The distribution of some selected alkali metals and ......The Stronghold Granite is located in the...
Transcript of The distribution of some selected alkali metals and ......The Stronghold Granite is located in the...
-
The distribution of some selected alkali metals and alkalineearths in the Stronghold granite, Cochise County, Arizona
Item Type text; Dissertation-Reproduction (electronic)
Authors Bock, Charles Mitchell, 1935-
Publisher The University of Arizona.
Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.
Download date 06/07/2021 16:04:46
Link to Item http://hdl.handle.net/10150/565605
http://hdl.handle.net/10150/565605
-
THE DISTRIBUTION OF SOME SELECTED ALKALI METALS
AND ALKALINE EARTHS IN THE STRONGHOLD
GRANITE, COCHISE COUNTY, ARIZONA
A Thesis Submitted to the Faculty of the
DEPARTMENT OF GEOLOGY
In P a rtia l Fulfillm ent of the Requirem ents For the Degree of
DOCTOR OF PHILOSOPHY
THE .UNIVERSITY OF ARIZONA
•r-'C harles Mi Bock
-
ERRATA
page 26, Table 4.Stronghold Granite
k2o CaO
Average
Stronghold Granite
5.75 0.50 should read
Average 4.95 0.59
page 27, Table 5 .Average o f rhyolite
dikes associated with the Stronghold
k2o CaO
Granite
Average o f rhyolitedikes associated with
5.75 0.31 should read
the Stronghold Granite
4.95 0.36
-
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my
direction by Charles M, Bock___________________________________
entitled The distribution of some selected alkali metals and alkaline
earths in the Stronghold Granite, Cochise County, Arizona_______
be accepted as fulfilling the dissertation requirement of the
degree of Doctor of Philosophy_______________________________
After inspection of the dissertation, the following members
of the Final Examination Committee concur in its approval and
recommend its acceptance:*
*This approval and acceptance is contingent on the candidate's adequate performance and defense of this dissertation at the final oral examination. The inclusion of this sheet bound into the library copy of the dissertation is evidence of satisfactory performance at the final examination.
Date / z
-
STATEMENT BY AUTHOR
This thesis has been submitted in p artia l fulfillment of req u ire m ents for an advanced degree at The University of Arizona and is deposited in The University L ibrary to be made available to borrow ers under ru le s of the L ibrary .
B rief quotations from this thesis a re allowable without special perm ission, provided that accurate acknowledgment of source is made. Requests for perm ission for extended quotation from or reproduction of th is m anuscript in whole or in p art may be granted by the head of the m ajor departm ent or the Dean of the Graduate College when in their judgment the proposed use of the m ateria l is in the in te rests of scholarship. In all other instances, however, perm ission m ust be obtained from the author.
-
THE DISTRIBUTION OF SOME SELECTED ALKALI METALS AND ALKALINE EARTHS IN THE STRONGHOLD
GRANITE, COCHISE COUNTY, ARIZONA
by
C harles M. Bock
ABSTRACT
X -ray fluorescent spectrographic analyses show the Stronghold
G ranite to be im poverished in Sr with respec t to other analyzed granites
of sim ilar Ca content and higher in the ratio . C a/S r. Rb and K/Rb values
for the Stronghold G ranite a re sim ilar to values obtained for other bio-
tite granites. Trend surface analysis techniques applied to the v a ri
ables m easured show that definite compositional trends exist in the
m assif. High order trend surfaces for Sr and Ca show negative cor
relation with the high order trend surface for the ra tio C a/S r. The
high order surfaces for C a/S r and K/Rb show negative correlation with
each other indicating that la te stage igneous events a re m ore dominant
in the northeast than in other p a r ts of the pluton.
ii
-
TABLE OF CONTENTS
Page
GLOSSARY ..................... ........................................................................... 1
INTRODUCTION ....................................................... ............... .............. 3
PROCEDURE........................... 7
GEOLOGICAL SETTING OF THE STRONGHOLD GRANITE . . . . 15
Country Rocks .................................................. 15Contact M etamorphism ............................................................... 17Rhyolite and Aplite Dikes A ssociated with the Stronghold
G ranite ....................... 18Xenoliths ..................... 19Petrography of the Stronghold G r a n i te ................ 19
M ajor M inerals ................................... 20A ccessory M inerals ............................. 20
RESULTS OF ANALYSES ..................................................................... 22
K and Ca Analyses ......................................................... .. 22Sr Analyses ................................... 27Rb Analyses ................................. 27
TREND SURFACES .............................................. 30
Assumptions .......................................... 30Sampling ..................................................... 31Computation .................................................. 32Discussion of Trend S u rfa c e s ...................................... ............... 34Significance of Trend Surfaces ............... ............................... .. 38
DEVIATION MAPS .................................................. 55
SUMB4ARY AND CONCLUSIONS . . . . . . . . . . . . . . o . . . . . . . . . . . . . 83
iii
-
Page
APPENDIX I—-TABULATION OF ANALYSES OF STRONGHOLD GRANITE SAMPLES EXCLUDING LOCATIONS .............................. 64
APPENDIX H— TABULATION OF ANALYSES OF RHYOLITE AND APLITE DIKES ASSOCIATED WITH THE STRONGHOLD GRANITE................ 74
APPENDIX HI— COEFFICIENTS FOR TREND SURFACE EQUATIONS ...................................... ........................................................ 77
APPENDIX IV— TABULATION OF U-V LOCATIONS AND ANALYSES OF STRONGHOLD GRANITE SAMPLES ...................... 80
APPENDIX V— SUMMATIONS OF COMPUTED AND OBSERVED VARIABLES, SUMS OF DEVIATIONS, SUMS OF SQUARES OF COMPUTED AND OBSERVED VARIABLES,AND SUMS OF SQUARES OF DEVIATIONS ASSOCIATEDWITH THE TREND SURFACES ............................. 86
SELECTED BIBLIOGRAPHY............................. 90
LIST OF FIGURES
Figure Page
1. Index map showing the location of the DragoonMountains ............................... 4
2. Topographic map of the central Dragoon Mountains . . . . . . 9
3. Example m easurem ent and calculation for Sr and Rbusing G -l as a standard ...................................................... 12
4. Geologic map of the central Dragoon M ountains................... 16
5. Frequency distributions for percent K and percent Ca inthe Stronghold G ra n i te ................ 23
6. Frequency distributions for ppm Rb and ppm Sr in theStronghold G ranite ........................... 24
iv
-
Figure Page
7. Frequency distributions for the ra tio s K/Rb and C a/Srin the Stronghold Granite ............................................ 25
8. Outline of the Stronghold Granite showing samplelocations and U-V coordinate s y s te m ............................ .... 33
9. Linear trend surface for ppm Sr in the StrongholdG ran ite ............. .............. ....................................................... .... 36
10. Linear trend surface for the ra tio C a/Sr in theStronghold Granite ............................................... .......... .. 37
11. Scatter plot of percen t Ca vs. ppm Sr in theStronghold Granite • ................. .......... .................................. .. 39
12. L + Q trend surface for percen t Ca in theStronghold Granite .......................................... 41
13. L + Q trend surface for ppm Sr in theStronghold Granite ................................ ................ .............. .. 42
14. L + Q + C trend surface for percent Ca in theStronghold Granite ....................... 43
15. L + Q + C trend surface for ppm Sr in theStronghold G ra n ite ............ ...................................................... 44
16. L + Q trend surface for the ra tio C a/Sr in theStronghold G ranite .......................................... 45
17. L + Q + C trend surface for the ra tio C a/Sr in theStronghold G ranite ..................... 46
18. L + Q trend surface for percent K in the StrongholdG ran ite ........................................................... 47
19. L + Q + C trend surface for percent K in theStronghold G ranite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
20. L + Q trend surface for ppm Rb in the StrongholdG ranite .................................... ....................... .. 50
v
-
Page
21. L + Q + C trend surface for ppm Rb in the StrongholdG ra n ite ................. . ................. .................. ............................... 51
22. L + Q trend surface for the ra tio K/Rb in the StrongholdG ra n ite ............................................................................................. 52
23. L + Q + C trend surface for the ra tio K/Rb in theStronghold G ranite ....................................................... .. 53 *
24. Map for deviations from the linear trend surface forpercen t K in the Stronghold G ra n ite .................................... 56
25. Map for deviations from the linear trend surface forpercen t Ca in the Stronghold G ra n ite .................................. 57
26. Map for deviations from the linear trend surface forppm Rb in the Stronghold Granite ...................................... 58
27. Map for deviations from the linear trend surface for ,ppm Sr in the Stronghold G ranite .......................................... 59
28. Map for deviations from the linear trend surface forthe ra tio K/Rb in the Stronghold Granite .......................... 60
29. Map for deviations from the linear trend surface forthe ratio C a/Sr in the Stronghold G ra n ite .............................. 61
LIST OF TABLES
Table Page
1. Instrum ental analysis d a ta ................................................. 10
2. P recision and accuracy of analyses ..................... .............. .. 13
3. Isotope dilution analyses and X -ray fluorescentanalyses ................................................ ................................. .... 14
4. Comparison of CaO and KgO contents of Nockolds’average biotite granite and the Stronghold Granite . . . . . 26
Figure
vi
-
Table Page
5„ Comparison of CaO and KoO contents of averagealkali rhyolite and rhyoute-obsidian with rh y o lite s" associated with the Stronghold G ra n ite ........... .. o . . . 27
6. Comparison of Sr contents and C a/S r ra tio s of lowCa granites and the Stronghold Granite ......... .. 28
7. Comparison of Sr contents and C a/Sr ra tio s of lowCa rhyolites and rhyolites associated with theStronghold G ran ite ................................................................ 28
8. Comparison of Rb contents and K/Rb ra tio s of 16South African biotite granites and the StrongholdG r a n i t e ........... ........................... ......................................... .. 29
9. Percentages of total sum s of squares associated withthe trend surfaces ............................................................. .... 35
10. Radii of the elem ents studied in the Stronghold G ranite . . 49
vii
-
GLOSSARY
DEVIATION TERMS. The algebraic difference between trend surface
values and values actually m easured a t data locations.
DIADOCHY. The substitution of one element for another element in a
given site in a crysta l structure .
G -l. A granite sam ple distributed by the U. S. Geological Survey for
which the chem ical composition is known precisely .
LINEAR SURFACE. A plane surface; a surface whose equation has no
te rm s higher, than f irs t degree.
LINEAR PLUS QUADRATIC SURFACE. A surface whose equation con
tains second degree te rm s plus f irs t degree te rm s.
LINEAR PLUS QUADRATIC PLUS CUBIC SURFACE. A surface whose
equation contains f irs t, second, and th ird degree te rm s.
NEGATIVE CORRELATION. R efers to a relationship between two v a ri
ables that causes one variable to increase while the other de
creases .
POSITIVE CORRELATION. R efers to a relationship between two v a r i
ables that causes one to increase when the other inc reases or
to decrease when the other decreases.
-
2
REGRESSION ANALYSIS. In this study, a m athem atical treatm ent of
the locations and magnitudes of a se t of variables to determ ine
an equation which best describes the magnitude of the variables
as a function of location.
TREND SURFACE. In this study, a surface which describes a variable
as a function of location.
X-RAY FLUORESCENT SPECTROGRAMHY. A spectrographic technique
in which X -rays a re used to excite fluorescent X -radiation
which is characte ris tic for each element.
-
INTRODUCTION
This paper is an attem pt to make a rea lis tic estim ate of the
p artia l composition of the Stronghold Granite and to investigate the
quantitative a rea l variations of K, Ca, Rb, Sr, K/Rb, and C a/S r using
trend surface analysis techniques. The elem ents selected for analysis
in this study were chosen because they a re readily amenable to quanti
tative analysis by X -ray fluorescent spectrography and they a re of geo
chem ical and petrologic moment.
The Stronghold Granite is located in the Dragoon Mountains of
Cochise County, Arizona (see Fig. 1).
The Stronghold Granite was chosen for study for the following
reasons:
1. The Stronghold G ranite is clearly in trusive to the surround
ing country rocks; i t can, therefore, be compared to other igneous
bodies.
2. The m assif is well exposed and only m oderately weathered.
3. Reliable geological work, e. g . , outcrop mapping, had a l
ready been accomplished.
4. F ine-grained texture of the granite sim plified sampling
and sam ple preparation because inadvertent inclusions of xenolithic
3
-
Figure 1. —Index map showing the location of the
Dragoon Mountains.
-
ARI ZONA
INDEXMAP
-
5
m ateria l or phenocrysts in hand specim ens was not a problem . That is,
a few cubic centim eters of a given hand specimen is as likely to be rep
resen tative of that hand specimen as any other sm all portion of that
hand specimen.
