, compiled
from records at Fresno and San Francisco, a close relation was not
evident, but an additive formula
rp _fc Rn-\-Rn-i+Rn-?>
Rn + Rn-l + Rn-2
was used with encouraging results. This formula was designed to
allow for strong conservation in the soil, not of the static type as in a
CORRELATION WITH RAINFALL.
71
pond, but of the moving type, as if a belated supply from the snows
came to hand and then passed on. The tree was assumed to receive
moisture from the current year and from the first and second preceding
years; and whichever of the three was greater, that one had the more
effect. The application of this formula is shown in figure 20.
1850
1860
1870
1880
1890
1900
1910
(Mms.
Measured 4-°°
growth of
Sequoias
3.50
3.00
Growth of
Sequoias
calculated
from rainfall as
described in text
Rainfall at
Fresno 10
San Francisco
0
FIG. 20. — Huntiugton's early curves of sequoia-growth and rainfall compared with growth calcu-
lated by a conservation formula.
But on identifying the rings in the trees collected from that locality
in 1915, and especially on finding the soft, delicate parts of the 1915
ring on D-5, it seemed fairly certain that the curve of growth given
in figure 20 is one year in error through the omission of a final ring. The
growth, then, which appeared to be 1902, for example, and for which a
pronounced conservation was necessary, really came the year before,
Rainfall
J?7V
Tree Growth '
1850 60 70 60 30 1900
Years
FIG. 21. — Comparison of Fresno rainfall (after Huntington) and sequoias D-l to 5.
h*
10
and less conservation or none was needed. The comparison of the
same rainfall curve with the old sequoias of the present series is given
in figure 21. In this the agreement is not as good as at Prescott, but
there is marked similarity in many details. My curve from very old
72 CLIMATIC CYCLES AND TREE-GROWTH.
trees is probably not as good in details as Huntington's samples from
young and sensitive trees. His material is well worth cross-identifying
and dating with care, and then comparing with any records of snowfall
which can be obtained from the sequoia groves. It is greatly to be
regretted that Fresno, 65 miles away and at 5,000 feet lower elevation,
is the nearest point where precipitation records can be obtained for a
period long enough to be of value.
Future work. — It will be very interesting to find whether the charac-
teristics of the correlation at Prescott are general in arid climates and
dry soils and whether practical formulas for conservation in moist
soils or climates can be worked out. When this is done the significance
of the study of annual rings will be greatly increased.
METEOROLOGICAL DISTRICTS.
The study above described raised emphatically the question as to
the extent of the region or district from which comparative rain
records should be selected. Such a meteorological district could be
defined as one in which homogeneous weather elements are found.
But we immediately ask ourselves the questions: must all weather
elements be alike in it or is it sufficient to have only rainfall (for
example) essentially the same throughout; will the district remain
constant through indefinite time or will it change; is the district for
short-period weather changes the same as the district covered by
secular changes. In the present discussion I have understood by
meteorological districts such regions as may show similar or identical
variations in some one weather element. It seems likely that a region
which may show unity in small or rapid variations may not do so in
large and slow variations, or more likely may be a small fraction of a
region which will show unity in large variations.
Meteorological districts and growth of trees. — The cross-identifica-
tion of trees over large areas has already suggested the use of annual
rings as a possible aid in delineating meteorological districts. This
function of the rings has received some exemplification in the present
study. For instance, the pine trees of Norway differed in such a way
that it was necessary to divide them into two classes, one of which came
from the outer coast near sea-level and the other from the inner fjords
and mountains. The trees from these different regions show strong
reversal with reference to each other. Again, the trees from the low-
lands about the Baltic Sea show marked similarity in their variations
and indicate, as we would expect, a homogeneous district. Further-
more, groups from near the Alps show strong differences from the
other European groups, as we might expect from our experience with
the five groups from the mountainous country about Prescott. A
rugged and mountainous region is very difficult to divide satisfactorily
CORRELATION WITH RAINFALL. 73
into meteorological districts. Yet, in spite of local differences, mountain
regions may be alike in major characteristics, for all the Prescott
groups, though differing among themselves, cross-identify excellently
with the Flagstaff trees 60 miles away. The sequoias also cross-
identify perfectly in mountain localities 50 miles apart, showing that
there is enough similarity in different parts of the high Sierras to cause
the trees to agree in many variations.
Arizona and California. — Fully 450 miles intervene between the
sequoias of California and the pines of Arizona, yet there are strong
points of identity between them in the last 300 years. The dates of
notably small rings are much alike in each. The details of this com-
parison have not yet been fully studied, but they support the idea long
since expressed (1909) that Arizona and California, especially its
southern half, form parts of a large district which has similarity in
certain variations. A long acquaintance with this region throws light
on the details of this similarity. The winter precipitation, which is
largely in the form of snow at the altitude of the trees studied, has the
major influence on tree-growth, for it is largely conserved near the
trees, whereas the summer rains are usually torrential and the water
quickly flows away. The winter storms moving in an easterly direction
reach the coast region first and after about 24 hours are felt in Arizona.
Thus, in spite of the coast range of mountains and the intervening
low-level deserts, each winter storm passes over both regions and
causes an evident similarity between them. In a large view they belong
to a single meteorological district.
Meteorological districts and solar correlation. — In searching for a
link of connection between solar variation and meteorological changes,
we must bear in mind the effect of possible reversals in neighboring
meteorological districts, such as noted above in Norway. It may be
the lack of such precaution which has caused many meteorologists to
condemn at once the suggested connection between the distant cause
and the nearby effect. We must remember that districts may be small
in area, and in combining many together we may neutralize the result
for which we are in search. Some illustration of correlation found in
small districts will be given in the final chapter.
VI. CORRELATION WITH SUNSPOTS.
Dry-climate tests. — In the work of 1907 (published 1909) upon the
first group of 25 yellow pines from 1700 to 1900 A. D., several long
sequences of variation in a 5 to 6 year period were noted. These were
compared with rainfall records at Prescott and in southern California
and the crests of rainfall and growth appeared to coincide in date. It
was then seen that the temperature curve of southern California had
a period and phase corresponding to the rainfall curve, but with the
second minimum almost entirely suppressed, and that finally this tem-
perature curve resembled in form and phase the inverted curve of sun-
spot numbers. In connection with the publication referred to (1909),
a set of curves was prepared to show these relationships. This set is
partly reproduced in figure 34, page 104. In the original drawing the
tree-curve was the least satisfactory, which was to be expected, as no
real certainty in the dating of rings existed at that time. After cross-
identification the tree-curve was again integrated for the 11-year period
and far better results were obtained. This new curve is given in the
figure referred to.
This type of integrated curve gives many facts in a very condensed
form. A differential or detailed form of presentation should accompany
it, as in figure 25, showing the full series of individual observations and
beside it the curve with which it is to be compared. The differential
study of the Arizona trees will be taken up in connection with cycles,
but can be summarized in the statement that in the last 160 years 10
of the 14 sunspot maxima and minima have been followed about four
years later by pronounced maxima and minima in the tree-growth.
Also, during some 250 years of the early growth of these trees, they
show a strongly marked double-crested 11 -year variation.
Wet-climate reaction. — In the very first group of continental trees
studied, those obtained at Eberswalde near Berlin, the remarkable
fact was recognized at once that 13 trees from one of those carefully
tended German forests show the 11 -year sunspot curve since 1830 with
accuracy. The variation in the trees is shown in plate 8. The arrows
on the photographs are not to call attention to the larger growth, but
to mark the years of maximum sunspots. The other trees of that
group do not show quite so perfect rhythm as do the marked radii
shown, but are like the other parts of these sections, showing strongly a
majority of the maxima. Taking the group as a whole, the agreement is
highly conspicuous, and the maximum growth comes within 0.6 year of
the sunspot maximum. The Eberswalde curves arranged in two groups
and compared with the sunspot curve were shown in figure 9, page 38.
In the group of six sections from south Sweden, which were measured
subsequently in Stockholm, a spruce (Picea excelsa) was discovered
which shows the sunspot rhythm with the same striking clarity as the
74
DOUGLASS
PLATE 8
A
B
A. Section of Scotch pine from Eberswalde, Prussia, showing solar rhythm.
B. Another section from the same forest, showing same rhythm.
CORRELATION WITH SUNSPOTS.
75
s.o
Measured rings
t\
Stanc/artf/zee/emd 'smoothed \
30 40 1850 60 70 80 90 1900 10
FIG. 22. — Sunspot numbers and annual rings in spruce tree from south Sweden.
\aso. 1900
Ebersvralcfe,
Prussia.
South
Sweden
Sun Spot;
ieso 1900
FIG. 23. — Six European groups, standardized and smoothed.
76 CLIMATIC CYCLES AND TREE-GROWTH.
best Eberswalde sections. In view of the as yet unsuccessful efforts
to obtain a photograph of this section, its measures have been plotted
and are found in figure 22 with the sunspot curve for comparison. In
the figure the upper curve gives the actual measures with the standard-
izing line drawn through them. The middle curve shows the same
measures reduced to percentage departures from the line and smoothed
by Hann's formula. The lowest curve shows the corresponding sun-
spot numbers. It would be highly interesting to know the exact
conditions under which a tree produced such a curve of growth as this.
In the opinion of the writer, it would not be impossible to find other
trees of this type, and even to identify them without real injury to the
tree, so th#t surrounding conditions could be studied.
The European groups. — For better comparison, the nine European
groups have been corrected for change of growth-rate with age, reduced
to percentages of their own means, smoothed by Hann's formula, and
plotted in figures 23 and 24 together with the sunspot curve. They do
not all follow the sunspot numbers with equal accuracy, and the six
groups showing best agreement are segregated in the first of the two
figures. The north German and south Sweden groups around the
Baltic Sea are the most satisfactory; the group from the west coast of
Norway is almost as good. Then come the Dalarne, Christiania, and
south of England groups. These six in figure 23 have the times of sun-
spot maxima indicated by broken lines carried straight upward from the
sunspot curve at the bottom. Of the other three groups, the trees from
the inner coast of Norway as a whole appear to show a reversed cycle,
probably because they were in deep inland valleys, while the southern
groups, northwest Austria, and southern Bavaria close to the Alps
have combined agreement and disagreement, so that they can not as
yet be considered to give a definite result. They are shown by them-
selves in figure 24.
However, in the 6 groups representing the triangle between England,
northern Germany, and the lower Scandinavian peninsula, a variation
in growth since 1820 showing pronounced agreement with the sunspot
curve is unmistakable. Every sunspot maximum and minimum since
that date appears in the trees with an average variation of 20 per cent.
This is shown in figure 25, which contains the mean of the 57 trees
of the six groups, with the sunspot curve placed below for comparison.
The agreement is at once evident. The apparent increase of tree-growth
with increase in the number of sunspots becomes still more striking
when the means are summated in a period of 11.4 years, as shown in
the lower part of the figure.
A second important feature of figure 25 is that five of the eight min-
ima show a small and brief increase in tree-growth. This suggestion of
a second maximum is of interest, because in it we find agreement with
Hann and Hellmann in their studies of European rainfall and sunspots,
and it lends added weight to results which each author obtained but
CORRELATION WITH SUNSPOTS.
77
which neither allowed himself to regard as conclusive. In the immense
work of Hellmann (1906) upon the rainfall of the North German
drainage area, it is this inconspicuous maximum which he finds the
more important of the two.
1850
1900
1.00
1.00
1.00
-HI. Norway, Inner Fjords
Sun Spots
Vffi. T1.W Austria
K.. 5.
Sun Spots, displaced
2 yrs. to left.
I85O '900
FIG. 24. — Three European groups, standardized and smoothed.
too.
o.
ISOO
isoo
125 Yrs.
iaee.9
i.oo
0.75
1.00
0.75
1.00
0.75
Mm.
i.ao
i.oo
0.80
FIG. 25. — Comparison between 57 north Europe trees (smoothed) and sunspot numbers. The
trees are from England, Norway, Sweden, and north Germany.
78
CLIMATIC CYCLES AND TREE-GROWTH.
In seeking further evidence of sunspot correlation, advantage was
taken of certain statistics recorded while measuring the various sec-
tions. Before making the measures or identifying the rings in any way,
the groups of rings larger than the average were sought out and
10
iZSP
ISOO
10
I85O
IQOO
FIG. 26. — Dates of large rings in 80 European trees compared with sunspot curves.
Ordinates give number of trees in total of 80 showing maxima in respective years.
1710
Windsor, Vermont, uroup
(II Sections)
(Sunspot curve displaced I year to left)
1810
(Sunspot curve
1850
displaced 3 years to left )
2.5
20
1.5
1.0
2.0
1.5
1.0
1^00 I9IO
FIG. 27. — Tree-growth at Windsor, Vermont, showing measures uncorrected; same
standardized and smoothed, and sunspot numbers displaced 3 years to left.
CORRELATION WITH SUNSPOTS.
79
crosses were placed upon the central ring, which was usually the largest
of the group. These crosses are well shown in plate 4, B. Their dates
were noted during the measuring. In figure 26 the ordinates give the
number of maximum marks found in each date throughout the whole
I&30
1850
I860
1870
1870
1880
/890
1900
1310
FIG. 28. — Smoothed quarterly rainfall (upper curve), sunspot numbers (center), and
tree growth (lower) at Windsor, Vermont, 1835 to 1912.
80 sections. The more recent dates show higher crests because there
are more trees. In the second line is the sunspot curve. The matching
of the crests of the two curves is unmistakable. The secondary tree-
crest at sunspot minimum is very regular, as would be expected from
the inclusion of the three groups of figure 24, some of which are evident
reversals. This test is only qualitative, but seems to the writer to offer
substantial support to the quantitative relation shown in figure 25.
Windsor (Vermont) correlation. — An interesting sidelight is thrown on
this type of correlation by the American curves from Windsor, Vermont.
80
CLIMATIC CYCLES AND TREE-GROWTH.
The original means of 11 trees are given in the upper line of figure 27.
In the middle line these are smoothed by Hann's formula and in the
lower line is the sunspot curve, displaced three years to the left in the
portions since 1810 and one year in the same direction before that date.
The tree crests anticipated the solar crests by three years when the
trees were large and making good growth, but when small this anticipa-
1834- etc.
Sun spots
displaced
-J years
— Tree Growth
(Windsor, Vt.)
Rain
Suns pots
FIG. 29. — Correlation curves of solar cycle, rainfall, and tree-growth at
Windsor, Vermont, 1835-1912.
tion of the sunspot maximum was considerably less. A correlation is
evident, but it is hard to give a satisfactory explanation of the phase
displacement. Figure 28 gives details of the time relation between
tree-growth, rainfall, and solar activity. In figure 29 the curves of
figure 28 have been summated on an 11.4-year period, as was done in
figure 25. At the bottom is the sunspot curve from 1834 to 1912 inclu-
sive; directly above it is the curve of rainfall for the vicinity of Windsor,
compiled chiefly from records at Hanover and Concord and covering
1835 to 1912; above that is the tree-growth from 1834 to 1912, and in the
upper line the sunspot curve is repeated with a displacement of — 3 years.
CORRELATION WITH SUNSPOTS. 81
THE SUNSPOTS AND THEIR POSSIBLE CAUSES.
If the sunspots are an index of some solar activity so far reaching as
to affect our climate and vegetation, it is well to note very briefly
their appearance and the suggested causes of their periodic character.
Appearance — At first view sunspots are small black areas appear-
ing from time to time on the sun. In actual size they vary from a few
hundred miles in diameter to more than a hundred thousand. Rarely
seen by the naked eye, the vast majority are only discovered through
the telescope; hence it was only after the invention of that instrument
that records of them were kept and their nature investigated. As Hale
(1908) has found, they are cooling places; they merely look black by
contrast with their more intensely bright background. His remark-
able photographs show that they often have a rotation about their own
center. They usually come in groups between latitude 5° and 25° in
each hemisphere of the sun and are almost continuously changing in
small details. Their life is usually less than one rotation of the sun.
Schwabe in 1851 announced their periodic character with maxima
every 11 years. During sunspot rnaximum a small telescope will show
5 to 20 spots, but during the minimum one may search for weeks
without finding a spot that can be certainly recognized. Records of
the numbers of spots were specially collected by Wolf for many years
and later by Wolfer of Zurich. At the present day many observatories
are taking daily photographs of them. The term relative sunspot
number was invented to convey an idea of the average number of spots
visible at any one time under favorable circumstances. The number
actually counted receives a simple correction for unfavorable weather
or small telescope, so that the published numbers shall be as nearly
standard as possible.
While the spot appears black and may possibly be sinking into the
sun, it is usually attended by intensely bright areas or faculse and even
by prominences which are often violently explosive, ejecting matter
hundreds of thousands of miles from the sun's surface. Thus the sun-
spot maximum indicates increased activity at the surface of the sun,
which, according to Abbot (1913 and 19132), is actually sending us
increased heat radiation. During the maximum the magnetic condi-
tion of the earth is profoundly affected, as evidenced by northern
lights, magnetic storms, earth currents, and variations of the earth's
magnetic constants. This relation to the earth's magnetism has been
recognized from the first discovery of the periodicity of sunspots. But
the effect of the change of solar radiation on climate and ordinary
weather elements is more obscure. General effects on climatic con-
ditions have been admitted as probable by Penck (1914), but in general
the great weight of opinion has been against a traceable effect of solar
activity on weather or climate.
82 CLIMATIC CYCLES AND TREE-GROWTH.
i
From the description above it is easily seen that the sunspots are
not likely to be in themselves the fundamental solar activity, but rather
an index of something else, and possibly a very sensitive index, for the
percentage change in spot numbers is hundreds of times as great as the
percentage changes in measured radiation between sunspot maxima
and minima.
