A Cooperative Investigation of 

Precision and Accuracy in 

Chemical, Spectroche~ical , 

and Modal Analysis of 

Silica.te Rocks 

GEOLOGICAL SURVEY BULLETIN 980 
A Cooperative Investigation· of 

Precision and AccuracY in 

Chemical, Spectrochemical 

and Modal Analysis of 

Silicat·e Rocks 

By H. W. FAIRBAIRN and others 

CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

GEOLOGICAL SURVEY BULLETIN 980 

.An investigation by staff membersj of 

Department of Geplogy, Massachussetts 

Institute of Technology, Cambridge, 

Mass. (in collaboration ·with Office of 

Naval Research, lf7 ashington, D. C.); 

Geophysical Laboratory, Carnegie Institution of lf7 ashington, lf7 ashington, 

__ D. C.; Geochemistry and Petrology 

Branch, U. S. Geological Survey, 

Washington, D. C. 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 195 I 
UNITED STATES DEPARTMENT OF THE INTERIOR 

Oscar L. Chapman, Secretary 

GEOLOGICAL SURVEY 

W. E. Wrather, Director 

For sale by the Superintendent of Documents, U. S. Government Pri.itin~ Office 

Washington 25, D. C. - Price 35 cents (paper cover) 
·coNTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

FOREWORD 

BY EARL INGERSON 

This bulletin is the second of the series "Contributions to Geochemistry" which was begun in 1946 with Bulletin 950, "Contributions 

to Geochen1istry, 1 942-45". This series is the successor to earlier 

ones, also published as U. S. Geological Survey Bulletins, "Report 

of work done in the Division of Chemistry and Physics" (1879-1893), 

"Contributions to chemistry and mineralogy from the laboratory 

of the United States Geological Survey" (1 900), "Contributions to 

mineralogy from the United States Geological Survey" (1905), and _ "Mineralogical Notes" (1911-16). A third member of the current 

series is essentially ready for publication and we hope still others 

will appear from time to time. 

"Contributions to Geochemistry, 1942-45" consisted entirely of 

reports of work .done by Survey staff members, as did most of the 

earlier series mentioned above. Much of the noteworthy progress 

in tho earth sciences is being made possible by the cooperation of 

scientists in different disciplines and in various institutions. It is 

particularly gratifying, therefore, to present in thi~ bulletin a report 

of cooperative work with geochemical laboratories throughout the 

world, studied, interpreted, and prepared for publication by spectrographers, geochemists, and petrologists. The results will give an 

insight into the current status of spectrographic and chemical analysis 

of silicate rocks that could not have been obtained by any amount 

of ~ork by one group of scientists working in one laboratory. 

It is a pleasure to express, on behalf of the staff mernbers of the 

Branch of Geochemistry and Petrology, our sincere thanks to the 

many scientists who, at considerable sacrifice of their special interests, 

participated so generously and conscientiously in this project. I 

also wish to express our appreciation to the other cooperating institutions, the lVIassachusetts Institute of Technology and the Geophysical Laboratory of the Carnegie Ins~itution of Washington. 

III 

CONTENTS 

Page 

PART 1. Preparation and distribution of the samples, by H. W. Fairbairn__ 1 

2. Results of chemical a.nalysis of samples of granite and diabase, by 

William G. Schlecht and Rollin E. Stevens__________________ 7 

3. Spectrochemical analysis of major constituent elements in minerals 

and rocks, by W. H. Dennen, L. H. Ahrens, and H. W. Fairba~n--------------------------------------------------- 25 

4. Spectrochemical analysis of some of the rarer elements in the 

granite and diabase samples, by L. H. Ahrens_~-------------- 53 

5. Modal analyses of the test rocks, by Felix Chayes ____ ...;_________ 59 

6. Summary of results, by H. W. Fairbairn_____________________ 69 

ILLUSTRATIONS 

Pnge 

PLATE 1. Analyses of the granite and the diabase______________________ 42 

FrouRE 1-2. Histograms based on chemical data in tables i, 2, and 4____ 32 

3. Diagram showing mutual relations of arithmetic mean and 

relative error for each constituent in the two standard 

rocks_______________________________________________ 36 

4. Working curves for iron and aluminum___________________ 46 

5. Working curve for manganese___________________________ 47 

6. Working curves for calcium_____________________________ 48 

7. Working curves for magnesium__________________________ 49 

8. Working curve for sodium_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 50 

9. ·Working curve for potassium (direct method) _ _ _ _ _ _ _ _ _ _ _ _ 51 

10. Working curve for potassium (indirect method)____________ 52 

TABLES 

Page 

TABLE 1. Results of analyses and calculated CIPW norms of granite 

sample, reported by 34 collaborators ____________________ ..:_ 8 

2. Results of analyses and calculated CIPW norms of diabase 

sample, reported by 30 collaborators______________________ 10 

3. Results with different inethods of determining Si02_ _ _ _ _ _ _ _ _ _ _ 13 

4. Results with different methods of determining total iron_______ 15 

5. Results with different methods of determining N a20 ________ _ : 16 

6. -Results with different methods of determining K20 _ _ _ _ _ _ _ _ _ _ _ 18 

7. Results with different methods of determining P20 6._ _ _ _ _ _ _ _ _ _ _ 20 

v 
VI CONTENTS 

Page 

TABLE 8. Results with ~ifferent method~ of determining MnO______ 21 

9. Results with different methods of determining total water_____ 2p 

10. "Good" summations with low-silica results__________________ 23 

11. Relative deviation (C) and relative error (E) for A120 3, FeO, 

MnO, and CaO __________________________________ ._,_______ 28 

12. Reproducibility data for Si02 in diorite______________________ 29 

1,3. Spectrochemical precision data for Na20 and K20 in gr.anite 

sample________________________________________________ 29 

14. Precision of determinations in rock analyses by 24 laboratories_ 37 

15. Precision of determinations in six partial chemical analyses of 

soda feldspar from six laboratories ____________ ~___________ 38 

16. Precision of determinations in four analyses of alkali metals by flame photometer ________________________ ·_______________ 38 

17. Precision of determinations in replicate rock analyses by one 

laboratory~-------------------------------------------- 38 

18. Comparison of intralaboratory precision on selected constituents 

in granite and diabase samples _________________ ·__________ 39 

19. Means of consensus groupings of constituents________________ 40 

20. Comparison of consensus and arithmetic means __ :____________ 41 

21. Comparison of measured and calculated modeR of granite sample_ 42 

22. Compilation of rejected determinations in chemical analyses of 

standard rock samples____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 44 

23. Comparison of spectrographic and chemical methods of analysis 

for rarer elements in the granite and diabase samples__ _ _ _ _ _ 54 

24. Diabase modes converted to percent by weight______________ 60 

25. Granite modes, by volume_________________________________ 61 

26. Average modes for the test rocks_-------------------------- 61 

27. Comparison of norms and modes of the test rocks____________ 63 
A COOP~RATIVE INVESTIGATION OF 

PRECISION AND ACCURACY IN 

CHEMICAL, SPECTROCHEMICAL, AND MODAL ANA'LYSIS OF 

SILICATE ROCKS 

PART 1. PREPARATION AND DISTRIBUTION OF THE 

SAMPLES 

BY H. w. FAIRBAIRN 1 

Whosoever shall entertain high and vaporous imaginations, instead 

of a laborious and sober inquiry of truth, shall beget hopes and 

beliefs of strange and impossible shapes. 

-Francis Bacon. 

The eminent Elizabethan author of the above lines doubtless 

had in mind a much broader horizon for his "sober inquiry of truth" 

than the limited level of inquiry which we will pursue in the pages to 

follow. Nevertheless his pronouncement is entirely apposite, whatever the scale, and characterizes in a single phrase the nature of the 

investigation we are presenting here. This investigation, in its present 

form, is concerned with the fundamental matter of precision and accuracy as applied to chemical, spectrochemical, and modal analyses of 

rocks. Despite the dependence of petrologists and geochemists on 

such analyses, there has been little attempt at critical evaluation 

of the procedures used. We arc presenting in this bulletin some 

facts and ideas which 1nay stimulate interest in this· aspect of quantiLive 1neasurement. 

Although the investigation as presented here is the work of many 

people, it had its immediate roots some 2 years ago in the Geology 

Department of the Massachusetts Institute of Technology as part of 

a progran1 of spectrographic research under H. W. Fairbairn, supervisor, and L. H. Ahrens, associate supervisor, and sponsored by the 

Office of Naval Research, Washington, D. 0. It was agreed at that 

ti1nc that the spectrograph might play a very useful role in quantitative work on the major elements of rocks, a role heretofore reserved 

for the minor elements. This minor-element role is in part a result of 

expediency, since chemists could not on the whole do satisfactory work 

with the low concentrations of the 1ninor elements, whereas the field 

t Massachusetts Institute of Technology. 

1 
2 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

of the major elements was tacitly recognized as their preserve. 

Since progress always involves intrusion into new ground, it was 

decided to reconnoiter this new field 2 of spectroscopy of the major elements, not with the idea of supplanting the chemists' work, but rather 

with the object of utilizing the economies in time and expense offered 

by the spectrograph. Chemical analyses of silicate rocks are at best 

expensive, if one has the work done by a reputable analyst, or are 

time-consuming if one has the skill and courage to make one's own. 

It is therefore tempting to pit the possibilities of the spectrograph 

against the unavoidable disadvantages of time and expense which 

handicap the chemist in his role as geological aide. 

Work in the Cabot Spectrographic Laboratory at Massachusetts 

Institute of Technology established the feasibility of quantitative 

analyses of most of the major elements: the analysis requires only a 

few hours to complete, and gives a precision-reproducibility-of 

about 5 percent. (See part 3 of this report.) Obviously the next step 

was to obtain a measure of the accuracy-degree of approach to the 

absolute value-of the ·determinations made. One way was to prepare synthetic sta:q.dards, in which the tolerances of each constituent 

would be known, and so provide a reference level for spectrographic 

determination of unknowns of the major elements. A second way 

was to prepare a provisional standard sample of a natural rock and 

have replicate chemical analyses made, the average value for each 

constituent to serve as control for the spectrographic determination. 

·The matter was decided in favor of the second method (part 3 of this 

report), as it was believed that lack of a natural rock matrix in a 

synthetic standard might lead to errors difficult or impossible to 

evaluate. There was the additional advantage that a large sto.ck of 

the natural rock could be made up as a standard and be available for 

calibration over ·a long period of time. On the other hand, the synthesis of a comparable rock in large quantities would be an imprac- ~ 

ticable task. 

Two factors entered into the selection of a natural rock standard: 

It seemed advisable to use a silicate rock of widespread occurrence, 

and there would be an advantage in using a massive, medium-grained 

homogeneous material so that statistical analysis of the mode could 

be undertaken. These demands could be met, for example, in many 

types of granite and diabase. By a fortunate coincidence we learned 

that Dr. Felix Chayes, of the Geophysical Laboratory, had already 

selected a granite from Westerly, Rhode Island, for modal analysis. 

We immediately joined forces with him and decided to use this rock 

for calibration purposes, since any chemical data we might obtain 

2 Reference to previous and contemporary work by other investigators will be found in Part 3 of this report, 

page 21. 
.... 

,.. 

!)REPARATION AND DISTRIBUTION' OF THE SAMPLES 3 

would obviously be of immense interest for his modal analyses. He 

immediately took steps to obtain additional material and have it 

processed for chemical study. Dr. Chayes' report on the work follows. 

The granite was purchased from the Smith Granite Co. of Westerly, R. I., 

and was quarried from their principal working as of June 1947. It was received 

as a single rough-finished strip with cross section about 6 inches by 6 inches and 

a little over 6 feet long. The strip was sand-blasted to remove dirt and paint. 

Eight slugs, approximately 4 inches by 2 inches by 2 inches were taken at 6-inch 

intervals along the strip. These were numbered consecutively, and a thin section 

was prepared from tablets sawed from each end of each slug in the plane of the 

hardway. , 

The remninder of the strip was broken into large pieces by sledge hammer, ' 

and these were passed through a 4-inch by 6-inch jaw crusher. The entire 

primary crusher product was then passed through a 2-inch by 3-inch jaw crusher 

and the product of this operation screened on a 10-mesh Hummer vibrating 

sereen. Oversize from this operation was put through a rolls cr-usher with stage 

screening until the entire product was minus 10-mesh. The complete sample 

was then screened, by hand on an SO-mesh S-inch sieve and the plus SO-mesh 

product ground in 2-pound batches in S-inch Abbe mills with mullite balls. 

The grinding operation was performed in 15-minute passes, undersize material 

being removed by sieve between successive passes. A 50-gram grab sample of 

the original undersize from the rolls, a 50-gram sample of the finished pebble-mill 

product-also grab-and the slugs mentioned above are stored in my laboratory. 

Of 106 pounds of granite available for the crushing, 96 pounds were recovered 

in -SO-mesh material. Most of the loss was encountered in the jaw crushing. 

During this operation pebbles up to 3 inches in diameter, but mostly smaller, 

were frequently thrown out of the machine by the wedging action pf the jaws. 

In order to reduce chances of contamination we decided at the outset to discard 

fragments lost in this fashion; most of the 10-pound loss could otherwise have been 

recovered. Using a hand lens I could detect no difference between fragments 

which popped out of the crushers and those that stayed in, and I do not believe 

the failure to retrieve them introduced any significant bias. 

The size reduction just described was performed by W. E. Warnke, of the 

Bureau of Mines, at the Eastern Experiment Station of the Bureau, College 

Park, Md., and most of the preceding discussion is a paraphrase of his report. 

For permission to use the facilities of the College Park Station we are indebted 

to Frank Lamb. 

The -SO-mesh powder was then delivered to Mr. R. A. Heindl, of the National 

Bureau of Standards, who arranged for the final mixing of roll and pebble-mill 

products, as there were no proper facilities for this operation at College Park. 

The entire 96 pounds of powder was tumbled for 5 hours in a large porcelainlined mill with a small load of carefully cleaned flint pebbles. 

At about this time we learned, through Dr. Chayes, that a few 

years earlier, Dr. W. T. Schaller, of the United States Geological 

Survey, had prepared a diabase sample with the intention of using it 

for control purposes in chemical work on rocks. By mutual agreement with Dr. Michael Fleischer, at present in charge of this type 

of investigation at the Geological Survey, the Massachusetts Institute 

of Technology and Geophysical Laboratory groups join~d with the 
4 CONTRIBUTIONS TO GEOCHEMISTRY, 1 9 50-51 

Federal Survey in an over-all spectrochemical-chemical-modal study 

based on both the granite and diabase standards. The powdered 

granite already prepared under the supervision of Dr. Chayes was 

turned over to W. G. Schlecht, of the Geological Survey, for bottling, 

distribution, and storage. Mr. Schlecht's report on this final aspect 

of the sampling is as follows: 

The 96 pounds of powdered granite received from Felix Chayes was heaped 

on a large canvas and di~ided into two equal parts. Grab samples were taken 

from one of the halves, as follows: Four 70-gram grab samples, labeled G-1-S, 

were taken for spectrographic analysis, as well as two additional 1-pound grab 

, samples, labeled G-1-A. These are being kept for comparison with the mixed 

sample, represented by G-1, in the event of suspicion that contamination. was 

introduced during .the mixing and bottling process. This half was again divided 

into two parts by quartering. One of these parts was split by passing through a 

Jones sample splitter, and the process wa~ repeated until two 1-pound samples, 

labeled G-1-B, were left; these are being kept as representative of the batch, 

in case any evidence is found. that either the unmixed sample, represented by 

G-1-A, or the mixed sample, represented by G-1, are inhomogeneous. 