The Dragoon Mountains a re a has been mapped as a p a rt of a
la rg e r regional study by Gilluly (1956). Gilluly’s work included petro
graphic descriptions of the Stronghold Granite as well as two chemical
analyses of the intrusion. C ederstrom (1946) described the structu ra l
geology of a sm all portion of the Stronghold Granite. Whitten (1959)
has dem onstrated that quantitative m ineralogic variation in granitic
bodies can be investigated successfully using trend surface analysis
techniques.
The w riter gratefully acknowledges technical support from Dr.
R. W. G. Wyckoff of the Physics Departm ent of the U niversity of
Arizona. X -ray fluorescent spectrographic analyses w ere ca rried out
using equipment made available to Dr. Wyckoff for other re sea rch
purposes under National Science Foundation Grant number 9760, and
National Institute of Health Grant number DE 01183. The w riter also
wishes to thank P ro fesso rs John W. Anthony and Spencer R. Titley for
many helpful suggestions during the course of the study. M r. R ichard
A. Bideaux operated the computer for the author, and wrote auxiliary
routines which aided the w riter m aterially . The Num erical Analysis
Laboratory of the U niversity of Arizona allowed the w riter use of their
-
equipment.
-
PROCEDURE
Early in the course of th is study the w riter established several
c r ite r ia which any granitic body would have to m eet to be successfully
studied with X -ray fluorescent spectrography combined with trend su r
face techniques. F irs t, the granite m ust be unequivocally in trusive so
that trends of trace element distribution observed in other igneous bodies
could be assum ed to be operative here. Second, the granite m ust be
well exposed with as little weathering a s possible. Third, the texture
m ust be fine enough so that 2 or 3 cubic centim eters of the rock would
be represen tative of any hand specimen, and further, each hand speci
men m ust be represen tative of the outcrop from which i t was taken.
The Stronghold Granite sa tisfied a ll of these requirem ents.
The location of sam pled s ites in th is study is best term ed
"haphazard” in the s ta tis tica l sense. At the inception of the study the
idea of collecting sam ples on a grid system was rejected because of the
extrem ely rugged topography. The sam ples a re biased as to ease of
accessib ility of outcrop and sta te of weathering. A sampling goal of 10
sam ples per square m ile was used a rb itra rily , and the w riter tr ied to
cover each square m ile as uniform ly as possible. Because of natural
obstacles a uniform coverage is lacking in some a reas .
7
-
8
Sample locations w ere m arked on a 1/62, 500 scale topographic
map made of p a rts of the U. S. Geological Survey St. David and P earce
15-minute quadrangles. Granite boundaries were traced from G illuly 's
geological map of central Cochise County on the newer topographic
se rie s and were corrected for location on the new map. No serious
relocation of the granite boundaries was necessary in tran sferrin g the
geology to the new map (see Fig. 2).
Samples were chipped from outcrops with a ham m er and m oil,
and rep resen t the fre sh est rock apparent to the worker at that location.
Dike rocks were sam pled a rb itra r ily whenever a dike was within approx
im ately 30 feet of a sample site and accessible. Approximately 3 cubic
cen tim eters of rock were chipped off each hand specimen and ground in
a P ica Blender m ill. The sam ple was reduced in the m ill for 1 minute,
and the pulverized and thoroughly mixed sample was then placed in a
p lastic "Caplug" and sealed with a l /4 -m il m ylar sheet held in place by
a drapery ring. Sieve analysis showed that in treating the sam ples in
th is manner over 80 percen t of the rock was reduced to -300 mesh.
Samples w ere irrad ia ted in specially constructed sam ple cups so that
the sam e a rea would be exposed to the exciting radiation for each sam ple.
A Norelco X -ray vacuum spectrograph with standard control
panel was used for analysis. Instrum ental analysis data is given in
Table 1. All peak height m easurem ents w ere made with the chart
reco rd e r. Signal intensity on the chart reco rd er was adjusted to give
-
Figure 2. —Topographic map of the central
Dragoon Mountains.
-
9
TOPOGRAPHIC MAP OF THECENTRAL DRAGOON MOUNTAINS
Composite mop of St. David and Peorce 15' Quod MopsScale
1 0 1 2 Miles
-
10
TABLE 1. INSTRUMENTAL ANALYSIS DATA*
Elem ents Rb and Sr K and Ca
Tungsten tube potential: 50 K.V. 30 K. V.
Tube current: 20 M. A. 25 M. A.
Analyzing crysta l: L iF EDDT
Radiation detector: Scintillation counter Flow proportional counterwith P-10 gas
Potential of rad ia tion monitor: 700 V. 1, 800 V.
Two-theta scan range: 24-28° C a ............... 43. 7-45. 5°
K ............. .. 48 ;7-50.7°
Two-theta position for background m easurem ent: A rb itrary C a ............... 43.7°
K ......... ......... 48.7°
♦All m easurem ents w ere made with base level discrim ination se t a t 20 volts. K and Ca m easurem ents were made in a vacuum of le ss than 500 m icrons m ercury p ressu re . Sr and Rb analyses w ere made in an a ir path. Scanning speed for a ll analyses was 1° tw o-theta per minute and the chart reco rd er speed was se t a t half an inch per minute. Tim e constant was se t at four.
-
11
optimum deflection from the baseline for the standard.
G -l, the U. S. Geological Survey standard granite, was used
a s the standard for a ll analyses by assum ing a linear relationship be
tween K-alpha X -ray peak height and composition for the sam ples. G -l
was run at least every tenth sam ple and at the beginning and end of each
se rie s of analyses. Ca and K peak heights were m easured from back
ground to the top of the g rea test deflection above background, and a
d irec t proportion was assum ed for the relation of peak intensity of the
unknown and the known G -l.
Sr and Rb contents w ere determ ined by constructing an a rb itra ry
baseline (see Fig. 3) and assum ing the ra tio of peak height to background
to be linear with variation in composition. The precision and accuracy
of these methods can be seen in Table 2. Sr and Rb analyses a re here
reported to the n ea rest 10 ppm (parts per million). Analyses on the
U. S. Bureau of Standards rocks were made by including them in day-
to-day runs and a re , therefore, an acceptable m easure of the accuracy
and precision which can be associated with analyses on the Stronghold
G ranite and associated rocks. Values used for G -l a re the values
recom m ended in U. 8. Geological Survey Bulletin 1113.
An independent check on the accuracy of the technique used for
Rb and Sr analyses was made by M r. Donald E. Livingston using isotope
dilution techniques. The re su lts of the isotope dilution analyses and
X -ray fluorescence techniques used in th is study appear in Table 3.
-
* 12 k.CO
X
degrees 2 0(LiF)
arbitrary background
chart baseline
Peak to background ratios(PBR)BCBA = 2L = 0-345 Rb:
3452 2 0 ,
P B R ^ ̂ppm Rbx
EF — =DE
§0 = 199 0-402,
^PBR for standards + PBR for unknown sample peaks ** unknown
Sr: P B R i2502 ppm Srx
1 ppm Rb ir, G-!2 ppm Sr in G-l
Figure 3.Example measurement and calculation for Sr and Rb
using G-l as a standard.
-
TABLE 2. PRECISION AND ACCURACY OF ANALYSES
13
P ercen t K P ercen t Ca ppm Rb ppm Sr
Chelm sford Granite (U .S .B .S . # 4979)
U. S.B . S. 4. 61 0.54
This study 4. 6640.08* 0.59+0.05* 328+13+ 47+12+
Turekian and C arr (1961) 65
M ilford Granite (U .S .B .S . # 4983)
U. 8. B. S. 3.32 0.40
This study 3.4140.06* 0.42+0.03* 60+13+ 131+10+
Turekian and C arr (1961) 125
G raniteville Granite (U .S .B .S . # 4981)
U. S .B .S . 3.82 0.46
This study 3.84+0.02* 0. 6840.06* 432+16+ 11+3+
Turekian and C arr (1961) 20
Recommended values for G -l (Stevens, 1960) 4. 51 0.97 220 250
♦R esu lts of 9 runs.
+R esults of 10 runs,
-
14
TABLE 3; ISOTOPE DILUTION* ANALYSES AND X-RAY FLUORESCENT ANALYSES
(Livingston, 1962)
Rb SrSample I. D.* X-Ray I. D.* X-Ray
Ruin Granite 279 330 158 150
Red Rock Rhyolite 205 260 226 220
Rhyolite (DEL-5-62) 173 200 250 230
-
GEOLOGICAL SETTING OF THE STRONGHOLD GRANITE
Country Rocks
The following is a b rief description of the rocks which surround
the Stronghold Granite. A detailed rep o rt on the region has been pub
lished as U. S. Geological Survey Professional Paper 281 by Jam es
Gilluly. The reader is re fe rre d to that paper for detailed stratigraphic
and struc tu ra l information.
The oldest unit exposed in contact with the granite is the P re -
cam brian Pinal Schist. Exposures of the sch ist along the central septum
(see Fig. 4) which divides the granite into two lobes a re characterized
by biotite, muscovite, quartz, and a little hornblende. A second type
of P inal Schist exposed along the eastern boundary of the pluton is
characterized by muscovite and occasional porphyroblasts of andalusite
averaging 5 mm in length.
Paleozoic rocks lie unconformably on the P recam brian Pinal
Schist and consist of the basal Cam brian Bolsa Q uartzite overlain by a
Devonian through Perm ian lim estone sequence in terrupted by occasional
shaly partings. The lim estone has suffered varying degrees of contact
m etam orphism , but seem s to have been predominantly unreactive to the
Stronghold Granite.15
-
Figure 4. —Geologic map of the central
Dragoon Mountains.
-
110*00'
j #
GEOLOGIC M A P % t _
% %
6 #r-j
EXPLANATION
V^V-:-y-J Quoternory ‘..‘dal..* alluvium
ii
f t
#
1 Tertiaryhr | Ts9 Stronghold
" " "
IvV-.VV-.V* --------- FormationC r ^ Trioesic or
W p . . w(.•:* Quartz
Monzonite%# ! H
j # '' :V.*:*•"•*;\V: Precombrion
OF THE CENTRAL
DRAGOON MOUNTAINS Modified from Gilluly(I956)
-
17
T riass ic or Ju rass ic Cochise Peak Q uartz Monzonite cuts the
Paleozoic rocks and is characterized by the presence of large well-
aligned m icrocline phenocrysts in a q u artz -rich m atrix . The author
observed an a rea north of the Stronghold Canyon Picnic A rea where the
quartz monzonite was sheared and apparently rem obilized at the tim e
of the Stronghold Granite emplacement.
The Cretaceous Bisbee Form ation overlies the Cochise Peak
Quartz Monzonite in depositional contact and consists dominantly of
e lastics with le sse r lim estone. The Bisbee Form ation does not have
an extensive exposed contact relationship with the Stronghold Granite
(see Fig. 4).
Contact M etamorphism
Contact m etam orphic activity is variable around the periphery
of the Stronghold Granite. At m ost contacts examined there appears to
have been a m ere "baking" of the country rocks with little reaction be
tween the granite and its host. However, there a re a few places where
lim estones have reac ted with the granite to produce dense hornblende
hornfels. Reaction was energetic enough to generate at least two pyro-
m etasom atic o re deposits (Wilson, 1951).
If one assum es the hornblende hornfels adjacent to the granite
as an indicator of maximum contact tem perature and p ressu re , the
granite probably intruded at a tem perature not higher than 700°C, and
-
18
with a partia l water p ressu re not g rea ter than 6 kilobars (cf. Fig. 107,
Fyfe, Turner, and Verhoogen, 1958). However, hornblende hornfels
zones a re not common, and the granite as a whole was probably cooler
o r, at least, le ss reactive than indicated by the hornblende hornfels at
the tim e of emplacement.
Rhyolite and Aplite Dikes Associated With the Stronghold G ranite"
Rhyolite dikes a re ubiquitous throughout the Stronghold Granite
m assif and show well-developed flow lines with m arked chilling a t their
bo rders. The rhyolite dikes a re usually 2 to 5 feet thick, but locally
may be as much as 50 feet thick.
Aplites occur as dikes cutting the granite and as zones within
the granite which appear to be segregations. Rhyolite dikes intrude
both granite and aplite and rep resen t the youngest igneous activity a s
sociated with the granite. Aplite dikes do not appear to be as numerous
as the rhyolites. They a re , however, especially well displayed half a
m ile north of Slavin Gulch (see Fig. 2) on the west side of the m assif.