Suggested causes of sunspots. — The cause of sunspots is still a matter
of conjecture, and there is no generally accepted hypothesis to explain
them. There is analogy to our clouds in that both indicate decreased
temperature. In their limitation to certain latitudes they resemble the
belts of Jupiter. The belts of Jupiter are roughly the lines of division
between the powerful easterly equatorial current and the slower moving
zones on either hand; and indeed this has been suggested as an expla-
nation of the particular location in latitude of the sunspots, for there
is an increase in speed of rotation of the sun's surface as the equator
is approached. Their periodic character is very difficult to explain.
Fundamental periodic changes in the body of the sun have been sug-
gested and, in the absence of better explanations, some such statement
hazily indicating the direction in which explanation is to be sought, is
perhaps the best that we can do. Planetary influence, however, has
often been proposed as the cause. The near agreement between the
revolution period of Jupiter and the sunspot period has naturally
attracted attention. Stratton (1911-1912) has made a very interest-
ing study of the appearance, continuance, and disappearance of spots
on portions of the sun facing toward or away from Jupiter and Venxiis.
A few per cent more spots do originate and disappear on the " after-
noon" of the side facing Venus than on other longitudes, but he con-
siders the case of physical relationship not proven.
Planetary influence is sought in a theory proposed by W. J. Spill-
man (1915). In this theory gravitation is assumed to be due to
pressure variations in the ether arising from electronic rotation in the
attracting body. The varying speed of a planet in its orbit between
perihelion and aphelion, involving varying quantities of energy, requires,
he says, an interchange between the kinetic energy of the plant and
the atomic energy of the central attracting body. This atomic energy
is in the vibrations of the electrons, but he thinks it is likely to affect
both the temperature and the electric activity of the central body.
The effect in this way of Jupiter and Saturn would exceed the sum of
all the other planets combined and is therefore the only one considered.
The effect of Jupiter with its substantial variations in distance between
perihelion and aphelion predominates, and we have a marked resem-
blance between the sunspot curves since 1770 and the differential
planetary effect. One notices that this interchange of energy would
presumably affect all parts of the sun alike and that therefore we could
not expect an excess of sunspots on the side facing Jupiter.
CORRELATION WITH SUNSPOTS. 83
H. H. Turner (1913; cf. Sampson, 1914) has worked out an hypothe-
sis which is stimulating, even if not yet acceptable. He supposes that
the Leonid swarm of meteors, revolving once in about 33 years in a
very eccentric orbit, is at the basis of the sunspot recurrence. These
meteors were observed in countless swarms, filling the sky for a
few nights in November 1799, and again in 1833 and 1866. In
1899 they were expected, but failed to appear in large numbers,
having probably been swerved to one side through the attraction of
some planet. Turner finds that they have passed near Saturn several
times in the last 2,000 years. At some of these encounters a quantity
of meteors may have been detached and losing their own velocity may
have fallen nearly straight toward the sun, grazing its outer surface
in their circuit at a velocity of 400 miles per second, then swinging out
to aphelion near their place of encounter, and completing their revolu-
tion in about 11 years. Successive returns of the main Leonid swarm,
approaches of Saturn, and perhaps even the influence of other planets
would be sufficient to perturb this meteoric swarm and cause the
variations in period observed. On their terrific flight close to the sun
many would be caught in the sun's outer atmosphere, thus in some way
causing sunspots.
This hypothesis attempts to explain the period and its irregularities,
including the double and triple period. I refer to it at some length
because the investigation of trees gives evidence not only of climatic
variations in the sunspot period, but of double and triple sunspot
periods and possibly of still larger fluctuations. Turner's hypothesis
warrants further discussion to explain why the spots appear in sub-
tropical latitudes but not at the solar equator. In the planetesimal
hypothesis of Chamberlin and Moulton, the rotation of the sun on its
axis is attributed to the material falling back upon it after receiving a
slight orbital motion from the visiting star. The authors state that
the process may still be going on. This view is sustained by arguments
based on the zodiacal light and on meteors, both of which seem best
explained as planetesimal matter not yet returned to the solar mass.
Matter as yet unabsorbed would very likely consist of particles which
had been given just enough orbital motion to escape the surface of the
sun on their periodic return. The particles for the most part would
then have extremely eccentric orbits and pass close to the sun's surface
at tremendous velocity. They would be moving largely in the plane
of the solar system and consequently would pass close to the sun's
equator. If finally caught in the sun's atmosphere, friction would
reduce their motion, turning a large part of it into heat and a part into
forward movement of the sun's atmosphere. Thus the planetesimal
hypothesis explains the equatorial acceleration. A large meteoric
group, as suggested by Turner, is therefore consistent with the hypoth-
esis. The undefined zone between the accelerated equator and the
84 CLIMATIC CYCLES AND TREE-GROWTH.
slower-moving latitudes on each side would present much mechanical
disturbance and favor the formation of local vortices. Such a process
as this would be accompanied by the increased radiation in sunspot
maximum which has been observed. If this hypothesis has a basis of
fact, it is probable that the increased radiation at that time would come
from the sun's equator, where there are no spots. Increased rotational
movement of the equatorial zone at the sunspot maximum should be
susceptible of observation by spectroscopic means. The meaning of the
slow movement of this spot-forming zone toward the equator, as sun-
spot maximum changes to minimum, is not clear under this hypothesis ;
nor does one see why the secondary spot described by Hale (1919)
should have its definite location following the principal spot, nor why
the magnetic polarity of spots changed near the last sunspot minimum.
These phenomena, recently observed by Hale and his collaborators,
point toward causes within the sun.
Length of the sunspot period. — For many years Newcomb's figure
of 11.13 years has been commonly quoted. However, recently some of
the best authorities say frankly that it may be anywhere from 1 1 years
to nearly 12 years. Schuster (1898-1906) discussed analytically the
best known sunspot numbers, those since 1750. This has been followed
by the work of Kimura (1913), and especially Turner (1913) and
Michelson (1913). In general, the analyses by Schuster and Kimura,
and by Turner in his earlier papers, produce a large number of possible
periods of small amplitude. Michelson, however, goes to the other
extreme. "Indeed," he says, "it would seem that with the exception
of the 11-year period and possibly a very long period (of the order of
100 years) the many periods found by previous investigators are
illusory." Turner in his hypothesis referred to above reduces the
number to a few, which supply a basis for his reasoning. Michelson had
favored a period of about 11.4 years and Turner says that only this
11.4-year period is sensible at the present time.
Tree-growth and solar activity. — The correlation shown in this chap-
ter suggests a possible use of the annual rings of trees in the study of
solar activity. There are two lines which such a study might take.
An intensive line already mentioned includes the search for wet-climate
trees showing the solar rhythm in their growth and the determination
of the conditions under which they produce this curve. An extensive
line of study is obviously possible also in reconstructing, as far as
possible, a history of the sunspot cycle from very old trees. The
yellow pines of Arizona give evidence that 500 years ago the cycle was
operating very much as now. The sequoias, if correctly interpreted,
already carry the history back over 3,000 years, and beyond that fossil
trees may stretch the time covered in part at least into millions of years.
VII. METHODS OF PERIODIC ANALYSIS.
Need for such analysis. — During these modern times of rainfall and
sunspot records we may compare such records with tree-growth and
obtain the interesting correlations exhibited in the last two chapters;
but the tree records extend centuries and even thousands of years back of
the first systematic weather or sun records of any kind. Without being
over-precise or exhaustive, it is interesting to note that California
weather records began about 1851. Records on the Atlantic coast
began largely in the half-century before that date. London has a
rainfall record since 1726, Paris since 1690, and Padua since 1725.
Good sunspot records began about 1750, but the number of maxima
and minima is known between 1610 and 1750, although the exact dates
are uncertain. All this does not carry us very far back, but it
serves as an excellent basis for the correct interpretation of the record
in the trees.
It would be possible to apply correlation formulas to the Arizona
tree records and perhaps to the sequoias and construct a probable
rainfall record for long periods of time, but apart from Huntington's
study of the " Climatic Factor in History," the chief use of such a
record would be in studying the laws which govern rainfall; and this
is best done through cycles. We shall find that the sunspot cycle plays
an important role in rainfall. But we find traces of the solar cycle in
nearly all of our tree groups, and evidently the way to read the trees
is to study first of all their alphabet of cycles. Hence the best methods
of identifying cycles must be used.
Proportional dividers. — If a short series of observations is to be
tested for a single period, it can be done by mathematics, but it will
take many hours and give a result in terms so precise as often to
deceive. This, for example, has been the difficulty with the mathe-
matical solution of the sunspot curve. It seems to the writer that the
safer way to solve such a curve is by a graphic process, plotting the
curve and applying equal intervals along it. An extremely good in-
strument for this purpose is the multiple-point proportional dividers.
By a system of pivots and bars, 16 or more points are maintained in
a straight line and at equal intervals, while the space between two
successive points may be drawn out from one-eighth inch to one inch.
The remarkable persistence of the half sunspot period in the early
Flagstaff trees was detected in this way.
The projection of equal spacing on curves as long as 12 to 15 feet
has been done by a 10-foot india-rubber band with small metal clips
pinched on at regular intervals. As the band was stretched all the
intervals were enlarged by equal amounts, and periodic phenomena
were detected. Similar use could be made of the sharp shadows cast
by the glowing carbon of an arc-light. The shadow of a transparent
85
86
CLIMATIC CYCLES AND TREE-GROWTH.
scale could easily be cast in all sizes upon a plotted curve. But all
these methods of equal spacing on a plotted curve leave far too much
to the individual judgment of the investigator.
THE OPTICAL PERIODOGRAPH.
A method of periodic analysis well adapted to the work in hand has
been developed by the writer as the need for it became more and more
evident. Along with the feeling of need for rapid analysis was the
increasing recognition of the desirability of some process which would
place mere individual judgment and personal equation as far in the
background as possible.
Schuster's periodogram. — In 1898, Schuster suggested the use of the
word " periodogram" as analogous to the word spectrogram; that is, a
periodogram is a curve or a photograph which indicates the intensity
of time periods just as the spectrogram indicates intensity of space-
periods or wave-lengths. The spectrogram commonly gives its inten-
sities by varying photographic density along a band of progressive
wave-lengths. For the periodogram Schuster made simply a plotted
curve, of which the abscissae represented progressive time-periods
and the ordinates represented intensities. He made a mathematical
analysis of the sunspot numbers and constructed a periodogram which
is reproduced in figure 30. It shows periods at its crest at 4.38, 4.80,
8.36, 11.125, and 13.50 years.
woo
3000
zooo
1000
FIG. 30. — Schuster's periodogram of the sunspot numbers.
The optical periodogram. — It is, of course, not necessary that the
periodogram should take the form of a plotted curve with intensities
represented by ordinates, nor yet need it be exactly like a spectrogram
showing intensities by density. The first periodogram produced by
the writer is shown in plate 9, A. It is an analysis of the sunspot num-
METHODS OF PERIODIC ANALYSIS. 87
bers from 1755 to 1911. The existence of a rhythm in any specified
period is indicated by a beaded or corrugated effect. A line across the
corrugations gives in fact the rhythmic vibrations of the cycle. On a
moment's examination this periodogram shows much of the informa-
tion which has been under discussion for many years. The 11-year
period is the most pronounced, but it is not so superior to all others as
would be expected. It may be of any duration from 11.0 to 11.8 years,
but 11.4 is a good average. There is obviously a period somewhere
between 9.5 and 10.5 years and one between 8.0 and 8.8, but it is less
conspicuous. Faint indications of periods are found near 14 years.
The double of 8.4 is seen between 16 and 17 years. The double of the
10-year period shows near the 20 and at 22 the double of the 11 begins.
The preliminary part of producing this periodogram is the constyuc-
tion of the "differential pattern" shown in plate 9, B. This pattern is
the optical counterpart of a set of columns of numbers arranged for
addition, as when one summates a series of annual measures on a
10-year period, for example. The series is arranged in order with the
first 10 years in the first line, the second 10 in the second line, and so on.
In the case of the pattern the lines are made indefinitely long, so that
the optical addition may be done in other directions than merely
straight downward, for by making the additions on a slant a different
period comes under test.
In order to produce this pattern the sunspot curve was cut out in
white paper and pasted in multiple on a black background. The left
end of each of the upper lines is the date 1755. Each successive line
is moved 10 years to the left, so that passing from above vertically
downward each line represents a date 10 years later than its pre-
decessor. This continues from 1755 to 1911, and the lower 10 lines
show the latter date at their right ends. It is not necessary that any
of the lines should be full length, as we use only a part of each. By
passing the eye downward from the top, a period near 10 years will
show itself at once by a succession of crests in vertical alinement. If
the crests form a line at some angle to the vertical, then the period they
indicate is not exactly 10 years. It is more if the slant is to the right
and less if to the left. The horizontal lines are spaced the equivalent
of 5 years. Hence, if we measure the angle made between a vertical line
and a line joining two crests in successive horizontal lines, we may
easily calculate by simple formulas the period indicated.
Since the photometric values of all the curves in the diagram are
proportional to the plotted ordinates, the photographic summation
of the whole pattern in a vertical direction is almost an exact analogue
of a numerical summation. This summation is simply done by a
positive cylindrical lens with vertical axis. This brings down on the
plate a series of vertical lines or stripes. If, now, we cut across these
lines with a horizontal slit, the light coming through this slit from one
end to the other will be the summation of the diagram in the vertical.
88 CLIMATIC CYCLES AND TREE-GROWTH.
But the photographic summation may be done at any slant instead
of only in the vertical, and therefore the sensitive plate may be made
to summate these curves through a long range of periods. In order to
get a long range of periods, the diagram was mounted on an axis with
clock-work and slowly rotated in front of a camera with a cylindrical
lens for objective, a horizontal slit in the focal plane, and a sensitive
plate passing slowly downward across the slit by clock mechanism.
In this way a full range of possible periods come under the summing
process, and when a real period is vertical the crests of the curves form
vertical lines which come down as a series of dots or beads in the slit.
When no period is in the vertical the light coming through the slit
is uniform. Of course, there is a practical limit to the different angles
at which the diagram may be viewed. An angle too far in one direction,
making the tested period very small, would require a great number of
duplications of the curve, while too great an angle the other way, mak-
ing the tested period very large, catches the curve in the nonsymmetri-
cal form a*nd introduces errors. In the periodograms actually made of
the sunspot curve the minimum period tested was 7 years and the
maximum 24. One notes especially that this is a continuous process
and that all periods from the minimum to the maximum are tested.
Application to length of sunspot period. — The interest in the sun-
spot period makes a special consideration of plate 9, c, worth while.
This figure is a photograph of plate 9, B, taken out of focus for the pur-
pose of calling attention to certain general features. In B the eye
naturally turns to the sharp outlines and notes its minute details. In
c the crests of B are changed into large blotches connecting somewhat
with their nearest neighbors and varying in intensity. The alinement
which they form in a nearly vertical direction is a graphic representa-
tion of the period. If the line were exactly vertical the period would be
10 years. The slant to the right shows more than 11. If the line were
straight the period would be constant. It is evident that there are
several irregularities in it. Having a number of exactly similar lines
side by side, the irregularities are repeated in each and thus strike the
consciousness with the effect of repeated blows. These irregularities
are the discontinuities referred to by Turner in connection with his
hypothesis. It is evident at a glance that the sunspot sequence
divides itself into three parts, namely, a 9.3-year period, 1750-1790;
then an interval of readjustment, 1800-1830, with a 13-year period;
and lastly an 11.4-year period lasting to the present time (values
approximate).1 But the latter is not perfectly constant, for after 1870
there is a change in intensity. The breaks thus shown and Turner's
dates of discontinuity are compared in table 6.
1 In discussing the periodicities of sunspots (19062, pp. 75-78) Schuster divided his 150 years,
from 1750 to 1900, into two nearly equal parts. He found in the first part two periods of 9.25
and 13.75 years acting successively, and in the second part, a period of 11.1 years.
DOUGLASS
PLATE 9
A. Periodogram of the sunspot numbers, 1755-1911. Corrugations show periods. The
numbers give length of period in years. The white line is the year 1830 and shows
phase.
B. Differential pattern used in making the periodogram, consisting of the sunspot curve
mounted in multiple.
C. Same pattern photographed out of focus to show discontinuities in the vertical lines.
D. Sweep of sunspot numbers, 1755-1911.
E. Differential pattern of sunspot numbers made by the periodograph process.
METHODS OF PERIODIC ANALYSIS.
89
sunspot cycle.
By means of this diagram one can discover at a glance the origin
of many of the periods which Michelson thought were illusory and in
which opinion he was largely right. We can plainly see a 9.3-year
period in the early part of the curve. TABLE 6.- Discontinuities in the
Let us call this part of the sequence An
and its broken continuation near the
center Bn, and the lower and later part
giving the 11.4-year period Cn. Thus we
get at once three periods, 9.3, 11.4, and
something over 13 years. If, now, we
bring the average An into line with the
average Cn as the periodograph does, we
Periodogram.
Turner.
1766
Between 1788 and 1804.
1796
Between 1830 and 1837 .
1838
Between 1870 and 1884.
1868
1895
get 11.4 years. If we bring the average An into line with the Cn_i, we
get close to 10 years. If we bring into line An and the heavier parts
of Cn_2, we get 8.4 years or thereabouts. And at 5.6 years we find
a period which is just half of Cn and at 4.7 the half of An, and so on.
It is like a checker-board of trees in an orchard ; they line up in many
directions with attractive intensity. But plate 9, c, helps remove some
of the complexity of the sunspot problem. It shows us that while these
various periods are apparent, they are improbable and needless com-
plications. The diagram supplies a basis for profitable judgment in
the matter. Hence to avoid just such awkward cases as the sunspot
curve, a differential pattern is considered to be a necessary accom-
paniment of the periodogram in doubtful cases.