Each of the original two halves of the 06-pound lot was mixed by shoveling 

and by shifting on the canvas. The two halves were combined in the original 

container and transferred to 562 jars. labeled G-1, containing about 76 grams 

each and totaling about 90 pounds of powder. 

Complete information on the processing of the diabase is not 

available owing to the death of one of the persons concerned. Mr. 

Schlecht has furnished the following: 

The diabase, of Triassic age, was collected December 6, 1946, by W. T. Schaller 

and Norman Davidson, at Bull Run Quarry, on U. S. Highway 211, 3% miles 

southwest of Centerville, Fairfax County, Va. Lumps of several pounds each, 

totaling 260 pounds, were picked from the quarry floor, taking care to avoid 

inclusions of secondary vein material. 

About a dozen of the lumps were saved for hand specimens, thin sections, and 

other purposes. The rest was reduced to about 10-mesh in the Geological Survey 

shop and ground in a ball mill at the National Bureau of Standards until it 

passed a 100-mesh screen. The powdered rock was heaped on ·a canvas and 

divided into two parts by quartering. Each half was again divided by quartering 

and each of the four resulting portions was mixed by shoveling and by shifting on 

the canvas. The whole lot was combined in the original container and transferred 

to 1,382 jars labeled w....:1, containing about 70 grams each and totalling about 

210 pounds of powder. 

The matter of contamination of the rock powders as a result of the 

processing is of no significance insofar as the material is used as a 

standard and is thoroughly mixed. Where the analytical results are 

to be used as a measure of the original composition of the rock, however, it must be remembered that alumina; silica, and iron may have 

entered the sample in' appreciable amounts because of the abrasion 

of the rolls and containers. There is no practical way of removing 

any of this extraneous material-except possibly tramp iron- and 
PREPARATION AND DISTRIBUTION OF THE SAMPLES 5 

allowance must therefore be made for it in terms of original rock 

composition. 

An indication that the mixing has been adequate and that the 

bottled samples are identical for practical purposes is shown by the 

low relative error for Si02 in the two rocks. (See pt. 3, table 14 for 

details.) The values obtained are very small relative to those for 

the other constituents. 

It was realized that, whatever the outcome of the present investigation, possession of a large store of such standard samples would be 

of immense future value to analysts of all kinds as a means of both 

intralaboratory and interlaboratory control. The chemical results 

discussed in parts 2 and 3 of this report indicate that the time for 

-· such control is long overdue. 

In order to obtain a broad coverage of chemical analyses it was 

decided to enlist the support of all types of laboratories-university, 

government, and commercial-in various parts of the world, and to 

request routine analysis of each prepared standard, in duplicate if 

possible. This task fell to the writer and all expense incurred was 

borne by the.Office of Naval Research. The response to our request 

for cooperation was unanimous and within a year 24 laboratories had 

furnished us with over 30 analyses of each rock, almost half of them 

in duplicate. ~1ost of the government laboratories made no charge 

for the work. To all participants, whether analysts or supervisors, 

goes our deep appreciation for their willing and prompt cooperation, 

without w~hich we would have been greatly l1andicapped. A list of 

the contributing laboratories and of the a.nalysts-as far as we know 

them-is given in part 2 (pp. 23-24). 

The results of the chemical work turned out to be more interesting 

than was anticipated, but not in a wa.y to solve completely the original 

spectrographic problem. In consequence part 2 and some of part 3 

are devoted to their evaluation. The original purpose of providing 

accurate calibration for spectrochemical work on the major elements 

was not realized except for a few constituents, since the spectrographic 

precision turned out to be superior in many respects to that obtained 

by chemical means (pt. 3 of this report). Similarly, the precision 

obtained by modal analysis proved superior to that shown by norms 

calculated from the individual chemical analyses (parts 2 and 4). 

These comparisons are unfair in the sense that in each example an 

interlaboratory (chemical) result is. contrasted with one of intralaboratory character only (spectographic, modal). Nevertheless, the 

relatively enormous discrepancies in some of the chemical results, 

part 3 (figs. 1-3) bespeak more than normal variations anq indicate 

an urgent need fo:r thorough interlaboratory standardization, 
6 CONTRIBUTIONS TO GEOCHEMISTRY,. 1 9 50-51 

An independent project on interlaboratory determination of minor 

elements in the two standard rocks has been supervised by Dr. 

Ahrens, with results to date shown in part 5. Although there is no 

easy way to eliminate systematic errors in minor-element determination, the results are distinctly encouraging. It is hoped that interlaboratory work on uranium and thorium will also be carried out. 

No part of the project under discussion in the following chapters 

is in any sense complete. In terms of the Baconian slogan which 

heads this chapter, our "sober inquiry after truth" would definitely 

"beget hopes and beliefs of strange and impossible shapes" were we 

to state otherwise. Since problems dealing with precision and 

accuracy literally have no final solution one must· be content with 

reports of progress. This bulletin is such a report of progress, pub- ·., 

lished at this time because we believe the topics under discussion are 

of surpassing interest to petrologists and geochemists. 
A COOPERATIVE lNVESTIGATION OF 

PRECISION AND ACCURACY IN 

cCHEMICAL, SPECTROCHEMICAL, AND MODAL ANALYSIS OF 

SILICATE ROCKS . 

PART 2. RESULTS OF CHEMICAL ANALYSIS OF SAMPLES 

OF GRANI)'E AND DIABASE 

BY WILLIAM G. ScHLECHT AND RoLLIN E. STEVENs 3 

This comparison of results reported by 34 -chemists analyzing the 

same rocks is the first step in :what is probably the most comprehensive 

study ever undertaken on rock analysis. Although the discrepancies 

in results may seem great, they are not surprising in view of previous 

. experience with rock analysis (Larsen, 1938). The results show what 

variability may be expected when a rock sample is analyzed by a large 

number of laboratories. In the absence of knowledge of the actual 

con1position of the rocks no very precise estimate can be made of the 

errors to be expected; the ranges of values give an idea of how large 

the discrepancies can be. 

When compared with the precision of spectographic procedures 

reported in part 3 of this report the precision of the chemical determinations may appear very low, but it should be noted that the 

estimates of spectrographic precision represent determinations made 

in a single laboratory, as contrasted with the chemical determinations 

.#' made in 25 laboratories. In part 3, table 18, chemical determinations 

made within a single laboratory are compared witp_ the spectrographic 

determinations. 

The disparity in results is too great at this preliminary stage to 

justify the assignment of "correct" values for the composition of the 

samples. Before they can be used as absolute standards on which 

calibrations are based, further work will have to be done to locate 

and correct the sources of the discrepancies in analytical results. It 

is hoped that further interlaboratory work will result in improvement 

of analytical procedures and in a more accurate estimate of the actual 

composition of the two rock samples. 

All 34 collaborators analyzed the granite sample (G-1), and 30 of 

them analyzed the diabase sample (W-1). Their reports are given in 

tables 1 and 2, in which each analyst is represented by a code number. 

aU. s. Geological Survey. 

'l 
TABLE I.-Results of analyses and calculated CIPW norms of granite sample (G-1), reported by 34. collaborators 

[Reports of collaborators are designated by numbers (1-34) in boxheads] 

4 5 6 7 8 19 110 Ill 12 13 114 115 116 117 ------------1 , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ____ , ___ , ___ , __ _ 

Si02--------------------------- 720 36 720 55 72019 720 74 720 52 720 68 720 40 720 04 72ol3 720 54 71.68 720 54 720 46 720 44 71.68 71.05 72,20' 

AhOs-------------------------- l4ol2 l4o 29 l4ol2 l3o 73 140 24 140 08 140 06 140 46 140 22 14o 40 14o 49 140 39 140 49 130 18 140 37 140 61 140 36 Fe20a __________________________ 1.01 o67 o97 1.07 o85 o82 o64 1.50 1.00 o82 1.23 o84 o79 1.48 1.50 o73 o97 

FeO___________________________ 1. 07 1. 05 1. 04 1.14 0 95 1.10 1.10 0 92 1. 04 0 99 0 93 0 95 0 98 0 78 0 87 1. 39 0 90 MgO __________________________ o36 o45 o48 o02 o41 o46 o45 o25 .33 o38 .76 .37 .39 .44 .24 .30 •. 45 

MnO__________________________ .03 o03 , .03 o03 .04 .01 003 .06 .04 .03 003 .03 .03 o03 •002 .02 .02 cao___________________________ 1.35 1.40 1.43 1.30 1.32 1.17 1.38 1.16 1.26 1.40 1.57 1.33 1.33 1.41 1.60 1.55 1044 Na20 __________________________ 3o18 3035 3o27 3o78 3o50 3o59 3o26 3o49 3o54 3o30 3o24 3o16 3o17 3o95 3053 2o84 3o47 K20 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5. 52 5. 51 5. 30 5. 44 5. 64 4. 99 5o 55 5o 38 5o 50 5o 46 5o 84 5o 43 5. 44 5o 52 5o 56 6 88 5o 54 

H20-------------------------- .04 .06 .04 .03 .05} 34 { .05 -------- .04 .01 .04 o05 .01 .07 .06 002 004 H20+------------------------- .32 .36 o38 .17 .22 · .38 .32 -------- .36 .19 .31 .37 .40 o30 .32 .28 Ti02--------------------------- .26 .29 .25 .24 .27 .20 .25 .31 .17 o24 .30 .26 026 .25 .18 029 .22 P20s--------------------------- . 09 .14 . 08 ol2 . 08 .10 . 08 .14 -------- .10 , . 09 . 08 . 08 . 08 .10 Tr. • 08 

BaO___________________________ ~-6;::==~~~~~~~~~~~~~=~~==~==== ----~~~- ======== ---~---- ======== ======== ----~~=- ----·-~- g ======== ==~===== ======== ======== ======== ========== ___ 0 ____ ======== ======== .10 ________________________ -------- . 09 .17 o 06 -------- __________________________________________________________ --------

SrO ____________________________ -------- -------- -------- -------- . 02 -------- -------- o 08 -------- ________________________ -------- ---------- -------- _______________ _ 

LbO ___________________________ -------- -------- -------- -------- . 03 -------- -------- -------- -------- -------- -------- -------- -------- ---------- -------- -------- -------- Cr20a __________________________ -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- ________ -------- -------- ---------- -------- -------- _______ _ 

V20s--------------------------- -------- -------- -------- -------- -------- -------- -------- -------- -------- ________ -------- -------- -------- ---------- -------- -------- -------- Zr02--------------------------- -------- -------- -------- -------- -------- . 07 -------- -------- -------- ________________________________ ---------- _______________________ _ 

TotaL_---------------------- 99. 82 I 1000 15 099.58 99.81 1000 14 99.72 I 6 990 82 I 100017 1--------1 1000 03 I 100 3~ 990 74 990 80 1000 03 I 1000 01 1000 00 990 97 

CIPWnorms 

00 

0 

0 

~ l:tl 

~· to 

q 

8 

~ 

0 

z 

[/). 

8 

0 

0 

t::t 

0 

0 

P:t 

i::'=j 

Quartz ________________________ 2903~ 27.78 29o28 27o90 27.18 29.40 27084 28.20 25.68 29o58 26064 30042 30o30 26004 26o46 23094 27.24 e 

Orthoclase __________ . ___________ 32o80 32.80 31.14 31.69 33o36 29o47 33o36 31.69 32080 32080 34o47 31.69 31.69 32.80 33o36 40o59 32o80 ~ 

Albite _________________________ 26072 28082 27.77 31.96 29o34 30o39 27077 29o34 32o49 27077 27025 26072 26072 33o54 29o34 24010 23o34 l:tl 

AJ?.ort~ite______________________ 6012 6.12 6012 4.45 6012 5o00 6o39 5o56 5o00 6012 7o23 5o56 5o5o 1.67 6095 6o67 6012 ~ DwpSide ______________________________________ -------- . 96 -------- -------- ________ ________ . 92 ________ ________ ________ ________ , 20 38 · . 22 . 92 -------- "" 

Hypersthene __________________ 1.69 2002 1.86 .40 1.79 2002 2.16 o73 o46 1.08 2004 1.53 166 .58? .63 1.79 1.63 

ilmenite.______________________ ~:~~;~~~=========~=========== ---~~~~- . 46 ----~~~- . 61 ---~~~~- . 59 ---~~~=- 0 46 ---~~~~- . 46 ---~~~~- . 46 ----~~~- . 46 ---=~~- . 61 ---~~~~- 0 30 ---~~~~- . 46 ---~~~~- o 61 ---~~~~- . 61 ---~~~~- o 61 1: . 46 ~~ ---=~~=- . 46 ----~~~- . 61 ----~~~= . 46 Apatite________________________ .34 .34 o34 .34 .34 .34 .34 o34 .04 .34 .34 .34 .34 .34 .34 Tr. .34 

Corundum __ ------------------ 0 61 . 41 0 71 ________ .10 . 92 . 20 . 92 -------- . 71 . 20 1. 33 1. 43 ---------- ________ -------- • 41 Zircon _________________________ -------- ________ --------------~-------- .18 -------- -------- -------- -------- ________ -------- -------- ---------- ________ -------- -------- Water_ ________________________ .36 o42 o42 .20 .27 .34 o43 032-------- o37 o23 .36 o38 .47 .36 .34 .33 

TotaL----------------------1 990 58 I 1000 25 I 99 62 I 990 75 I 100012 I 990 68 I 990 88 I 990 80 I 990 08 I 1000 39 I 1000 87 I 990 72 I 990 85 

Classification: I Class, Order ________________ _ Rang, Subrang _____________ _ I, 41 I, 41• I, 41 2,3 2,3 2,3 1,41 . 1,41 1, 3 2, 3 I, 41 I, 41 I, 41 I, 41 I, 41 I, 41 I, 41 I, 41 ~3 ~3 ~3 ~3 ~3 ~2 ~3 ~3 

,_ .i 

1000 30 I 1000 21 I 990 89 I 100. 06 

I, 41 1, 3 1,41 2, 3 I, 41 2, 3 

I, 4 

2, 3 

....... 