A large podlike aplite m ass is exposed on the sheer cliffs
north of the entrance to the Stronghold Picnic A rea, but its boundaries
could not be determ ined because of inaccessibility of the te rra in .
M iarolitic cavities displaying euhedral quartz and m icrocline a re
especially abundant in th is aplitic m ass. Such cavities a re common
-
19
also in the granite north of West Stronghold Canyon. In some places
m icrocline and quartz have completely filled the voids yielding sm all
pegm atitic pods ranging from a few inches to several feet in diam eter.
Xenoliths
P laty b io tite -rich xenoliths 2 to 3 inches in diam eter w ere ob
served in a roadcut approximately halfway up Slavin Gulch. These
xenoliths a re probably rem nant products of reaction of the granite with
blocks of Pinal Schist which were observed to be ro tated out of position
along the w estern contact of the cen tra l septum.
Petrography of the Stronghold Granite
Thin sections of 15 specim ens of the Stronghold G ranite were
studied with a petrographic m icroscope. No effort was made to get uni
form coverage of the pluton with thin sections. The specim ens examined
a re characterized by their cataclastic texture and late growth of m icro
cline.
Average estim ated volume percentages a re : 50-60 percent
quartz, 30-40 percent K- spar, 10-20 percent plagioclase, and 0 to 3
percen t biotite. M ineralogically the Stronghold G ranite corresponds
to an alaskitic biotite granite (cf. Gilluly, 1956, p. 107).
-
20
M ajor M inerals
K -spar is represen ted as perth itic m icrocline in euhedral to
subhedral c ry sta ls 1 to 5 mm long which a re commonly observed re -
sorbing plagioclase cry sta ls . Large m icrocline c ry sta ls a re m ost
commonly poikiloblastic with quartz blebs which appear to have been
partia lly replaced by K -spar. Some of the large crysta ls also show
growth rings which m ay be outlined by quartz blebs or K -spar with a
slightly different optical orientation.
Subhedral to anhedral lath-shaped crysta ls of plagioclase range
from l / 4 to 2 mm long, and in m ost of the specim ens studied the c ry s
ta ls have been replaced to a g rea te r or le sse r degree by K -spar. An-
orth ite molecule percentage, a s determ ined by the M ichel-Levy method,
with a universal stage ranges from An^g to Angg. Values of An^g to
An^g a re m ost common.
Quartz c ry sta ls range from 1/4 to 5 mm in diam eter in an
hedral, commonly strained grains. Small blebs of quartz a re often a r
ranged in inclusion zones in K -spar and quartz also often has in te rs titia l
appearance to large K -spar c ry sta ls .
A ccessory M inerals
L ight-green to yellow and yellow-brown laths of biotite range
from l /8 to 3 mm long and a re not uncommonly being replaced by
-
21
m uscovite or K -spar. Opaques a re often in close proxim ity to the bio-
tite being replaced and a re probably reaction products of the rep lace-X
ment. Shreds of se ric ite were observed replacing plagioclase occa
sionally, and le ss commonly as a replacem ent of K -spar. Muscovite
usually occurs as a replacem ent of biotite, but a few isolated laths a re
found without associated opaques. A few irreg u la r peripheral patches
of chlorite, probably pennine, were observed replacing biotite. Euhedral
to subhedral c ry sta ls of zircon w ere observed as inclusions in biotite.
Haloes a re found around some zircon cry sta ls , but a re not characte r
is tic . Anhedral to euhedral c ry sta ls of fluorite a re commonly associ
ated with biotite and le ss commonly as apparent void fillings.
Other accessory m inera ls include epidote, apatite, opaques,
and clays. Epidote occurs as vein fillings in a few locations, but is not
quantitatively im portant as an accessory m ineral in the granite. A few
apatite cry sta ls a re occasionally associated with opaques. Magnetite,
ilm enite, and hem atite observed in the Stronghold Granite appear to be
associated with the breakdown of biotite. Clay m inera ls were observed
as occasional alteration products of both K -spar and plagioclase.
-
RESULTS OF ANALYSES
The re su lts of 243 X -ray fluorescent spectrographic analyses
on the Stronghold Granite a re tabulated in Appendix I. For convenience
of com parison with other data, oxide as well as elem ental percentages
a re lis ted for K and Ca. Frequency distributions of the variables w ere
made and appear in F igures 5, 6, and 7. C lass in tervals in the f re
quency distributions were selected a rb itra rily , but in all cases exceed
the rela tive standard deviation of analysis for the variable involved.
Analyses of aplites and rhyolite dikes associated with the granite a re
tabulated in Appendix IL
K and Ca Analyses
The KgO and CaO content of the Stronghold Granite do not ap
pear to be significantly different from Nockolds’ averages for sim ilar
granitic rocks (Nockolds, 1954; Table 4). However, i t has been pointed
out that Nockolds* averages a re represen tative only for the hand speci
m ens which w ere analyzed, and a re not necessarily represen tative of
the composition of the plutons from which the sam ples were taken. This
c ritic ism may apply to a ll averaged rock analytical data until m ore r e
a listic estim ates of the composition of rock units a re available.
22
-
Arithmetic mean = 4 11% Standard deviation = 0 41
Frequency distribution for %K
Figure 5. Frequency distributions for Stronghold Granite.
Arithmetic mean - 0 42 % Standard deviation = 0-13
Frequency distribution for % Co
%K and % Ca in the
3
-
6 0.. Arithmetic mean = 3 9 0 PPm Geometric m eon = 375 ppm Standard deviation = 120
5 0..
4 0 1
3 0..
2 0 ..
f !|om1oCM
— 1. I - i. .4- 4—1- -1—1__I__l _ 4 _ 4 - L i . n n 4-4 -4-4—4. 1-4- 4Frequency distribution for ppm Rb
Figure 6. Frequency distributions forStronghold Granite.
Arithmetic mean = 30 ppm Geometric mean = 2 0 ppm Standard deviation = 2 0
Frequency distribution for ppm Srppm Rb and ppm Sr in the
-
6 0
5 0
4 0
30
20
10
Arithmetic mean = 110 Geometric mean = HO Standard deviation = 25
4 0 IArithmetic mean = 2 6 0 Geometric mean = 2 0 0Standard deviations 2 0 0
2 0
io
oGO
1 JA i . m - i
requency distribution for K/Rb Frequency distribution for Ca/Sr> 7. Frequency distributions for K/Rb and Ca/Sr in the Stronghold Granite.
-
TABLE 4. COMPARISON OF CaO AND K20 CONTENTS OF NOCKOLDS' AVERAGE BIOTITE GRANITE AND
THE STRONGHOLD GRANITE
26
k 2o(percent)
CaO(percent)
Nockolds* average biotitegranite (Nockolds, 1954) 5.01 0.56
Stronghold G ranite average 5.75 0.50
Whitten (1962b) has proposed a new method for determ ination
of the average composition of a granitic m assif based on trend surface
analysis. This method will be applied to the Stronghold G ranite at a
la te r date.
The rhyolite dikes intruding the granite a re m ore potassic and
le s s calcic than Nockolds* (1954) averages for alkali rhyolite and
rhyolite-obsidian, as seen in Table 5.
Three rhyolite dikes have sufficiently higher K content to
w arrant further study, that is, samples Sgd 16, 17, and 24 (see Appen
dix Ha).
Too few aplites were analyzed in th is study to make any mean
ingful com parisons with other data (see Appendix Bb).
-
27
TABLE 5. COMPARISON OF CaO AND K2O CONTENTS OF AVERAGE ALKALI RHYOLITE AND RHYOLITE-
OBSIDIAN WITH RHYOLITES ASSOCIATED WITH THE STRONGHOLD GRANITE
k 2o(percent)
CaO(percent)
Nockolds1 average alkali rhyolite and rhyolite- obsidian (Nockolds, 1954) 4. 73 0.61
Average of rhyolite dikes associated with the Stronghold G ranite 5. 75 0.31
Sr Analyses
The Sr content of the granite appears to be significantly lower
than the average given by Turekian and Kulp (1956) for granites in the
0 .1 -1 . 0 percent Ca range (see Table 6). The lower Sr content also
affects the C a/S r ra tio causing that param eter to be higher than the
average C a/S r ra tio for rocks of sim ila r composition. Rhyolite dikes
associated with the granite also run low in Sr when com pared with other
data (see Table 7). The C a/Sr ra tio for the rhyolites is also higher
than the average for rocks of sim ila r Ca content (see Table 7).
Rb Analyses
Rb values appear to be in good agreem ent with data obtained
-
TABLE 6. COMPARISON OF Sr CONTENTS AND C a/Sr RATIOS OF LOW Ca GRANITES AND THE
STRONGHOLD GRANITE
28
Sr(ppm) C a/Sr
Average for granitic rocks with 0 .1 -1 .0 percent Ca (Turekian and Kiulp, 1956) 100 60 (re
ported %s Sr X 10 V Ca)
Average for the StrongholdG ranite 30 260
TABLE 7. COMPARISON OF Sr CONTENTS AND C a/Sr RATIOS OF LOW C a RHYOLITES AND RHYOLITES
ASSOCIATED WITH THE STRONGHOLD GRANITE
Sr(ppm) Ca/Sr
Average for rhyolites with le ss than 1 .0 percen t Ca (Turekian and Kulp, 1956) 178 19.6
(reported as Sr X 103/Ca)
Average for rhyolites a s sociated with the Stronghold Granite 30 160
-
29
from other granites. Ahrens, Pinson, and Kearns (1952) investigated
the Rb-K relationship in rocks, but did not identify the dark m inerals
in the granites so that valid com parison is not p ractical. Butler,
Bowden, and Smith (1962) have made a study of a se rie s of South African
granites and their data for K/Rb and Rb in biotite granites agree well
with data gathered in th is study (see Table 8).
Frequency distributions for Ca and K show the expected norm al
distributions (cf. Ahrens, 1954a) for m ajor elements (see Fig. 5). Sr
and C a/S r show apparent lognorm al distributions (see Figs. 6 and 7).
The distribution for Rb is not clearly norm al or lognormal, but the
distribution for K/Rb is apparently norm al (see Fig. 7).
TABLES. COMPARISON OF Rb CONTENTS AND K/Rb RATIOS OF 16 SOUTH AFRICAN BIOTITE
GRANITES AND THE STRONGHOLDGRANITE
Rb(ppm) K/Rb
Average for 16 South African biotite granites (Butler, Bowden, and Smith, 1962) 400 116
Average for the Stronghold G ranite 390 110
-
TREND SURFACES
Assumptions
Whitten (1959) has outlined the assum ptions necessary to a
study of this nature, but i t seem s advantageous to review then here.
F irs t , i t is assum ed that a hand specimen is represen tative of a broad
a re a of rocks around it. Second, i t is assum ed that the laboratory anal
yses a re tru ly represen tative of the composition of the rocks in question;
and third, it is assum ed that there is a rational, m easurable trend in
the granitic body. The f ir s t assum ption is perhaps the weakest of the
th ree and, as far a s is known, no attem pt has been made to rigorously
establish the relationship. Sampling plans have been proposed which
allow equal chance for each outcrop to be sampled, but the w riter does
not know of any attem pt to dem onstrate that a hand specimen is re p re
sentative of a rock outcrop.
The confidence that can be placed in the laboratory work is
high, since the several analyses of the U. S. Bureau of Standards rocks
com pare favorably for the known components. The w riter satisfied
him self early in the study that a few chips from a hand specimen were
rep resen tative of the hand specim en by making duplicate analyses of
30
-
31
the sam e specimen. In th is respect, however, perhaps m ore confidence
can be placed in the ra tio s of elem ents than in the absolute quantities.
The ra tio s may be m ore re liab le because inadvertent inclusion of a
sam ple rich e r in quartz than the hand specimen would cause the absolute
amount of K, Ca, Rb, and Sr to be low, but the ra tio s of K/Rb and
C a/S r should be unchanged, assum ing that the ra tio s a re constant for
any given hand specimen.
The assumption that th e re is a rational trend in the Stronghold
G ranite and that it can actually be portrayed by trend surface can only
be supported by the fact that trend surface analyses dem onstrate that
trends do exist for the param ete rs m easured.
Sampling
Trend surface analyses have been critic ized because sam ples
w ere not collected randomly in a rigorous sta tistica l sense (Link and
Koch, 1962). Sampling models have been proposed based on a rec tan
gular grid and random number scheme. However, the end re su lt of
such schem es is that the worker m ust make a subjective decision con
cerning the accessib ility of the sam ple site, weathering, and other r e l
evant details. One m ajor problem that is commonly overlooked by
designers of such plans is the identification of a sam ple site in the field
from a grid intersection on a topograjiic map or ae ria l photo. In th is
study a grid sampling procedure was re jected because of rugged
-
32
topography. Every effort was made to obtain uniform coverage on the
outcrop of the pluton, and the w riter feels that the sampling is re p re
sentative of the Stronghold Granite, even though it may not be s ta tis tica l
ly valid in a rigorous sense (see Fig. 8). For detailed argum ents on
sampling see Link and Koch (1962) and Whitten (1962a).