Production of differential pattern. — The work described above, con-
sisting particularly in the production of a periodogram from the differ-
ential pattern, was done at Harvard College Observatory in 1913. The
next fundamental improvement in the apparatus was in 1914, and con-
sisted in a method of producing the differential pattern without all the
labor of cutting out the curves. It was simply the combination of a
certain kind of focal image called a " sweep" and an analyzing plate.
A single white or transparent curve on a black background is all that
is now needed as a source of light. An image of this is formed by a
positive cylindrical lens with vertical axis. In the focal plane image so
produced each crest of the curve is represented by a vertical line or
stripe and the whole collection of vertical lines looks as if it has been
swept with a brush unevenly filled with paint and producing heavy
and faint parallel lines. Each of these lines represents in its brightness
the ordinate of the corresponding crest. The sweep of the sunspot
numbers is shown in plate 9, D. Any straight line whatever in any
direction across this sweep truly represents the original curve, not as a
rising and falling line but in varying light-intensity. A plate with
equally spaced parallel opaque lines, called the analyzer or analyzing
plate, is placed in the plane of this sweep. These lines may be seen in
90 CLIMATIC CYCLES AND TREE-GROWTH.
plate 9, E. When the analyzer is turned at a small angle to the lines
of the sweep, each transparent line shows the full curve or a substantial
part of it in its varying light intensities. These numerous reproduc-
tions are all parallel to each other, separated by equal dark lines, and
each one is displaced longitudinally with reference to its neighbors,
thus presenting the characteristics of the differential pattern. By
twisting the analyzer with reference to the sweep while the two remain
in parallel planes, different periods may be tested; for as the analyzer
twists, each reproduction varies in respect to its length and its dis-
placement from its adjoining neighbors above and below. When a
period is formed it shows itself, just as in the original differential
pattern, by rows of dark and light spots in alinement more or less
perpendicular to the analyzing lines, as in plate 9, E. These light and
dark rows are analogous to interference fringes and are identical with
the elaborate but provokingly useless designs on a wire screen in front
of its reflection in a window, or with the parallel fringes when two sets
of parallel lines are held at a slight inclination to each other.1 Aline-
ments are always best recognized by holding the paper edgewise and
looking at the diagram at a low angle rather than in a perpendicular
direction.
The analyzing plate resembles a coarse grating with equally spaced
parallel lines. Much difficulty was experienced in making it. It is
most satisfactory if made on glass with strong contrast between the
opaque and transparent parts. The grating now in use was produced
by photographing a 10-foot sheet of coordinate paper upon which 165
lines of black gummed paper had been carefully fastened. The coor-
dinate lines permitted the spacing to be done with exactness. The
width of the transparent space throughout was three-tenths of the
distance from center to center. This was carefully photographed by a
good lens at different distances. Glass prints were made from each
negative and are still in use.2
Theory. — The formula for the period is very simple :
Let y = length of curve in years or other time-unit employed.
1 = length of curve image across sweep lines in centimeter or
other unit of length.
s = spacing center to center of analyzing lines in unit of length.
Then - = number of analyzing lines in curve when lines are parallel to
sweep.
— = number of years in 1 line when lines are parallel to sweep.
i
1 Roever (1914), has used somewhat similar interference patterns to illustrate very beautifully
certain lines of force.
2 A very superior analyzing plate has recently been made from a ruled screen such as is com-
monly employed in half-tone engraving.
METHODS OF PERIODIC ANALYSIS.
91
Now, taking analyzing lines aa1 and bbl in figure 31 as horizontal, and
letting the sweep be inclined as a small angle 5 with the analyzing
lines, the number of lines required to cross the sweep in the direction
ab perpendicular to analyzing lines will be increased and hence the
value in years between two analyzing lines will be decreased; hence
— cos 5 = years per line from a to 6.
If the fringe is perpendicular to the analyzing lines, its period is the
distance ab in years and we have for this special case:
ys ,,
p\=— cos o.
i
FIG. 31. — Diagram of theory of differential pattern in periodograph analysis.
If, however, the fringe takes some other slant, as the direction ac,
making the angle 6 with the analyzing lines, then the period desired
is the time in years between a and c. That equals the time between
a and 6 less the time from b to c. Now be in years would equal ab cot 6
except for the fact that the horizontal scale along be is greater than the
vertical scale along ab in the ratio - '— and therefore a definite space
sin o
interval along it means fewer years in the ratio of !!E_. Hence we have :
cos d
be (in years) = ab (in years) tan 5 cot 6
or
P = pi(i — tan 5 cot 6)
which is the period required.
The separation of the fringes needs to be known at times in order to
find whether one or more actual cycles are appearing in the period
under test. In figure 31
ab =
ad =
sin 5
— s sin (0—5)
ae = —
sin d
which is the width required.
92 CLIMATIC CYCLES AND TREE-GROWTH.
THE AUTOMATIC OPTICAL PERIODOGRAPH.
The present apparatus combines the two processes whose develop-
ment has been described above. The second process developed is
really the first one in the present instrument.
The curve. — The curve is prepared by cutting it out in a thick
coordinate paper. The space between the curved line and the base is
entirely removed and the curve becomes represented by area. In
order to make the density still greater, the paper is painted with an
opaque paint so that the brilliant light passing through will come
through only the curve itself and not the paper. A special window-
shutter is made to occupy the lower 2 feet of the window, whose width
is some 50 inches. The curtain can be drawn down to the top of this,
excluding the light around the edges. This window-shutter has a door
in the upper part to give access to the interior. Within this box is a
sloping platform upon which a mirror 8 by 46 inches is placed. This
mirror is about 35° from the horizontal position and when looked at
from a horizontal direction it reflects the sky from near the zenith.
On the side of this box toward the room is a slit 45 by 3 inches in size.
This extends horizontally and is on a level with the mirror. Below this
slit is a narrow groove for taking the lower edge of the curve paper and
above this slit is a strip of wood on hinges, so that when the lower edge
of the curve is placed in the narrow groove below, this hinged strip
closes down on the top and holds the curve in place directly in front of
the mirror. Looked at from a horizontal direction within the room,
the curve is seen brightly illuminated by light from the sky not far
from overhead.
Track and moving mechanism. — About 7 -feet from the curve the
track begins and extends back 45 feet in a perpendicular direction.
The track consists of 3 rails. The center rail is of uniform height and
takes the single rear wheel, whose motion controls the movement of
the film at the back of the camera. The right-hand rail is also uniform
in height and supports one of the front wheels. The left rail is variable
in height and supports the driving-cone, which serves as the other
front wheel. The cone is 6 inches long and 3 inches in greatest diameter.
It rests on a side rail whose elevation and distance from the center can
be altered. The purpose of this particular mechanism is to vary the
speed with which the camera travels along the track, for the time of
exposure is approximately proportional to the square of the distance
from the curve, and therefore when the camera travels from the near
position to the far position it must slow down in rate as it goes along.
The left rail, therefore, at the near position is close to the center and
low down; in the middle and outer parts of the track it gets farther
away and higher up, since the parts of the cone near the vertex travel
on it. The axis of the cone carries a bevel gear meshing with another
METHODS OF PERIODIC ANALYSIS. 93
bevel attached to a vertical axis with a worm gear at the top, which the
electric motor drives with a belt connection. In order to aid the motion
of the camera, a cord passes from its back to the outer end of the track
and by a system of pulleys and weights exerts a slight constant force.
The motor is so connected that the camera travels away from the curve.
The details here described may be seen in plate 10.
The differential pattern mechanism. — The camera is divided into
three separate compartments, to each of which access is obtained by a
sliding door moving in grooves on the side. The front compartment
produces the differential pattern. It is about 7 inches long by 5 inches
wide in the clear and 4 inches high. It is nearly divided into two parts
by a partition which comes down from the top at about 2 inches from
the front end. This partition does not go down to the floor of the com-
partment, but leaves a space of about an inch. A hole 1.5 inches in
diameter is cut through the front of this compartment a little above its
center, and another hole of the same size to match is cut through this
partition, while at the back of this compartment a large opening is
made a little over 2.5 inches wide and about 2 inches high. The lens
is carried on a special carriage consisting of a horizontal and a vertical
part. The vertical piece has a hole 1.5 inches in diameter cut in it,
and the lens is mounted over the hole. The lens now in use consists
of a spherical lens concavo-convex 2 inches in diameter and 12 inches
in focus placed on the inside, and a positive cylindrical lens of the same
size and focus placed on the outside with axis vertical. The convex side
of each lens is placed outward. The lens carriage is placed partly under
the partial partition and the lens in its holder comes directly between
the two holes mentioned. When the sliding door of the compartment
is down, the compartment is sufficiently light-tight to fulfill all the
requirements of a camera. The movable carriage of the lens is mounted
on two small glass tubes and runs between guides. A spring at its back
end pulls it toward the position of focus for distant objects, where its
motion is stopped by a pin. A long screw is passed through a hole in
the bottom of the camera box and enters the bottom of this lens car-
riage, so that an automatic arrangement outside and underneath the
camera can regulate the focus. This consists of a vertical axis with
two lever arms. The upper lever arm is a short one connected to the
screw which comes from the lens board. The lower lever arm is some
4 inches below the upper and goes off in a direction nearly at right
angles; it carries on its end a wheel in a horizontal position. This
wheel is so placed that it runs on an especially arranged track attached
to the side of the center rail of the main track. By varying the eleva-
tion of this special focussing track in different parts of the main track,
the focus of the lens can be automatically controlled.
At the back of this first compartment is the analyzing plate, the same
plate used in previous work. The spacing of its lines is 0.5 mm. from
94 CLIMATIC CYCLES AND TREE-GROWTH.
center to center. The proportionate transparent part is about three-
tenths of the center-to-center measurement. The area covered by
these lines is 1 by 3 inches, making about 156 lines. The photograph
is transparent with dense black lines in it. The glass has been cut
down to a convenient size, and this plate is mounted at the back of the
first compartment with the film side of the plate toward the back.
This plate is over the large opening at the back of the first compart-
ment. The differential pattern is formed automatically by the lens on
this plate. The plate is held in a fixed position with its lines nearly
vertical but inclined about 12° to the lines of the sweep formed by the
lens. This produces fringes more or less horizontal in direction. Vary-
ing periods are tested by changing the distance from the curve which
alters the scale of the sweep while the analyzing lines are unchanged.
As the scale of the sweep changes, the fringes appear to rotate about
the center of the differential pattern. Immediately behind the analyz-
ing plate are two condensing lenses described in the next topic. They
bring the general beam of light to a focus about 6 inches back of the
plate. For visual work a movable mirror, just back of the plate,
reflects the beam outside the camera box, through an eyepiece to the
eye. For photographic work a small total-reflection prism and simple
lens are inserted about 5 inches back of the analyzing plate. These
throw the beam outside into a special camera attachment in which
ordinary films or plates may be used.
The periodogram mechanism. — The remainder of the camera is
especially for the purpose of producing the periodogram from the
differential pattern. Almost in contact with the analyzing plate is a
condensing lens consisting of two cylindrical lenses about 2 inches in
diameter and 6 inches focus ; these are mounted with vertical axes and
with their convex sides toward each other. The aperture of the con-
denser is about 0.75 inch in vertical height and 1.75 inches in length.
The purpose of these condensers is to coverge the light which comes
through the analyzing plate on the slit at the back. The second com-
partment is nearly the same size as the first, namely, about 6.5 inches
long. At its front end is the analyzing plate with the condensers and
at its back in the same optical axis is a vertical slit about 1 inch long
and 1 mm. wide. The sides of this slit are beveled so that the slit
itself is at the back. In the middle of this compartment is a powerful
cylindrical lens or combination of lenses with horizontal axis. This
lens is made up of 4 separate positive cylindrical lenses, each 2 inches
in diameter and 6 inches focus. These all have their convex sides
toward the common center. They are mounted on a movable carriage
of wood which slips in place or may be removed entirely. The aperture
of this lens system is about 1.5 inches long by 0.75 inch high. The
effect of the condensing lens and of this cylindrical lens is to cast in
the plane of the slit an area of light whose size is essentially a repro-
DOUGLASS
PLATE 10
A.
B.
A. The automatic optical periodograph.
B. Differential patterns of Sequoia record, 3200 years at 11.4.
B.C
-1300
B.C.
-1000
B.C.
1-500
AD
•500
A.D.
-1000
A.D.
-1500
A.D.
-1900
METHODS OF PERIODIC ANALYSIS. 95
duction of the aperture of the objective, namely, 1 inch high by 0.25
inch wide, but the detail in this area of light is brought in focus by the
cylindrical lens and integrates the horizontal lines of the differential
pattern. When, therefore, the differential pattern shows a series of
horizontal fringes, they become reproduced by a series of horizontal
lines crossing the slit, while in the slit itself they appear as a series of
dots. When a period is disclosed by proper position of the camera, it
will produce horizontal lines on the analyzing plate. A series of black
and white dots, therefore, go through the slit into the final compartment;
but when the distance is such that the lines on the differential pattern
are at some slant, then, the integration carried into the slit being still
horizontal, the illumination in the slit is uniform. In this way the
beaded or corrugated effect in the slit indicates a period at that partic-
ular distance from the curve.
In order to read off periods directly in the final result without the
necessity of making exact measures, an automatic signal or period
indicator is introduced in this second compartment. Above the upper
and lower ends of the slit are placed small pieces of mirror at 45°, and
corresponding to these there are two small holes 0.25 inch in diameter
in the side of the box. Outside of these holes again is a mirror at 45°
reflecting light from the curve in the window. So long as the holes are
open, direct light from the curve is reflected by the two sets of mirrors
through the slit on to the film beyond, as will be described. A shutter
is placed over the outer holes in the box with a lever carried down to
the vicinity of the central rail. On the end of the lever arm is a wheel.
At proper intervals small pieces of wood are placed in the side of the
track, so that as the wheel passes over them the shutter is opened and
light passes to the mirrors and makes a dot or a line on each side of
the film in the third compartment. In this way marks can be placed on
the film independent of the periodogram, and yet they can be spaced
exactly to represent the different periods tested. Special periods, for
example 5 or 10 years, etc., are indicated by the extra length and
density of the marks produced. These appear on the margins of the
periodograms in plate 11.
The final compartment at the rear contains a drum on a vertical
axis which is slowly rotated as the whole mechanism moves along the
track. The rear wheel resting on the center rail is connected by
gearing to the drum, so that 1 mm. on the drum represents 42.7 mm. or
1.7 inches on the track. This makes a convenient length for the final
periodogram. The drum can be detached, carried to a dark room to
have a film pinned to its periphery, returned in a special light-tight
box, and mounted on its axis for an exposure. The times of exposure
depend on characteristics of the curve under test, but it is necessary
to allow about 35 minutes for the range from 4 to 15 years, and several
times that for the range from 15 to 25 years. Plates 10, 11, and 12
illustrate the apparatus and the periodic analysis produced.
96 CLIMATIC CYCLES AND TREE-GROWTH.
Periodograms. — Plate 11, which has been arranged to illustrate the
work of the periodograph, shows several of the early periodograms
which are comparatively free from obvious instrumental defects. In
each the range of periods is marked on the left margin. Periods are
indicated by the vertical band or ribbon breaking up into a series of
horizontal dots or beads. For example, plate 11, A, is a periodogram
of the 5-year standard period made for the purpose of calibrating the
work of the periodograph. The 5-year period is very prominent near
the top of the diagram in the plate. At 10 years its first harmonic
appears with double crest, showing still that it is a 5-year period. At
15 years the second harmonic shows with a triple crest, and at 7.5
years the 3/2 overtone is evident with 3/2 crests. These overtones
are always readily distinguished from the fundamental on the differ-
ential pattern. The differential pattern of this 5-year standard is
shown in plate 12, Q. The instrument is set for analysis at 5.0 years.
In this position the integrating lens sums up the rows of light crests as
a series of dots on the periodogram.
Plate 11, B, is the analysis of a mixed standard used for calibrating
the instrument. The curve contains sharp triangular crests at intervals
representing periods of 7, 9, 11, 13, and 17 years, all mixed together and
no two starting intentionally from the same point. These are all
separated in the periodogram and the overtones of some may be seen.
Such overtones can be distinguished from the fundamental on the
differential pattern.
Plate 11, c, gives a periodogram of the sunspot numbers from 1610
to 1910, using before 1750 the probable times of maxima suggested
by Wolfer. The best period is at 11.1 as usually quoted. If the varia-
tion from 1750 only is taken, the best period comes at 11.4. This
periodogram shows a period at about 8.6. The degree of accuracy with
which one can pick out the periodic point is a real criterion of the
accuracy of the result selected. The differential pattern of this same
series of sunspot numbers will be found in plate 12, A, in which the
vertical rows of crests are readily distinguished. The sudden change
in direction of the lines a little below the center of this and the two
following periodograms is an instrumental defect due to slight uneven-
ness in the track and therefore is without significance.
Plate 11, D and E, give an analysis of the Arizona 500-year record.
The chief points of interest are the well-defined double-crested 11.6-
year period and the 19-year and 22-year periods. Other weaker periods
may be seen from place to place.
Resolving power of the periodograph. — The accuracy with which a
period can be determined by the periodograph may be readily observed
in the differential pattern and the periodogram. The pattern indicates
a period by showing a row of light spots or crests in line. The accuracy
PLATE 11
E
A. Periodogram of standard 5-year period.
B. Periodogram of mixed periods.
C. Periodogram of sunspot numbers, 1610-1910.
D. Periodogram of Flagstaff 500-year record, to show cycles
between 4 and 15 years of length.
E. Periodogram of same continued to 25 years.
METHODS OF PERIODIC ANALYSIS. 97
of the period is the accuracy with which the direction of this line can be
ascertained. This depends on the length of the row of crests, on the
shortness of each crest, and on their individual regularity or alinement.