0:0 

c:;r 

0 

I 

c:;r 

....... 
~ -. 

liS 119 I 20 21 22 23 24 125 26 127 28 29 30 I 31 132 33 2 34 

------------1 l---1---1---1---1---1---l---1---1---1---1---1---l----1-----·---·---

SiOz--------------------------- 71.54 72.46 72.23 72.45 72.40 72.04 72.30 72.46 _71.60 _ 72.34 72.36 72.43 72.48 71.88 72.17 72.37 72.34 . Ah03-------------------------- 15.96 14. OS 14.88 14.13 15.40 14.50 14.13 14.42 14 59 14.31 13.96 14.04 14.31 13. SO 14.93 14.30 14.34 Fe203-------------------------- .53 .70 .S2 .so .82 .77 .92 .72 .74 .91 .85 1.17 1.01 1.66 .28 1.05 .68 FeO___________________________ 1.32 1.04 .98 .93 1.05 .96 .9S 1.00 1.05 .93 .96 .84 .97 1.20 .91 .99 1.13 MgO __________________________ .52 .42 .43 .38 .19 .45 .52 .26 .15 .40 .45 .23 .22 .42 .42 .48 .37 

MnQ__________________________ . 04 . 025 . 02 . 03 . 03 . 03 . 02 . 02 . 05 . 03 . 03 . 02 -------- . 03 . 02 . 06 . 02 cao___________________________ 1.34 1.30 1.52 1.34 1.52 1.42 1.37 1.40 1.90 1.25 1.30 1.49 1.45 1.22 1.34 1.35 1.52 

Na20-------------------------- 3.48 3.13 3.25 345 2.61 3.26 3.29 3.04 3.16 3.35 3.30 3.17 3.3S 2.7S 3.41 2.98 3.37 K20--------------------------- 4.4S 5.74 5.34 6.23 3.85 5.48 5.37 5.86 5.74 5.49 5.46 5.42 5.54 5.62 5.30 5.51 5.47 H20-----------------,-------- .14 .07 .00 .02 .02 .11 } 3 52 { .10 .OS .05 .06 .04 } 3 44 { .10 .01 (') .06 H20+------------------------- .38 .36 .40 .33 1.42 .38 · .42 .28 .35 .57 .49 · .68 .26 .35 .30 TiOz___________________________ . 20 . 2S . 26 . 26 .16 . 25 . 35 . 24 . 26 . 26 . 25 . 26 . 23 . 27 . 50 . 31 . 26 

P205--------------------------- Tr. .11 .10 .12 .41 .06 .10 .08 .20 .08 .27 .16 .09 .03 .04 .04 .12 s______________________________ ________ ________ ________ . 02 ________ ________ ________ ________ ________ ________ ________ ________ ________ __________ . oo _______________ _ 

C02- -------------------------- 0 -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- ---------- -------- -------- -------- BaO ___________________________ -------- -------- -------- .10 -------- -------- -------- -------- -------- -------- -------- -------- -------- ---------- 5. 28 -------- -------- SrO ___________________________ -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- ---------- •. 002 -------- -------- LbO ___________________________ -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- -------- ---------- 5. 08 -------- --------

CrzOa-------------------------- -------- -------- -------- . 01 -------- -------- -------- -------- -------- -------- -------- -------- -------- ---------- 5 009 -------- -------- V20s--------------------------- -------- -------- -------- -----~-- -------- -------- -------- -------- -------- -------- -------- -------- -------- ---------- 5. 04 -------- -------- Zr02--------------------------- -------- -------- -------- ________ -------- -------- -------- ________ -------- -------- -------- ________ -------- ---------- 5. 00 -------- _______ _ 

TotaL ___________ . __________ _! 99.93 99.71 I 100.23 liiQO. 59 99.88 99.71 99. 87 I 100. 02 99.80 99.75 99.S2 99. 76 I 100. 12 99.69 IS 100. 00 99.79 99.98 

CIPWnorms 

Quartz ________________________ 29.58 28.32 29.16 24.84 39.66 28.50 28.80 28.74 26.82 29.04 29.40 30.18 28.44 30.54 27.12 30.18 28.20 

Orthoclase_____________________ 26.69 33.92 31.14 37.25 22.80 32.25 31.69 35.03 33.92 32.25 32.25 31.69 32.80 33.36 32.80 32.80 31.69 

Albite_------------------------ 29.34 27.25 27. 77 2!l. 34 22.01 27. 77 28.30 25.68 26. 72 28.30 27.77 26.72 28.30 23.58 28.82 25.15 28.30 Anorthite______________________ 6. 67 5. 56 6. 67 4. 45 5. 00 6.12 5. 56 6 12 8. 62 5. 00 4. 73 6. 67 6. 39 6.12 7. 23 6. 39 6. 67 Diopside ______________________ -------- -------- ________ 1. 57 ________________________________ -------- -------- ________________________ ---------- ________________ --------

Hypersthene__________________ 2.88 1.89 1.76 ."66 1.42 1.76 1.83 1.49 1.46 1.53 1.76 .S6 1.16 1.40 1.66 1.50 1.82 

Magnetite_-------------------- . 70 . 93 1.16 1.16 1.16 1.16 1. 39 . 93 . 93 1. 39 1.16 1. 62 1. 39 2. 32 . 46 • 1. 62 1.16 

Hematite ______________________ ------------------------------------------------------------------------------------------------------------------------------------------ Ilmenite----------------------- .46 .61 .61 .61 .30 .61 ".61 .61 .61 .46 .46 .46 .46 .46 .91 .61 .46 Apatite ________________________ -------- . 34 . 34 . 34 1. 01 . 34 . 34 . 34 . 34 . 34 . 67 . 34 . 34 ---------- ________ ________ . 34 

Corundum ____________________ 2.96 .51 1.33 -------- 5.10 .92 .61 .71 -------- 1.02 .92 .51 .41 .S1 .61 .92 .41 

Zircon _________________________ ----------------------------------------------------------------------------------------·-------------------------------------------------- Water_________________________ .51 .43 .41 .35 1.44 .49 .52 .51 .36 .40 .63 .53 .44 .7S .27 .35 .36 

TotaL----------------------1 99. 79 I 99. 76 I 100.35 I 100.57 I 99.90 I 99.92 I 99.65 I 100.16 I 99 78 I 99.73 I 99.75 I 99.58 I 100.13 99. 37 I 99. ss I 99. 52 

Classification: Class, Order_________________ I I, 4 ~- Rang, Subrang ______________ · 2,3 I, 41 I, 41 2, 3 2,3 I,41 1, 3 I, 31 I, 41 I, 41 I, 41 I, ~ I I, 41- ~. 41- -I, 41 I, 41 I. 41 I, 41 I, 41 ~3 ~3 ~3 ~3 ~3 ~3 ~3 ~3 ~3 ~3 ~3 ~3 

99.41 

I,4 

2, 3 

1 Mean of two analyses. 2 Received too late for inclusion in calculations in Part 3. 3 Loss on ignition. ' Sample dried at 100° C. 6 Spectrographic determination. a Corrected for sulfur ( -0.02). 7 Corrected for sulfur (-0.01). s Also reported PbO, 0.004 (spectrographic determination). 

0 

~ t_:::j 

e 

0 

> t" 

> 

z 

> t" 

~ 

U1 

H 

U1 

0 

~ 

0 

~ 

> z 

H 

1-3 

t_:::j 

~ t;:j_ 

t:=' 

H 

> bj 

> U1 

t_:::j 

eo 
TARLE 2.-Results of analyses and calculated CIPW norms of diabase sample (W-1), reported by 30 collaborators 

[Reports of collaborators are designated by numbers (1-5, 7-24, 26-28, 31-34) in boxheads) · 

4 8 I 9 110 Ill 12 13 I 14 I 15 1}6 

·---·---·---·---·---1---·---·---·---·---·---·---·---·---·---

Si02-------- __ ------------------------------------- 52.56 52. 58 52. 12 53.01 52.59 52.59 52.48 52.38 52.45 51. 71 52.35 52.42 52.55 51.38 AhOa--------------------------------------------- 13.91 14.91 15.07 15.09 14.99 15.13 15.19 15.34 15.66 14.86 15.37 15.35 13.70 14.57 Fe20a _____________ -------------------------------- 2. 28 1. 38 1. 44 . 92 1. 08 1. 35 1. 73 1. 35 3. 46 4. 00 1. 31 1. 31 2. 64 2. 00 FeO----------------------------------------------- 8. 92 8. 78 8 81 9.16 8. 89 8. 78 8. 42 8. 66 6. 90 7.14 8. 67 8. 69 8.16 8. 26 MgO·--------------------------------------------- 6. 67 6. 70 6. 74 5. 69 6. 54 6. 64 6. 52 6. 60 6. 52 6. 69 6. 59 6. 60 6. 68 6.18 MnO·-------------------------------------------- .17 .16 .16 .13 . 21 .16 .10 .11 .18 .16 .17 .17 .18 . 53 CaO______________________________________________ 10.82 11.00 11.04 10.86 lO. 88 10.98 10.55 11.19 11.04 10.79 10.95 10.95 10.89 11.42 

Na20---------------------------------------------- 2.09 2.14 2.09 2.40 2.28 2.15 2.17 1.98 1.88 2.15 2.01 2.09 2.28 2.48 K20----------------------------------------------- .74 .68 .60 .66 .69 .71 .61 .60 .65 .82 .63 .68 1.17 •. 82 H20---------------------------------------------- .12 , 18 .13 .15 . 20 .18 -------- . 07 . 02 • 24 .17 .17 . 05 .18 H20+--------------------------------------------- . 52 . 44 . 46 . 41 . 39 . 48 . 67 . 77 • 62 • 20 . 49 . 47 . 52 . 71 

Ti02---------------------------------------------- 1.12 1.00 1.02 1.01 1.00 1.01 ·1.04 1.05 .91 1.12 1.08 1.09 1.18 1.41 P20s---------------------------------------------- .13 .18 . 14 .17 .13 .13 . 24 .12 .11 .18 .13 .13 .14 .10 

8-------------------------------------------------- . 04 -------- -------- ------"- -------- -------- 0 -------- -------- -------- -------- -------- -------- -------· 002----------------------------------------------- -----· -- -------- -------- -------- -------- -------- 0 -------- -------- -------- -------- -------- -------- 0 

51.28 

16.32 . 28 9. 38 

6. 67 

.12 

11.29 

2.06 

1. 30 

.32 

. 06 1. 15 0 (?) 

BaO _ _ ___ _ _ __ _ _ _ __ __ __ __ _ __ ____ ___ _ _ ___ __ ___ _ __ _ _ _ . 06 ______________ -- ____ -- ________ -- ____ --- _ . 04 _______ . -------- _ -~- ____________________________________ 

1 

_______ _ 

SrO _ __ _ _ __ _ __ _ __ _ ____ _ _ __ _ _ _ __ _ ___ _ ____ _ _ _ __ _ ____ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ __ _ _ _ _ _ _ __ _ __ _ . 02 _ _ __ _ _ _ _ . 09 ____________________________________________________________ . __ _ 

~~m~~~===~====~================================== TotaL __ ----------------------------------------1 ======== 2100. 11 I ======== 100. 13 ======== 99.82 ===~==== 99.66 =====~;=_ 99. 92 I ======== 100. 30 ----~~~- 99. 90 I ======== 100. 22 I ======== 100. 40 I ======== 100. 06 ======== 99. 92 I ======== 100. 12 I ======== 100. 14 I ======== 100. 04 =====.=== 100.23 

CIPW norms 

......... 

0 

(') 

0 

z 

8 

::u 

>-f 

td 

0 

8 

>-f 

0 

z 

w 

8 

0 

0 

t:=l 

0 

0 

~ ~ >-f 

U2 Quartz____________________________________________ 4. 74 3. 60 4. 56 3. 72 2. 88 3. 84 4. 20 4. 02 6. 66 4. 50 4. 02 3. 60 2. 82 1. 32 ________ ~ 

Orthoclase_______________________________________ 3.89 3.84 3.34 3.89 4.45 3.89 3.34 3.34 3.89 5 00 3.34 3.89 7.23 5.00 7.78 ~ 

Albite ___________ ---------------------------------- 17.82 18.34 16. 77 20.44 18.86 18.34 18.34 16. 77 16.24 17.82 16. 77 17.82 19.39 20.96 17.82 .... Anorthite.---------------------------------------- 26.41 28.91 30.58 28.36 28.63 29.47 30.02 31.14 32. 25 28.36 31.41 30.30 23.35 26.13 31.14 Diopside__________________________________________ 21.64 20.98 19.16 20.69 20.10 20.37 18.46 19.97 17.30 19.99 18.80 18.95 24 .• 11 24.39 20.62 

Hypersthene-------------------------------------- '19.15 19.98 20.84 18.47 20.50 19.52 19.65 19.68 16.24 15.35 20.68 20.64 16.07 15:30 15. On 

Olivine ____________________________________________ ---------------------------------------------------------------------------------------- -------- -------- -------- 4. 97 Magnetite _______________________ ------------------ 3. 25 2. 09 2. 09 1. 39 1. 62 2. 09 2. 55 2. 09 5.10 5. 80 1. 86 1. 86 3. 71 . 3. 02 . 46 llmenite __________________________________________ 2.13 1.98 1.98 1.98 1.98 1.98 1.98 2.13 1.67 2.13 2.13 2.13 2.2R 2.74 2.13 Apatite ___________________________________________ .34 .34 .34 .34 .34 .34 .34 .34 .34 .67 .34 .34 .34 .34 _______ _ 

Water _____________________________________________ .64 44 .59 .56 .59 .66 .67 .84 .64 .44 .66 .62 .56 .89 .38 

TotaL-----------------------------------------1100.01 1100.551100.251 99.841 99.951100.50 I 99.551100.321100.331100.061100.01 1100.151100.261100.091 100.36 

018'i:S~~~~~~------------------------------------I III,51 III,51 III,51 III,51 III,51 III,51 III,51 III,51 III,51 III,51 III,51 III,51 III,51 III,51 III,5 Rang, Subrang_________________________________ 4,4 4,4 4,4 4,4 4,4 4,4 4,4 4,4 4,4 4,4 4,4 4,4 . 4,4 4,4 4,4 

, 

.... 

tO 

01 

0 

I 

C11 

.... 
.. \> 

I 17 I 18 I 19 120 21 22 23 I 24 26 127 28 I 31 132 33 3 34 

·---·---·---·---·---·---·---·---·---·---·---·---·---·---·--- if 8102----------------------------------------------- 52.31 52. 66 52.61 52.32 52.43 52.21 52.42 52.45 52.09 . 52.28 52.49 52.20 52.51 52.22 52.25 ~Ah03---------------- ---------------------------- 15.18 14.96 14.66 15.41 14.86 16.56 15.04 14.83 18.57 14.92 14.51 14.50 15.28 15.19 15.13 c:::~Fe20a--------------------------------------------- 1.74 1.08 1.32 1.22 1.57 4.26 1.43 1.13 1.33 3.86 1.19 1.45 1.51 1.92 1.02 cn

1 

FeO----------------------------------------------- 8.55 9.22 8.80 9.12 8.67 6.80 8.80 8.95 8.81 7.02 8.98 9.10 8.57 R45 9.07 

MgO---------------------------------------------- 6. 79 7. 09 6. 66 6. 76 6. 70 5. 49 7. 09 6. 75 4. 67 6. 61 6. 69 6. 57 6. 68 6. 60 6. 74 cnMnO _____________________________________________ .18 .26 .17 .12 .17 .21 .18 .20 .23 .22 .20 .16 .13 .18 .17 

.... , cao __________ ----------------------------------- 11.15 10. 70 10.88 10.88 10.91 11.12 11.06 10.86 10.64 10.92 10.90 11.02 10.81 11.07 10.98 Na20--------------------------------------------- 2.20 1.91 1.96 2.02 2.62 1.61 1.94 1.78 1.98 1.98 2.18 1.78 2.09 1.82 2.11 K20----------------------------------------------- . 60 . 41 . 84 . 64 . 67 . 66 . 62 . 64 . 75 . 5S . 66 . 57 . 54 . 74 . 60 l':IH20------------------------------------------- __ .16 .13 .23 .03 .16 .09 .18 .08 .23 .18 .16 .10 .04 (4) .16 H20+--------------------------------------------- . 50 . 58 . 46 . 61 . 56 1. 17 . 62 51.04 . 67 . 48 . 72 1.16 38 . 54 . 46 Ti02---------------------------------------------- 1.13 .94 1.14 1.03 1.13 .53 1.11 1.09 .10 1.00 1.21 1.37 1.28 .95 1.03 P205--------:------------------------------------- .15 . 08 .16 .12 .11 . 08 .13 .10 .15 .16 .17 .18 . 06 . 09 . 22 