Computation
Trend surfaces were generated using an IBM 650 computer
with a program (IBM file No. 8.3.001) described by Krumbein (1959).
Information requ ired by the computer includes the location of each data
point in te rm s of an a rb itra ry U-V coordinate system and data from that
location. From reg ression analyses coefficients for general equations
w ere generated for linear (L), linear plus quadratic (L + Q), and linear
plus quadratic plus cubic (L + Q + C) surfaces. General equations
(Krumbein and Faulkner, p. 6) for trend surfaces have the form
XL - A + BU + CV (L)
Xq = Aq + Bq U + CQ + D2QU + Eq UV + Fq V2 (L + Q)
Xq - Aq + BCU + CCV + DCU2 + ECUV + F CV2 + GCU3 +
H c u V + J CUV2 + Kq V3 (L + Q + C)
where X is the computed value a t a location given by U and V, and A,
B, C, etc. a re coefficients for the respective surfaces. Coefficients
for the surfaces generated in th is study a re listed in Appendix ILL The
U-V location of each sample and the raw data are lis ted in Appendix IV.
-
Figure 8= —Outline of the Stronghold Granite showing
sample locations (.) and U-V coordinate
system .
-
A23C K 2 4 E
T.ii s.
COCO
-
34
"Raw data" were converted to ra tio s and oxide percentages by an auxil
ia ry computer program .
Computed values were com pared with m easured values at each
data point to yield deviation termso
Trend surface and deviation m aps were contoured by inspec
tion after computed values were manually plotted against U-V coordi
nates.
Discussion of Trend Surfaces
The linear surfaces for K, Ca, Rb, and K/Rb all a re essen tial
ly horizontal surfaces, that is , the differences in the variables ac ross
the surfaces is le ss than the expected analytical e rro r of any individual
analysis. F rom the percentages of sum s of squares accounted for by
these surfaces, i t appears that the data fitted by the linear surfaces
a re noisy (see Table 9). "Noise" may be attributed to analytical e rro r
or to natural variations within the granite.
The percentage of the totaled sum of squares accounted for by
any surface is one appraisal of a surface (Dawson and Whitten, S62).
This param eter is actually a m easure of "goodness of f i t , " that is ,
when a high percentage of the sum of squares is accounted for by a su r
face, the surface p asses through a large number of data points. The
percentage of total sum of squares accounted for by a surface was
calculated from the equation given by Dawson and Whitten (1962):
-
35
TABLE 9. PERCENTAGES OF TOTAL SUMS OF SQUARES ASSOCIATED WITH THE TREND SURFACES
ComponentK
(percent)Ca
(percent)Rb
(ppm)Sr
(ppm) K/Rb C a/Sr
L inear 0 .5 0.1 6.6 9.0 4.6 8.4
L inear plusquadratic 9.25 3.19 24.7 16.2 21.5 17.6
Quadratic alone (8.75) (2.09) (18.1) (7.2) (16.9) (9.2)
L inear plus quadratic pluscubic 11.8 7.30 42.0 20.3 33.6 25.3
Cubic alone (2.65) (4.11) (17.3) (13.9) (12.1) (7.7)
100 (Sum of computed- (Sum X computed) V n)9 9(Sum observed-(Sum X observed) /N)
This number is norm ally calculated as a p a r t of the computer program ,
but for some unknown reason, the computer recorded absurd values for
Sum X observed. Since th is number is used in the above calculation,
the percentage was calculated by hand after an auxiliary program deter
mined the tru e value for Sum X^ observed (see Appendix V).
The linear surfaces for Sr and C a/Sr do show appreciable dif
ferences in variab les ac ro ss the surfaces (see F igs. 9 and 10).
L inear plus quadratic p artia l trend surfaces show appreciable
-
Figure 9. —Linear trend surface for ppm Sr in the
Stronghold Granite.
-
ppm Sr line
GOoa
-
Figure 10. —Linear trend surface for the ra tio C a/S r
in the Stronghold Granite.
-
38
gains in percentages of sum s of squares (see Table 9), but a re essen
tially no better at approximating the average variable than the f irs t su r
face (see Appendix VI). The f ir s t approximation of the average of the
variable is improved with higher o rder trend surfaces, but i t is doubt
ful that improvem ent past the f i r s t th ree decimal p laces has any d irec t
geological significance. Strike and dip symbols showing the attitude of
the linear trend surface a re shown on the linear plus quadratic surfaces
for com parison of trend. In all cases except K, the s trik e sense for
the linear plus quadratic surface is sim ilar to the s trik e of the linear
surface suggesting that the attitude of the linear surface is significant.
L inear plus quadratic plus cubic trend surfaces show appreci
able gains in sum s of squares, but for a ll surfaces except the percent
Ca surface the gain is le ss than the gain from linear to linear plus
quadratic. Further, the linear plus quadratic plus cubic surface re ta in s
the sam e sense of dip and strik e a s that of the linear plus quadratic su r
face.
Significance of T rend Surfaces
Turekian and Kulp (1956, Fig. 10) have established a positive
correlation between Ca and Sr in rocks, and a sim ilar correla tion is
suggested in the Stronghold G ranite, although a lim ited range of Ca
values tends to m ask th is interdependence in a sca tte r plot (see Fig.
11). Heier and Taylor (1959b, p. 297) note that Sr proxies for K as
-
I 3 0
120 -
I 10 -
100 ’
/
•90
•80
•70
•60
;30oo
•4055
•30
•20
•10
tir-!4 ':
Is•e
• • •
4
4
3
5 10 20 30 40 50 6 0 70 80 90ppm S r ------ =""»
Figure II. Scatter plot of % Co vs. ppm
100 150
Sr in the Stronghold Granite.W*
-
40
well as Ca and diadochy of th is so rt would also tend to obscure co rre la
tion of Sr with Ca. The substitution of Sr++ for K* is a capture mech
anism resulting from the sm aller divalent Sr ion (see Table 10) being
included instead of the monovalent K ion.
Trend surface analysis suggests a crude positive correlation
between Ca and Sr, but the sim ilarity is only slight for the L + Q + C
surfaces and even m ore obscure for the L + Q surfaces (see F igs. 12-
15). The ra tio C a/Sr is apparently strongly controlled by the gradients
of the Ca and Sr trends. The C a/S r ra tio trend surface shows a strong
negative correlation with trend surfaces for the absolute amounts of Ca
and Sr (see Figs. 14, 15, 16, and 17). This negative correlation be
tween the ra tio C a/Sr and Ca and Sr had been noted previously by
Turekian and Kulp (1956) and Heier and Taylor (1959).
An increasing ra tio of C a/S r is considered an index of in c reas
ing differentiation in igneous rocks (Heier and Taylor, 1959, p. 298).
If the L + Q + C trend surface for C a/S r tru ly rep resen ts a trend in the
Stronghold G ranite, then la te stage igneous events p rog ressed toward
the northeastern p a rt of the pluton (see Fig. 17).
The distribution of K throughout the pluton is apparently uni
form because all the trend surfaces for absolute amount of K have a
highly sym m etric relation to the outline of the intrusion (see F igs. 18
and 19). By contrast, the Rb distribution is uniform for the linear su r
face, but the second and th ird degree surfaces show pronounced r is e s
-
Figure 12. —L + Q trend surface for percen t Ca in the
Stronghold Granite.
-
0 4 0
% C a I t q
-
Figure 13. —L + Q trend surface for ppm Sr in the
Stronghold Granite.
-
Figure 14. —L + Q + C trend surface for percent Ca in the
Stronghold Granite.
-
Figure 15. —L + Q + C trend surface for ppm Sr in the
Stronghold Granite.
-
ppm Sr l + q + c
+
-
Figure 16. —L + Q trend surface for the ra tio C a/Sr in the
Stronghold Granite.
-
5 0 0
f t
-
Figure 17. —L + Q + C trend surface for the ra tio C a/S r
in the Stronghold Granite.
-
CD
-
Figure 18, —L + Q trend surface for percen t K in the
Stronghold Granite.
-
4 0 0
-
Figure 19. —L + Q + C trend surface for percent K in the
Stronghold Granite.
-
z z
3 80
%K l+q + c
+00
-
TABLE 10. RADII OF THE ELEMENTS STUDIED IN THE STRONGHOLD GRANITE
4 9
Cation . K* • Ca++ • Rb+ Sr++
o o o oRadius (Green, 1.42 A 1.03 A 1.57 A 1.16 A
1959)
in Rb values to the northeast (see Figs. 20 and 21).
Rb values apparently strongly control the trend of the K/Rb
ra tio for both L + Q and L + Q + C surfaces (see Figs. 22 and 23). As
Rb values increase , K values decrease, so that the K/Rb ra tio s de
c rease rapidly. The strong trend of lower values for the ra tio toward
the northeast p a rt of the m assif is striking, and since the param eter of
K/Rb is also considered as a differentiation index (Butler, Bowden, and
Smith, 1962, p. 93), the idea that late stage igneous events p rogressed
toward the northeast is reinforced.
In noting that late stage igneous events p rogressed toward the
northeast in the Stronghold Granite, the w riter does not mean that dif
ferentiation in the granite p rog ressed la terally . Consideration of v e rti
cal position of sampled sites in trend surface analyses would alm ost
certainly a lter the configuration of the trend surfaces so that vertical
trends may be distinguished. Further, from rela tions with the country
rocks the w riter gained the im pression that the pluton is unroofed only
-
Figure 20. —L + Q trend surface for ppm Rb in the
Stronghold Granite.
-
Figure 21. —L + Q + C trend surface for ppm Rb in the
Stronghold Granite.
-
5 0
400450ppm Rb l + q + c
-
Figure 22, —L + Q trend surface for the ra tio K/Rb in the
Stronghold Granite.
-
Figure 23„ —L + Q + C trend surface for the ra tio K/Rb
in the Stronghold Granite.
-
!
120
K/Rb l+q+c
-
/
54
to a shallow depth. Thus, the weathering surface of the pluton in places
may be very close to the original in terface between the m assif and the
country rocks. P erterbating influences of reactions between the granite,
country rocks, and la te stage differentiates will becloud the p ic tu re of
the granite* s history until m ore is learned about the geology of the in
trusion.
-
DEVIATION MAPS
Deviations from calculated linear values w ere plotted and con
toured (see F igs. 24-29). Deviations from higher o rder surfaces were
not trea ted because higher o rder te rm s account for m ore and m ore
sum s of squares thereby reducing deviations,, Im plicit in th is study is
the assum ption that a linear trend surface is an adequate representation
of any regional trend, while higher order trend surfaces may m ask im
portant anom alies removing them from deviation te rm s. Deviations a re
probably not significant unless they a re m ore than one standard deviation
away from the surface, where the standard deviation is computed from
frequency distributions of the variables. Significant deviations may
also be surrounded by deviations of the sam e sign and of a le sse r or
g rea ter magnitude.
In th is study deviations from the regional trend (linear trend
surface) apparently have no sim ple relationship to the surrounding
country rocks. Since lack of reaction of the granite with the country
rocks seem s to be characte ristic , lack of correla tion of the deviations
with contiguous country rocks is not su rprising (cf. Fig. 4 with F igs.
24-29). The Paleozoic rocks surrounding the m assif a re largely lim e
stones, and one might expect positive Ca anom alies a t contacts of the
55
-
Figure 24. —Map for deviations from the linear trend
surface for percent K in the Stronghold
Granite.
-
m m
SB
-
Figure 25. —Map for deviations from the linear trend
surface for percent Ca in the Stronghold
Granite.
-
DEVIATIONSE X P L A N A T I O N
P o s i t i v e N e g a t i v e
-
Figure 26. —Map for deviations from the linear trend
surface for ppm Rb in the
Stronghold Granite.
-
'' ’•X’X-Xv!
Rb LINEAR DEVIATIONS
E X P L A N A T I O NP o s i t i v e
o x 0-200
CJI00
-
Figure 27, —Map for deviations from the linear trend
surface for ppm Sr in theK *
. Stronghold Granite.
-
CJi
-
Figure 28. —Map for deviations from the linear trend
surface for the ra tio K/Rb in the
Stronghold Granite.