These characteristics may be noted in the plates and especially in
plate 12, Q. Expressed in other terms, these resolving features are
respectively as follows: (1) Number of cycles covered by the given
curve. (2) Shortness of maxima in relation to length of cycle; if the
maximum is sudden and sharp, as in rainfall, the accuracy may be very
great; if the maximum is long, as in a sine curve, the accuracy is less.
(3) Regularity in the maxima and freedom from interference. These
features all appear in the differential pattern and hence the accuracy
of any period is its most evident feature and all observers can judge it
equally well. It is exactly analogous to the accuracy of a straight line
passed through a series of plotted points which theoretically ought
to form a straight line but which do not do so exactly.
The most important part of the constructed instrument which may
alter the accuracy of analysis is the analyzing plate. The accurate
spacing and parallelism of the lines is a mechanical feature and can be
produced with care and attention to details, but the relation of width
of transparent line to center-to-center spacing of the lines is a matter
of judgment and the necessities of photography. As this relative width
increases, the length of each crest in the pattern becomes longer and
the row of crests becomes wider and less definite in direction. If the
maxima in the curve under test are of the sine-curve type this relation
is less important, for the light crests in the pattern will be long in any
case, but for sharp, isolated maxima resolution is lost if the width of the
transparent line is too great. In the instrument now constructed the
ratio of transparent line to center-to-center spacing is 3: 10, but a
smaller ratio such as 1 : 10 could advantageously be used in certain
cases if there is sufficient light to make photography easy.
The accuracy in reading a periodogram is at once apparent on its
face. When the number of cycles is great as in plate 11, A, the rhythmic
or beaded effect is short and very limited in extent, as in the 5-year
period there indicated, and the period is accurately told. But if the
number of cycles is reduced (as in plate 11, B or c) the periodic effect
in the photograph extends over a greater range and its center can not
be told with the same precision. The accuracy of estimation in the
periodogram is therefore the actual accuracy of the result.
VIII. CYCLES.
Significance of cycles. — It has already been stated that three charac-
teristics were observed in the curves of tree-growth: (1) correlation
with rainfall; (2) correlation with simspots; (3) general periodic
variation. In the first and second of these the trees are compared
directly with existing records, but in the third the tree record is avail-
able over hundreds and even thousands of years during which no
human observations were recorded. Thus, if previous inferences are
correct, the trees may reasonably be expected to give us some knowl-
edge of prehistoric conditions. In the first attempt to secure such
knowledge, the method which promises the most certain results is the
analysis of ring variations in terms of cycles.
Correlatively, the study of cycles is of special value in climatic
investigations. Such studies are undertaken for the purpose of pre-
dicting the future. The basis of daily or short-distance prediction is
found in the conditions existing about the country at a given moment
and a knowledge of the usual movement of storm areas. A basis for
long-distance prediction is now generally sought in climatic cycles.
Such cycles may or may not be permanent. Perhaps they are nothing
more enduring than a series of wave systems on a water surface. Yet
for the navigator a knowledge of the existing system is important, and
so for the purpose of weather prediction we need to know the nature
of the pulsations actually operating, and each one should be studied
minutely. For this purpose the very long tree records and their pre-
sumably fair accuracy seem especially advantageous, since they give
us a range in centuries which the meteorological records, with few
exceptions, give only in decades.
A special and rapid method of carrying on the study of cycles has
been developed in the periodograph which has been used in checking
fully all the results in the present chapter. But after its recent com-
pletion and trial the fact became clear to the writer that its real
service will be in a complete and thorough examination of all curves
obtained, in order to derive a quantitative statement of the extension
in time and space shown by each cycle. This in itself is a long process.
Moreover, preliminary analysis of many tree curves reveals a very
complex system of short-period variations in the trees, some of evident
significance and some of little-known value as yet. The study of this
complex of short periods together with other problems naturally sug-
gested in the course of the work is reserved for the future; we shall
now touch upon a few of the most important results reached in the
analyses already accomplished.
Predominant cycles. — With the understanding that the study of
cycles is not yet complete, it may be stated at once that the more
98
CYCLES. . 99
conspicuous and general cycles at once apparent in the trees are directly
related to the solar period. They are as follows:
5 to 6 years approximate half sunspot period.
10 to 13 " " full
21 to 24 " double "
32 to 35 " triple "
100 to 105 " " triple-triple "
There are few if any periods over 20 years not in this list, but under
20 years several are fairly persistent, such as 19-, 14-, 10-, and 7-year
periods. There is also a period of about 2 years which causes a frequent
alternation of size in successive rings, giving a " see-saw" or " zig-zag"
effect in the appearance of the curve. The discussion in this chapter,
however, will be confined to the solar group of periods above listed and
to a preliminary statement regarding the 2-year period. As the larger
of these solar periods are very nearly simple multiples of the 11-year
period, it is naturally suspected that they are or should be real multiples
of the sunspot period. Hence I feel at liberty to speak of the " double
sunspot period" or the " triple sunspot period" without committing
myself to its exact length.
Locality and solar cycles. — Compared to the multitudes of meteoro-
logical districts about the world, the few isolated localities which have
here been investigated seem very insignificant. The wet-climate trees
near the Baltic Sea show variations following almost perfectly the
curve of sunspot numbers. The Scotch pines just south of the sea have
had good care since they were planted about 90 years ago. This care
has prevented the excessive competition between individuals which
characterize natural forests, and perhaps for that reason they give this
remarkable record of external conditions. The trees to the north of
the Baltic include spruces as well as Scotch pines, and show the same
reaction. Both these groups are in comparatively level country and
far from mountains. The group of pines from the Swedish province of
Dalarne show the 11-year period somewhat less clearly. They were
nearer the backbone of mountains which extends down the Scandi-
navian peninsula. The older trees of this group show evidence of a
triple sunspot period. The groups growing in the mountains and in the
inner fjords of Norway show extensive variations and even reversals.
Some of the individual trees exhibit the sunspot period very well,
while some show it inverted and some divide it into two crests. The
older trees show evidence of an inverted double period.
The trees near sea-level, both at Christiania, and on the outer coast
of Norway, return again to the 11-year period. The former do not
cross-identify well and the latter show occasional variations, such as
double-crested period, inversion, etc. Variations of this kind were
noted in different radii of the same tree. The trees from the south of
100 CLIMATIC CYCLES AND TREE-GROWTH.
England show slight relation to the solar cycle. They show more
prominently other variations, which, taken between 1870 and 1900, may
have given rise to Lockyers 3.8-year period (1905, 1906). The full
tree record becomes more accordant on a 3.5-year period. In this
group there appears to be a slight relation to London rainfall of a
direct character, that is, the growth is larger with increased rain.
Naturally in such a well-cultivated region there may have been large
differences due to treatment of the soil, drainage, and so forth. The
other two European groups, one from Pilsen in Bohemia and one from
the north slopes of the Alps in southern Bavaria, do not show consistent
agreement with the solar variation. Yet the former shows a double
sunspot period which is illustrated below.
Coming to the American continent, the Vermont group may also
be considered as growing in a wet climate. It shows a very strong
single-creasted solar period, but the maxima come 3 years early during
the last century. During the preceding century, when the trees were
younger, the tree maximum is only 1 year early. The rainfall in this
region shows the solar period also, but it is roughly inverted with
respect to the tree curve. The Oregon group must be considered as in
the wet climate of the temperate zone. It is near the Pacific coast and
has abundant rain or snow. The solar cycle is probably in it, but it is
not so conspicuous as other short cycles. When these trees are summed
up on the 11-year period, they show about 10 per cent total variation
with maximum and minimum coinciding with the Vermont group and
therefore anticipating the sunspot maximum by 3 years.
The sequoias grow farther south and experience the heavy pre-
cipitalion of the temperate-zone winter combined with dry-climate
summer conditions — that is, the summers are mostly clear, but have
occasional sharp local showers, often with lightning The tree-growth
shows a relation to the rainfall in the great valley below and therefore
we could expect some similarity to the Arizona pines. This does exist,
but the exact 11.4-year cycle shown in the pines is less evident in the
sequoias, though unmistakably there. The analysis of the long
sequoia record will be shown below. In it several cycles between 7 and
15 years predominate in places. The 11 -year period is plainly evident
through most of the record and for some centuries is the predominant
cycle, but for long periods other slightly differing cycles, such as 10
years, 12.6 years, or 13 years, are more evident. It is as yet impossible
to say whether at these times there was a real change in the sunspot
period, whether some subordinate period is operating in the sun, or
whether only local conditions of some kind are the controlling factor.
The yellow pines of northern Arizona are dry-climate trees. They
have a modified winter precipitation of the temperate zone. Spring
and autumn have the complete dryness of the " horse latitudes," and
the summers have the characteristic subtropical torrential thunder-
CYCLES. 101
storms. Rain is the controlling factor in these trees. The trees show a
double-crested 11.4-year period through nearly all the 500 years of
their record. This will be illustrated below. A 7-year period is also
frequently observed, and the combination of the 7-year and 11-year
periods may be the cause of these trees showing the double sunspot
period prominently through most of their record by interfering to
suppress alternate 11-year maxima. A triple sunspot period is very
evident in the last 200 years, but is practically lost in the preceding
300. The pines and sequoias agree in showing a long period of about
100 years. The record of the pines is not long enough to give it much
precision, and 120 years fits it more nearly. The 3,200 years of the
sequoias analyze best at 101 years.
Illustrations of cycles — Two methods of illustrating cycles in the
tree curves are used here. One is the usual method of showing the
plotted curves together with another curve indicating the cycle, so
that agreements and disagreements may be noted. To this method
also belongs the integrated or summated curve, which shows the mean
variation in the desired period. The other method is by aid of various
periodograph diagrams. These diagrams may similarly be divided
into the differential pattern, in which variations from the cycle at any
time may be noted, and the periodogram proper, which gives roughly
the mean form of the cycles in a considerable range of periods. This
form of presentation, being new and yet carrying more information
than the former, will be given with some explanation after the curves
themselves have been shown.
The 11-year cycle. — Only two tree records, the yellow pine and the
sequoia, extend back of the first telescopic observations of sunspots.
It is of peculiar interest to see whether the trees which carry the rainfall
record back so far with a comparatively high degree of accuracy show
the same cycle. In nearly all parts of the yellow-pine curve there are
suggestions of an 11-year cycle. By tracing this throughout the record,
the period is found to have a length of about 11.4 years, which is
sufficiently close to the length of the sunspot cycle to be considered
identical with it. This exact figure is not yet considered final, as future
intensive study of the short-period variations in the trees may throw
more light upon it. Taking 11.4 years as the probable length, the
average total variation is found to be some 16 per cent of the mean
growth. The period is generally double-crested with two well-developed
maxima and minima, but they are rarely symmetrical. During the
120 years from 1410 to 1530 it shows most remarkable regularity.
This feature, which was observed as soon as the smoothed curve was
examined, is shown in figure 32. The tree curve in this diagram has
been reduced to departures from its own mean and smoothed by Hann's
formula. The short period is immediately evident, even without the
5.7-year cycle plotted below. This bit of record in the yellow pines
102
CLIMATIC CYCLES AND TREE-GROWTH.
and the 90 years of record in the wet-climate Scotch pines near the
Baltic Sea give the finest examples of rhythmic growth yet found in the
trees.
MO
[AAAAAAAA/VV
20 1530
FIG. 32. — Smoothed curve of Arizona pines showing the half-sunspot period for 120 years.
H-70 80 30 ISOO JO
Years
In order to test for possible variations in the sunspot curve during
these 500 years, the tree record from 1420 to 1909 has been divided
into 8 periods of approximately 60 years each and the form of the
11 -year period obtained in each. This is shown in figure 33. From
this it appears that the 11 -year cycle is not uniform throughout the
whole 490 years covered by the curve. In general the cycle shows 2
maxima and 2 minima. From 1420 to 1660 the second minimum is
generally the deeper. For the next 60 years the curve flattens out in a
striking manner. From 1730 to 1790 the curve again shows variations,
but they are not well related to this cycle. After 1790 there are again
2 minima, but on the whole the first is more conspicuous.
The 11-year cycle in sequoia. — The question of agreement between
the sequoia and the yellow pine is a vital one. Although the sequoias
grow in a locality some 450 miles distant, there is a similarity in the
rainfall of the two places. Some attempt has been made to cross-
identify the rings in the two groups, and the puzzling fact was revealed
that from 1400 to about 1580 no certain identity could be found,
though after that date it was evident in many places. The difficulty
has been partly removed by applying this same method of analysis to
the last 500 years of the sequoia. The result is shown in the dotted
lines of figure 33. It is evident that from 1420 to 1476 the second
maximum of the pines is almost entirely lacking in the sequoias. The
same is true of the interval from 1602 to 1658. The sequoias show
strikingly the flattening of the curve from 1670 or 1680 to 1727. In
the remainder of the curves the sequoias show better rhythm in the
sunspot cycle than do the pines.
Taking the evidence as a whole, it seems likely that the sunspot
cycle has been operating since 1400 A. D., with some possible inter-
ference for a considerable interval about the end of the seventeenth
century.
CYCLES.
103
Correlation curves. — Figure 34 is arranged to show certain relations
of special interest in this connection. At the top was found the mean
pine and sequoia curves for 490 years averaged on an 11.4-year period.
Below these the mean 11.4-year period for the last 60-year interval is
given for each tree. This is required for proper comparison with the
short interval of climatic records. Next the rainfall and temperature
observed on the southern California coast are plotted, and last of all the
inverted sunspot curve for a corresponding period. There appears to
be a marked relationship between these curves. Even the subordinate
crest, which sometimes shows in the change from maximum to mini-
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FIG. 33. — Changes in the 11-year period in 500 years. Solid line, Arizona pine;
dotted line, sequoia.1
mum of sunspots, matches the suppressed second crest of temperature
and the full second crest of rainfall and tree-growth. This would seem
impossible in the absence of a physical relation between them.
Double and triple cycles. — The first tabulation of the Arizona pines
covered a period of only 200 years and included 25 trees. There were a
few errors of identification in some of these trees, sufficient to flatten
JThe correction for the ring 1580 was made too late for insertion in this figure. The two
dotted curves between 1420 and 1533, therefore, should be moved one year to the left, while
the third dotted curve between 1534 and 1601 becomes slightly modified. A slight change in
the first Arizona curve is required by a correction at 1463 A. D.
104
CLIMATIC CYCLES AND TREE-GROWTH.
the curve a little but not enough to change the pronounced fluctuations
amply shown in recent analysis. This 200-year record showed a very
clear combination of the double and triple sun-spot periods. This
was illustrated at the time in a drawing which is largely reproduced
in figure 35. Curve No. 1 is a triple solar cycle 32.8 years in length;
/ //J7/7T.
FIG. 34. — Correlation curves in the 11-year cycle.
No. 2 is a double cycle 21.2 years long, and the third curve is a simple
combination of the two. The fourth curve is the tree-growth, showing
fluctuations which admirably combine these two periods. All sub-
sequent analysis of these trees has entirely supported this result, as
shown in the periodograph work below. When the length of curve was
extended from 200 years to 500 years, the double solar period was
found to prevail through almost the entire length, but the triple period
does not appear to have affected the tree-growth in the earlier 300 years.
Two other plain examples of the double solar type are illustrated in
figures 36 and 37. The former gives the double cycle shown in a scat-
CYCLES.
105
tered group of trees of considerable age from the inner fjords and
mountains of Norway. The earlier half of the curve includes 6 trees
and the later half 8. The cycle beneath makes evident a well-developed
rhythm in these trees. Figure 37 shows a very regular double sun-spot
rhythm in the sequoias. There are many similar rhythms apparent
in the sequoias, but as yet little study has been made of them. This
one shows 80 years of the section D-12, whose identification was for a
noo
nso
1850
1300
1800
Years
FIG. 35. — Early curve of Arizona pines from 1700 to 1900 A. D. (No. 4), compared with double
and triple sunspot cycles combined (No. 3).
175O
1800
1850
I9OO
FIG. 36. — Double sunspot period in tree-growth at inner fjords of Norway;
lower curve a 22.8 year cycle.
2 1
2.80
300
10
20
Years
30
350
FIG. 37. — Double sunspot rhythm in sequoia, D-12 about 300 A. D.
(Material obtained in 1919 shows the dates in this figure to be too large by 27 years.)
long time uncertain on account of its complacent character and badly
compressed rings. The rhythmic character is so evident that no cycle
needs to be placed below the curve. The period is estimated at 20
to 22 years.
A triple solar cycle is shown in figure 38, giving the condensed curve
of a single 400-year-old Norwegian tree. The upper curve gives the
mean growth, and the lower curve is a simple 34-year cycle. The
rhythmic character of the growth was clearly seen in the measures
106
CLIMATIC CYCLES AND TREE-GROWTH.
immediately after their completion, and the period at once suggested
the Bruckner cycle of 35 years. This interesting tree has been men-
tioned on pages 34 and 41.
A 2-year cycle. — In the cross-identification of the trees used in this
investigation, a constantly recurring feature has been a marked alter-
nation in size of successive rings, giving them an appearance of being
arranged in pairs. In the plotted curves this produces a zig-zag or
see-saw effect. Usually such effect lasts a few years and then disap-
pears or reverses, but the example illustrated in figure 39 shows unusual
persistence. It is taken from D-22 from 750 B. C. to 660 B. C. The
even dates show less growth than the odd almost continuously for
60 years, but for the next 30 years the reverse is the case. This is
•mm.
- 1.5
I5OO
IfcOO
I70O
I8OO
I9OO
FIG. 38. — Triple sunspot cycle in a single tree from northern Norway.