8-------------------------------------------------- -------- -------- -------- -------· . 03 -------- -------- -------- -------- -------- -------- -------- . 00 -------- -------- co,_______________________________________________ ________ o ________________________________________________________________________________________________________ _ BaO _____ ---- __ · _______________ . _ _ _ _ __ __ ___ _ ____ _ __ _ ___ _ __ _ _ __ _ _ _ __ __ _ _ _ ___ __ ___ ___ . 02 _ --- _______________________________________ . _ _ _ _ _ ___ _ __ _ 6 • 03 ____ -- ___ . ------

SrO _______________________________________________ -------- -------- ______ :_ -------- -------- -------- -------- -------- -------- -------- ·------- -------- 6. 001 -------- -------- LhO _ -------- _____________________________________________________________ -~-- ____________________ ---- ______________________________________ c _ _ __ 6 • 02 -------- --------

Cn03--------------------------------------------- ________________________ -------- . 02 ________________ -------- ________ ________ ________ ________ 6. 01 ________ --------

V20a---------------------------------------------- -------- -·------ -------------------------------------------------------------------------------- 6.07 ----------------

TotaL _____ ------------------------------------ 100. 64 I 100. 02 I 99. 89 I 100. 28 11100. 62 I 100. 79 I 100. 62 I 99. 90 I 100. 22 I 100. 21 I 100. 06 I 100. 16 18100. 01 I 99. 77 I 99. 94 

CIPW norms 

Quartz_------------------------------------------- 3. 36 4. 68 3. 96 3. 661 1. 50 8. 82 4.14 5. 22 3. 96 6. 90 3. 54 5. 64 4 62 5. 10 3. 36 . Orthoclase __ -------------------------------------- 3. 34 2. 22 5. 00 3. 34 3. 89 3. 89 3. 34 3. 34 4. 45 3. 34 3. 89 3. 34 2. 78 3. 89 3. 34 Albite--------------------------------------------- 18.34 1624 16.77 16.77 22.01 13.62 16.24 15.20 16.77 16.77 18.34 15.20 17.82 15.20 17.82 Anorthite _________________________________________ 30.02 30.86 28.63 31.41 26.97 36.14 30.58 30.58 39.48 30.02 27.80 29.75 30.86 31.41 30.02 

Diopside__________________________________________ 20.03 17.59 20.31 18. 27· 21.64 14.68 19.13 18.46 10.51 18.88 21.02 19.52 11:99 18.66 21.93 

Hypersthene-------------------------------------- 19.85 24.09 20.31 22. 16 18.85 14.88 21. 77 21. 96 21.81 15.68 20.21 20.21 20. 54 20.01 18.77 Olivine ____________________________________________ ------------------------------------------------------------------------------------------------------------------------ Magnetite _________________________________________ 2.55 1.62 1.86 1.86 2.32 6.26 2.09 1.62 1.86 5.57 1.86 2.09 2.0912.78 1.39 Ilmenite ________________________ : _________________ 2.13 1.67 2.13 1.98 2.13 1.06 2.13 2.13 .15 1.98 2.28 2.74 2.43 1.82 1.98 

Apatite------------------------------------------- .34 .34 .34 .34 .34 .34 .34 .34 .34 .34 .34 .34 .34 .34 .67 Water------------------------------------~-------- . 67 . 71 . 70 . 64 . 72 1. 26 . 80 1. 12 . 90 . 66 . gg 1. 27 . 42 . 54 . 62 

TotaL-----------------------------------------1 100.63 I 100.02 1100.01 }100.43 }100.35 }10G.95 }100.56 I 99.97 1100.23 1100.14 1100.161100.10 I 99.89 I 99.75 I 99.90 

Classification: Class, Order------------------------------------I III, 5 I III, 5 I III, 5 I III, 5 I III, 5 I 

Rang, 8ubrang_________________________________ 4,4 4,3 4,4 4,4 4,4 II, 41 III, 51 III, 51 4,4 4, 4 4, 4 II, 51 III, 51- III, 51 III, 51 III, 51 III, 51· III, 5 4, 4 4, 4 4, 4 4, 4 4, 4 4, 4 4, 4 

(") 

Ill 

t?:l 

~ H 

(") 

> t-« 

> z 

> t-« 

~ 

U1 

H 

U1 

0 

~ 

0 

:;:o 

H 

~ 1-3 

t?:l 

~ t;; 

t;; 

~ > U2 

t?:l 

t Mean of 2 analyses. ' Corrected for sulfur ( -0.02). a Received too late for inclusion in calculation in chap. 3. 4 Dried at 100° C. 5 Loss on ignition. 6 Spectrographic deter- ~ 

mination. 7 Corrected for sulfur ( -0. 01). 8 Also reported PbO, 0.002, and NiO, 0.001 (spectrographic determinations). ~ 
12 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

If the analysis was made in duplicate, the code number is marked 

with a footnote reference and the mean of the two analyses is given. 

Tables 1 and 2 also give the petrographic "norm," computed from 

each analysis by the mineralogical staff of the Trace Elements Section 

of the Geochemistry and Petrology Branch, United States Geological 

Survey, under the direction of Theodore Botinelly. The CIPW norm 

is a conventional assignment of the elements in a rock to an arbitrarily 

designated set of "normative minerals," which may or may not 

actually be present in the rock. Rules for calculating the CIPW 

norm from the chemical analysis of a rock are given in textbooks of 

petrology and petrography (Johannsen, 1931, vol. 1, ch. 8). The 

norms are discussed in this report by Felix Chayes. (See pt. 5.) 

The "consensus" of results is shown graphically in plate 1, where 

each analyst's result is shown by a point on the histograms for each 

constituent. Exper!ence with collaborative analysis of other materials has shown that the correct values may be quite different from 

the most frequent ones. (Lundell, 1933.) 

All collaborators did not report their analytical procedures. Examination of those results for which procedures were reported shows 

few regularities in relations between the methods and the results. 

At the present stage of the study it is not possible to estimate how 

much of the variation is caused by personal errors of the analyst, and 

how much by errors inherent in the procedures. It may be worth while, 

however, to describe briefly the course of a silicate rock analysis, 

pointing out tendencies to be high or low and their causes, and also 

to list the results by different methods .of accomplishing the various 

steps of the analysis. 

RESULTS OBTAINED BY DIFFERENT PROCEDURES 

For many of the constituents one method was considerably more 

popular than others, and so the results of that method decide what is 

to be taken as a normal value. This is particularly shown in results 

for potassium, where weighing as I\:2Pt016 is by far the most popular 

method. It is possible, of course, that a value far removed from the 

most popular range of values may be nearest the truth. 

Silica (Si02) .-Silica is determined by fusing the sample with 

sodium carbonate, dissolving the product in acid, usually HOI, and 

evaporating to dryness to dehydrate the silica and make it insoluble. 

After a single evaporation several milligrams of Si02 escape dehydration and remain in soluble' form. A second dehydration recovers 

most of this, and the remainder can be recovered by dissolving 

the R20 3 group and dehydrating with H2S04• Perchloric and sulfuric 

acids are used by some analysts for second or third dehydrations. 

Platinum or porcelain dishes are used for the evaporations; one 

analyst used pyrex beakers. With porcelain dishes results may be 
CHEMICAL ANALYStS OF~ GRANITE AND DIABAS:E 13 

low because of failure to remove all of the .tightly adhering silica from · 

the surface of the dish, or they may be high because of removal of the 

glaze. Two of the seven workers who used porcelain vessels for the 

dehydration took extraordinary precautions to remove all silica from 

the dish, and their results agree more closely than the rest with those 

obtained in platinum vessels. After the silica is col~ected, it must be 

ignited at sufficiently high temperature to assure complete dryness 

for weighing. The silica is then volatilized with HF, the crucible 

and residue weighed, and the weight of Si02 obtained by difference. 

Results tend to be low, because negativ~ errors due to failure to 

collect all Si02 generally are greater than positive errors from failure 

to drive off all water before weighing. 

Processes used for determining Si02 on the two rocks are as follows 

(table 3): 

1. Double dehydration with HCl only. This would tend to give 

low resalts because of failure. to remove all silica. 

2. Double dehydration with HCl, and recovery of Si02 in the R20 3 

group. This should recover essen~ially all the Si02 • 

3. Single dehydration with HCl, followed by a second dehydration 

with HCl04: This i's generally considered a sound procedure although 

the results here reported are low. 

Results of determinations of Si02 by these procedures are given in 

table 3. 

TABLE 3.-Results with different methods of determining Si02, in percent 

[Numbers assigned to methods agree with nu~bcrs in text.] 

Granite smnple (0-1) 

Ann.lyscs by method indicated 

I. 2 HOI 2. 2 HOI de· 

dchydm· hydrations, 

tions only recovery of 

Si02in H20a 

I 71.05 2 71.60 8 71.54 3 71.88 8 71.68 8 72.13 3 72.04 I 72.17 I 72.19 I 72.23 I 72.20 . 72.30 I 72.34 I 72.34 I 72.36 I 72.36 3 72.46 I 72.40 I 72.54 I 72.43 8 72.54 72.45 

72.46 

72.46 

I 72.48 

I 72.52 

I 72.55 

I 72.68 

I 72.74 

I Dchydmtion in plutinum vessel. ~Dchydmtion in pyrex beaker. 1 Dehydration in porcelain vessel. 

3.1 HOI de· 

hydration; 

1 HOI04 dchydmtion 

8 71.68 

- Diabase sample (W-1) 

Ann.lyscs by method indicated 

1.2HCI 2. 2 HOI de· 3. 1 HOI de· 

dchydm· hydrations, hydration, 

tions only recovery of 1 HOI04 Si02 in H20a dehydration 

I 51.28 2 52.09 3 51.71 3 51.38 3 52.20 I 52.12 I 52.25 I 52.28 I 52.32 I 52.31 3 52.38 3 52.35 52.43 3 52.42 52.45 8 52.42 I 52.49 152.45 I 52.51 I 52.56 I 52.58 3 52.66 I 52.59 

I 52.59 

52 61 53.01 
14 CONTRIBUTIONS TO GEOCHEMISTRY, 19 50-51 

Alumina (Al20 3) .-In most of the analyses alumina was calculated 

by subtracting from the · R20 3 group-elements precipitated by 

neutralizing the acid solution with NH40H-the Fe20 3, Ti02, and 

P20 5 • Unusual procedures and their results are as follows: 

1. Separation of iron group from R20 3 by double precipitation with 

N aOH, reprecipi~ation with NH40H. Al20 3 was calculated by subtracting iron group from total R20 3 • Ti02 and P20 5 were considered 

part of iron group. Percent alumina: granite sample (G-1), 14.13; 

diabase sample (W-1), 14.83. _ 

2. Separation of iron group from R20 3 by double precipitation with 

KOH, reprecipitating with NH40H. Al20 3 was calculated by subtracting iron group and P20 5 from total R20 3 • P205 was considered 

not part of iron group. Percent alumina: granite sample (G-1), 

13.18; diabase sample (W-1), 13.70. 

3. Oupferron separation of Fe and Ti. Al20 3 and P20 5 were 

precipitated from filtrate and weighed. Percent alumina: .granite 

sample (G-1), 14.49; diabase sample (W-1), 14.86. 

· Total iron (Fe).-Iron in solution, obtained either from the R20 3 

or from a separate safil:ple, is reduckd to the ferrous state and titrated 

to the ferric state. An alternate to this process is to titrate from the 

ferric to the ferrous state with ·titanous ion. Essential variations in 

procedure have principally to do with the means of reduction. The 

different methods of reduction used are as follows: 

1. Reduction of iron in HOI solution with stannous chloride 

(Zimmermann-Reinhardt method). Results are low if the titration 

is delayed owing to air-oxidation of ferrous ion, and they are high if 

titration is too rapid owing to oxidation of chloride ion to free chlorine 

if permanganate is used as oxidant. 

2. Reduction with H 2S. Results are high if all H 2S is not ren1oved. 

3. Reduction with zinc amalgam. Sulfuric acid solution of iron 

is passed down a column of zinc amalgam (Jones' reductor) to reduce 

ferric ion to ferrous; this also reduces titanium ion. Titanium may 

be oxidized before the titration is made by aerating the solution, 

preferably in the presence of a trace of copper as catalyst. If this 

is not done, the results are high. 

4. With silver reductor. Iron in HOI solution is reduced by passing the solution down a column of metallic silver. Titanium ion is 

not reduced and so does not interfere. 

5. Reduction with S02. 

6. Titration of ferric ion with titanous ion. 

Results by these methods of determining iron are given in table 4'. 
•• 

,;,. 

CHEMICAL ANALYSIS OF GRANITE AND DIABASE 15 . 1: I ·I II 

TABLE 4.-Results with different methods of determining total iron, in percent. 

[Total Fe determined as Fc20s. Numbers of methods refer to text] 

1. SnCh I 2. H2S reduction 1 rcduction2 

1. 29 1. 86 1. 91 1. 92 2.04 1.94 2. 34 1. 99 3 2.47 2.01 

2.10 

2.16 

2. 26 

2. 99 

11.03 10.97 11.10 11.08 

11.10 ll. 12 11.10 8 11.18 11.17 11.56 

'11.82 

11.93 

1 Titration with K2Cn07. I 'l'itration with KMnOc. a 'l'itratlon method not stated. 

13.Zn amm-1 4 s·t I gam (Jones' · 5. SOs I'· Titmtion of 1 ver 1 ferric ion with reductor) 2 reductor reduction titanous ion ' 

Granite Sample (G-1) 

1. 84 1.88 I 2.00 1. 83 1. 84 1.90 1.83 1. 86 1. 92 1. 91 1. 94 1. 91 1. 97 2.13 

2.20 

2. 2i 

Diabase Sample (W-1) 

10.70 10.95 I 11.33 11.21 10.96 10.97 

11.11 11.13· 11.14 11.24 11.21 11.66 11.23 

11.36 

12.19 

· Ferrous oxide (FeO).-The sample is dissolved in a mixture of sulfuric and hydrofluoric acids in a large crucible with tight-fitting lid; 

the crucible and its contents are placed in a large beaker containing 

dilute.. sulfuric acid, and usually boric acid, and the solution is titrated 

at once with standard oxidizing agent. Use of different oxidizing 

_ agents-for example, KMn04, K 2Cr20 7-for titrating the ferrous 

ion should not give differing results if they are properly standardized. 

Air oxidation during solution of the sample in HF is usually prevented 

by the steam generated (simple method) or by an atmosphere of C02. 

Only three analysts definitely stated that they used a 002 atmosphere. 

Their results. are: granite sample (G-1), 0.93,' 1.04, and 1.05 percent; 

diabase sample (W-1), 6.80, 7.14, and 8.80 percent. 

Calcium oxide (OaO).-Nearly all the reporting analysts precipitated 

calcium oxalate froin the filtrate of the R20 3 separation and ignited it 

to the oxide. One analyst weighed calcium as CaS04 and reported: 

granite sample (G-1), 1.37 percent; diabase sample (W-1), 10.86 

percent. Another laboratory determined calcium volumetrically 

by titrating the calcium oxalate, after solution in acid, with permanganate solution, reporting: granite sample (G-1), 1.57: diabase 

sample (W-1), 10.79 percent. 
16 CONTRIBUTIONS TO GEOCHEMISTRY, 1 9 50-51 

Magnesium oxide (MgO).-All reporting analysts precipitated 

magnesium as magnesium ammonium phosphate all:d weighed it as the 

pyrophosphate (Mg2P 207). 