-
Figure 29, —Map for deviations from the linear trend
surface for the ra tio C a/Sr in the
Stronghold Granite,
-
Ca/Sr LINEA
DEVIATIONSE X P L A N A T I O N
N e g a t i v e
B ,
-
62
granite and the Paleozoic country rocks, but no such sim ple re la tion
ship is apparent in the deviation m aps.
Speculations concerning deviation m aps m ust await processing
of complimentary petrographic data by trend surface analysis.
-
SUMMARY AND CONCLUSIONS
1. X -ray fluorescent spectrographic analysis is a re liab le
method for p a rtia l analysis of granitic rocks, and it is especially
amenable to the analyses of elem ents such as Sr and Rb which a re dif
ficult to tre a t using norm al chem ical techniques.
2. Trend surface analysis can be used to establish chemical
trends in granitic bodies where such trends a re not otherw ise clear in
raw data. Such trends can be used to establish a rea s within a granite
pluton which are characterized by la te stage igneous activity.
3. The Stronghold G ranite is an alkali granite im poverished
in Sr and higher in the ra tio C a/S r with respec t to other analyzed
granites of sim ilar Ca content. Rb and K/Rb values of the Stronghold
G ranite a re not s ignificantly different from sim ilar rocks. Reported
negative correlation between Ca and Sr, and the ra tio C a/Sr is co r
roborated. C a/S r and K/Rb trend surfaces show negative correlation
and indicate that la te stage igneous activity p rogressed toward the
northeast in the Stronghold G ranite pluton.
6 3
-
APPENDIX I
TABULATION OF ANALYSES OF STRONGHOLD GRANITE SAMPLES EXCLUDING LOCATIONS
NOTE: All data a re listed here in p a rts per million, that is ,
to read percentages count four p laces over from the right.
EXAMPLE: Read 0000044800 as 4.48 percent. Read
0000000010 as 10 ppm.
F or purposes of computation, Sr values originally recorded as
le ss than 10 ppm a re reported as 5 ppm. Oxide percentages and ra tio s
of the elem ents were computed by mi auxiliary program on the IBM 650
computer.
6 4
-
65
-
Sample No.
0000000001
0000000002
0 0 0 0 0 0 0 0 0 3
0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 5
0 0 0 0 0 0 0 0 0 6
0 0 0 0 0 0 0 0 0 7
0 0 0 0 0 0 0 0 0 8
0 0 0 0 0 0 0 0 0 9
0000000010
0000000011
0000000012
0 0 0 0 0 0 0 0 1 3
0 0 0 0 0 0 0 0 1 4
0 0 0 0 0 0 0 0 1 5
0 0 0 0 0 0 0 0 1 6
0 0 0 0 0 0 0 0 1 7
0 0 0 0 0 0 0 0 1 8
000000001Q
0000000020
0000000021
0000000022
0 0 0 0 0 0 0 0 2 3
0 0 0 0 0 0 0 0 2 4
0 0 0 0 0 0 0 0 2 5
0 0 0 0 0 0 0 0 2 6
0 0 0 0 0 0 0 0 2 7
0 0 0 0 0 0 0 0 2 8
% K
0 0 0 0 0 4 4 8 0 0
0 0 0 0 0 4 3 6 0 0
0 0 0 0 0 4 2 4 0 0
0 0 0 0 0 3 9 2 0 0
0 0 0 0 0 4 0 7 0 0
0 0 0 0 0 4 4 2 0 0
0 0 0 0 0 4 4 8 0 0
0 0 0 0 4 0 0 0 0
0 0 0 0 0 4 2 7 0 0
0 0 0 0 0 3 8 9 0 0
0 0 0 0 0 3 2 8 0 0
0 0 0 0 0 4 3 0 0 0
0 0 0 0 0 3 8 9 0 0
0 0 0 0 0 3 9 8 0 0
0 0 0 0 0 4 3 0 0 0
0 0 0 0 0 3 3 3 0 0
0 0 0 0 0 4 5 7 0 0
0 0 0 0 0 4 3 4 0 0
0 0 0 0 0 4 6 7 0 0
0 0 0 0 4 0 0 0 0
0 0 0 0 0 4 3 7 0 0
0 0 0 0 0 4 2 7 0 0
0 0 0 0 0 4 2 0 0 0
0 0 0 0 0 3 7 3 0 0
0 0 0 0 4 0 0 0 0
0 0 0 0 0 3 7 7 0 0
0 0 0 0 0 3 5 6 0 0
0 0 0 0 0 4 1 4 0 0
% k 2o
0 0 0 0 0 5 3 9 7 0
0 0 0 0 0 5 2 5 2 0
0 0 0 0 0 5 1 0 8 0
0 0 0 0 0 4 7 2 2 0
0 0 0 0 0 4 9 0 3 0
0 0 0 0 0 5 3 2 4 0
0 0 0 0 0 5 3 9 7 0
0 0 0 0 0 4 8 1 8 0
0 0 0 0 0 5 1 4 4 0
0 0 0 0 0 4 6 8 6 0
0 0 0 0 0 3 9 5 1 0
0 0 0 0 0 5 1 8 0 0
0 0 0 0 0 4 6 8 6 0
0 0 0 0 0 4 7 9 4 0
0 0 0 0 0 5 1 8 0 0
0 0 0 0 0 4 0 1 1 0
0 0 0 0 0 5 5 0 5 0
0 0 0 0 0 5 1 0 8 0
0 0 0 0 0 5 6 2 5 0
0 0 0 0 0 4 8 1 8 0
0 0 0 0 0 5 2 6 4 0
0 0 0 0 0 5 1 4 4 0
0 0 0 0 0 5 0 5 9 0
0 0 0 0 0 4 4 9 3 0
0 0 0 0 0 4 8 1 8 0
0 0 0 0 0 4 5 4 1 0
0 0 0 0 0 4 2 8 8 0
0 0 0 0 0 4 9 8 7 0
% Ca
0 0 0 0 0 0 4 7 0 0
0 0 0 0 0 0 4 4 0 0
0 0 0 0 0 0 6 4 0 0
0 0 0 0 0 0 4 9 0 0
0 0 0 0 0 0 4 2 0 0
0 0 0 0 0 0 7 6 0 0
0 0 0 0 0 0 3 2 0 0
0 0 0 0 0 0 7 0 0 0
0 0 0 0 0 0 5 1 0 0
0 0 0 0 0 0 4 2 0 0
0 0 0 0 0 0 4 4 0 0
0 0 0 0 0 0 4 0 0 0
0 0 0 0 0 0 4 4 0 0
0 0 0 0 0 0 4 5 0 0
0 0 0 0 0 0 5 7 0 0
0 0 0 0 0 0 7 7 0 0
0 0 0 0 0 0 5 0 0 0
0 0 0 0 0 0 6 6 0 0
0 0 0 0 0 0 3 3 0 0
0 0 0 0 0 0 4 8 0 0
0 0 0 0 0 0 4 5 0 0
0 0 0 0 0 0 4 7 0 0
0 0 0 0 0 0 4 2 0 0
0 0 0 0 0 0 4 9 0 0
0 0 0 0 0 0 3 4 0 0
0 0 0 0 0 0 5 6 0 0
0 0 0 0 0 0 5 2 0 0
0 0 0 0 0 0 4 7 0 0
% CaC
0 0 0 0 0 0 6 5 8 0
0 0 0 0 0 0 6 1 6 0
0 0 0 0 0 0 8 9 5 0
0 0 0 0 0 0 6 8 6 0
0 0 0 0 0 0 5 8 8 0
0 0 0 0 0 1 0 6 3 0
0 0 0 0 0 0 4 4 8 0
0 0 0 0 0 0 9 7 9 0
0 0 0 0 0 0 7 1 4 0
0 0 0 0 0 0 5 8 8 0
0000006160
0 0 0 0 0 0 5 6 0 0
0 0 0 0 0 0 6 1 6 0
0 0 0 0 0 0 6 3 0 0
0 0 0 0 0 0 7 9 8 0
0 0 0 0 0 1 0 7 7 0
0 0 ^ 0 0 0 7 0 0 0
0 0 0 0 0 0 9 2 3 0
0 0 0 0 0 0 4 6 2 0
0 0 0 0 0 0 6 7 2 0
0 0 0 0 0 0 6 3 0 0
0 0 0 0 0 0 6 5 8 0
0 0 0 0 0 0 5 8 8 0
0 0 0 0 0 0 6 8 6 0
0 0 0 0 0 0 4 7 6 0
0 0 0 0 0 0 7 8 4 0
0 0 0 0 0 0 7 2 8 0
0 0 0 0 0 0 6 5 8 0
ppm Rb
0 0 0 0 0 0 0 3 5 0
0 0 0 0 0 0 0 3 4 0
0 0 0 0 0 0 0 3 2 0
0 0 0 0 0 0 0 4 2 0
0 0 0 0 0 0 0 3 9 0
0 0 0 0 0 0 0 6 5 0
0 0 0 0 0 0 0 3 5 0
0 0 0 0 0 0 0 3 0 0
0 0 0 0 0 0 0 3 6 0
0 0 0 0 0 0 0 3 4 0
0 0 0 0 0 0 0 3 0 0
0 0 0 0 0 0 0 3 4 0
0 0 0 0 0 0 0 3 6 0
0 0 0 0 0 0 0 4 2 0
0 0 0 0 0 0 0 3 4 0
0 0 0 0 0 0 0 2 4 0
0 0 0 0 0 0 ^ 3 5 0
0 0 0 0 0 0 0 3 4 0
0 0 0 0 0 0 0 4 1 0
0 0 0 0 0 0 0 4 7 0
0 0 0 0 0 0 0 3 7 0
0 0 0 0 0 0 0 3 8 0
0 0 0 0 0 0 0 3 8 0
0 0 0 0 0 0 0 3 0 0
0 0 0 0 0 0 0 4 6 0
0 0 0 0 0 0 0 3 5 0
0 0 0 0 0 0 0 2 8 0
0 0 0 0 0 0 0 3 6 0
ppm Sr
o o n o o o o o i o
0000000020
0 0 0 0 0 0 0 0 3 0
0000000010
0000000010
0000000010
0000000010
0 0 0 0 0 0 0 0 6 0
0 0 0 0 0 0 0 0 3 0
0000000020
0 0 0 0 0 0 0 0 3 0
0 0 0 0 0 0 0 0 3 0
0000000010
0000000010
0000000010
0 0 0 0 0 0 0 0 4 0
0000000010
0 0 0 0 0 0 0 0 6 0
0000000010
0 0 0 0 0 0 0 0 0 5
0000000010
0 0 0 0 0 0 0 0 3 0
0000000010
0 0 0 0 0 0 0 0 5 0
0000000010
0 0 0 0 0 0 0 0 6 0
0 0 0 0 0 0 0 0 5 0
0000000020
K/Rb
0 0 0 1 2 8 0 0 0 0
0 0 0 1 2 8 2 0 0 0
0 0 0 1 3 2 5 0 0 0
0 0 0 0 9 3 3 0 0 0
0 0 0 1 0 4 4 0 0 0
0 0 0 0 6 8 0 0 0 0
0 0 0 1 2 8 0 0 0 0
0 0 0 1 3 3 3 0 0 0
0 0 0 1 1 8 6 0 0 0
0 0 0 1 1 4 4 0 0 0
0 0 0 1 0 9 3 0 0 0
0 0 0 1 2 6 5 0 0 0
0 0 0 1 0 8 1 0 0 0
0 0 0 0 9 4 8 0 0 0
0 0 0 1 2 6 5 0 0 0
0 0 0 1 3 8 8 0 0 0
0 0 0 1 3 0 6 0 0 0
0 0 0 1 2 4 7 0 0 0
0 0 0 1 1 3 9 0 0 0
0 0 0 0 8 5 1 0 0 0
0 0 0 1 1 8 1 0 0 0
0 0 0 1 1 2 4 0 0 0
0 0 0 1 1 0 5 0 0 0
0 0 0 1 2 4 3 0 0 0
0 0 0 0 8 7 0 0 0 0
0 0 0 1 0 7 7 0 0 0
0 0 0 1 2 7 1 0 0 0
0 0 0 1 1 5 0 0 0 0
Ca/Sr
0 0 0 4 7 0 0 0 0 0
0002200000
0 0 0 2 1 3 3 0 0 0
0 0 0 4 9 0 0 0 0 0
0 0 0 4 2 0 0 0 0 0
0 0 0 7 6 0 0 0 0 0
0 0 0 3 2 0 0 0 0 0
0 0 0 1 1 6 7 0 0 0
0 0 0 1 7 0 0 0 0 0
0002100000
0 0 0 1 4 6 7 0 0 0
0 0 0 1 3 3 3 0 0 0
0 0 0 4 4 0 0 0 0 0
0 0 0 4 5 0 0 0 0 0
0 0 0 5 7 0 0 0 0 0
0 0 0 1 9 2 5 0 0 0
0 0 0 5 0 0 0 0 0 0
0001100000
0 0 0 3 3 0 0 0 0 0
0 0 0 9 6 0 0 0 0 0
0 0 0 4 5 0 0 0 0 0
0 0 0 1 5 6 7 0 0 0
0 0 0 4 2 0 0 0 0 0
0 0 0 0 9 8 0 0 0 0
0 0 0 3 4 0 0 0 0 0
0 0 0 0 9 3 3 0 0 0
0 0 0 1 0 4 0 0 0 0
0 0 0 2 3 5 0 0 0 0
-
66
-
0 0 0 0 0 0 0 0 5 7
0 0 0 0 0 0 0 0 5 8
0 0 0 0 0 0 0 0 5 9
0 0 0 0 0 0 0 0 6 0
0 0 0 0 0 0 0 0 6 1
0 0 0 0 0 0 0 0 6 ?