Lower curve, a 34-year cycle.
evidently due to a short period of about 2 years in length. It has not
yet been fully studied, but it is prominent in the European groups and
in the Vermont group. It frequently shows a duration of a little less
than 7 years in one phase, with odd dates greater in growth than even
dates, and then for the next 7 years reverses its phase. This 14-year
cycle is the series of beats the 2-year cycle produces by interfering with
10 700
Year- B.C.
FIG. 39. — D-22 at 750 to 660 B. C., showing a 2-year period.1
the exact annual and biennial effects in the tree. Hence, by a simple
process, its length is found to be in effect frequently 21 or 28 months.
Comparison has been made with the rainfall records near the Vermont
group (Douglass, 1915 : 181) and a variable period has been found
!. The corrections found in 1919 make these dates one year earlier.
CYCLES. 107
averaging near the larger figure. It should more properly be called a
"broken" period perhaps, since it is made up of different periods for
different intervals, first one and then another predominating. The
methods used in the search for this 2-year period have revealed frequently
a solar cycle also, and there seems to be some obscure connection between
the two.
PERIODOGRAPH ANALYSES.
Differential patterns. — The periodograms, as already shown, indicate
the different cycles operating within a certain range. Any one cycle
together with others close to it may be studied more minutely on the
differential pattern produced when the instrument is set at the desired
period. Plates 12 and 10, B, are arranged to illustrate this and at the
same tune show the solar cycles in several of the groups. A periodic
effect equal in length to the setting of the instrument is indicated by a
vertical row of light crests or dark spaces. These rows may be seen in
any of the patterns. If the row of crests points downward to the
right, its period is greater than the setting of the instrument; if to the
left, the period is less. The straightness of the row indicates the
regularity of the period. Plate 12, Q, is made from the standard 5-year
period with a setting at 5.0 years. The first pattern in plate 12 shows
the regularity of the sunspot period since 1610 A. D. The interval in
the latter part of the eighteenth century, when the cycle was reduced
to less than 10 years, is distinguished by a bending of the row toward
the left. This is followed by a deflection toward the right during the
interval of readjustment from 1790 to 1830. The direction of any
row becomes an exact measure of its period.
If a period is constant, the row of crests is straight. A zigzag row
made up of short, straight parts means that one period after another
becomes predominant. A curved row means a constantly changing
period. Some examples of apparent curved rows may be picked out
in the sequoia pattern. A curved row may indicate some other func-
tion than a simple period. Pattern R in plate 12 is made to illustrate
a logarithmic variable, beginning at the top as a 5-year period and
changing by a constant percentage increase to a 10-year period at the
bottom. The instrument is set at 8.0 years.
The 11-year cycle. — The first 6 patterns in plate 12 illustrate this cycle.
The first gives the sunspot numbers from 1610 to 1910, including the
uncertain ones from 1610 to 1750. Pattern B gives the fine vertical
row shown by the 6 groups of trees from north Europe. This was
shown as a curve in figure 25, page 77. The qualitative test of the
entire 80 European trees is shown in pattern C. This may be seen as
a curve in figure 26. The small secondary maxima at several of the
minima show as light crests between the main rows. Pattern D shows
a 12-year period in south Sweden during the past 50 years, preceded by
108
CLIMATIC CYCLES AND TREE-GROWTH.
several maxima at about 8.5-year intervals. Pattern E gives the Ver-
mont analysis. The solar cycle shows well for the last 150 years, but
is preceded by a 9.2-year cycle for about 50 years, and then by the
solar cycle again. This tree curve is shown in figure 27, page 78.
The Arizona pines are given in pattern F. The double-crested solar
cycle shows in the larger part of it, but is best developed in the upper
and lower thirds. By sighting along these vertical rows, a dark line
in the upper third, indicating the more pronounced minimum, comes
in straight line with the lesser dark minimum line in the lower third,
indicating a transfer of emphasis from one-half of the 11 -year cycle to
the other half in passing the seventeenth century. This was noted
above in connection with the analysis of the same record by a series
of curves in figure 33, page 103. Further study of this pattern, how-
ever, gives information as to how and when that change took place.
Changes in the 11-year tree-cycle of Arizona — A careful examina-
tion of an early differential pattern of the Flagstaff tree record gave the
following probable history of the 11-year variation in Arizona:
TABLE 7. — Changes in the 11 -year tree-cycle of Arizona.
Years.
1395-1550
1550-1595
1595-1661
1661-1677
1677-1770
1770-1793
1793-1817
1817-1910
Period.
11.3
14.3
11.0=t0.5
16. 0(?)
12.5
9.0
11.6
Remarks.
Double crests throughout, except 1476 and
1487, where the second crest fails.
Heavy double crest.
Heavy single crests with trace of double
diminishing to small variable singles.
Possibly 1 long interval.
Double crests mostly; going to 10.8 from
1702 to 1722.
Sharp single crest continuing second crest
of preceding double.
Doubtful.
Rather broad, heavy crests, sometimes
double; 1864 has too little and 1875 too
much crest.
The interval from 1830 to the present time divides also extremely
well on a 21.0-year period, and fairly well in one of 7.3 years.
In obtaining this result no comparison was made with the sunspot
record. So the following is of interest:
TABLE 8. — Changes in tree and sunspot cycles compared.
Trees.
Sunspots.
Years.
Period.
Years.
Period.
1595-1661
11.0±0.5 years.
1615.5 to 1660.0
11.1 (?) years.
1661-1677
16(?)
1660.0 to 1675.0
15.0
1677-1770
12.5 mostly and 10.8
1675.0 to 1769.7
10.5
1770-1793
9.0
1769.7 to 1788.1
9.2
1793-1817
Doubtful.
1788.1 to 1816.4
14.15
1817-1910
11.6, 21.0, or 7.3
1816.4 to 1905
11.08
DOUGLASS
PLATE 12
DIFFERENTIAL PATTERNS.
rr.^Sunspot Nos. 1610-1910 at 11.4.
b. 57 European trees, 1830-1910 at 11.4.
80 European trees, 1800-1910 at 11.4.
South Sweden, 1830-1910 at 12.0.
Vermont group, 1650-1910 at 11.3.
Flagstaff group, 500 years at 11.4.
Flagstaff group at 23.5 years.
Norway, 1740-1910 at 23.8 years.
?'.f Austria, 1830-1910 at 22.0 years.
c.
d.
e.
f.
Norway, N-2, 400 years at 33.0.
Vermont, 250 years at 32.5.
Sweden, 1740-1910 at 37.0.
Sequoia, 1300-250 B. C. at 33.0.
Flagstaff, 500 years at 33.0.
Sequoia, 3200 years at 101.
Flagstaff, 500 years at 120.
q. Standard 5-year period at 5.0 years.
r. 5 to 10 year logarithmic variable
period at 8.0.
J-
k.
I.
m
o.
P.
CYCLES.
109
The agreement seems to the writer to justify the conclusion that
the tree record may indicate a possible sunspot period of 11.3 years
from 1400 to 1550 and of 14.3 from the latter date to 1600.
Sequoia pattern. — Pattern B in plate 10, opposite page 94, is naturally
the most interesting in respect to age, as it gives the sequoia analysis
for 3,200 years. The solar cycle subject to slight variations may be
dimly seen in large parts of it. It shows with some prominence during
the first 500 years of our era, then for a few hundred years near the
year 1000 A. D., and for a long interval in the first 500 years of the
record. There is opportunity for extensive study of these short periods,
interpreting them by the aid of more widely scattered groups and other
kinds of trees, and when possible by weather records.
5O
6O
I2O
130
lOO
90
9O
tOO
3O 4-Q 5O 6O 7O QO
FIG. 40. — Two differential patterns of Huntington's preliminary 2000-year sequoia record. The
most prominent cycle is about 105 years in length, shown in the upper diagram.
Other solar cycles. — Plate 12, G to p, shows the multiples of the solar
cycle. Pattern G gives the Arizona tree record analyzed at 23.5 years.
It shows a slightly irregular vertical row of crests. This is best seen by
tipping the pattern so that the eye views it from a low angle instead of
perpendicularly as in ordinary reading. A line slanting down to the
left giving a period at nearly 22.2 years would answer quite as well.
The lower third is somewhat broken by the triple sunspot period
showing in it. The same record is analyzed at 33.0 years in pattern
N. In this pattern the lower third shows the triple cycle in vertical
rows and the double cycle shows in rows slanting strongly down to the
left. Patterns H and I in plate 12 show the excellent double sunspot
110 CLIMATIC CYCLES AND TREE-GROWTH.
rhythm in the long Norwegian and shorter Austrian records, whose
curves were given in figures 36 and 24 respectively, pages 105 and 77.
Pattern J shows the 33-year cycle of the 400-year tree, N-2, from near
the Arctic Circle in Norway. The Vermont hemlocks are shown in
pattern K. Here is found a good rhythm with a change in phase about
100 years ago. The Swedish curve shows a good rhythm at 37 years.
Several intervals of triple solar cycle appear in the 1,000 years of early
sequoia growth in pattern M. All the 8 patterns G to A7 are taken
from special curves prepared on a one-fifth scale, using 5-year sums
in the plot.
The 100-year cycle. — Only two tree records are long enough to be
tested for a cycle of this length. The sequoia gives a very excellent
alinement at a period of 101 years, shown even better in the upper
pattern of figure 40. The pattern of the present plate shows an
increase to about 125 years in the last 600 years, which corresponds to
the best analysis of the 500-year Arizona curve. This latter is at 120
years as shown in pattern P. Both of these are made from special
curves plotted on one twenty-fifth of the usual scale.
Illustration by the periodograph.— The illustrations of periodograph
analysis given above are practically the first made with this instrument
and are therefore crude in many respects. Its advantage in the study
of simple and obvious cycles such as the sunspot numbers is not at
once apparent to the eye and its efficiency becomes evident only when
one tries to select the exact period and state its accuracy. But one can
foresee a useful application of this instrument in the study of mixed
periods, such as appear in tree-growth here considered or in rainfall
and other meteorological elements, a field as yet almost untouched on
account of its complexity. However, in the brief presentation of its
work given above, it is evident that the periodograph is found to
corroborate and extend the results of the previous direct study of
curves and to confirm the evidence there given of the great extent and
importance of the solar cycles in the growth of trees.
CLIMATIC CYCLES AND TREE-GROWTH. Ill
SUMMARY.
In the foregoing investigation the following conclusions have been
reached :
(1) The variations in the annual rings of individual trees over considerable
areas exhibit such uniformity that the same rings can be identified in nearly
every tree and the dates of their formation established with practical certainty.
(2) In dry climates the ring thicknesses are proportional to the rainfall
with an accuracy of 70 per cent in recent years and this accuracy presumably
extends over centuries; an empirical formula can be made to express still
more closely this relationship between tree-growth and rainfall; the tree records
therefore give us reliable indications of climatic cycles and of past climatic
conditions.
(3) The tree's years for such records begins in the autumn.
(4) Double rings are caused by spring drought and are indicative of the
distribution of rainfall throughout the year.
(5) Tree records may be used in the intensive study of the location of homo-
geneous meteorological conditions and in outlining meteorological districts.
(6) Certain areas of wet-climate trees in northern Europe give an admirable
record of the sunspot numbers and some American wet-climate trees give a
similar record, but with their maxima 1 to 3 years in advance of the solar
maxima. It is possible to identify living trees giving this remarkable record
and to ascertain the exact conditions under which they grow.
(7) Practically all the groups of trees investigated show the sunspot cycle
or its multiples; the solar cycle becomes more certain and accurate as the area
of homogeneous region increases or the time of a tree record extends farther
back ; this suggests the possibility of determining the climatic and vegetational
reaction to the solar cycle in different parts of the world.
(8) A most suggestive correlation exists in the dates of maxima and minima
found in tree-growth, rainfall, temperature and solar phenomena. The preva-
lence of the solar cycle or its multiples, the greater accuracy as area or time
are extended, and this correlation in dates point toward a physical connec-
tion between solar activity and terrestrial weather.
(9) The tree curves indicate a complex combination of short periods includ-
ing a prominent cycle of about 2 years.
(10) An instrument has been constructed which promises special facility
in the analysis of such periods.
The items enumerated above point to the general conclusion that
near at hand and readily available in our forest areas is written a story
of climatic cycles and solar relationship which in part at least is inter-
preted by the methods illustrated in the foregoing pages.
ADDENDUM.
In the summer of 1919 a trip was made to the sequoia groves with
three objects in view: (1) settling an uncertainty regarding the ring
provisionally called 1580 A ; (2) gathering material bearing on the relation
of short-period cycles to topography; (3) investigating the causes of
enlarged or gross rings. It is only the first of these topics which has
an important bearing on the foregoing chapters.
The region near the General Grant National Park was visited and
12 new trees were very carefully selected as to their water-supply,
drainage, and distance from other trees, and short radial samples
were cut from them. It did not seem necessary to have these include
more than the last 500 years of growth. The radial piece, therefore,
was made very small, but especial attention was given to procuring a
continuous and reliable record. Critical examination showed at once
that occurrence of the ring 1580 A was dependent on locality. The
trees from the uplands, where identification was easy, largely failed
to show the ring, but in specimens from swampy basins, where cross-
identification was difficult and sometimes uncertain, the ring was
nearly always present. A complete decision, therefore, in favor of
its real existence was satisfactorily obtained and the necessary correc-
tions were made in the foregoing text and in the tabular matter which
follows. It seems likely that the year 1580, which this ring repre-
sents, was phenomenally deficient in moisture in the locality of these
giant trees.
In addition to the 12 new trees added to the sequoia group, a
cutting was made from the stump D-12, which had hitherto defied all
attempts at satisfactory dating. A small piece going back about 800
years was cut from a part of the circumference, entirely free from
compressed rings, about 4 feet away from the full sample cut in 1915.
At the time of cutting, great care was taken to insure proper cross-
identification between the inner end of the new piece and the former
sample. But in the laboratory the new piece proved to carry a very
excellent series of rings and the identification was everywhere very easy
and sure, and all doubt about the dating of that particular tree to its
earliest ring in 135 A. D., several inches away from its original cen-
ter, was removed; therefore, it may now be included among those
whose dating is entirely reliable.
A new group of 5 very old trees from near Flagstaff, has settled an
uncertainty regarding the years 1463 and 1464 in the yellow pines
(too late, however, to rectify figure 3 on page 25). It is now possible
to carry a very fair cross-identification between the pines of Arizona
and the sequoias of California through the whole five centuries of the
former.
112
APPENDIX.
TABLES OF MEAN TREE-GROWTH, BY GROUPS.
The tables give the mean growth of the group for each year in
millimeters. The decade number in the left column applies to the
growth in the adjacent column, and the succeeding 9 years follow along
the horizontal line.
Flagstaff 500-year measures: 2 to 19 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1390
1.55
2.25
2.50
1.75
2.20
2.30
2.20
2.10
1400
2.55
2.75
2.00
2.10
1.95
1.90
2.30
1.50
2.35
1.65
1410
1.65
2.25
1.90
1.80
1.85
1.30
2.25
1.30
1.90
1.10
1420
0.80
0.70
0.90
1.90
1.45
1.40
1.20
1.35
1.55
1.80
1430
1.25
1.65
1.15
1.45
1.95
0.75
1.20
1.35
0.80
0.90
1440
1.35
1.25
0.60
0.65
1.40
1.10
1.00
1.05
0.95
1.60
1450
1.25
1.40
1.85
1.60
1.15
0.85
1.35
1.65
1.20
0.80
1460
0.80
1.25
1.75
1.40
0.55
0.95
1.40
1.45
1.10
1.60
1470
1.25
1.05
1.10
1.65
1.00
1.00
1.25
1.40
1.40
1.45
1480
1.20
1.10
1.35
1.00
1.05
0.60
1.05
0.40
0.60
1.05
1490
1.40
1.80
1.10
0.85
1.40
0.70
1.10
1.35
1.65
0.60
1500
0.40
1.55
1.15
0.70
1.35
0.80
0.50
1.25
1.10
1.05
1510
0.55
1.05
0.55
1.05
0.90
0.90
0.65
0.45
0.75
1.32
1520
1.06
0.96
0.72
0.96
0.98
1.36
1.56
1.22
0.82
1.50
1530
1.38
1.16
0.74
0.92
0.94
1.10
1.54
1.22
0.74
1.34
1540
1.50
1.40
0.86
1.14
1.32
1.00
1.62
1.28
1.10
1.72
1550
1.66
1.76
2.02
1.80
1.60
1.56
1.32
1.18
0.78
1.34
1560
1.48
1.34
1.72
1.84
1.70
1.68
1.20
1.30
1.94
1.80
1570
1.20
1.68
1.44
1.02
1.08
1.00
0.98
1.34
1.04
1.08
1580
0.78
1.18
1.34
1.26
0.36
0.22
0.88
1.30
1.76
1.76
1590
0.92
0.70
1.14
1.68
1.66
1.70
1.28
1.44
1.34
1.60
1600
0.34
0.84
0.96
1.44
1.22
1.20
1.38
1.14
1.20
1.72
1610
1.66
1.14
1.10
0.78
1.18
0.98
1.48
1.62
1.72
1.48
1620
1.78
1.60
1.22
0.70
1.04
1.18
0.88
0.90
0.80
1.08
1630
0.98
0.70
0.26
0.72
0.82
0.98
0.80
0.68
0.62
0.86
1640
1.16
0.90
1.08
1.02
1.04
0.84
0.76
0.76
0.60
0.78
1650
1.10
1.12
0.86
0.64
0.36
0.80
0.72
0.74
0.82
0.96
1660
0.94
0.96
0.96
1.24
0.86
0.92
0.68
0.68
0.64
0.46
1670
0.32
0.54
0.80
1.04
1.38
1.06
0.86
0.94
0.96
0.88
1680
1.26
1.26
0.74
1.04
0.72
0.74
0.62
1.00
1.00
1.06
1690
0.86
0.96
0.98
0.96
1.14
0.94
0.84
0.94
1.06
1.14
1700
1.18
1.08
0.98
0.86
1.28
1.30
1.48
0.74
0.94
1.02
1710
1.06
0.80
1.02
1.12
0.94
1.04
0.98
1.00
1.36
1.10
1720
1.24
0.82
0.86
1.12
0.98
1.40
1.40
0.62
0.64
0.42
1730
0.56
0.72
0.82
0.64
0.86
0.32
0.88
0.56
0.96
0.54
1740
0.82
0.80
0.76
0.90
0.74
0.78
1.06
0.84
0.40
0.86
1750
0.70
0.66
0.10
0.68
0.62
0.62
0.44
0.74
1.00
0.76
1760
0.80
0.92
0.90
0.88
1.22
0.94
0.86
0.86
0.68
0.66
1770
0.80
0.68
0.76
0.36
0.60
0.74
0.72
0.64
0.48
0.48
1780
0.36
0.52
0.32
0.74
1.02
0.50
0.60
0.86
0.54
0.50
1790
0.58
0.72
0.76
0.90
0.86
0.80
0.58
0.70
0.42
0.74
1800
0.58
0.44
0.78
0.56
0.50
0.78
0.78
0.54
0.58
0.80
1810
0.76
0.76
0.62
0.22
0.42
0.58
0.64
0.52
0.36
0.62
1820
0.36
0.62
0.04
0.46
0.48
0.50
0.72
0.68
0.74
0.42
1830
0.94
0.88
0.82
0.64
0.56
0.66
0.64
0.60
0.54
0.64
1840
0.60
0.44
0.30
0.56
0.52
0.34
0.42
0.36
0.66
0.56
1850
0.68
0.22
0.82
0.86
0.90
0.76
0.62
0.70
0.64
0.70
1860
0.88
0.52
0.74
0.62
0.62
0.56
0.86
0.64
0.94
0.62
1870
0.86
0.68
0.64
0.52
0.80
0.56
0.52
0.46
0.52
0.26
1880
0.34
0.44
0.36
0.36
0.42
0.46
0.32
0.40
0.48
0.46
1890
0.54
(0.47)
(0.35)
(0.35)
(0.45)
(0.40)
(0.54)
0.40
0.60
0.40
1900
0.40
0.54
0.20
0.36
0.20
0.32
0.42
(0.53)
(0.60)
(0.66)
1910
(0 73)
\ \J . • U J
113
114
CLIMATIC CYCLES AND TREE-GROWTH.