Sodi1Lm oxide (Na20).--A. Decomposition. No systematic differt::nces are apparent in results from different methods of decomposition. 

Most reporting analysts decomposed the sample by sintering with a 

a mixture of CaC03 and NH4Cl-the J. Lawrence Smith procedure. 

Three analysts substituted BaCl2 for NH4Cl in the sinter mixture; this 

sinters more easily than the usual mixture, and automatically removes 

sulfate. Four analysts decomposed the samples with HF and H2S04• 

This should give a more complete recovery of alkalis, as it is a complete decomposition of the sample, while the J. Lawrence Smith procedure is an extraction. Of the four samples decomposed by the acid 

treatment, three were analyzed by the flame photometer. 

B. Determination. Usually the mixed chlorides of potassium and 

TABLE 5.-Results with different methods 

GRANITE SAMPLE (G-1) 

By difference from mixed chlorides (4) (5) (6) (7) 

a~s~~r~! By difference 

(l) (2) (3) Weighed as from mixed Flame 

Na2S04 uranyl zinc sulfates, K photometer K weighed K weighed K weighed as weighed as as K2PtClo as KCI04 K2NaCo(N02)6 acetate K2PtCl6 

Decomposed by J. Lawrence Smith method 

2. 78 2. 61 3.47 3. 24 -3.13 3.04 3. 30 2.M I - 3.16 3.35 I 3.18 

3. 25 I 3. 26 3.37 

3. 41 3.45 

3.48 

3.53 

3. 54 3. 95 

Decomposed by J. Lawrence Smith method, using BaCb instead of ~H4Cl 

3. 591 I I 3. 261 I I 3. 27 

Decomposed with HF and H2S04 

3.W I 

I I I I I 

3.35 

3.50 

3. 78 

I Weighed as platinum sponj!"e. 
CHEMICAL ANALYSIS OF GRANITE AND DIABASE 17 

sodimn are weighed, the potassium is separated and weighed a.s (1) 

l{2Pt0l6, (2) KC104, or t3) potassium cobaltinitrite, and the sodium 

obtained by difference. Sodium may also be weighed separately as 

(4) Na2S04, or (5) sodium uranyl zinc acetate. The determination 

1nay also be made (7) with a flmne photometer. All these proc~dures 

1nay give good results when used by skilled analysts. One analyst 

reported (6) weighing the mixed sulfates and calculating the sodium 

by difference after weighing K2Pt016• The low solubility of Na2 804 in 

alcohol may cause low results in this procedure owing to inclusion of 

Na2 804 in the l{2PtCl6• • 

The three ·determinations made by method (2) and the one determination n1ade by method (6) are low, but this is not evidence enough 

to establish any systematic error. 

Results of deter1ninations by the above seven procedures are given 

in table 5. 

of determining Na20, in percent 

DIABASE SAMPLE (W-1) 

By difference from mixed chlorides (4} (5) (6) 

Weighed By difference 

(1) (2) (3} Weighed as . as sodium from mixed 

Na2S04 uranyl zinc sulfates, K 

K weighed K weighed K weighed as weighed as as K2PtClo as KClO, K2NaCo(N02)o acetate K2PtClo 

Decomposed by J. Lawrence Smith method 

1. 78 1.61 2.20 1. 88 2.06 1. Ill 1. 98 1. 94 2.15 1. 96 

1. 98 1. 98 2.02 

2.09 

l 2.09 

2.11 

2.28 

2.48 

2.62 

Decomposed by J. Lawrence Smith method, using BaCh instead of NH,Cl 

I I ·I . 2.151 I 

Decomposed with HF and H2S04 

I 

(7) 

Flame 

photometer 

2.09 

2.14 

2. 28 2.40 
18 CONTRIBUTIONS TO. GEOCHEMISTRY, 1 9 50-51 

Potassium oxide, (K20.)-A.Decomposition. Procedures were the 

same as for N a20, which is determined in the same portion of sample 

used for the K20 determination. As with the determinations of Na20, 

there are no significant deviations associated with the modified decomposition procedures. 

B. Determination: Potassium is weighed as (I) K2PtCl6, (la) 

platinum sponge separated from K2PtCl6 (Hicks' method), (2) KC104, 

or (3) potassium cobaltinitrite. One analyst reported (4) K2PtCl6 

separated from solution of the mixed sulfates, a procedure that would 

give high results from inclusion of N a2804 in K2PtCl6, due to low 

soluoility of Na2804 in alcohol. The flame photometer (5) is an additional method. _ 

One of the three determinations made by method (2) is low, and 

both of the determinations by method (4) are high, but this is not 

enough evidence to establish systematic error. 

TABLE 6.-Results with different 

GRANITE SAMPLE CO-l) 

(1) (2) (3) (4) (5) 

As K2PtC16 from AsKClOt As K2NaCo(N02)6 As K2PtCIG Flame photometer mixed chlorides 

Decomposed by J. Lawrence Smith method 

4. 48 3.85 5. 54 6.88 5.30 5.86 5.34 

5 42 5.46 

5. 46 5.47 

5.49 

5. 50 5. 52 I 5:52 

5. 56 5. 62 5. 74 5. 74 5.84 

6. 23 

Decomposed by J. Lawrence Smith method, using BaCh instead of NHtCI 

-

·~I I I I 5.30 5. 55 

Decomposed with HF and H2S04 

,, I 

I I I 

5. 44 5. 51 5. 64 

1 Weighed as platinum sponge. 

... 
CHEMICAL ANALYSIS OF GRANITE AND DIABASE 19 

Results of determinations of K20 by different procedures are given 

in table 6. 

Determination of alkalis by flame photometer.-A.dditiona1 work on 

alkali determinati.ons with the flame photometer is reported in part 3, 

table 16. 

Phosphorus pentoxide (P205).-Phosphate is separated from nitric 

acid solution by precipitation as ammoni~m phospho-molybdate. rrhe 

precipitate can be· (1) weig~ed directly, (2) converted to Mg2P201 and 

weighed, (3) converted_ to PbMo04 and weighed, or (4) determined 

volumetrically by alkalim.etric titration. All four methods give 

good results. One an.alyst (5) converted to P20 5.24Mo03 by heating 

... at500 0 before weighing (method of w·oy; Dittler, Gesteinsanalytisches 

Praktikum, Berlin & Leipzig, w·alter de Gruyter & Co., 1933, pp. 

54-56). 

·methods of determining K20, in percent 

DIABASE SAMPLE (W-1) 

(1) (2) (3) (4) (5) 

As K2PtCio from As KCI04 As K2NaCo(N02)o As K2PtClo Flame photometer mixod chlorides 

Decomposed by J. Lawrenc11 Smith method 

0. 41 0. GG 0. GO 1.30 . 54 

.57 

• 58 

.60 

. 60 

. 62 

.64 

. 65 

. 66 

. 67 

•. 74 

. 75 

.82 

.82 

.84 

1.17 

Decomposed by J. Lawrence Smith method, using BaCis instead of NHcCI 

• 71 I I I 

\ 

I 0. 60 

Decomposed with HF and H2SOc 

OMI 

I I I 

0. 66 

.68 

.69 
20 CONTRIBUTIONS TO GEOCHEMISTRY, 19 50-51 

Results of determinations of P20 5 are given in table 7. 

. . 

T 4-BLE 7.-Results with different methods of determining P20 5, in percent 

(1) (2) (3) (4) (5) 

Weighed as Weighed as Converted to Weighed as (NH4)3P04. PbMo04 Volumetric 12Mo0a Mg2P~07 and weighed P206.24Mo0a 

Granite sample (G-1) 

0 03 0.08 0.10 "Traces" 0.10 .04 .08 0. 06 .08 .08 .09 .08 .08 .12 .08 .08 . 20 .08 .09 .10 .09 .14 .10 

.10 

.11 

.12 

. 12 

. 16 

. 27 

. 41 

Diabase sample (W-1) 

0.06 0.08 0.10 0.08 0.10 .11 .11 . 13 .13 . 12 . 15 .13 .13 .17 . 14 . 13 . 18 .16 .13 . 18 .14 . 18 .15 

.16 

.17 

. 22 

Manganese oxide (MnO) .-The small percentages of ma.nganese in 

the granite and diabase· were determined colorimetrically after 

oxidizing the manga.nese to permanganate using (1) perioclate, (2) 

bismuthate, or (3) persulfate in the presence of silver ion as catalyst. 

Four reporting analysts determined manganese volumetrically, after 

oxidizing to permanganate with persulfate and silver ion, by adding 

an excess of ferrous sulfate and titrating the excess with standard solution of oxidizing agent. It is possible to get good results by all four 

methods. 

Results of determinations of lvinO by the different methods are 

assembled in table 8. Some of the results are so aberrant as to suggest 

the possibility of arithmetical errors in the dilution factors used. 
CHEMICAL ANALYSIS OF GRANITE AND DIABASE 21 

TABLE s.-Res1tlts with differ:ent methods of determining MnO 

Colorimeti ic method (4) 

(1) 

I 

(2) 

I 

(3) PersniCate 

(volumetric 

Periodate Bismnthato Persulfato method) 

Granite sample (G-1) 

0.01 0.02 0.02 0.02 .02 .02 .02 .03 .02 .03 .03 .03 .02 .04 .05 .04 .02 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

.03 

.03 - .04 

Diabase sample (W-1) 

0.13 0.11 0.12 0.13 .16 .17 .12 .16 .10 . 20 .18 .18 . 16 .23 . 26 .16 

.17 

.17 

.17 

.17 

.17 

.18 

.18 

. 21 

. 21 

. 22 

. 53 

Titania (Ti02) .-Titania was invariably determined colorimetrically 

after oxidation to the amber color by peroxide in sulfuric acid solution 

containing phosphoric acid to reduce color due to ferric ion. The 

results reflect the care and skill of the analyst rather than differences 

of n1ethod. As with manganese, blunders in dilution factors are suspected in.some of the results. · 

Total water.-Uncon1bined water (H20-) was invariably taken as 

the percentage loss in weight at. 105 to 110° C. For total water, 

from which combined water (H20+) is calculated by subtracting 
22 CONTRIBUTIONS TO GEOCHEMISTRY, 1 9 50-51 

H20-, a number of methods were 1.1-sed: (1) Loss on ignition, corrected for oxidation of ferrous oxide. If FeO is not completely oxidized to Fe203, the results obtained are high; (2) volatilization and 

isolation in a Penfield tube without a flux; (3) the Penfield tube 

method using anhydrous sodium tungstate, N a2W04, as a flux to 

,decompose the sample; (4) the Penfield tube with basic lead chromate 

as a flux; (5) the Penfield tube with lead oxide as a flux; and (6) 

volatilization and the absorption of water in a desiccant. 

Results. of determinations of tota~ water using these methods are 

·given in table 9. 

TABLE 9.-Results with different methods of determining total water (total H20), 

in pe_rcent 

[Numbers in box heads refer to text] 

(1) (2) (3) (4) (5) (G) 

Ignition loss Penfield Penfield Volatiliza- (corrected Penfield (basic learl Penfield (Na2W04 tion and for FeO (no flux) chromate (PbO flux) 

oxidation) flux) flux) absorption 

Granite sample (G-1) 

0. 52 0. 20 0.35 0. 36 0. 27 0.36 . 53' .23 . 37 .34 .43 .63 . 27 . 38 . 36 .49 . 78 . 32 . 40 . 42 . 52 .34 .42 . 36 

.36 

.40 

. 43 

.47 

.52 

1. 44 

Diabase sample (W-1) 

0.88 0.38 0. i2 0.64 0.59 0.69 1.12 .42 .. 64 . 59 .so 1. 26 .44 .66 .62 .90 . 56 .66 .64 .57 

.62 

.64 

.66 

.66 

.71 

.84 

.89 

1. 26 

Summation.-The traditional practice of inspecting the summation 

of a rock analysis is a necessary test of its correctness, but a summation near to 100.0 percent is no assurance of its correctness. For 

example, several analyses may be seen to have very low results for 

silica, although their summations are satisfactor;y. 
CHEMICAL ANALYSIS OF GRANITE AND DIABASE 23 

TABLE 10.-"Good" summations with low-silica results 

Sample ~aterial 

Granito (Q-1) ___________________________ ---------------- { 

Diabase (W-1) ..... ------------------------------------- { 

Analyst 

No. 

15 

16 

11 

15 

Si02 (percent) 

71.68 

71.05 

51.71 

51.38 

Summation 

(percent) 

100.01 

100.00 

100.06 

100.04 

Elements seldom determined.-Some analysts reported in one or both 

rocks determinations of elements commonly ignored. By chemical 

methods barium was determined by five analysts, sulfur was determined by seven, strontium, lithium, and chromium by two, and zirconium by one of the analysts. One analyst determined all these 

clements except sulfur, and in addition lead and nickel, spectrographically. The foregoing includes those who reported "none" or 0.00 percent. A special comparative study of the rarer elements in the granite and diabase samples is reported in Part 4 of this report. 

LIST OF PARTICIPATING ANALYSTS 

United States: . 

F. A. Gonyer, Harvard University, Cambridge, Mass. 

Eileen K. Oslund} M" t R k L b t M. r M" Lee C. Peck____ mneso a oc a ora ory, mneapo 1s, mn. 

Ledoux & Co., New York, N. Y. 

W. W. Brannock __ 

M. K. Carron ____ _ 

J. J. Fahey ______ _ 

Charles Milton ____ U. S. Geological Survey, Washington, D. C. 

Leonard Shapiro __ _ 

Ann Vlisidis _____ _ 

Charlotte Wa1shaw 

Canada: 

· R. J. C. Fabry, Canada Department of Mines, Ottawa. 

D. A. Moddle, Ontario Department of Mines, Toronto. 

H. Boileau and C. Tousignant, Quebec Department of Mines, Qu~bec. 

United Kingdom: . 

J. H. Scoon, Department of Mineralogy and Petrology, Cambridge University, 

Cambridge, England. · 

Lars Lund, Leeds University, Leeds, England. 

0. von Knorring, Leeds University, Leeds, England. 

W. F. Waters, Geological Survey and Museum, London, England. 

A. H. Clarke, Geochemical Laboratories, Wembley, England. 

W. H. Herdsman, Glasgow, Scotland. 

Finland: H. B. Wiik, Geological Survey of Finland, Helsinki. 

Sweden: Naima Sahlbom, Stockholm. 

Switzerland: · . .. 
24 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

J. Jakob, Eidg. Technischen Hochschule, Zurich. 

Th. Hiigi, Universitat Bern, Bern. 

Germany; Chemisches Laboratorium Fresenius, Wiesbaden. 

South Africa: C. F. J. van der Walt, Department of Agriculture, Pretoria. 

Australia: 

J. N. A. Grace} G Ch . I L b p h 

W I 1

. overnment emiCa a oratory, ert . . ng Is ____ _ 

S. B. Watkins, Government Chemical Laboratory, Brisbane. 

G. Ampt, University of Melbourne, Victoria. 

F. F. Field, Mines Department, Melbourne, Victoria. 

E. N. Reidy, Department of Mines, Sydney, New South Wales. 

W. St. C. Manson, Department of Mines, Hobart. 

New Zealand: F. T. Seelye, Dominion Laboratory, Wellington. 