0 0 0 0 0 0 0 0 6 3
0 0 0 0 0 0 0 0 6 4
0 0 0 0 0 0 0 0 6 5
0 0 0 0 0 0 0 0 6 6
0 0 0 0 0 0 0 0 6 7
0 0 0 0 0 0 0 0 6 8
0 0 0 0 0 0 0 0 6 9
0 0 0 0 0 0 0 0 7 0
0 0 0 0 0 0 0 0 7 1
0 0 0 0 0 0 0 0 7 2
0 0 0 0 0 0 0 0 7 3
0 0 0 0 0 0 0 0 7 4
0 0 0 0 0 0 0 0 7 5
0 0 0 0 0 0 0 7 6
0 0 0 0 0 0 0 0 7 7
0 0 0 0 0 0 0 0 7 8
0 0 0 0 0 0 0 0 7 9
0 0 0 0 0 0 0 0 8 0
0 0 0 0 0 0 0 0 8 1
0 0 0 0 0 0 0 0 8 2
0 0 0 0 0 0 0 0 8 3
0 0 0 0 0 0 0 0 8 4
0 0 0 0 0 4 1 3 0 0
0 0 0 0 0 3 8 4 0 0
0 0 0 0 0 4 9 0 0 0
0 0 0 0 0 4 2 6 0 0
0 0 0 0 0 4 3 7 0 0
0 0 0 0 0 4 ? 3 0 0
0 0 0 0 0 4 3 0 0 0
0 0 0 0 0 3 7 3 0 0
0 0 0 0 0 4 4 4 0 0
0 0 0 0 0 4 5 6 0 0
0 0 0 0 0 4 1 5 0 0
0 0 0 0 0 4 3 8 0 0
0 0 0 0 0 3 8 1 0 0
0 0 0 0 0 3 7 6 0 0
0 0 0 0 0 4 1 8 0 0
0 0 0 0 0 3 6 6 0 0
0 0 0 0 0 3 9 7 0 0
0 0 0 0 0 4 3 3 0 0
0 0 0 0 0 4 0 4 0 0
0 0 0 0 0 4 6 7 0 0
0 0 0 0 0 3 4 3 0 0
0 0 0 0 . 3 0 0 0 0
0 0 0 0 0 3 7 5 0 0
0 0 0 0 0 3 9 8 0 0
0 0 0 0 0 4 5 6 0 0
0 0 0 0 0 4 1 8 0 0
0 0 0 0 0 3 9 9 0 0
0 0 0 0 0 4 1 0 0 0
0 0 0 0 0 4 9 7 5 0
0 0 0 0 0 4 6 2 6 0
0 0 0 0 0 5 9 0 3 0
0 0 0 0 0 5 1 3 2 0
0 0 0 0 0 5 2 6 4 0
0 0 0 0 0 5 0 9 5 0
0 0 0 0 0 5 1 8 0 0
0 0 0 0 0 4 4 9 3 0
0 0 0 0 0 5 3 4 8 0
0 0 0 0 0 5 4 9 3 0
0 0 0 0 0 4 9 9 9 0
0 0 0 0 0 5 2 7 6 0
0 0 0 0 0 4 5 9 0 0
0 0 0 0 0 4 5 2 9 0
0 0 0 0 0 5 0 3 5 0
0 0 0 0 0 4 4 0 9 0
0 0 0 0 0 4 7 8 2 0
0 0 0 0 0 5 2 1 6 0
0 0 0 0 0 4 8 6 7 0
0 0 0 0 0 5 6 2 5 0
0 0 0 0 0 4 1 3 2 0
0 0 0 0 0 3 6 1 4 0
0 0 0 0 0 4 5 1 7 0
0 0 0 0 0 4 7 9 4 0
0 0 0 0 0 5 4 9 3 0
0 0 0 0 0 5 0 3 5 0
0 0 0 0 0 4 8 0 6 0
0 0 0 0 0 4 9 3 9 0
0 0 0 0 0 0 3 7 0 0
0 0 0 0 0 0 4 1 0 0
0 0 0 0 0 0 4 2 0 0
0 0 0 0 0 0 4 0 0 0
0 0 0 0 0 0 4 0 0 0
0 0 0 0 0 0 3 9 0 0
0 0 0 0 0 0 4 8 0 0
0 0 0 0 0 0 4 9 0 0
0 0 0 0 0 0 4 2 0 0
0 0 0 0 0 0 4 4 0 0
0 0 0 0 0 0 4 9 0 0
0 0 0 0 0 0 5 0 0 0
0 0 0 0 0 0 4 8 0 0
0 0 0 0 0 0 3 9 0 0
0 0 0 0 0 0 3 1 0 0
0 0 0 0 0 0 4 3 0 0
0 0 0 0 0 0 5 3 0 0
0 0 0 0 0 0 4 8 0 0
0 0 0 0 0 0 5 2 0 0
0 0 0 0 0 0 3 6 0 0
0000002000
0 0 0 0 0 0 1 4 0 0
0 0 0 0 0 0 3 0 0 0
0 0 0 0 0 0 6 1 0 0
0 0 0 0 0 0 3 6 0 0
0 0 0 0 0 0 5 0 0 0
0 0 0 0 0 0 1 8 0 0
0 0 0 0 0 0 3 3 0 0
0 0 0 0 0 0 5 1 8 0
0 0 0 0 0 0 5 7 4 0
0 0 0 0 0 0 5 8 8 0
0 0 0 0 0 0 5 6 0 0
0 0 0 0 0 0 5 6 0 0
0 0 0 0 0 0 5 4 6 0
0 0 0 0 0 0 6 7 2 0
0000006860
0 0 0 0 0 0 5 8 8 0
0 0 0 0 0 0 6 1 6 0
0 0 0 0 0 0 6 8 6 0
0 0 0 0 0 0 7 0 0 0
0 0 0 0 0 0 6 7 2 0
0 0 0 0 0 0 5 4 6 0
0 0 0 0 0 0 4 3 4 0
0 0 0 0 0 0 6 0 2 0
0 0 0 0 0 0 7 4 2 0
0 0 0 0 0 0 6 7 2 0
0 0 0 0 0 0 7 2 8 0
0 0 0 0 0 0 5 0 4 0
0 0 0 0 0 0 2 8 0 0
0 0 0 0 0 0 1 9 6 0
0 0 0 0 0 0 4 2 0 0
0 0 0 0 0 0 8 5 4 0
0 0 0 0 0 0 5 0 4 0
^ 0 0 0 0 0 7 0 0 0
0 0 0 0 0 0 2 5 2 0
0 0 0 0 0 0 4 6 2 0
0 0 0 0 0 0 0 4 3 0
0 0 0 0 0 0 0 4 1 0
0 0 0 0 0 0 0 4 7 0
0 0 0 0 0 0 0 3 9 0
0 0 0 0 0 0 0 3 5 0
0 0 0 0 0 0 0 4 5 0
0 0 0 0 0 0 0 4 6 0
0 0 0 0 0 0 0 4 1 0
0 0 0 0 0 0 0 4 0 0
0 0 0 0 0 0 0 3 2 0
0 0 0 0 0 0 0 3 7 0
0 0 0 0 0 0 0 3 4 0
0 0 0 0 0 0 0 4 1 0
0 0 0 0 0 0 0 3 9 0
0 0 0 0 0 0 0 4 7 0
0 0 0 0 0 0 0 4 2 0
0 0 0 0 0 0 0 3 5 0
0 0 0 0 0 0 0 3 3 0
0 0 0 0 0 0 0 3 2 0
0 0 0 0 0 0 0 4 8 0
0 0 0 0 0 0 0 2 7 0
0 0 0 0 0 0 0 2 8 0
0 0 0 0 0 0 0 3 0 0
0 0 0 0 0 0 0 3 2 0
0 0 0 0 0 0 0 3 9 0
0 0 0 0 0 0 0 3 2 0
0 0 0 0 0 0 0 7 3 0
0 0 0 0 0 0 0 3 2 0
0000000020
0000000020
0000000020
0000000010
0000000020
0000000010
0000000010
0000000010
0000000020
0 0 0 0 0 0 0 0 1 0
0000000010
0000000010
0000000010
0 0 0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 2 0
0000000010
0 0 0 0 0 0 0 0 3 0
0000000010
0000000020
0000000010
0 0 0 0 0 0 0 0 4 0
0 0 0 0 0 0 0 0 3 0
0000000020
0000000020
0 0 0 0 0 0 0 0 0 5
0000000010
0 0 0 0 9 6 0 0 0 0
0 0 0 0 9 3 7 0 0 0
0 0 0 1 0 4 3 0 0 0
0 0 0 1 0 9 2 0 0 0
0 0 0 1 2 4 9 0 0 0
0 0 0 0 9 4 0 0 0 0
0 0 0 0 9 3 5 0 0 0
0 0 0 0 9 1 0 0 0 0
0001110000
0 0 0 1 4 2 5 0 0 0
0001122000
0 0 0 1 2 8 8 0 0 0
0 0 0 0 9 2 9 0 0 0
0 0 0 0 9 6 4 0 0 0
0 0 0 0 8 8 9 0 0 0
0 0 0 0 8 7 1 0 0 0
0 0 0 1 1 3 4 0 0 0
0 0 0 1 3 1 2 0 0 0
0 0 0 1 2 6 3 0 0 0
0 0 0 0 9 7 3 0 H O
0 0 0 1 2 7 0 0 0 0
0 0 0 1 0 7 1 0 0 0
0 0 0 1 2 5 0 0 0 0
0 0 0 1 2 4 4 0 0 0
0 0 0 1 1 6 9 0 0 0
0 0 0 1 3 0 6 0 0 0
0 0 0 0 5 4 7 0 0 0
0 0 0 1 2 8 1 0 0 0
0 0 0 1 8 5 0 0 0 0
0 0 0 2 0 5 0 0 0 0
0002100000
0 0 0 4 0 0 0 0 0 0
0002000000
0 0 0 3 9 0 0 0 0 0
0 0 0 4 8 0 0 0 0 0
0 0 0 4 9 0 0 0 0 0
0002100000
0 0 0 4 4 0 0 0 0 0
0 0 0 4 9 0 0 0 0 0
0 0 0 5 0 0 0 0 0 0
0 0 0 4 8 0 0 0 0 0
0 0 0 1 9 5 0 0 0 0
0 0 0 0 7 7 5 0 0 0
0 0 0 4 3 0 0 0 0 0
0 0 0 2 6 5 0 0 0 0
0 0 0 4 8 0 0 0 0 0
0 0 0 1 7 3 3 0 0 0
0 0 0 3 6 0 0 0 0 0
0001000000
0 0 0 1 4 0 0 0 0 0
0 0 0 0 7 5 0 0 0 0
0 0 0 2 0 3 3 0 0 0
0 0 0 1 8 0 0 0 0 0
0 0 0 2 5 0 0 0 0 0
0 0 0 3 6 0 0 0 0 0
0 0 0 3 3 0 0 0 0 0
-
6 7
-
0 0 0 0 0 0 0 0 5 7 0 0 0 0 0 4 1 3 0 0 0 0 0 0 0 4 9 7 5 0 0 0 0 0 0 0 3 7 0 0 0 0 0 0 0 0 5 1 8 0 0 0 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 9 6 0 0 0 0 0 0 0 1 8 5 0 0 0 0
0 0 0 0 0 0 0 0 5 8 0 0 0 0 0 3 8 4 0 0 0 0 0 0 0 4 6 2 6 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 5 7 4 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 9 3 7 0 0 0 0 0 0 2 0 5 0 0 0 0
0 0 0 0 0 0 0 0 5 9 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 5 9 0 3 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 5 8 8 0 0 0 0 0 0 0 0 4 7 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 4 3 0 0 0 0 0 0 2 1 0 0 0 0 0
0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 4 2 6 0 0 0 0 0 0 0 5 1 3 2 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 5 6 0 0 0 0 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 9 2 0 0 0 0 0 0 4 0 0 0 0 0 0
0 0 0 0 0 0 0 0 6 1 0 0 0 0 0 4 3 7 0 0 0 0 0 0 0 5 2 6 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 5 6 0 0 0 0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 2 4 9 0 0 0 0 0 0 2 0 0 0 0 0 0
0 0 0 0 0 0 0 0 6 ? 0 0 0 0 0 4 2 3 0 0 0 0 0 0 0 5 0 9 5 0 0 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 5 4 6 0 0 0 0 0 0 0 0 4 5 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 9 4 0 0 0 0 0 0 0 3 9 0 0 0 0 0
0 0 0 0 0 0 0 0 6 3 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 5 1 8 0 0 0 0 0 0 0 0 4 8 0 0 0 0 0 0 0 0 6 7 2 0 0 0 0 0 0 0 0 4 6 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 9 3 5 0 0 0 0 0 0 4 8 0 0 0 0 0
0 0 0 0 0 0 0 0 6 4 0 0 0 0 0 3 7 3 0 0 0 0 0 0 0 4 4 9 3 0 0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 6 8 6 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 9 1 0 0 0 0 0 0 0 4 9 0 0 0 0 0
0 0 0 0 0 0 0 0 6 5 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 5 3 4 8 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 5 8 8 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 1 0 0 0 0 0 0 0 2 1 0 0 0 0 0
0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 4 5 6 0 0 0 0 0 0 0 5 4 9 3 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 6 1 6 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 4 2 5 0 0 0 0 0 0 4 4 0 0 0 0 0
0 0 0 0 0 0 0 0 6 7 0 0 0 0 0 4 1 5 0 0 0 0 0 0 0 4 9 9 9 0 0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 6 8 6 0 0 0 0 0 0 0 0 3 7 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 2 2 0 0 0 0 0 0 4 9 0 0 0 0 0