South of England: 11 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1850
3 1
1860
5.1
4.6
4.7
3.8
3.53
4.18
4.29
5.25
4.27
4.32
1870
3.65
5.19
5.21
4.32
4.34
4.87
4.04
3.79
4.94
4.72
1880
3.26
3.75
3.93
3.50
3.12
2.78
3.08
2.23
2.06
1.75
1890
2.41
1.74
1.81
1.81
2.30
2.22
2.06
1.83
1.48
1.45
1900
1.71
1.90
1.63
2.35
2.29
1.83
1.84
1.65
1.72
1.51
1910
2.28
1.71
1.65
Outer Coast of Nonvay: 10 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1820
0.75
0.62
1830
0.38
0.38
0.38
0.25
0.50
0.50
0.75
0.75
0.50
0.62
1840
0.50
0.75
0.75
0.88
1.38
1.53
1.57
1.68
1.44
1.47
1850
1.50
1.39
1.59
1.22
1.74
1.29
1.17
1.01
1.28
1.57
1860
1.57
1.24
1.26
1.28
1.27
1.40
1.54
1.52
1.85
1.77
1870
1.57
1.87
2.18
1.83
2.10
1.35
1.38
1.22
1.58
0.98
1880
1.25
0.73
1.11
1.14
1.64
1.09
1.29
1.20
1.17
1.27
1890
0.86
1.07
1.05
1.21
1.18
0.97
1.07
1.16
1.20
1.02
1900
0.85
0.90
0.69
1.14
1.24
1.34
1.20
1.05
1.13
0.66
1910
1.03
0.70
0.94
Inner Coast of Norway: 8 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1820
1.81
2.38
2.09
2.22
2.25
2.00
2.12
1.89
2.04
1.88
1830
2.00
1.89
1.72
2.01
1.80
1.45
1.30
1.64
1.81
1.65
1840
1.60
1.78
1.92
2.15
2.08
1.94
1.94
1.81
1.81
1.81
1850
1.71
1.66
1.79
1.40
1.69
1.58
1.40
1.54
1.49
1.22
1860
1.56
1.31
1.52
1.65
1.62
1.68
1.74
1.65
1.66
1.34
1870
1.56
1.26
1.38
1.44
1.75
1.60
1.48
1.76
2.16
1.68
1880
1.89
1.34
1.52
1.38
1.36
1.29
1.25
1 22
1.34
1.36
1890
1.44
1 .44
1.51
1.45
1.79
1.30
1.10
1.05
1.08
1.00
1900
0.95
1.19
1.14
1.30
1.29
1.20
1.10
1.00
1.14
Christiania: 5 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1820
1.12
1.06
1.10
1.10
1.16
1.10
1.60
1.54
1.60
1.48
1830
1.28
1.12
0.94
0.86
0.96
1.12
1.22
1.20
1.08
1.68
1840
1.52
1.70
2.32
1.76
1.82
1.58
1.36
1.44
1.66
1.40
1850
1.54
1.60
1.36
1.26
1.72
1.36
1.20
1.32
1.32
1.52
1860
1.66
1.48
1.58
1.40
1.72
1.52
1.58
1.50
1.96
1.94
1870
2.00
1.60
1.14
1.50
1.62
1.64
1.20
1.68
1.84
1.18
1880
1.70
1.84
2.10
1.86
2.26
2.12
2.08
1.88
1.42
1.42
1890
1.24
1.10
1.28
1.62
1.60
1.48
1.56
1.44
1.14
1.22
1900
1.14
1.24
1.00
1.36
1.16
1.30
1.36
1.28
1.86
1.88
1910
2.68
2.36
2.34
APPENDIX.
115
Central Sweden: 12 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1820
0.92
0.92
1.05
1.08
1.16
0.98
1.12
1.08
1.12
0.84
1830
0.97
0.92
0.74
0.93
1.04
0.65
0.72
0.72
0.72
0.69
1840
0.71
0.65
0.78
0.71
0.77
0.66
0.72
0.62
0.81
0.77
1850
0.78
0.70
0.66
0.46
0.73
0.62
0.82
0.89
0.98
1.12
1860
1.30
1.14
1.04
1.04
0.96
0.95
1.02
0.87
1.09
0.97
1870
1.28
1.03
1.02
0.85
0.88
0.87
0.87
0.86
0.93
0.76
1880
0.84
0.66
0.86
0.68
0.77
0.88
0.84
0.88
0.76
0.74
1890
0.74
0.76
0.81
0.78
0.92
0.89
0.92
0.77
0.62
0.70
1900
0.67
0.74
0.50
0.59
0.58
0.53
0.51
0.47
0.47
0.46
1910
0 55
South Sweden: 6 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1820
1.90
1.75
1.85
1.98
2.15
2.25
1.78
1.82
1.58
1.72
1830
2.37
2.37
1.68
1.83
1.95
1.58
1.55
1.58
1.85
1.87
1840
1.93
2.07
1.82
1.23
1.35
1.27
1.45
1.02
1.87
1.38
1850
1.25
1.23
1.23
1.20
1.08
1.48
1.20
1.28
1.42
1.35
1860
1.35
1.28
1.68
1.65
1.35
1.43
1.42
1.07
1.42
1.23
1870
1.45
1.37
1.32
1.08
1.00
1.03
0.95
0.93
1.03
1.02
1880
1.23
1.12
1.38
1.02
1.28
1.02
0.90
0.72
0.82
0.78
1890
0.72
0.88
0.88
1.03
1.02
0.90
0.97
0.92
0.87
0.70
1900
0.78
0.93
0.68
0.77
0.63
0.72
0.73
0.77
0.82
0.80
1910
0 70
Eberswalde, Prussia: IS trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1830
2.70
2.56
2.78
2.26
2.52
2.38
2.79
3.22
3.74
3.04
1840
2.63
2.38
1.56
2.11
2.55
2.06
2.55
1.82
2.82
2.88
1850
2.08
2.15
1.55
1.96
1.66
1.05
1.06
0.87
1.28
1.92
1860
1.98
2.15
1.88
1.51
1.49
1.40
1.22
1.68
1.33
1.54
1870
1.59
1.58
1.52
1.16
1.35
1.46
1.25
0.83
1.25
1.23
1880
1.12
1.31
2.13
1.47
2.06
1.68
1.29
1.05
0.99
0.91
1890
1.12
1.37
0.97
0.85
0.55
0.63
0.79
0.63
0.78
0.73
1900
0.69
0.62
0.73
1.17
1.03
1.12
0.91
0.93
0.57
0.42
1910
0 47
0 35
0 58
Pilsen, Austria: 7 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1830
4.03
3.99
2.74
3.60
3.49
2.59
2.06
3.36
2.47
2.43
1840
2.79
3.01
1.66
2.29
2.66
1.63
2.17
1.64
1.34
0.89
1850
1.13
1.54
1.50
1.60
1.59
1.54
1.70
1.06
1.33
1.23
1860
1.44
1.31
1.54
1.43
0.74
0.99
1.27
1.39
0.99
1.20
1870
1.09
1.29
1.44
1.19
0.87
1.14
1.30
1.14
1.51
1.24
1880
1.50
1.37
1.70
1.56
1.70
1.33
1.37
0.93
1.00
0.87
1890
1.17
1.16
1.26
1.16
1.31
1.41
1.49
1.70
1.40
1.50
1900
1.47
1.40
1.20
1.19
0.97
1.04
1.09
1.04
0.89
1.03
1Q10
1 23
0 91
1 31
116
CLIMATIC CYCLES AND TREE-GROWTH.
Southern Bavaria: 8 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1840
3.20
3.42
1850
3.36
3.71
3.31
3.64
3.41
2.80
2.62
2.42
2.14
1.95
1860
1.91
2.35
2.38
1.98
1.90
1.08
1.38
1.28
1.35
1.42
1870
1.09
1.75
1.71
1.62
1.39
1.39
1.52
1.58
1.68
1.66
1880
1.65
1.55
1.50
1.44
1.26
1.05
1.00
0.92
1.09
0.96
1890
1.11
0.99
1.04
0.76
0.81
0.96
0.95
0.96
0.95
0.72
1900
0.81
0.82
0.74
0.86
0.90
0.81
1.02
1.19
0.92
0.66
1910
0.79
0.76
Six old Norway trees: Group A; inner coast.
A. D.
0
1
2
3
4
5
6
7
8
9
1740
1.10
0.98
0.82
0.84
0.78
1.00
1.03
1.40
1.30
1.25
1750
1.52
1.35
1.73
1.55
2.07
1.83
1.15
1.85
1.55
1.45
1760
1.77
1.48
1.20
1.30
1.11
0.98
1.45
1.43
1.60
1.52
1770
1.30
1.52
1.48
1.45
1.42
1.95
1.80
1.75
1.47
1.43
1780
1.43
1.30
0.97
0.87
0.82
0.78
0.68
0.82
0.72
0.80
1790
0.97
1.02
1.23
1.02
0.97
1.08
1.22
1.07
1.35
1.50
1800
2.03
1.70
1.35
1.27
1.08
1.23
1.33
1.15
1.17
1.02
1810
1.00
0.82
0.90
1.28
1.32
1.22
1.13
1.58
1.23
1.18
1820
1.73
2.05
1.77
1.67
1.82
1.63
2.02
1.82
2.00
1.77
1830
1.73
1.84
1.80
1.88
1.64
1.28
Eight old Sweden trees; Group B; Dalarne.
A. D.
0
1
2
3
4
5
6
7
8
9
1740
0.70
0.54
0.54
0.73
0.85
0.90
0.87
0.90
1.00
0.87
1750
1.09
0.90
1.07
0.79
0.80
0.78
0.55
0.61
0.65
0.87
1760
0.80
0.86
1.00
0.92
0.87
0.90
0.99
0.95
0.92
0.76
1770
0.62
0.66
0.71
0.75
0.68
0.82
0.88
0.90
0.93
0.97
1780
0.89
0.86
0.92
0.89
0.95
0.86
0.79
0.86
0.81
0.68
1790
0.68
0.78
0.67
0.62
0.68
0.59
0.68
0.63
0.63
0.63
1800
0.56
0.52
0.61
0.55
0.58
0.58
0.52
0.60
0.57
0.59
1810
0.58
0.65
0.71
0.74
0.71
0.73
0.68
0.73
0.81
0.79
1820
0.66
0.63
0.66
0.66
0.75
0.61
0.81
0.75
0.82
0.65
1830
0.62
0.65
0.55
0.70
0.79
0.55
Windsor, Vermont; 11 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1650
0.6
0.8
0.7
0.72
0.47
1.03
0.77
0.67
0.75
1660
0.68
0.62
0.28
0.38
0.45
0.35
0.55
0.40
0.28
0.53
1670
0.22
0.38
0.29
0.35
0.45
0.37
0.40
0.39
0.50
0.48
1680
0.57
0.52
0.38
0.35
0.40
0.37
0.42
0.41
0.49
0.72
1690
0.76
0.40
0.57
0.73
0.73
1.06
0.79
0.65
0.57
0.72
1700
0.67
0.64
0.54
0.50
0.26
0.20
0.34
0.36
0.37
0.45
1710
0.37
0.47
0.49
0.45
0.60
0.47
0.66
0.75
1.03
0.84
1720
0.70
0.90
0.83
0.57
0.88
0.99
0.92
1.15
0.79
0.68
1730
0.87
0.89
0.54
0.51
0.66
0.69
0.68
0.60
0.67
0.56
1740
0.51
0.34
0.47
0.37
0.52
0.65
0.56
0.72
0.41
0.47
1750
0.55
0.71
0.76
0.62
0.53
0.51
0.81
1.04
0.92
1.12
APPENDIX.
117
Windsor, Vermont; 11 trees — continued.
A. D.
0
1
2
3
4
5
6
7
8
9
1760
1.12
0.96
0.73
0.78
1.00
1.05
0.65
0.62
0.74
0.91
1770
0.44
0.45
0.53
0.54
0.59
0.58
0.67
0.81
0.86
0.80
1780
0.67
0.77
0.86
0.75
0.51
0.53
0.74
0.60
0.71
0.81
1790
0.57
0.54
0.58
0.69
0.63
0.69
0.61
0.50
0.46
0.47
1800
0.66
0.82
0.72
0.77
0.61
0.96
0.82
1.25
1.94
2.02
1810
1.96
2.09
1.95
1.85
1.75
1.86
1.47
1.46
1.28
1.43
1820
1.21
0.79
2.06
1.81
2.41
1.88
1.40
2.05
2.62
2.18
1830
2.56
2.66
2.17
2.71
2.65
1.85
1.62
1.74
2.26
1.85
1840
2.00
1.75
1.51
1.70
2.07
1.95
1.90
2.11
2.06
1.74
1850
1.77
2.33
1.66
1.36
1.39
1.50
1.70
1.77
1.99
1.45
1860
1.63
2.12
1.37
1.76
1.61
1.79
1.78
1.75
2.33
1.55
1870
1.67
1.32
1.25
1.04
1.76
1.73
1.49
1.21
1.97
1.58
1890
2.23
1.68
1.97
1.15
1.68
0.93
1.49
1.73
1.50
2.37
1890
2.04
2.31
2.76
2.11
2.75
1.23
1.38
2.01
2.11
1.06
1900
1.19
1.35
1.61
1.79
1.43
1.38
1.39
1.25
1.13
1.20
1910
1.51
0.95
1.76
Oregon group; 17 trees.
A. D.
0
1
2
3
4
5
6
7
8
9
1710
4.21
4.04
3.91
4.30
4.44
4.81
5.21
4.30
3.63
4.38
1720
4.57
4.08
4.31
4.10
4.06
4.21
3.84
3.84
3.62
3.67
1730
3.69
3.39
3.63
3.49
3.14
2.80
2.89
2.74
2.97
3.46
1740
2.34
2.19
2.02
2.16
2.29
2.17
1.91
2.09
2.14
2.36
1750
2.29
2.57
2.52
2.67
2.17
1.92
2.00
1.98
1.90
1.99
1760
2.33
2.18
2.33
2.28
2.49
2.18
2.27
2.33
2.26
2.32
1770
2.69
3.16
3.15
3.01
3.32
2.85
3.22
2.84
3.04
3.25
1780
3.15
3.23
2.72
2.52
2.62
3.05
3.58
3.35
2.58
3.28
1790
2.74
2.46
2.59
2.74
3.00
2.78
2.59
2.36
2.29
2.50
1800
2.45
2.44
2.57
2.61
2.65
2.81
2.97
2.52
2.57
2.31
1810
2.37
2.31
2.06
2.11
2.35
2.71
2.77
2.62
2.48
2.54
1820
2.99
2.72
1.96
2.36
2.10
2.38
2.37
2.54
2.22
2.05
1830
2.19
2.21
2.06
2.80
2.72
2.29
2.53
2.15
2.21
2.35
1840
2.22
2.00
1.82
1.88
1.52
1.86
2.08
2.42
1.93
1.94
1850
1.33
1.66
1.74
1.75
1.76
1.84
2.05
2.11
1.93
1.77
1860
1.88
2.24
2.32
1.84
1.92
1.81
1.76
1.88
2.31
2.01
1870
1.76
1.61
1.56
1.60
1.66
1.75
2.07
2.08
2.13
2.15
1880
2.12
1.88
1.62
1.50
1.08
1.09
1.16
1.44
1.34
1.88
1890
1.54
1.25
1.62
1.84
1.68
1.68
1.48
1.19
0.98
1.62
1900
1.54
1.89
1.78
1.61
1.87
1.77
1.31
1.28
1.39
1.34
1910
1.11
1.11
Sequoia record: Group of 1918; 1 to 4 trees.