REFERENCES CITED 

Johannsen, Albert, 1931, A descriptive petrography of the igneous rocks, vol. 1, 

ch. 8, Chicago, Univ. Chicago Press. 

Larsen, E. S., Jr., 1938, The accuracy of chemical analyses of amphiboles and 

other silicates: Am. Jour. Sci. 5th ser., vol. 35, pp. 94-103. 

Lundell, G. E. F., 1933, The chemical analysis of things as they are: Ind. Eng. 

Chern., Anal. Ed., vol. 5, pp. 221-225. 
A COOPERATIVE INVESTIGATION OF 

PRECISION AND ACCURACY IN 

CHEMICAL, SPECTROCHEMICAL, AND MODAL ANALYSIS OF 

SILICATE ROCKS 

PART 3. SPECTROCHEMICAL ANAYLSIS OF MAJOR 

CONSTITUENT ELEMENTS. IN ROCKS 

AND MINERALS 

BY w. H. DENNEN, L. H. AHRENs, AND H. vv. FAIRBAIRN 4 

CONTENTS 

Page 

Introduction______________________________________________________ 25 

Precision (reproducibility) in spectrochemical analysis_______ _ _ _ _ _ _ _ _ _ _ _ _ 26 

Accuracy in spectrochemical analysis __________________ · ________ -.-_____ 27 

Procedure and precision in determination of Ca, AI, Mg, Mn, and Fe_____ 30 

Procedure nnd precision in determination of SL____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 31 

Procedure and precision in determination of Na and K_________________ 31 

Statistical analysis of the chemical data _______ ·- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 32 

. Statistical analysis of flame photometer data for alkali metals___________ 36 

Relative precision of chemical and spectrochemical analysis_____________ 37 

Tho arithmetic mean and the consensus moan_________________________ 39 

The working curves----~------------------------------------------- 44 

References cited___________________________________________________ 45 

INTRODUCTION 

Spectrochemical analysis has long been recognized as a sensitive 

and rapid method of qualitative analysis for some 70 elements, and as 

an invaluable quantitative method for these elements at low concentrations. Its application in this respect has been p-articularly valuable 

in geology. With the marked improvement in the precision and accuracy of spectrochemical methods during the past 2 decades attention 

has been drawn to its possible use for the quantitative analysis of the 

major constituent elements. The question of course arises as to 

whether any useful purpose would be served by using spectrochemical 

procedures. For minor constituent analyses the reason is obvious, 

but for the major constituents chemical analysis has served us well. 

· In attempting to answer the question a few points should be borne 

in mind. 

• Massachusetts Institute of Technology. 

25 
26 CONTRIBUTIONS TO GEOCHEMISTRY, 19 50-51 

1. Spectrochemical analysis is much more rapid than chemical 

analysis, and because of this it becomes possible to investigate many 

geological problems which one would hesitate to attempt were only 

the relatively slow chemical procedures available-see for example 

discussion of various geological applications by Ahrens (1950, 

ch. 23). 

2. The. precision and accuracy of spectrochemlcal analysis is reasably high, comparing favorably. with chemical methods. 

. 3. The cost of a quantitative spectrochemical analysis is small 

compared with that of a chemical analysis. 

4. The spectrum of a specimen provides a permanent record of the 

presence of several other elements that may be of interest. Thus it 

is possible to determine several major constituent el~ments and also 

a number of minor ones from a single spectrogram. 

5. Where material for analysis is difficult to prepare, as in many 

mineralogical investigations, the small sample required for spectrochemical analysis-as little as 3 mg is sufficient-is a considerable advantage over chemical analysis. 

Bearing in mind these points, it is clearly evident that quantitative 

spectrochemical analysis offers some definite advantages, provided 

that both precision (reproducibility) and accuracy (degree of approach to the absolute value) are adequate. First we will discuss 

the precision and accuracy of spectrochemical methods in general; 

secondly, we will record some observations and provide statistical 

data on some major constituent analyses, mainly on the diabase and 

gran~te provisional standards, as a basis of comparison with chemical 

methods. 

PRECISION (REPRODUCIBILITY) IN SPECTROCHEMICAL 

ANALYSIS 

Many sources of excitation are used in spectrochemical analysis. 

For the analysis of minerals, rocks and related materials the directcurrent arc is most -commonly employed and the discussion here applies to this source in particular. Many reports in the literature describe the arc method as "semi-quantitative." These reports, which 

are unfortunately misleading, at one time caused the direct-current 

arc method t0lapse into disrepute, from which, however, it has strongly 

recovered. Unlike many other sources, however, the choice of an 

internal standard is usually very critical and much depends, therefore, upon the internal standard used and on the smoothness of the 

arc burn. (For discussion on internal standardization in the directcurrent arc, see Ahrens (1950), ch. 7.) Provided an ideal internal 

standard has been used, meticulous care has been given the various 

operational details, and conditions in general are ideal, a reproduci-
SPECTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 27 

bility of 2 percent, expressed as relative deviation, may be attained. 

In practice, this value is frequently approached and relative deviations of 3 to 5 percent are quite commonly obtained (tables 11, 12, 13); 

occasionally relative deviations of 2 to 3 percent are reported. 

The following summarizes the statistical terminology used in this 

chapter. 

n, number of observations, analyses, etc. 

x, arithmetic mean. 

d, deviation of an observation from the mean. 

s, standard 4evi~tion=.J"Pd;, the uncertainty of a single observation. 

8:;,. standard error= Jn' the error of the arithmetic mean. 

0, relative deviation=~X 100, also known as the coefficient of 

X 

variation. 

E relative error= Q_. ~ .fii 

The quantities 0 and E permit comparison of data on a percentage 

basis, which is not possible if s and 8:; only are used. 

Accuracy in spectroche\mical analysis 

Spectrochemical methods of powder analysis are particularly liable 

to systematic error (bias). Such an error has several causes (see 

Ahrens, 1950, ch. 8) and is associated with the fact that the general 

physical and chemical composition of a specimen influences the 

intensity of line emission. Error due to compositional variation may 

be introduced where synthetic standards have to be used-usually 

causing a. systematically high result in the naturally occurring unlmowns-and when the mineralogical and chemical composition of 

the unknowns varies greatly. If systematic error is absent in a 

precise method, the method will then be accurate. 

Error due to the use of synthetic standards may be overcome by 

using naturally occurring standards that have been carefully analyzed 

che~ically. For the major.constituents this procedure may invariably 

be employed, but for relatively rare elements it is usually impossible. 

This is one use of the diabase and granite standards described in 

part 1. The second source of error-wide variation in the general 

composition of the unknown-would .appear if the standard diabase 

and granite were used as standards for the analysis of markedly 

d~fferent rock types. To overcome errors of this type it is probably 

safest to use a separate batch of standards for each composition type; 

947795-51-3 
TABLE 11.-Relative deviation (C) and relative error (E) for Al20 3, Fe 0 , MnO, and GaO 

[All measurements by W. H. Dennen. Lines used in observations: Sr, 2931 (internal standards); Mg, 2779; Fe, 2929; AI, 2652; Mn, 2801; Ca, 3006 and 3158. Italicized figures indicate poor results attributable to very low or very high line intensities. Figures in parentheses indicate values determined spectrographically] 

Sample mate- rial 

Reference No. 

Constituents 

Ab03 Fe 0 MnO MgO I CaO 

Concen-1 I Concen-1 I I ConcenNum- I ber of 

obser- I 

vations1 Concentration 

(percent) 

c E 

Concentration 

(percent) 

c E I tration C E tration C E tration I C I E (percent) (percent) (percent) ------ ----~·1 , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , __ _ 

Granite__________ G-L ________ 9 14.44 4. 7 1.6 1. 44 4. 7 1.6 0. 03 12.4 4.1 0.39 6. 5 2. 2 1. 42 4. 6 1.5 Diabase __________ W-L _______ 12 15.23 5.8 1.7 7.88 6. 2 1.8 .19 9.0 2. 6 6. 52 6. 7 1. 9 10.95 5. 8 1.7 Granite __________ D-23 ________ 27 (17. 5) 5. 2 1.0 (4. 2) 3. 9 .8 (. 34) 4.1 .8 (.42) 6. 4 1. 25 (1. 7) 4. 7 .9 Obsidian ________ R-1580 ______ 5 12.64 5. 5 2. 5 .88 5.4 2. 4 .03 4. 9 2. 2 .04 14.7 6. 6 .59 6.3 2.8 

Limestone _______ BS 1a _______ 4 4.16 5. 0 2. 5 1.14 5. 0 2. 5 .038 3. 6 1.8 2.19 6. 7 3 4 41.32 8. 0 4. 0 

~~cix-ite~=== == == == 

BS 98. ______ 5 25.54 7. 9 3. 5 1. 43 3. 4 1.5 .005 10.6 4. 7 . 72 5.6 2. 5 . 21 8. 0 3. 6 BS 76. ______ 5 37.7 6.8 3.0 1. 67 7.4 3. 3 ---------- 7.6 3. 4 (. 5) 7.4 3. 3 ---------- 7.1 3. 2 Glass. ___________ BS 93.------ 5 1. 94 5. 4 2. 4 . 053 14.0 6. 3 (. 001) 8. 4 3. 7 . 026 -------- -------- (.16) s. 2 2. 8 Olivine __________ R-1579 ______ 5 1. 07 22.3 10.0 8. 72 3.9 1.8 .16 1.3 . 6 46.27 ----2:9- . 36 7. 3 3. 2- Pyroxene ________ R-1096 ______ 5 3. 67 4. 0 1.8 3. 25 2.6 1.2 .14 2. 5 1.1 18.28 1.3 20.13 3.8 1.7 Amphibole ______ R-1110 ______ 5 11.33 3. 5 1.6 10.45 4. 0 1.8 .19 5.4 2. 4 12.41 6. 3 2. 7 12.03 1.5 .7 Biotite ___________ R-1578 ______ 5 14.58 4. 3 1.9 8.17 5. 3 2.4 ---------- -------- -------- 11.84 -------- -------- . 31 5.8 2. 6 Microcline _______ BS 70. ______ 4 18.03 3. 6 1.8 . 21 """38:2· ---16:6· (. 01) 12.5 6. 3 .013 (.07) 13.5 6. 8 

Albite._--------- BS 99. ______ 4 19.06 6. 5 3.1 .47 .0003 11.5 5.8 . 53 3. 4 1.7 .38 5. 6 2.8 

Fe0 indicates total Fe as metallic iron. 

·& 

1.\j 

00 

() 

0 

z 

1-3 

::u 

H 

t:d 

q 

1-3 

1-1 

0 

z 

Ul 

1-3 

0 

0 

t':1 

0 

c 

~ 

1-1 

~ 

[/). 

1-3 

::u 

,.1-<1 

~ 

co 

01 

0 

I 

01 

~ 
SPE·CTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 29 

for example, one for granitelike rocks, one for gabbroic types, one 

for ultramafics, and one each for feldspar, mica, pyroxene, and so on. 

This will of course necessitate building up a large collection of 

accurately analyzed rock and mineral types. The same procedure 

may be applied to soil types. 

TABLE 12.-Reproducibility data jo1· Si02 in diorite 

[All measurements by Lorraine G. Gorfinkle. Lines used in observations: Be, 2494 (internal standard); 

fH, 2528. Computations: :;, 62.5; s, 2.19; C, 3.5; Si, 0.50; E, 0.80] • 

ConcentmAnalysis No. tion 

(percent) Analysis No. 

l____________________ 61.5 7 ___________________ _ 

2 ••..• ·--------------- 63.0 g ___________________ _ 

3____________________ 59.7 !) ___________________ _ 

4____________________ 66.5 10 __________________ _ 

5____________________ 63.8 11. _________________ _ 

6_,__________________ 61.0 12. ________ ----------

Concentration 

(percent) 

61.0 

62.0 

63.8 

62.5 

64.7 

66.9 

ConcentmAualysis No. tiou 

(percent) 

13___________________ 63.8 14___________________ 63.4 15___________________ 60.2 1(j___________________ 58.7 1 7___________________ 63.0 

18___________________ 62.5 

TABLE 13.-Spectrochemical precision data for Na20 and K20 (five analyses each) 

in granite sample (G-1) 

Na20 K20 1 Na20 K20 1 

3.30 __________________________ 5. 57 3.3!) __________________________ 5. 28 

3.32_-- ----------------------- 5. 50 3.45_------------------------- 5. 64 

3. 24_------------------------- 5. 30 

t One extremely low analysis of 4.25 percent was discarded from this group. 

NoTg.-All measurements by Margaret Kearns, Department of Geology, Massachusets Institute of 

'J'eehnology. Lines used in observations: Li, 4073 (internal standard); Na, 5682; K, 6030. Computations: 

Na~O: x, 3.34; C, 2.55; E; 1.14, K~O: x~ 5.46; C, 2.05; E, 1.32. 

Another approach to the elimination of error due to compositional ... 

variation is the use of a compound which aats as a flux and buffer. The 

fitLxing action breaks down mineral structure and quicldy converts 

all the powder to a n1e)t, while buffer action aids in keeping arc temperature constant. To buffer successfully, the metal in the buffer 

compound should have a relatively low ionization potential. LhC03 

has been used for this purpose, and gern1anium metal may also be 

employed (Strock, 1948). 

Apart fron1 the use of chen1ical1y an~lyzed, naturall.Y occurring 

standards, there are other factors which tend to improve over-all 

accuracy of a major-constituent analysis when compared with a 

minor-ele1nent analysis. Fundamentally, of course, thei·e is no difference and no sharp dividing line. All spectrochemical methods are 

based on the same principle, namely, the variation of line intensity 

with the concentration of emitting atoms in the source. In minorelement techniques, lwwever, much emphasis has to be placed on 

developing a method that will provide the utmost sensitivity so as 

not to overlook a trace of elements, and in so doing puantitative 
30 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

reproducibility may be impaired. This does not hold for majorconstituent analyses. Th~re is usually much sensitivity to spare 

and nearly all attention can be focused on developing a very smoothburning and reproducible arc. A high dilution in an appropriate 

matrix-powdered graphite or carbon, CuO, or NiO, for exampleaids in this_ respect and also tends to improve accuracy by buffering 

-this would not apply to carbon because of its high ionization potential-and by reducing selective volatilization (fractional distillation) differences. Furthermore, relatively small anodes may be 

used for holding the specimen and through their use the reproducibility 

of the arc method can sometimes be improved. This does_ not apply to 

cathode-layer excitation where small cathodes must in any case be 

used for holding the sp~cimen in order to obtain proper cathode-layer 

enrichment. 

Several methods have been described for the spectro-chemical 

analysis of major .constituents in minerals, rocks and allied materials, 

using the direct-current arc. In the sections which follow we will present data on reproducibility and discuss the accuracy of working 

curves for certain elements, using (a) a method described by Kvalheim 

(1947) which has been modified in a few minor respects for the analysis 

of Ca, Mg, Fe, Mn, AI, and Mg; (b) a method modified after K valheim 

(1947) for silicon; and (c) a method developed in the Cabot Spectro- _ 

graphic Laboratory, Massachusetts Institute of Technology, for the 

analysis of N a and K. . 

The reader may obtain further information on the reproducibility 

•of these and other spectrochemical methods of major-element analysis 

by referring to the bibllography given by Ahrens and others (1952?). 