0 0 0 0 0 0 0 0 6 8 0 0 0 0 0 4 3 8 0 0 0 0 0 0 0 5 2 7 6 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 3 4 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 2 8 8 0 0 0 0 0 0 5 0 0 0 0 0 0
0 0 0 0 0 0 0 0 6 9 0 0 0 0 0 3 8 1 0 0 0 0 0 0 0 4 5 9 0 0 0 0 0 0 0 0 4 8 0 0 0 0 0 0 0 0 6 7 2 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 9 2 9 0 0 0 0 0 0 4 8 0 0 0 0 0
0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 3 7 6 0 0 0 0 0 0 0 4 5 2 9 0 0 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 5 4 6 0 0 0 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 9 6 4 0 0 0 0 0 0 1 9 5 0 0 0 0
0 0 0 0 0 0 0 0 7 1 0 0 0 0 0 4 1 8 0 0 0 0 0 0 0 5 0 3 5 0 . 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 4 3 4 0 0 0 0 0 0 0 0 4 7 0 0 0 0 0 0 0 0 0 4 0 ... 0 0 0 0 8 8 9 0 0 0 0 0 0 0 7 7 5 0 0 0
0 0 0 0 0 0 0 0 7 2 0 0 0 0 0 3 6 6 0 0 0 0 0 0 0 4 4 0 9 0 0 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 6 0 2 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 8 7 1 0 0 0 0 0 0 4 3 0 0 0 0 0
0 0 0 0 0 0 0 0 7 3 0 0 0 0 0 3 9 7 0 0 0 0 0 0 0 4 7 8 2 0 0 0 0 0 0 0 5 3 0 0 0 0 0 0 0 0 7 4 2 0 0 0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 3 4 0 0 0 0 0 0 2 6 5 0 0 0 0
0 0 0 0 0 0 0 0 7 4 0 0 0 0 0 4 3 3 0 0 0 0 0 0 0 5 2 1 6 0 0 0 0 0 0 0 4 8 0 0 .. 0 0 0 0 0 0 6 7 2 0 0 0 0 0 0 0 0 3 3 0 .. 0 0 0 0 0 0 0 0 1 0 ....0 0 0 1 3 1 2 0 0 0 ..0 0 0 4 8 0 0 0 0 0
0 0 0 0 0 0 0 0 7 5 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 4 8 6 7 0 0 0 0 0 0 0 5 2 0 0 0 0 0 0 0 0 7 2 8 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 1 2 6 3 0 0 0 0 0 0 1 7 3 3 0 0 0
0 0 0 0 0 0 0 0 7 6 0 0 0 0 0 4 6 7 0 0 0 0 0 0 0 5 6 2 5 0 0 0 0 0 0 0 3 6 0 0 0 0 0 0 0 0 5 0 4 0 0 0 0 0 0 0 0 4 8 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 9 7 3 0 0 0 0 0 0 3 6 0 0 0 0 0
0 0 0 0 0 0 0 0 7 7 0 0 0 0 0 3 4 3 0 0 0 0 0 0 0 4 1 3 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 8 0 0 0 0 0 0 0 0 0 2 7 0 . 0 0 0 0 0 0 0 0 2 0 0 0 0 1 2 7 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 7 8 0 0 0 0 ^ 3 0 0 0 0 0 0 0 0 0 3 6 1 4 0 0 0 0 0 0 0 1 4 0 0 0 0 0 0 0 0 1 9 6 0 0 0 0 0 0 0 0 2 8 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 7 1 0 0 0 0 0 0 1 4 0 0 0 0 0
0 0 0 0 0 0 0 0 7 9 0 0 0 0 0 3 7 5 0 0 0 0 0 0 0 4 5 1 7 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 2 5 0 0 0 0 0 0 0 0 7 5 0 0 0 0
0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 3 9 8 0 0 0 0 0 0 0 4 7 9 4 0 0 0 0 0 0 0 6 1 0 0 0 0 0 0 0 0 8 5 4 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 1 2 4 4 0 0 0 0 0 0 2 0 3 3 0 0 0
0 0 0 0 0 0 0 0 8 1 0 0 0 0 0 4 5 6 0 0 0 0 0 0 0 5 4 9 3 0 0 0 0 0 0 0 3 6 0 0 0 0 0 0 0 0 5 0 4 0 0 0 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 6 9 0 0 0 0 0 0 1 8 0 0 0 0 0
0 0 0 0 0 0 0 0 8 2 0 0 0 0 0 4 1 8 0 0 0 0 0 0 0 5 0 3 5 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 3 0 6 0 0 0 0 0 0 2 5 0 0 0 0 0
0 0 0 0 0 0 0 0 8 3 0 0 0 0 0 3 9 9 0 0 0 0 0 0 0 4 8 0 6 0 0 0 0 0 0 0 1 8 0 0 0 0 0 0 0 0 2 5 2 0 0 0 0 0 0 0 0 7 3 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 5 4 7 0 0 0 0 0 0 3 6 0 0 0 0 0
0 0 0 0 0 0 0 0 8 4 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 4 9 3 9 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 4 6 2 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 2 8 1 0 0 0 0 0 0 3 3 0 0 0 0 0
-
68
-
0 0 0 0 0 0 0 0 8 5 0 0 0 0 0 3 5 2 0 0 0 0 0 0 0 4 2 4 0 0 0 0 0 0 0 1 3 7 0 0 0 0 0 0 0 1 9 1 7 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 7 3 0 0 0 0 0 0 6 8 5 0 0 0 0
0 0 0 0 0 0 0 0 8 6 0 0 0 0 0 4 4 2 0 0 0 0 0 0 0 5 3 2 4 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 5 7 4 0 0 0 0 0 0 0 0 3 1 0 o o n o o o o o i o 0 0 0 1 4 2 6 0 0 0 0 0 0 4 1 0 0 0 0 0
0 0 0 0 0 0 0 0 8 7 0 0 0 0 0 4 1 8 0 0 0 0 0 0 0 5 0 3 5 0 0 0 0 0 0 0 3 6 0 0 0 0 0 0 0 0 5 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 4 5 0 0 0 0 0 0 1 8 0 0 0 0 0
0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 4 1 7 0 0 0 0 0 0 0 5 0 2 3 0 0 0 0 0 0 0 2 7 0 0 0 0 0 0 0 0 3 7 8 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 4 3 0 0 0 0 0 0 1 3 5 0 0 0 0
0 0 0 0 0 0 0 0 8 9 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 4 6 9 8 0 0 0 0 0 0 0 2 5 0 0 0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 4 0 0 0 0 0 0 2 5 0 0 0 0 0
0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 4 0 6 0 0 0 0 0 0 0 4 8 9 1 0 0 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 5 4 6 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 3 5 3 0 0 0 0 0 0 1 9 5 0 0 0 0
0 0 0 0 0 0 0 0 9 1 0 0 0 0 0 4 1 4 0 0 0 0 0 0 0 4 9 8 7 0 0 0 0 0 0 0 4 8 0 0 0 0 0 0 0 0 6 7 2 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 2 9 4 0 0 0 0 0 0 4 8 0 0 0 0 0
0 0 0 0 0 0 0 0 9 2 0 0 0 0 0 4 4 8 0 0 0 0 0 0 0 5 3 9 7 0 0 0 0 0 0 0 3 8 0 0 0 0 0 0 0 0 5 3 2 0 0 0 0 0 0 0 0 3 6 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 2 4 4 0 0 0 0 0 0 1 9 0 0 0 0 0
0 0 0 0 0 0 0 0 9 3 0 0 0 0 0 4 7 8 0 0 0 0 0 0 0 5 7 5 8 0 0 0 0 0 0 0 3 7 0 0 0 0 0 0 0 0 5 1 8 0 0 0 0 0 0 0 0 3 8 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 2 5 8 0 0 0 0 0 0 1 8 5 0 0 0 0
0 0 0 0 0 0 0 0 9 4 0 0 0 0 0 4 5 1 0 0 0 0 0 0 0 5 4 3 3 0 0 0 0 0 0 0 4 6 0 0 0 0 0 0 0 0 6 4 4 0 0 0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 0 3 0 0 0 0 1 2 8 9 0 0 0 0 0 0 1 5 3 3 0 0 0
0 0 0 0 0 0 0 0 9 5 0 0 0 0 0 4 3 4 0 0 0 0 0 0 0 5 2 2 8 0 0 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 3 7 2 0 0 0 0 0 0 0 0 3 6 0 0 0 0 0 0 0 0 0 0 5 0 0 0 1 2 0 6 0 0 0 0 0 0 4 6 0 0 0 0 0
0 0 0 0 0 0 0 0 9 6 0 0 0 0 0 4 5 1 0 0 0 0 0 0 0 5 4 3 3 0 0 0 0 0 0 0 1 8 0 0 0 0 0 0 0 0 2 5 2 0 0 0 0 0 0 0 0 3 7 0 0 0 0 0 0 0 0 0 0 5 0 0 0 1 2 1 9 0 0 0 0 0 0 3 6 0 0 0 0 0
0 0 0 0 0 0 0 0 9 7 0 0 0 0 0 4 1 3 0 0 0 0 0 0 0 4 9 7 5 0 0 0 0 0 0 0 5 1 0 0 0 0 0 0 0 0 7 1 4 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 2 5 2 0 0 0 0 0 0 1 2 7 5 0 0 0
0 0 0 0 0 0 0 0 9 8 0 0 0 0 0 4 3 4 0 0 0 0 0 0 0 5 2 2 8 0 0 0 0 0 0 0 3 8 0 0 0 0 0 0 0 0 5 3 2 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 1 3 5 6 0 0 0 0 0 0 1 2 6 7 0 0 0
0 0 0 0 0 0 0 0 9 9 0 0 0 0 0 4 3 8 0 0 0 0 0 0 0 5 2 7 6 0 0 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 3 2 2 0 0 0 0 0 0 0 0 3 1 0 0000000020 0 0 0 1 4 1 3 0 0 0 0 0 0 1 1 5 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 4 1 4 0 0 0 0 0 0 0 4 9 8 7 0 0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 0 4 2 0 0000000010 0 0 0 0 9 8 6 0 0 0 0 0 0 3 5 0 0 0 0 0
0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 4 1 6 0 0 0 0 0 0 0 5 0 1 1 0 0 0 0 0 0 0 5 1 0 0 0 0 0 0 0 0 7 1 4 0 0 0 0 0 0 0 0 3 6 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 1 5 6 0 0 0 0 0 0 1 2 7 5 0 0 0
0 0 0 0 0 0 0 1 0 7 0 0 0 0 0 4 2 3 0 0 0 0 0 0 0 5 0 9 5 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 8 0 0 0 0 0 0 0 0 0 3 0 0 0000000010 0 0 0 1 4 1 0 0 0 0 0002000000
0 0 0 0 0 0 0 1 0 3 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 5 3 4 8 0 0 0 0 0 0 0 3 7 0 0 0 0 0 0 0 0 5 1 8 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 4 8 0 0 0 0 0 0 0 3 7 0 0 0 0 0
0 0 0 0 0 0 0 1 0 4 0 0 0 0 0 3 9 6 0 0 0 0 0 0 0 4 7 7 0 0 0 0 0 0 0 0 4 7 0 0 0 0 0 0 0 0 6 5 8 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 4 0 0 0 0 1 2 3 8 0 0 0 0 0 0 1 1 7 5 0 0 0