B. C.
0
9
8
7
6
5
4
3
2
1
1310
ll.W
2.90
2.50
1.50
2 40
2 60
1300
2.45
1.40
1.30
1.25
1.25
1.00
0.90
1.30
1.20
1.30
1290
1.50
1.40
1.45
1.15
1.10
0.95
0.90
1.00
0.90
0.85
1280
1.15
1.20
1.05
1.20
1.00
0.75
0.60
0.75
0.65
0.90
1270
0.65
0.40
0.55
0.55
0.50
0.70
0.90
0.55
0.55
0.80
1260
0.90
0.55
0.70
0.80
0.80
0.95
1.05
0.60
0.50
0.45
1250
0.70
0.70
0.60
0.70
0.80
0.80
0.60
0.90
0.70
0.60
1240
0.70
0.45
0.75
0.85
1.15
0.85
0.90
1.00
0.90
1.15
1230
1.25
1.35
1.40
1.40
1.55
2.10
2.20
2.85
3.45
3.10
1 1306 B. C. is incomplete.
118
CLIMATIC CYCLES AND TREE-GROWTH.
Sequoia record: Group of 1918; 1 'to 4 trees — continued.
B. C.
0
9
8
7
6
5
4
3
2
1
1220
3.25
3.45
2.85
3.00
3.50
3.65
4.55
3.50
3.80
3.35
1210
3.35
3.95
3.10
4.20
4.00
3.90
2.95
2.75
3.20
2.20
1200
2.50
3.20
2.80
3.35
3.75
3.25
2.85
3.35
3.35
4.30
1190
3.35
2.90
3.65
3.95
3.95
3.05
3.05
3.00
3.45
4.25
1180
4.10
3.95
4.00
3.10
3.25
3.75
4.40
3.70
5.00
4.20
1170
3.60
3.10
2.50
2.85
3.65
4.10
3.15
3.50
3.10
2.40
1160
2.30
2.65
2.80
3.10
2.65
2.30
2.30
2.30
3.15
2.50
1150
2.20
2.55
3.10
3.05
3.80
2.85
2.75
2.80
2.80
3.10
1140
3.25
2.50
2.50
2.75
2.65
2.90
3.50
3.15
2.40
2.35
1130
2.80
2.45
3.00
2.75
2.55
3.50
3.25
2.35
2.18
2.59
1120
2.26
2.12
2.09
1.71
1.86
2.04
2.09
2.54
1.76
2.06
1110
1.72
1.99
2.42
2.23
1.98
1.90
1.55
1.85
2.04
2,23
1100
2.15
2.30
2.58
2.53
2.42
1.84
1.99
1.93
2.32
2.14
1090
1.55
1.67
1.78
1.69
1.91
1.78
1.62
1.44
1.59
1.68
1080
1.68
1.66
1.51
1.64
1.48
1.77
1.88
2.72
2.71
2.66
1070
2.04
2.76
1.01
1.08
1.30
0.97
1.18
1.14
1.34
1.43
1060
1.34
1.38
1.22
1.32
1.74
1.76
1.77
1.54
1.31
1.13
1050
1.34
1.31
1.53
1.69
1.63
1.41
1.45
1.60
1.59
1.31
1040
1.79
1.41
1.45
1.27
1.23
1.25
1.29
1.01
1.68
1.68
1030
1.66
1.92
1.65
1.74
1.53
1.56
1.50
1.19
1.09
1.33
1020
0.99
1.22
1.27
1.24
1.67
1.33
1.66
1.92
2.12
2.10
1010
1.87
1.64
1.22
1.29
1.12
1.08
1.24
1.44
1.39
1.33
1000
1.29
1.28
1.28
1.20
1.24
1.24
1.29
1.65
1.31
1.29
990
1.24
1.29
1.19
1.34
1.39
1.28
1.21
1.24
1.10
1.15
980
1.06
1.14
1.00
1.38
1.21
1.25
1.12
1.20
1.24
1.32
970
1.37
1.27
1.30
1.04
1.27
1.24
1.16
1.20
1.36
1.18
960
1.25
1.30
1.32
1.43
0.76
0.83
1.03
0.93
1.10
1.07
950
1.35
1.56
1.55
1.30
1.32
1.64
1.43
1.83
1.51
1.38
940
1.44
1.16
1.50
1.37
1.63
1.91
2.35
2.20
2.17
1.74
930
2.09
2.79
3.23
2.66
1.77
2.06
1.76
1.78
2.13
1.85
920
2.14
2.02
1.69
1.71
1.70
1 .22
1.46
1.71
1.88
1.64
910
1.86
1.87
2.18
1.72
1.44
1.77
1.92
1.82
1.80
1.87
900
2.25
2.35
2.29
1.98
2.10
2.37
2.32
2.07
2.45
2.10
890
1.89
1.96
1.94
1.95
2.40
2.18
2.12
2.24
2.33
1.95
880
2.17
2.29
2.48
2.13
2.11
2.33
1.99
1.77
1.83
1.67
870
1.62
1.72
2.17
1.58
1.43
1.19
1.31
1.36
1.30
1.38
860
1.30
1.42
1.33
1.25
1.14
1.13
1.09
1.15
1.11
0.74
850
1.02
1.23
1.14
1.07
1.04
1.39
1.32
1.45
1.42
1.58
840
1.32
1.51
1.54
1.40
1.40
1.36
1.40
1.43
1.44
1.28
830
1.57
1.51
1.28
1.16
1.57
1.65
1.54
1.32
1.22
1.26
820
1.06
1.12
1.11
0.97
0.97
1.00
0.98
1.11
1.00
1.01
810
1.15
1.25
1.30
1.04
1.18
1.10
0.88
1.07
1.13
1.20
800
1.10
1.18
1.27
1.20
1.14
1.26
1.26
1.26
1.08
1.26
790
1.10
1.04
1.19
1.07
1.16
1.21
1.02
1.08
1.08
1.10
780
1.03
1.21
1.16
0.92
0.91
1.12
1.23
1.08
0.89
1.03
770
1.06
1.25
1.07
1.02
1.12
1.14
1.09
1.28
1.17
1.31
760
1.27
1.22
1.41
1.04
1 22
1.12
1.08
1.06
1.23
1.27
750
1.27
1.35
1.38
1.12
1.15
1.59
1.37
1.10
1.44
1.48
740
1.53
1.33
1.30
1.25
1.46
1.29
1.32
1.30
1.47
1.28
730
1.26
1.40
1.62
1.46
1.17
1.23
1.49
1.38
1.21
0.94
720
1.52
1.46
1.39
1.02
1.19
1.20
1.34
1.30
1.22
1.44
710
1.37
1.43
1.58
1.52
1.72
1.32
1.51
1.26
1.60
1.33
700
1.82
1.56
1.30
1.43
1.45
1.66
1.40
1.45
1.79
1.81
690
1.78
1.75
1.79
1.78
1.36
1.46
1.42
1.52
1.28
1.40
680
1.21
1.26
1.09
1.41
1.25
1.30
1.44
1.63
1.28
1.51
670
1.25
1.38
1.06
1.20
1.30
1.25
1.34
1.70
1.44
1.15
660
1.35
1.20
1.22
1.01
0.96
1.13
1.44
1.36
1.20
1.32
650
1.18
1.22
0.86
1.18
0.97
1.03
1.12
0.98
1.01
1.14
640
1.14
1.32
1.17
1.08
1.12
1.18
1.16
1.14
1.04
0.94
630
1.22
1.02
0.98
1.02
1.00
1.24
1.21
1.18
1.10
1.39
620
1.24
1.22
1.26
1.13
1.13
1.20
1.22
1.08
1.08
1.19
610
1.08
0.90
1.02
0.95
1.07
1.15
1.05
1.04
0.96
1.21
APPENDIX.
119
Sequoia record: Group of 1918, 1 to 4 trees — continued.
B. C.
0
9
8
7
6
5
4
3
2
1
600
1.25
1.20
0.95
1.10
0.90
0.90
1.05
1.08
0.94
0.99
590
0.94
1.06
0.83
0.82
0.97
0.92
0.60
0.64
0.45
0.68
580
0.83
0.96
0.75
0.78
0.96
0.80
0.82
0.83
0.90
0.86
570
0.76
1.02
0.91
0.74
0.86
0.93
0.93
0.86
0.78
0.81
560
0.66
0.80
0.82
0.95
0.88
0.95
0.96
1.11
1.03
1.10
550
1.21
1.44
1.38
1.32
1.29
1.26
1.10
1.18
1.34
1.19
540
1.10
0.94
1.07
0.76
0.79
0.89
0.66
0.77
1.05
1.04
530
1.00
0.88
0.90
1.01
0.81
0.90
0.80
0.82
0.88
0.94
520
0.60
0.74
1.01
0.99
0.93
0.92
0.83
0.87
0.50
0.96
510
1.08
0.96
0.91
1.02
1.06
1.12
1.04
1.01
1.10
1.29
500
0.98
1.00
1.01
0.89
0.90
1.10
1.10
1.09
1.02
0.91
490
1.14
1.10
1.06
1.03
0.90
0.92
1.00
0.94
1.05
1.12
480
1.17
1.12
1.10
1.11
1.22
1.04
1.08
0.88
0.82
0.90
470
0.91
1.03
0.99
1.01
1.16
0.76
0.96
0.80
0.82
0.94
460
0.96
0.91
0.79
0.84
0.79
0.90
0.84
0.82
0.69
0.86
450
0.84
0.60
0.66
0.79
0.83
0.86
0.77
0.78
0.86
0.77
440
0.84
0.94
0.94
0.78
0.79
0.80
0.80
1.02
1.09
1.12
430
1.16
0.81
0.97
0.86
0.82
0.75
0.88
0.69
0.63
0.58
420
0.90
0.60
0.73
0.83
0.58
0.77
0.88
0.78
0.74
0.84
410
0.89
0.59
0.82
0.90
1.05
0.93
0.82
0.90
0.83
0.83
400
0.83
0.75
0.80
0.67
0.66
0.55
0.71
0.75
0.58
0.78
390
0.90
0.74
0.66
0.77
0.80
0.76
0.69
0.99
0.83
0.80
380
0.75
0.95
1.02
0.99
1.04
0.91
0.95
0.88
0.92
1.09
370
1.00
1.00
0.90
0.97
0.92
1.01
0.87
0.81
0.67
0.87
360
0.93
0.90
0.79
0.87
0.81
0.84
0.82
0.76
0.71
0.72
350
0.66
0.68
0.69
0.73
0.82
0.69
0.73
0.70
0.59
0.73
340
0.71
0.77
0.72
0.74
0.69
0.61
0.78
0.84
0.84
0.60
330
0.68
0.67
0.72
0.68
0.54
0.70
0.38
0.54
0.64
0.85
320
0.86
0.83
0.79
0.93
0.98
0.93
0.94
0.90
0.93
0.88
310
0.82
0.69
0.72
0.87
0.86
0.89
0.97
0.78
0.88
0.84
300
0.92
0.88
0.93
0.95
0.74
0.84
0.78
0.72
0.81
0.73
290
0.82
0.86
0.69
0.76
0.82
0.73
0.70
0.85
0.83
0.62
280
0.70
0.81
0.66
0.84
0.87
0.72
0.72
0.72
0.65
0.70
270
0.65
0.70
0.84
0.77
0.70
0.74
0.72
0.68
0.67
0.86
260
0.82
0.74
0.64
0.64
0.78
0.69
0.69
0.71
0.72
Sequoia record: Group of 1915; 11 trees.
B. C.
0
9
8
7
6
5
4
3
2
1
280
3.82
4.38
3.78
2.87
270
2.96
2.59
2.73
2.55
0.84
2.85
2.27
2.70
2.76
3.56
260
3.16
3.08
3.71
2.92
2.54
2.41
2.20
2.16
2.37
2.73
250
2.66
2.47
2.13
2.32
1.67
1.29
0.87
1.42
1.72
1.83
240
1.53
1.52
1.61
1.15
1.09
0.63
1.19
1.19
1.51
1.05
230
1.30
1 .22
1.29
1.22
1.12
1.48
1.55
1.40
1.06
1.35
220
1.55
1.52
1.64
1.75
1.26
1.21
1.25
1.65
2.06
1.77
210
2.33
2.11
2.02
2.71
2.88
2.40
2.58
2.23
1.82
2.16
200
2.19
2.23
2.40
2.61
2.35
2.38
2.62
2.72
2.02
2.28
190
3.10
2.85
2.80
3.15
3.01
2.98
2.17
2.48
1.92
1.86
180
2.33
2.78
2.44
2.20
2.50
2.59
2.35
2.40
2.11
1.97
170
1.77
2.00
1.52
2.51
2.96
2.89
1.89
1.93
1.47
1.76
160
1.20
1.10
1.42
1.77
2.02
2.00
2.20
2.14
1.90
2.87
150
2.26
2.28
2.74
2.58
2.60
2.36
2.34
2.06
2.66
1.70
140
2.78
2.54
2.25
2.42
2.28
2.07
2.20
2.34
2.36
2.52
130
2.00
2.01
2.18
2.44
2.04
2.18
1.87
2.00
2.23
2.23
120
2.20
2.48
2.66
2.34
2.16
2.29
2.54
2.33
2.15
2.28
110
2.64
2.66
2.33
2.24
2.85
2.55
2.44
2.16
2.21
1.91
100
1.62
2.08
2 22
1.96
1.85
1.75
1.65
1.85
1.90
1.80
120
CLIMATIC CYCLES AND TREE-GROWTH.
Sequoia record: Group of 1915; 11 trees — continued.
B. C.
0
9
8
7
6
5
4
3
2
1
90
1.74
1.80
1.89
1.68
1.68
1.56
1.80
1.37
1.92
2.27
80
2.34
2.16
2.25
2.17
2.00
2.63
2.16
2.08
2.16
2.27
70
2.26
1.85
2.20
2.13
2.18
1.87
2.43
2.22
1.64
1.70
60
2.22
2.35
2.48
2.52
2.00
1.90
1.89
1.58
1.54
1.85
50
1.75
1.58
1.42
1.31
1.24
1.60
1.81
1.78
1.72
1.66
40
1.75
1.64
1.59
1.59
1.70
1.68
1.57
1.35
1.53
2.14
30
1.86
1.71
1.50
1.62
1.50
1.54
1.34
1.62
1.79
1.38
20
1.78
1.38
1.46
1.71
1.44
1.70
1.23
1.23
1.04
1.24
10
1.44
0.98
1.38
1.52
1.44
1.42
1.40
1.29
1.56
1.60
A. D.
0
1
2
3
4
5
6
7
8
9
0
1.68
1.58
1.70
1.93
1.83
1.56
1.67
1.24
1.39
1.65
10
1.92
1.60
1.30
1.21
1.33
0.89
1.24
1.72
1.96
1.58
20
1.57
1.68
1.74
1.80
1.71
1.82
1.83
1.78
2.01
1.94
30
1.87
1.76
1.76
1.74
1.80
2.06
2.39
1.74
1.69
2.00
40
2.11
1.75
1.83
1.64
1.88
2.06
2.00
1.72
1.60
1.61
50
1.44
1.27
1.19
1.40
1.44
1.45
0.98
1.00
1.42
1.54
60
1.21
1.17
1.26
1.09
1.03
1.23
1.38
1.31
1.36
0.86
70
1.42
1.20
1.49
1.55
1.41
1.33
1.25
1.21
1.27
1.32
80
1.28
1.59
1.52
1.48
1.54
1.77
1.48
1.38
1.50
1.44
90
1.50
1.42
1.46
1.35
1.15
1.15
1.25
1.33
1.06
1.23
100
0.86
1.25
1.11
1.18
1.17
1.14
0.80
1.17
0.99
0.44
110
1.04
1.28
1.82
1.85
1.26
1.16
1.26
1.38
1.31
1.38
120
1.13
1.07
1.20
1.06
0.99
1.05
1.05
1.06
0.92
1.13
130
0.98
0.96
0.92
0.90
0.92
0.93
1.19
1.14
1.12
1.07
140
1.02
1.00
0.93
1.10
1.10
1.10
1.12
1.14
1.27
1.12
150
1.01
0.98
0.59
0.99
1.16
0.92
1.19
0.93
1.08
1.10
160
0.93
0.98
1.04
1.24
1.02
1.04
1.06
0.79
0.54
0.55
170
0.81
0.99
0.79
0.74
1.00
1.20
1.01
1.17
0.87
0.91
180
0.98
0.86
1.15
1.02
1.00
1.13
1.12
1.16
0.98
0.49
190
0.87
1.29
1.52
1.59
1.47
1.40
1.35
1.42
1.28
1.39
200
1.25
1.42
1.37
1.58
1.58
1.81
1.68
1.19
1.18
1.30
210
1.40
1.40
1.28
1.11
1.06
1.07
1.30
1.06
1.98
0.94
220
0.82
1.10
1.09
1.04
1.10
0.90
0.77
1.00
1.15
0.92
230
0.93
Q. 94
1.10
1.09
1.03
1.06
0.66
0.99
0.98
0.75
240
0.98
1.07
0.88
0.91
1.02
0.94
1.06
1.04
0.98
0.97
250
1.00
0.89
0.95
0.82
0.96
0.90
0.74
0.81
0.80
0.91
260
1.02
1.00
0.92
0.97
1.01
0.95
0.89
1.02
1.03
1.01
270
0.84
0.61
0.92
0.92
0.60
0.90
0.84
0.96
0.91
0.88
280
1.04
0.85
0.95
0.98
0.94
0.88
0.98
0.96
0.92
0.99
290
1.08
1.10
0.74
0.87
0.85
1.14
0.96
0.84
1.14
0.98
300
0.91
1.08
1.00
1.03
0.96
0.56
0.60
0.76
0.87
0.96
310
0.98
1.09
0.92
0.60
1.02
0.89
0.85
0.91
1.04
0.85
320
0.92
0.82
0.99
0.86
0.89
0.87
0.83
0.85
1.04
0.78
330
0.78
0.84
0.78
0.46
0.68
0.88
0.76
0.82
0.80
0.68
340
0.62
0.75
0.91
0.81
0.54
0.78
0.74
0.82
0.97
0.68
350
1.04
0.86
0.90
0.78
0.93
0.88
0.88
0.72
0.98
0.89
360
0.91
0.80
1.00
1.05
1.21
1.12
1.35
1.32
1.07
0.74
370
0.81
1.08
1.23
1.47
1.73
1.79
1.56
1.08
1.34
1.68
380
1.83
1.89
1.95
1.82
1.79
1.75
1.13
1.30
1.60
1.62
390
1.59
1.64
1.54
1.63
1.66
1.60
1.40
1.44
1.26
1.31
400
1.79
1.92
1.88
1.53
1.43
1.76
1.77
1.62
1.61
1.68
410
1.68
1.83
1.73
1.68
1.52
1.81
2.03
1.91
1.90
2.09
420
2.19
1.92
1.92
1.82
1.64
1.76
2.14
2.34
2.19
2.12
430
2.07
1.92
1.79
1.66
1.78
1.66
1.90
1.80
1.59
1.62
440
1.68
1.89
1.27
1.55
1.58
1.89
1.69
1.48
1.20
1.39
450
1.37
1.24
1.18
1.21
1.28
1.34
1.59
1.60
1.44
1.36
460
1.38
1.32
1.26
1.35
1.30
1.39
1.21
1.29
1.29
1.30
470
1.50
1.47
1.29
1.41
1.23
1.56
1.52
1.27
1.48
1.65
480
1.57
1.61
1.67
1.73
1.76
1.66
1.70
1.68
1.54
1.76
APPENDIX.