PROCEDURE AND PRECISION IN DETERMINATION OF 

Ca, AI, Mg, Mn, AND Fe 

Only a brief outline of the above method for determination is given 

here. Details may be obtained by reference to Ahrens and others 

(1950). . . . 

In a procedure slightly modified after Kvalheim (1947) strontium 

is used as the internal standard for the determination of the above 

elements. T4is internal standard appears generally suited to the 

analysis of the above group of elements. K valheim also employed it 

for Na and K, but because of the much greater volatility of the alkali 

metals, strontium is usually not an ideal internal standard for them. 

Using Kvalheim's procedure we found a poorer precision for the 

alkali metals than for the above elements. Consequently, a separate 

procedure was developed for the alkali metals. (Seep. 31.) 

Reproducibility data giving relative deviation and relative error in 

analyses are shown in table 11. In general, the relative deviations are 
SPE'CTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 31 

reasonably satisfactory. Relatively poor reproducibility in determina-

"' tion of AI in olivine and Fe and Ca in plagioclase is attributed to the 

low concentration of these elements. This has caused a marked weakening of the analysis lines and makes microphotometry less accurate. 

This error could undoubtedly be Teduced by usirig some other more 

intense lines at the low concentrations. 

The materials listed in table 11 were chosen in order that the effect 

of different matrices might be observed. The results show that a 

change of matrix composition has no apparent effect on the precision. 

~ Matrix composition might, however, introduce a systematic error, 

but the plotted points in figures 4 to 7 do not appear to show 'any 

effect of composition for the specimen types investigated. The point 

should be explored further, however, and if one were in doubt the 

safest procedure would be to employ separate standards for each 

unknown type. 

PROCEDURE AND PRECISION IN DETERMINATION OF 

SILICON 

The method described by K valheim (194 7) using beryllium as the 

internal standard gives a relatively high precision provided, as described by Ahrens and. others (1950), the sample is greatly diluted 

with carbon. Much dilution with carbon serves to make the volatilization rates of beryllium and silicon almost identical; otherwise beryllium is much less volatile. 

· The reproducibility data given in table 12 refer to a specimen of 

diorite. They apply generally to all rocks in the range of 5 to 100 

percent Si02• This wide range in silicon concentration can be handled 

with equal precision because there are several closely-spaced silicon 

lines of varying intensity at the analyst's disposal. These measurements were made before diabase (W-1) and granite (G-1) were 

· available for comparison. 

PROCEDURE AND PRECISION IN DETERMINATION OF 

Na AND K 

A satisfactory spectrochemical method for the analysis of N a and K 

in rocks is of considerable value, first because an analysis for alkali 

metals 'necessitates a separate operation-usually aJ. Lawrence Smith 

fusion-and secondly, because chemical reproducibility may be poor, 

particularly at relatively low concentrations-potassium in diabase, 

for example (fig. 2A). A method has been developed at the Cabot 

Spectrographic Laboratory, Massachusetts Institute of Technology 

(see Ahrens and others, 1952?), which provides a satisfactory precision 

and ac~uracy, for Na and K in most silicate r9cks; with little extra 
32 CONTRIBUTIONS TO GEOCHEMISTRY, '1 9 50-51 

effort the other alkali metals, Li, Rb, and Cs may be detennined with 

about equal precision. All alkali metals behave much in the same• 

way in the arc·, and highest accuracy is usually attainable when one 

alkali metal is 'used as an internal standard for another; this forms the 

basis of the spectrochemical procedure which has been developed. 

Spodumene is added to each specimen as a source for lithium, which· 

is the internal standard. Sodium may be determine<! over a co~centration range of about 0.5 to 15 percent. For potassium, lithium is 

used as the internal standard for relatively high concentrations (more 

than 3 percent). Below this concentration use is made of a double 

procedure. Sodium is first determined in the usual way, using 

lithium as the internal standard. The specimen-the same portionis then arced using a different procedure, in which sodium is used 

as a variable internal standard. In this second procedure potassium may be determined down to 0.5 percent and Li, Rb, and sometimes Cs may be determined accurately at the -same time. 

Table 13 shows son1e typical reproducibility data for sodiwn and 

potassium in the granite specimen. The relative error for sodium is 

about 2.5 percent, which is highly satisfactory; the relative error for 

potassium, is about 3.5 percent. At lower concentrations of potash, 

for which the double procedure is used, the relative error is about 6 

percent. 

STATISTICAL ANALYSIS OF THE CHEMICAL DATA 

In the preceding chapter the chemical data for the two provisional 

standards are given and the ·procedures used by the analysts are 

tabulated and discussed in some detail. The data are there presented 

as histograms. It was concluded that differences in methods of 

analysis could not explain the dispersion of values obtained. Additional discussion of these analyses is now desirable in order to test 

theiT usefulness for calibration of the spectrochemical investigation. 

EXPLANATION OF FIGURES 1 AND 2 

Histograms based on chemical data of tables 1 and 2 and table 14. Vertical scale showing frequency is 

simih'ir throughout-one block equals one analysis. 'l'he class interval shown by the horizontal scale is an 

a1 bitrary fraction of the mean and is given for each figure. The num bets at the ends of each histogram are 

the lowest and highest values reported for each constituent. 'l'he intermediate number is the arithmetic 

mean, placed approximately at its correct position in the histogram. The cross-lined blocks at the ends of 

some of the histograms represent those analyses which on statistical grounds alone could reasonably be 

rejected (sec p. 43). 

FIGURE 1.-A, Class interval for Si02 is 0.5 percent of the arithmetic mean; that for AhOs is I percent. B, 

Class interval for Fe0 , F~, and Fc20s is 5 percent ot the respective arithmetic means. C, Class interval 

for CaO and MgO is 5 percent of each arithmetic mean. 

FIGURE 2.-A, Class interval for Na20 and K20 is 5 percent of each arithmetic mean .. B, Class interval for 

MnO and PsOo is 33.3 percent of each arithmetic mean. C, Class interval for 'l'i02 and H20 is 10 percent of 

each arithmetic mean. · 
SPECTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 33 

14 .44 

1""'~1>1.9 ___ ,_.1 "''' • ~ W-1'-:Ac:-lz~--,---------'""' 

A 

1 7 4 

W-1 Fe• 

'!] 'I Ill! =._ _ _... G-llflel• •• _ _j~ 

·II ~-W-1 feO 

~...,__ ____ ._.1 ~G~-~1 ·~I ~~-20~3---L--~~_J~ • I ~ 

W-1 CoO 

Figure 1. 
34 CONTRIBUTIONS TO GEOCHEMISTRY, 19 50-51 

551 

0.02 

G-1 MnO 

i 

- 1.17 

Figure.2. 
SPECTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 35 

In the histogrmns of part 2 (pl. 1) the class interval is 0.1 percent 

regardless of the concentration o~ the constituent-MnO in granite 

excepted. All analyses are included in this compilation, irrespective 

of the number from any given laboratory. 'Another method of presenting the chemical data is shown in figures 1 and 2 (pt. 3). The 

class interval in eacJ;t histogram is fixed at some convenient percentage 

of the mean-5 percent for most-and only one value from each 

laboratory is included-the mean, where more than one analyst per 

laboratory made an analysis. Analyst 34 reported too late to be 

included in thMe calculations. This method of determining class 

interval allows direct visual comparison of the granite and diabase 

for any one constituent and, for constituents plotted with the same 

class interval, direct comparison of the dispersion of different· constituents. The "laboratory mean" method prevents undue weighting 

of the histograms in favor of laboratories which furnished a number of 

analyses. This may be an important factor where, as in this investigation, the chemical results were intended as calibration for the spectrochemical data. o 

The high degree of dispersion shown in the histograms for some constituents casts immediate doubt on their usefulness for calibration 

purposes. The means_ commonly do not coincide wi.th the highestfrequency columns and only one histogram (CaO in diabase standard, 

W-1) shows a symmetrical distribution of values on either side of the 

mean. The problem is similar to that encountered by Larsen (1938) 

i~ his smaller-scale study of replicate amphibole analyses. 

Statistical data are assembled in ·table 14 and include the standard 

deviation, standard error, and relative error for each constituent. 

For most of the constituents the relative error of the mean varies 

inversely with the ·magnitude of the mean. That is, the relative error 

tE) for CaO in the diabase (10.95 percent CaO) is lower than in the 

granite (1.42 percent CaO). These relations are shown in figure 3. 

The exceptions, shown by AbOa, Fe20a,. MnO and H20, are of less 

significance than the trend followed by the majority. Petrologists 

who make use of chemical data may st.udy this figure with much 

profit to themselves. Low error with high concentration, and high 

error with low concentration are taJten for granted by che1nists, but 

arc little appreciated by petrologists. 

In fairness to analytical chemists, it should be said that much 

greater precision can be obtained than that shown in tabl~ 14 if a 
36 

90 20 

19 

18 

17 

16 

IX 80 15 

14 z 

<( 13 1U 

:::!: 12 

(.) II i= 

1U 70 10 :IE 

::c 

..... 9 

0:: 

<( 8 

7 

6 

60 5 

4 

3 

2 

I 

50 0 

0 

Sl02 

CONTRIBUTIONS TO GEOCHEMISTRY, 1 9 50-51 

2 3 4 5 

Scale for MnO and P205 at nght 

Scales for others at left 

6 7 8 9 

RELATIVE ERROR Sl!/X 

0.3 

10 II 

FIGURE 3.-Diagmm showing mutual relations of the arithmetic mean and relative error for each constituent 

in the two standard rocks-filled circles, W-1; open circles, G-1. The lines connecting W-1 and G-1 for 

, each constituent draw attention to the inverse relation of the mean and the relative erroi-high concentration and low error; low concentration and high error-which holds for most of the constituents. 

careful selection of analysts is made and special precautions are taken. 

·For example," the accompanying table 15 shows admirable precision 

for certain constituents in a soda feldspar analyzed by the Bureau 

of Standards ·and their collaborators. For every constituent E is 

superior to its counterpart in table 14, after making due allowance 

for the relative concentration levels. This restricted type of test 

was not desired for the granite and diabase analyses and is quoted 

here as a reminder that the procedures used by analytical chemists are 

capable of high precision and accuracy. 

·sTATISTICAL ANALYSIS OF FLAME PI-IOTOMETER DATA 

FOR ALKALI METALS 

The increasing use of the flame photometer for routine determination 

of Na and I~ makes it advisable to include some results on the two 

standard rocks. In addition, determinations have been made on two 

standard samples of feldspars from Bureau of Standards. The data 

at hand are listed in table 16. For the two standard rocks the E 

values for the alkali metals (table 14) obtained from 24 laboratories 

• 
• 

• 

SPECTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 37 

arc nuwh inferior to the flame-phot01neter values; for the soda feldspar 

(albite smnple, BS 99) the precision of the Bureau of Standards 

chcn1ists (table 15) is somewhat better than the fl_ame photometer for 

Na20, but the reverse is true for K20. 

RE:i,JA'l.,IVE PRECISION OF CHEMICAL AND SPECTROCI:IEMICAL ANALYSIS 

A thorough comparative test 9f reproducibility in chemical and 

spectrochemical analysis has not yet been made. The comparison 

presented in table 18 is based on ·chen1ical determinations, shown in 

table 17, by seven analysts from a single laboratory and on spectrochemical determinations by two analysts, also from a single laboratory. 

The chemical determ.inations are included in th~ histograms of part 2 

and were n1ade by analysts of the United States Geological Survey. 

·Table 17 gives the 1nean, the standard deviation, and the relative 

deviation for each constituent in the two standard rocks. The 

relative deviation is large where the concentration of the constituent 

is low,· as in MnO and P205, and sn1all where the concentration is 

high, as in Si02• Table 18 compares those constituents which have 

been investigated by spectrochemical means. It is to be particmarly 

noted that the chem.ical rule relating to concentration and precision 

(fig. 3 and table 17) does not hold for spectrochemical analysis, in 

which reproducibility is essentially independent of concentration. 

Spectrochemical precision is therefore usually superior to che1nical 

where concentration is low but is inferior where concentration is high. 

(Sec "remarks" column in table 18.) 

TARLE 14.-P?·ecision of determinations in rock analyses by 24- laboratories t 

[Computations: x, ari.thmetic men~;~; s, standard deviation; s;, standard error; E, relative errot] 

Granite (0-1) 

s;; E 

------------- Si02----------------- 72.22 0. 43 0.09 0.125 

'l'i02---------------- . 26 . 067 . 01 5. 38 

AhOs .. -------------- 14.44 . 541 .11 . 79 

Fc20s-- ------------- .04 . 34 .07 7. 45 FcO _____ . ____ -- ___ -- 1.00 .135 .03 2. 81 Fco 2 _________________ 

MnO 1.44 . 231 . 05 3.35 ________________ . 03 . 0122 .003 8. ()() l\1g0 ________________ . 39 .135 .03 7. 20 cao _________________ 1. 42 .152 . 03 2. 25 

Na20---------------- 3. 2() . 284 .06 1. 81 

K20----------------- 5. 51 . 549 .11 2.07 

H20+--------------- . 37 .104 . 02 6.00 

P:!O~-- ·-------------- .10 . 045 . 01 10.3 

• Analyses rcculculatcd to 100 percent, omitting H20-. 

----

52.25 

1.09 

15.23 

1. 85 8. 51 7.88 

.19 

6. 52 10.95 

2.05 

.71 

.62 

.13 

Diabase (W-1) 

----

0. 41 

.179 

.938 

. 053 

. 707 

.180 

.086 

.520 

.197 

. 230 

.196 

. 245 

. 0414 

s-z 

---

0.09 

. 04 

. 20 

. 21 

.15 

.04 

.02 

.11 

.04 

.05 

.04 

. 05 

. 01 

2 l?o0 indicates total Fe as metallic iron. Percent not included in summation. 

E 

0.167 

3.59 

1. 31 11.24 

1.77 

. 50 9. 47 

1. 70 

.38 

2.39 

5.89 

8.42 

6. 93 
38 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

TABLE 15.-Precision of determinations in six partial chemical analyses of soda 

feldspar (BS99} from sii laboratories 1 

[Computations: x, arithmetic mean; 8, standard deviation; s-;;, standard error; E, relative error]' 

c E c E 

----------------------------------- Si02- _ ---------- . 68.66 · Fe20a. ---------- . 67 cao____________ . 36 

0.047 

.004 

. 092 

0.07 

6. 5 6.1 

0. 03 Na20----------- 10.73 2. 9 K20. _ ---------- . 41 2. 7 

I u.s. Bureau of ?tandards analyses, issued 1931. 