0 0 0 0 0 0 0 1 0 5 0 0 0 0 0 3 3 5 0 0 0 0 0 0 0 4 0 3 5 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 5 7 4 0 0 0 0 0 0 0 0 3 4 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 9 8 5 0 0 0 0 0 0 1 3 6 7 0 0 0
0 0 0 0 0 0 0 1 0 6 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 4 9 5 1 0 0 0 0 0 0 0 3 6 0 0 0 0 0 0 0 0 5 0 4 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 5 0 0 0 1 2 8 4 0 0 0 0 0 0 7 2 0 0 0 0 0
0 0 0 0 0 0 0 1 0 7 0 0 0 0 0 4 0 9 0 0 0 0 0 0 0 4 9 2 7 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2 0 OOOl363nnn O n o l 5 n n o o o
0 0 0 0 0 0 0 1 0 8 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 5 3 0 0 0 0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 0 3 6 0 0 0 0 0 0 0 0 0 2 0 0OO12220nn 0 0 0 1 7 5 0 0 0 0
0 0 0 0 0 0 0 1 0 9 0 0 0 0 0 4 1 5 0 0 0 0 0 0 0 4 9 9 9 0 0 0 0 0 0 0 5 4 0 0 0 0 0 0 0 0 7 5 6 0 0 0 0 0 0 0 0 3 4 0 0 0 0 0 0 0 0 0 3 0 0 0 0 1 2 2 1 0 0 0 0 0 0 1 8 0 0 0 0 0
0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 4 9 2 0 0 0 0 0 0 0 5 9 2 7 0 0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 0 3 5 0 0000000010 0 0 0 1 4 0 6 0 0 0 0 0 0 3 5 0 0 0 0 0
0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 4 9 3 9 0 0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 6 8 6 0 0 0 0 0 0 0 0 3 4 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 2 0 6 0 0 0 0 0 0 2 4 5 0 0 0 0
0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 4 8 6 7 0 0 0 0 0 0 0 4 5 0 0 0 0 0 0 0 0 6 3 0 0 0 0 0 0 0 0 0 3 7 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 9 2 0 0 0 0 0 0 2 2 5 0 0 0 0
-
69
-
0 0 0 0 0 0 0 1 1 3 0 0 0 0 0 4 0 3 0 0 0 0 0 0 0 4 8 5 5 0
0 0 0 0 0 0 0 1 1 4 0 0 0 0 0 3 9 0 0 0 0 0 0 0 0 4 6 9 8 0
0 0 0 0 0 0 0 1 1 5 0 0 0 0 0 4 1 6 0 0 0 0 0 0 0 5 0 1 1 0
0 0 0 0 0 0 0 1 1 6 0 0 0 0 0 4 1 7 0 0 0 0 0 0 0 5 0 2 3 0
0 0 0 0 0 0 0 1 1 7 0 0 0 0 0 4 5 5 0 0 0 0 0 0 0 5 4 8 1 0
0 0 0 0 0 0 0 1 1 8 0 0 0 0 0 5 6 6 0 0 0 0 0 0 0 6 8 1 8 0
0 0 0 0 0 0 0 1 1 9 0 0 0 0 0 3 9 9 0 0 0 0 0 0 0 4 8 0 6 0
0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 4 2 7 0 0 0 0 0 0 0 5 1 4 4 0
0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 4 0 8 0 0 0 0 0 0 0 6 9 1 5 0
0 0 0 0 0 0 0 1 2 2 0 0 0 0 0 4 1 9 0 0 0 0 0 0 0 5 0 4 7 0
0 0 0 0 0 0 0 1 2 3 0 0 0 0 0 3 7 0 0 0 0 0 0 0 0 4 4 5 7 0
0 0 0 0 0 0 0 1 2 4 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 5 3 4 8 0
0 0 0 0 0 0 0 1 2 5 0 0 0 0 0 4 1 3 0 0 0 0 0 0 0 4 9 7 5 0
0 0 0 0 0 0 0 1 2 6 0 0 0 0 0 4 3 6 0 0 0 0 0 0 0 5 2 5 2 0
0 0 0 0 0 0 0 1 2 7 0 0 0 0 0 3 6 4 0 0 0 0 0 0 0 4 3 8 5 0
0 0 0 0 0 0 0 1 2 8 0 0 0 0 0 3 2 1 0 0 0 0 0 0 0 3 8 6 7 0
0 0 0 0 0 0 0 1 2 9 0 0 0 0 0 3 6 3 0 0 0 0 0 0 0 4 3 7 3 0
0 0 0 0 0 0 0 1 3 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 8 1 8 0
0 0 0 0 0 0 0 1 3 1 0 0 0 0 0 4 4 6 0 0 0 0 0 0 0 5 3 7 3 0
0 0 0 0 0 0 0 1 3 2 0 0 0 0 0 3 9 1 0 0 0 0 0 0 0 4 7 1 0 0
0 0 0 0 0 0 0 1 3 3 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 5 3 0 0 0
0 0 0 0 0 0 0 1 3 4 0 0 0 0 0 4 9 1 0 0 0 0 0 0 0 5 9 1 5 0
0 0 0 0 0 0 0 1 3 5 0 0 0 0 0 4 2 8 0 0 0 0 0 0 0 5 1 5 6 0
0 0 0 0 0 0 0 1 3 6 0 0 0 0 0 4 1 8 0 0 0 0 0 0 0 5 0 3 5 0
0 0 0 0 0 0 0 1 3 7 0 0 0 0 0 3 5 6 0 0 0 0 0 0 0 4 2 8 8 0
0 0 0 0 0 0 0 1 3 8 0 0 0 0 0 4 0 3 0 0 0 0 0 0 0 4 8 5 5 0
0 0 0 0 0 0 0 1 3 9 0 0 0 0 0 3 9 3 0 0 0 0 0 0 0 4 7 3 4 0
0 0 0 0 0 0 0 1 4 0 0 0 0 0 0 3 9 6 0 0 0 0 0 0 0 4 7 7 0 0
0 0 0 0 0 0 1 7 0 0 0 0 0 0 0 0 2 3 8 0 0 0 0 0 0 0 0 3 2 0
0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 1 1 1 9 0 0 0 0 0 0 0 0 3 3 0
0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 0 4 1 0
0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 6 8 6 0 0 0 0 0 0 0 0 4 0 0
0 0 0 0 0 0 1 9 0 0 0 0 0 0 0 0 2 6 6 0 0 0 0 0 0 0 0 3 4 0
0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 3 0 8 0 0 0 0 0 0 0 0 4 2 0
0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 4 4 0
0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 6 8 6 0 0 0 0 0 0 0 0 4 2 0
0 0 0 0 0 0 2 8 0 0 0 0 0 0 0 0 3 9 2 0 0 0 0 0 0 0 0 6 9 0
0 0 0 0 0 0 3 8 0 0 0 0 0 0 0 0 5 3 2 0 0 0 0 0 0 0 0 6 6 0
0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 5 6 0 0 0 0 0 0 0 0 0 7 9 0
0 0 0 0 0 0 5 3 0 0 0 0 0 0 0 0 7 4 2 0 0 0 0 0 0 0 0 3 2 0
0 0 0 0 0 0 3 8 0 0 0 0 0 0 0 0 5 3 2 0 0 0 0 0 0 0 0 3 6 0
00 0 0 0 0 4 8 00 0 0 0 0 0 0 6 7 2 0 0 0 0 0 0 0 0 4 3 0
0 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 6 0 2 0 0 0 0 0 0 0 0 5 5 0
0 0 0 0 0 0 1 9 0 0 0 0 0 0 0 0 2 6 6 0 0 0 0 0 0 0 0 6 7 0
0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 3 0 8 0 0 0 0 0 0 0 0 5 9 0
0 0 0 0 0 0 5 9 0 0 0 0 0 0 0 0 8 2 6 0 0 0 0 0 0 0 0 3 3 0
0 0 0 0 0 0 5 1 0 0 0 0 0 0 0 0 7 1 4 0 0 0 0 0 0 0 0 3 5 0
0 0 0 0 0 0 4 7 0 0 0 0 0 0 0 0 6 5 8 0 0 0 0 0 0 0 0 3 1 0
0 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 6 0 2 0 0 0 0 0 0 0 0 3 7 0
0 0 0 0 0 0 4 6 0 0 0 0 0 0 0 0 6 4 4 0 0 0 0 0 0 0 0 3 2 0
0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 7 000 0 0 0 0 0 0 0 3 2 0
0 0 0 0 0 0 4 5 0 0 0 0 0 0 0 0 6 3 0 0 0 0 0 0 0 0 0 4 9 0
0 0 0 0 0 0 3 7 0 0 0 0 0 0 0 0 5 1 8 0 0 0 0 0 0 0 0 3 9 0
0 0 0 0 0 0 5 5 0 0 0 0 0 0 0 0 7 7 0 0 0 0 0 0 0 0 0 3 3 0
0 0 0 0 0 0 3 5 0 0 0 0 0 0 0 0 4 9 0 0 0 0 0 0 0 0 0 3 5 0
0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 4 6 8 0 0 0 0 0 0 0 0 4 5 0
0 0 0 0 0 0 0 0 3 0 0 0 0 1 2 5 9 0 0 0 0 0 0 0 5 6 7 0 0 0
0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 8 2 0 0 0 0 0 0 0 7 2 7 0 0 0
0 0 0 0 0 0 0 0 8 0 0 0 0 1 0 1 5 0 0 0 0 0 0 0 4 3 8 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 4 3 0 0 0 0 0 0 2 4 5 0 0 0 0
0 0 0 0 0 0 0 0 4 0 0 0 0 1 3 3 8 0 0 0 0 0 0 0 4 7 5 0 0 0
0 0 0 0 0 0 0 0 8 0 ..0 0 0 1 3 4 8 0 0 0 0 0 0 0 2 7 5 0 0 0
0 0 0 0 0 0 0 0 3 0 0 0 0 0 9 0 7 0 0 0 0 0 0 1 6 6 7 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 1 7 0 0 0 0 0 0 2 4 5 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 5 9 1 0 0 0 0 0 0 2 8 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 6 3 5 0 0 0 0 0 0 3 8 0 0 0 0 0
0 0 0 0 0 0 0 0 0 5 0 0 0 0 4 6 8 0 0 0 0 0 0 8 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 1 3 8 8 0 0 0 . 0 0 0 5 3 0 0 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 4 7 0 0 0 0 0 0 1 9 0 0 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 1 4 0 0 0 0 0 0 2 4 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 6 6 2 0 0 0 0 0 0 4 3 0 0 0 0 0
0 0 0 0 0 0 0 0 0 5 0 0 0 0 4 7 9 0 0 0 0 0 0 3 8 0 0 0 0 0
0 0 0 0 0 0 0 0 0 5 0 0 0 0 6 1 5 0 0 0 0 0 0 4 4 0 0 0 0 0
0 0 0 0 0 0 0 0 4 0 0 0 0 1 2 1 2 0 0 0 0 0 0 1 4 7 5 0 0 0
0 0 0 0 0 0 0 0 4 0 0 0 0 1 2 7 4 0 0 0 0 0 0 1 2 7 5 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 1 2 6 1 0 0 0 0 0 0 47 0 0 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 1 1 8 9 0 0 0 0 0 0 2 1 5 0 0 0 0
0 0 0 0 0 0 0 0 3 0 0 0 0 1 5 3 4 0 0 0 0 0 0 1 5 3 3 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 1 3 3 8 0 0 0 0 0 0 2 5 0 0 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 0 8 5 3 0 0 0 0 0 0 2 2 5 0 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 0 9 1 3 0 0 0 0 0 0 1 8 5 0 0 0 0
0 0 0 0 0 0 0