121
Sequoia record: Group of 1915; 11 trees — continued.
A. D.
0
1
2
3
4
5
6
7
8
9
490
1.48
1.47
1.60
1.52
1.76
1.92
1.94
1.51
1.50
1.88
500
1.55
1.48
1.44
1.61
1.85
1.70
1.52
1.31
1.47
1.62
510
1.61
1.92
1.39
1.27
1.19
1.26
1.39
1.07
0.68
1.10
520
0.94
1.33
1.45
1.14
1.02
1.15
1.08
1.11
1.24
1.29
530
1.14
1.27
1.24
1.26
1.18
1.27
1.30
1.33
1.21
0.78
540
0.94
0.99
0.86
0.91
0.96
1.19
1.15
1.16
1.08
0.98
550
0.97
1.03
0.72 .
0.48
0.45
0.82
1.09
0.79
1.07
1.34
560
1.61
1.23
1.45
1.21
1.20
1.07
1.13
1.27
1.08
1.14
570
0.84
0.98
1.03
1.08
1.16
1.04
0.99
0.92
0.94
1.09
580
0.94
1.04
0.78
0.99
0.99
0.98
0.77
1.29
1.16
1.12
590
1.16
0.95
1.22
1.09
1.06
1.10
1.27
1.00
0.98
0.95
600
1.17
1.19
0.97
1.29
1.22
1.27
1.12
1.06
1.45
1.30
610
1.36
1.40
1.02
1.28
1.54
1.52
1.61
1.74
1.67
1.72
620
1.28
1.46
1.62
1.71
1.35
1.30
1.23
1.54
1.53
1.20
630
1.28
1.24
1.28
1.24
1.47
1.35
1.36
1.28
1.26
1.14
640
0.84
1.10
1.16
1.45
1.64
1.43
1.30
1.36
1.50
1.62
650
1.22
1.07
1.38
1.52
1.49
1.57
1.31
1.27
1.46
1.03
660
1.23
1.21
1.57
1.78
1.37
1.51
1.41
1.50
1.52
1.32
670
1.54
1.39.
1.49
1.44
1.49
1.51
1.21
1.10
1.41
1.07
680
1.54
1.55
1.53
1.14
1.20
1.19
1.25
1.35
1.28
1.21
690
1.33
1.15
1.53
1.67
1.49
1.36
1.17
1.22
1.38
0.55
700
1.20
1.58
1.37
1.41
1.50
1.47
1.60
1.01
1.29
1.30
710
1.30
1.34
1.22
|1.16
1.04
0.93
1.15
1.23
1.00
0.74
720
1.08
1.18
0.97
1.09
0.96
1.25
1.19
1.08
0.80
1.14
730
1.27
1.24
1.33
1.49
1.32
1.27
1.33
1.59
1.34
1.10
740
1.25
1.22
0.84
[1.41
1.31
1.51
1.13
1.22
1.08
1.24
750
1.16
0.87
1.04
0.96
0.88
0.90
1.04
1.08
1.19
1.20
760
0.88
0.96
0.56
0.82
0.75
1.00
0.91
0.95
0.94
1.10
770
1.16
1.39
1.48
1.29
1.20
1.50
1.34
1.39
1.47
1.17
780
1.62
1.12
1.04
1.23
1.36
1.17
0.96
1.11
0.87
1.10
790
1.40
1.13
1.16
1.12
0.99
1.18
1.39
0.75
1.17
1.20
800
1.19
1.11
1.18
1 . 19
0.88
1.01
1.42
1.04
1.11
0.73
810
0.99
1.22
1.23
1.15
1.24
1.28
1.26
1.17
1.02
0.83
820
1.10
1.17
1.32
0.89
1.09
1.08
1.25
1.30
1.29
1.16
830
1.10
1.24
1.38
1.07
1.18
1.26
1.25
1.32
1.27
1.13
840
0.99
1.10
1.10
1.35
1.19
0.97
1.21
0.92
1.23
1.23
850
1.15
1.16
1.16
1.22
1.09
0.99
1.06
1.01
1.13
1.14
860
1.19
1.00
1.04
1.04
1.12
0.67
1.23
1.20
0.63
1.14
870
1.32
1.08
1.03
0.97
1.18
1.10
0.98
1.12
1.17
1.18
880
1.24
1.35
1.41
1.13
1.22
1.53
1.42
1.08
1.29
1.15
890
1.00
1.05
1.33
1.33
1.10
1.13
1.24
1.31
1.11
1.21
900
1.03
1.25
1.10
1.07
1.12
1.13
1.03
1.01
1.10
1.00
910
1.06
1.15
1.10
0.84
1.17
0.97
1.15
1.28
1.06
1.09
920
1.20
1.08
1.24
1.05
0.87
1.04
1.09
1.09
1.03
0.90
930
0.74
0.98
1.00
0.72
1.05
1.01
1.02
1.29
1.05
1.21
940
1.24
1.20
1.15
0.99
0.91
1.06
1.19
1.28
1.01
1.01
950
1.20
1.09
0.94
0.97
0.47
0.91
1.08
0.71
0.89
1.07
960
1.22
0.87
0.92
1.15
1.06
1.07
0.98
1.16
1.33
1.28
970
1.50
1.14
1.09
1.22
1.15
1.01
1.08
1.14
1.00
0.82
980
0.62
0.76
0.92
0.96
1.19
1.36
1.15
1.24
1.21
1.33
990
1.28
1.41
1.36
1.40
1.17
1.04
1.04
1.39
1.42
1.24
1000
1.30
1.44
1.45
1.55
1.35
1.20
1.46
1.36
1.35
1.31
1010
1.11
1.34
1.22
1.20
1.20
1.37
1.58
1.54
1.36
1.60
1020
1.49
1.38
1.38
1.56
1.56
1.10
1.31
1.32
1.16
1.13
1030
1.14
1.08
0.98
1.10
1.19
1.08
1.12
1.22
1.21
1.06
1040
1.00
1.23
1.28
1.03
0.99
1.20
0.99
0.88
0.93
0.95
1050
1.02
1.02
0.76
0.70
0.79
0.84
0.94
0.81
0.82
0.58
1060
0.58
0.91
0.89
0.92
1.19
1.17
1.08
1.25
1.36
1.13
1070
0.90
1.24
0.99
1.08
1.21
1.32
1.30
1.15
1.08
1.16
122
CLIMATIC CYCLES AND TREE-GROWTH.
Sequoia record: Group of 1915; 11 trees — continued.
A. D.
0
1
2
3
4
5
6
7
8
9
1080
1.17
1.08
0.71
1.11
1.09
1.10
0.95
1.14
1.05
1.07
1090
0.88
0.89
0.82
0.64
0.99
1.13
0.93
1.06
0.76
0.83
1100
1.11
1.04
1.05
0.92
0.90
1.00
0.87
0.84
0.86
1.05
1110
0.93
0.96
0.96
1.01
1.00
1.10
1.24
1.17
1.24
1.07
1120
1.18
1.17
1.11
0.93
1.02
1.19
0.57
0.70
0.99
1.00
1130
1.00
0.88
0.90
0.91
0.90
0.97
1.11
0.96
0.95
0.94
1140
0.92
0.92
1.08
0.96
0.89
0.83
0.89
0.97
0.89
1.07
1150
0.88
0.76
0.52
0.63
0.83
0.84
0.34
0.65
0.85
0.99
1160
1.00
0.93
0.80
1.06
0.87
1.00
1.02
1.05
0.85
1.12
1170
0.84
0.81
0.87
0.82
0.91
0.63
0.72
0.60
0.80
0.89
1180
0.88
1.06
0.92
0.71
0.99
0.87
1.06
0.93
1.12
1.10
1190
1.00
1.00
0.98
0.90
1.04
1.06
0.91
0.98
0.94
1.04
1200
1.09
1.08
0.96
0.94
1.00
1.04
0.79
0.85
0.82
1.02
1210
0.98
0.86
0.93
0.92
1.06
0.86
0.96
0.84
0.74
1.00
1220
0.93
0.83
0.82
0.87
0.87
0.91
0.82
0.73
0.91
0.97
1230
0.95
0.73
0.83
0.91
0.80
0.78
0.64
0.62
0.78
0.79
1240
0.84
0.86
0.76
0.74
0.77
0.64
0.93
0.87
1.04
0.80
1250
0.57
0.70
0.84
0.84
0.70
0.71
0.99
0.88
0.97
1.00
1260
0.97
0.85
0.80
0.57
0.54
0.85
0.92
0.86
0.79
0.70
1270
0.97
0.99
0.96
0.81
1.06
1.05
0.87
0.97
1.10
0.72
1280
0.83
0.91
0.94
1.00
0.74
0.58
0.86
0.94
0.85
0.87
1290
1.00
1.00
0.71
0.85
0.98
0.74
0.48
0.85
0.78
1.01
1300
0.91
0.97
1.03
1.01
1.17
1.20
1.21
1.27
1.15
0.95
1310
1.17
1.06
1 .22
1.28
1.14
1.24
0.85
1.03
1.20
1.20
1320
1.03
1.07
1.12
1.17
1.04
0.92
1.24
1.34
1.19
1.18
1330
1.35
1.31
1.02
1.05
1.16
0.90
1.14
1.20
1.23
1.14
1340
1.25
1.26
1.16
1.09
1.15
1.17
1.11
1.06
1.01
1.26
1350
1.03
0.93
0.66
0.97
0.96
1.10
1.27
1.09
0.96
1.03
1360
1.05
0.97
1.10
1.21
1.15
0.83
1.06
1.22
1.20
1.15
1370
1.06
1.05
1.15
1.14
1.05
1.01
0.95
0.76
0.99
1.04
1380
1.21
1.21
1.03
1.09
1.04
1.09
1.04
0.97
1.00
1.13
1390
0.81
0.87
0.98
1.03
1.01
0.87
0.81
0.91
0.90
0.92
1400
0.84
0.86
0.74
0.80
0.86
0.88
0.88
0.84
0.76
0.91
1410
0.72
0.89
0.94
0.75
1.05
1.10
1.11
1.10
1.11
1.05
1420
1.27
1.02
1.25
1.16
1.13
0.92
0.70
0.90
0.85
0.90
1430
0.83
0.81
0.83
0.85
0.81
0.78
0.84
0.80
0.80
0.79
1440
0.80
0.81
0.74
0.72
0.75
0.88
0.79
0.74
0.78
0.71
1450
0.77
0.75
0.66
0.74
0.71
0.77
0.73
0.68
0.75
0.78
1460
0.77
0.79
0.81
0.76
0.70
0.74
0.73
0.84
0.66
0.77
1470
0.91
0.76
0.72
0.61
0.73
0.71
0.68
0.86
0.87
0.57
1480
0.77
0.86
0.88
0.94
1.00
0.78
0.88
0.82
0.94
0.94
1490
0.88
0.87
0.84
0.86
0.88
1.00
0.96
0.82
0.89
0.66
1500
0.63
0.85
1.06
0.94
0.94
0.95
1.00
0.98
1.05
1.07
1510
0.85
0.86
1.04
1.06
0.97
0.84
0.82
0.93
0.66
0.91
1520
0.94
0.97
0.94
0.99
1.09
1.11
1.05
0.95
1.03
0.60
1530
0.90
1.06
0.64
0.70
1.03
1.03
0.87
0.89
0.96
1.12
1540
0.88
0.68
0.80
0.88
0.94
0.87
0.96
1.04
0.73
0.94
1550
0.84
0.97
0.92
0.95
0.77
0.82
0.88
0.85
0.89
0.82
1560
0.87
0.85
0.77
0.78
0.90
0.87
0.76
0.81
0.89
0.78
1570
0.82
0.48
0.70
0.80
0.77
0.76
0.68
0.78
0.70
0.50
1580
0.12
0.53
0.66
0.78
0.68
0.66
0.72
0.80
0.75
0.87
1590
0.68
0.75
0.77
0.81
0.76
0.76
0.80
0.81
0.79
0.75
1600
0.69
0.88
0.89
0.85
0.98
0.99
0.87
0.81
0.88
0.88
1610
0.94
0.97
0.86
0.67
0.86
0.92
0.89
0.94
0.84
0.79
1620
0.86
0.90
0.77
0.96
1.01
1.04
0.90
0.89
0.97
0.89
1630
0.91
0.78
0.45
0.63
0.75
0.87
0.93
0.66
0.81
0.92
1640
1.02
1.01
0.96
0.95
1.00
1.00
0.92
0.87
0.91
0.94
1650
0.77
0.86
0.82
0.74
0.52
0.58
0.78
0.75
0.84
0.74
1060
0.83
0.83
0.79
0.81
0.79
0.85
0.86
0.67
0.82
0.70
APPENDIX.
123
Sequoia record: Group of 1915] 11 trees — continued.
A. D.
0
1
2
3
4
5
6
7
8
9
1670
0.68
0.73
0.81
0.86
0.89
0.91
0.77
1.03
0.89
0.85
1680
0.94
0.78
0.73
0.82
0.76
0.83
0.71
0.80
0.78
0.73
1690
0.72
0.54
0.78
0.76
0.79
0.79
0.73
0.79
0.65
0.67
1700
0.64
0.63
0.90
0.65
0.72
0.89
0.64
0.72
0.80
0.95
1710
0.74
0.67
0.68
0.76
0.73
0.70
0.84
0.88
0.74
0.71
1720
0.86
0.70
0.70
0.83
0.82
0.93
0.91
0.84
0.83
0.48
1730
0.85
0.89
0.97
0.95
1.01
0.99
0.86
0.91
0.98
0.73
1740
0.92
1.04
0.96
0.96
0.96
1.10
0.90
1.01
0.83
0.88
1750
1.11
0.99
0.96
0.94
0.91
0.85
0.69
0.79
0.93
1.00
1760
1.06
1.13
1.01
1.08
1.05
0.85
1.14
1.21
1.25
1.05
1770
1.10
1.16
1.16
1.08
1.17
1.06
0.85
0.48
0.73
0.90
1780
0.97
0.87
0.52
0.67
0.93
0.98
1.05
1.00
0.82
0.95
1790
1.04
1.03
1.07
0.95
0.83
0.57
0.63
1.12
1.14
1.19
1800
1.06
1.13
1.09
1.07
0.96
0.99
0.93
0.91
0.83
0.81
1810
0.84
0.99
0.79
0.88
1.03
0.92
0.99
1.03
0.78
0.88
1820
0.88
0.84
0.74
0.75
0.71
0.97
0.94
0.78
0.77
0.55
1830
0.77
0.89
0.98
0.83
0.81
0.80
0.86
0.87
0.90
0.81
1840
0.77
0.52
0.73
0.69
0.83
0.95
0.90
0.97
0.89
0.95
1850
0.92
0.80
0.96
1.03
0.82
0.85
0.79
0.91
0.69
0.74
1860
0.91
0.88
0.86
0.84
0.61
0.76
0.87
0.91
0.88
0.80
1870
0.78
0.80
0.83
0.87
0.79
0.86
0.99
0.80
1.11
0.99
1880
1.08
1.23
1.01
1.17
1.19
1.14
1.10
0.99
1.12
1.16
1890
1.20
1.12
0.94
1.11
1.10
1.11
1.09
1.10
0.84
0.90
1900
1.11
0.98
0.76
0.82
0.96
0.91
0.90
0.93
0.82
0.89
1910
0.78
0.90
0.87
0.83
0.85
* NOTE. — The dates in table 4 on page 45 should be altered by one year to agree
with those in table 5 on page 52.
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