0.059 

.025 0. 55 ' 0. 24 6. 2 2.8 

TABLE 16.-Precision of determinations in four analyses of alkali metals by flame 

photometer 

All measurements by Geraldine Sullivan, Departme: · · ,-• Computations: x. arithmetic mean; 1, :·. · 

Material Reference No. Number of 

observations 

c E c E 

·--------1------1·--------------------------

Granite._----------- G-L __________ 8-------------- 3. 58 1.40 0.50 5.42 0.83 0.29 

Diabase.------------ W-1 __________ 8.------------- 2. 29 2. 85 1. 01 .693 2. 28 .81 

Mlcrocline_. -------- BS70 __________ 5 and s _____ 2. 33 1. 73 .71 12.42 1.38 .49 Albite_. _________ . ___ BS99..-------- 5 and 7 ________ 10.75 1. 39 .62 .504 5. 57 2.10 

TABLE 17.-Precision of determinations in replicate rock analyses by one laboratory 

( U. S. Geological Survey) 

[Analyses recalculated to 100 percent, omitting H20-. Computations: z, arithmetic mean; 8, standard . deviation; C, relative deviation] 

Granite, G-1 (7 analysts) Diabase, W-1 (6 analysts) 

x c x c 

Si02.------------------------- 72.64 0. 23 0. 31 52.66 0.34 0.64 

Ti 02.-------..• --------------- .25 .03 11.2 1.03 .04 4.15 

Ah Oa. ------------------------ 14.13 .17 1. 22 14.87 .48 3.23 

Fc20a .. -.--------------------- .86 .17 19.3 1. 41 .47 33.4 

FeO .• ------------------------ 1.06 .06 5. 7-2 8. 91 .16 1. 82 

Fe0 -------------------------- 1. 43 .13 9.30 7. 91 .31 3.92 

MnO __ ----------------------- .03 .01 30.5 .17 ,\Jl3 15.6 

MgO--- ---------------------- .44 .04 9.90 6. 51 .40 6.00 

CaO -------------------------- ]. 34 .09 6.53 10.95 .09 .83 

Na20 1_. ---------------------- 3.43 . 21 6.23 2.20 . 13 5. 72 

!{20 I ________ ------------------ 5.43 . 21 3.83 .68 .05 7.06 

H20+------------------------ .31 .08 26.7 . 45 .05 10.5 

P20G------ -------------------- .10 .02 23.4 .15 .03 18.7 

1 Three analysts determined alkalis with flame photometer. 

The relative deviation of 3.5 percent for Si02 is reasonably good, 

but it does not suffice as a basis for rock classification and is definitely 

poorer than the chemical reproducibility, even if comparison is made 

with the interlaboratory chemical determin.ations shown in table 14. 

By making a quadruplicate analysis, the relative deviation could be 

reduced to a little less than 2 percent. There are a few geological 

applications of a spectrochemical method of silicon where a relatively 

coarse variation in the sili~on content suffices as, for example, in the 

investigation of the geochemical association of Ge and Si in rocks. 
.• 

SPECTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 39 

For low concentrations of Si, as in a limestone, where precision of 

chemical analysis is probably lower than. with igneous rocks, the 

. spectrochemical method could successfully compete with the chemical 

procedure: Data on this aspect of the P.roblem are not yet at hand. 

When attempting to compare relative precision of chemical and 

spectrochemical analysis, it should be borne in mind that whereas 

personal error in a spectrochemical method is invariably slight, this 

cannot be said about chemical analysis. Therefore, although all 

spectrochemical determinations were made by only two analysts, the 

reproducibility would probably have been affected only a little had 

several other spectochemists also made analyses. 

In working with the alkali metals additional .comparison of precision can be made using the flame photometer data already listed in 

table 16. Even though some of the determinations of the Geological 

Survey chemists were made with the flame photometer, the over-all 

precision is considerably less than that obtained from flame photometric data only. 

TilE AH.ITIIMETIC MEAN AND THE CONSENSUS MEAN 

Since the histograms of the chemical data show little approach to 

symn1etrical form the task of selecting mean values for construction 

of spectrochemical working curves becomes a formidable one. If one 

assumes that the clustered values represent superior determinations 

and that the remaining vf).lues are inferior in quality, then a consensus 

mean-the mean of an arbitrarily selected cluster-should be used. 

If, on the other hand, one assumes that experimental error alone is 

responsible for the disper~ion which is astonishingly large for certain 

constitutents, then the arithmetic mean, computed from all the 

TABLE lB.-Comparison of intralaboratory precision on selected constituents in 

granite (G-1) and diabase (W-1) samples 

[Precision stated as rollltive deviations (C)] 

Percent Spectra- Chemical conccntm- precision 1 tionofcon- chemical Remarks 

stituent precision t 

. 

1?6~~---------------~---------- 0.3-0. 6 . 5Q-70 3.5 Chemical analysis much superior. 1-3 14-15 5-6 Chemical analysis superior. 

Fo0 

Mno ---------------- 4-9 1-8 4-6 Spectrochemical analysis slightly superior. ______________ 15-30 .03-.2 !H3 Spectrochemical analysis much superior. MgO .......•.•.••.. 6-10 . 4-7 6. 5 Spectrochemical analysis superior in G-1. cao _______________ .8-6.5 1-11 4-6 Chemical analysis superior in W-1. 

N.,o ____ ----------1 3 6 } 2-4 2.5 Spectrochemical analysis superior to chemical; 4 1. 5-3.0 . about the same as flame photometer. 

1{20 •••••••••• : ••••• a 4-7 } . 7-5 3-5 Spectrochemical analysis about the same as 4 1.0-2. 5 chemical; inferior to flame photometer. 

I Except for AhOa, precision in these chemical analyses increases directly ( C becomes smaller) with in· crease in concentration of the constituent. 2 Spectrochemical precision is independe.nt of concentration of constituent. a Includes three flame photometer determinations noted in table 17. 1 Flame photometer only. (Massachusetts Institute of Technology values.) 
TABLE 19.-Means of consensus groupings of constituents 

Constituent 

SiQz_----------------------------------, ___ -------------------- TiQz _________________ : ________________________________________ _ 

Alz03-- __ ------------------------------------------------------ Fe20l---------------------------------------------------------- FeO--- -------------------------------------------------------- MnO _______ --------------------------------------------------- MgO _- ___________ -- _____ ------------------------------ _- _- ----

CaO ___ -------------------------------------------------------- Na20 __ -------------------------------------------------------- I\:zO--- --------------------------------------------------------

Mean 

based on fig. 1 

72.45 

.25 

14.30 

.85 

1. 00 

.025 

.45 

1. 35 

3.35 

5 45 

.35 

.05 

.10 

HzO+--- __ ---------------------------------------------------- H20-------------------------------------.--------------------- PzOs-----------------------------------------------------------.===1 

Totf!.l 99 98 

Total Iron as Fe203--------------------------------------------1 1 90 

G-1 

Dispersion 

of consensus 

values 

(±mean) 

0.05 

.05 

. 20 

.15 

.10 

.005 

.05 

. 05 

.15 

.05 

. 05 

.05 

.05 

Fraction of 

total analyses in consensus 

grouping 

~-

o/Jo 

~~ 

% 

% 

%-

~~ 

% 

% 

~ 

%-

All 

o/Jo+ 

Mean 

based on fig.3,4 

72.40 . 25 14.30 

. 90 

1 00 

.03 

. 50 1 40 

3 40 5.50 

.40 

--------:iii-

--

100.15 

.10 I ~+ j_ ___________ 

Mean 

based on fig. 1 

52.50 

1. 05 15 15 

1.40 

8. 75 

.17 

6 65 10 95 

2.10 

. 65 

. 55 

.15 

.15 == 

100. 12 

1110 

• 

W-1 

Dispersion 

of consensus 

values 

(±mean) 

0.10 

.05 

. 25 

.30 

.05 

. 01 

.05 

. 05 

.10 

.05 

.15 

. 05 

. 05 

===== 

----------------

0.10 

~ 

Fraction of 

total analyses in consensus 

grouping 

~+ 

~~ 

?5 

~~ 

~~ 

~ 

% 

% 

% 

?4-

7~+ 

~{!-

All 

----------------

~~ 

Mean 

based on figs. 3, 4 

52.35 

1.10 

15.10 

1 50 

8.60 

.19 

6. 60 10 95 2.10 

. 65 

. 55 

------------ .13 

99 82 

~ 

0 

0 

0 

z 

8 

~ ~ 

td 

q 

8 

~ 

0 

z 

Ul 

8 

0 

0 

M 

0 

0 

~ M 

~ ~ 

Ul 

8 

~ 

--~ 

...... 

co 

01 

0 

I 

01 

...... 
I 

•. 

SPEC'l'ROCHEMICA.L ANALYSIS-MAJOR CONSTITUENTS 41 

analyses, should be u_sed. This mean has already been computed 

(table 14), and its relative position has been indicated on the histograms (fig. 1, 2). 

Any consensus mean will be arbitrary and should therefore be 

selected carefully and used with caution. Two sets of consensus 

means taken independently and several weeks apart turned out, 

however, to be practically identical. One was taken from the histograms of part 2 and the other from those in this chapter. Table 19 

shows these values, as well as arbitrary dispersion values, and the 

fraction of the total analyses occurring within the consensus grouping. 

The last-mentioned two columns were compiled from the histograms 

in part 2. If there is therefore any virtue in a consensus mean the 

selection shown in table 19 is probably as free from bias as any. The 

two sets of means are compared in table 20. The discrepancies are 

small, but should not be ignored on that account. 

TARLE 20.-Comparison of consensus and arithmetic means 

G-1 W-1 

Consensus Arithmetic Consensus Consensus Arithmetic Consensus mean Mean mean less mean Mean mean less 

greater by by greater by by 

Si02 .. ------------------------ 0. 23 ._72. 22 0. 20 ._52. 25 

'l'i02-------------------------- . 26-> 0. 01 1 09~ 0. 02 

Ah03------------------------- 14.44~ .14 15. 23~ . 13 

l<'c203-------------------- .94~ .09 1.85~ .40 J?cO. __ ... ---------------. ~~~~ .0 1.00 .0 . 21 ._g, 25 l\1n0 _________ : ------ _________ .0 .03 .0 .19~ • 01 

~1?.. ~ === == ==== ==== == =~======- .OG <-.39 . 13 <-G .. 52 1. 42 .07 .0 10.95 .0 Na20 .• .09 <-3. 2G . 05 <-2. 05 

K20 ... -= = = = = = = = = = = = = = = = = = ~ = = = 5.51~ .OG .71~ .OG 

1-hO+------------------------ .0 . 37 .0 .02~ .07 

1'206-------------------------- .0 .10 .0 .01 <-.13 

'fhrec tests may now be applied toward a solution of the problem 

of whether the arithmetic or the consensus mean more nearly represents the theoretical composition of the two rocks. The first test 

involves comparison of the measured and calculated mode; the second 

is concerned with the problem of rejecting certain chen1ical determinations; the third involves a new set of analyses on a synthetic rock 

sample. . 

The first ·test makes use of the detailed modal investigation presented in part 5. These measured modes were made from thin 

sections prepared from the same slab of granite as was used for 

chemical analyses. It was thought that comparison of calculated 

n1odcs-one based on aritlunetic means, the other on consensus 

means-with these thin-section modes 'might give some indication 

. as to the. preferred set of means. The results of such calculations 
42 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

are shown in table 21. Both calculated modes approximate the 

measured modes very closely, particularly for total feldspar. Both 

show somewhat higher. quartz and lower mica than the thin section 

modes. The Al203 remainder 'is negligible in each case. The test 

is therefore inconclusive for present purposes, but nevertheless useful 

in showing that neither set of means is very far from the theoretical 

composition of the rock. 

The calculated modes were made as follows: 

(1) All Fe20a was assigned to magnetite. 

(2) FeO not required for magnetite was assigned to biotite. ,.., 

(3) All MgO _ was assigned to biotite. The proportions of 

MgO and FeO thus available were about normal for 

biotite in granites. 

(4) Spectrochemical analysis of Al20 3 in this biotite gave 16 

percent, corresponding to a biotite formula K20 

5.6(Mg, Fe)O 1.4Al20a 5.6Si02 2H20. 

(5) Since the water available for muscovite after completion 

of the biotite calculation was far in excess of that 

required (ratio of muscovite to biotite, in measured 

mode, equals 2:5), the excess was disregarded and the 

muscovite calculation was based on the measured mode. 

TABLE 21.-Comparison of measured and _calculated modes of granite (G-1) sample 

Minerals 1 

Measured modes 

(converted to weight percent) Calculated modes 

Mean of Mean of Based on an measurements M. I. T. meas- arbitrary con- by Chayes on urements by 5 sensus mean 

Hi sections ope~~;t~~~~n 5 for s~ft~~n~onBased on the 

computed mean for each 

constituent 

Quartz __________________ --------------- 28.0 26.8 28.9 29. 1 

Total feldspar__________________________ 65.9 66.7 65.8 66.3 

Muscovite._--------------------------- 1. 4 1. 4 1.1 1. 0 Biotite_________________________________ 3. 6 3. 4 3.1 2. 9 

Magnetite ______________ --------------- 1. 5 1. 7 1. 3 1. 4 

1---------1----------1----------1---------

TotaL___________________________ 100.4 100.0 100.2 100.7 

I====~~======= I~=======!======== AlzOa remainder ________________________ -----------~--------------------- 0. 9 0. '! 

t Nonopaque accessories omitted. 

(6) K20 not required for biqtite and muscovite was assigned to 

orthoclase. 

(7) All N a20 was assigned to albite. 

(8) All CaO was assigned to anorthite. 

(9) Si02 not required for the above calculations was assigned 

to quartz. ' 
GEOLOGICAL SURVEY 

I • 

71 

GRANITE 

. . . .. . . . . . . . . . . . . . . . . . . ' .... ' .. 

I • 

13 

15 

0.0 

1~0 

72 

. 

... • 

. .. . . .. . ....... . .. , ....... . 14 15 

.. .. . .. . ...... .. • I ...... , ••• 

16 17 

. . . . . . . . . . . . . 

73 

. . . . . . ..... ' .. o.s 1.0 

. . . • 

. • 

. . . . . . ... 

16 

' . 18 

. 

1.5 ' 

0.5 0 1.5 

1.5 

. 

. . . •• 

. . . . . . . . . . . . . . , . . . ,. 210 2,5 

. . . .. . . .. 

. . . . . . . . . . . . . . . . . . . . . .. ' o.o 015 1.0 

.. . . . . . . 

. . . . ... . . . . . . . . . . . . . • • • • • 

1,0 I I 5 

. . 

. . . . . . , . 0~00 0.05 

• 

2.0 

0.10 

19 

210 

3.0 

Si Oz 

. . 51 

13 

Fe 0 

6.5 7.0 715 

10.0 

MgO 

4.5 510 515 

CoO 

MnO 

26 

52 

DIABASE 

. .. . ... ..... . .... ... ~ .. 

. . ..... . . ..... 

53 

• • I ..... ,.... • • • 

14 15 16 17 

..... 

. .... . , ..... ·-···· 27 28 29 

. .. 

18 

• I 

30 

... ...... ......... . , . ., . 0 

8.0 

. .. . . 

2 

. . . . . . . ........... 

3 

8,5 910 9~5 

. . . .. . . . . 

• • e • ' •••• I •••• 

10.5 1110 11.5 12.0 

6.0 

. 

.. • .. . . . . .... . . . . . ' . . . . 6.5 7.0 

. . .. . . . . . . . . . . ..... . .. ' .... 10.5 11.0 1115 

. ... ... ... .. ... .. ,.. .... , ... 0.10 0.2 0 0.30 

715 

OAO 

4 

12.5 

0150 

19 

3 

5 

• 0.60 

GRANITE 

. . . . . . ... . .. . . . . . ... . . .. , .... ,. 215 310 315 410 

4 

. • 

. • 

.. ... .... ..... 5 6 ' ····-·. 

. . . . . . . 

. . 

• • 

. ' 010 0.5 

o.o 

. 

• 

. • 

. 

. 

• • • 

. • 

' 

• • 

. . 

• 

0~0 

. . . 

• • • • . • . • 

.. . . 

.. • • 

. . .. 

• • • • • • 010 015 

. . • . . . . . . . . . . . . . . . 

0.5 

110 

, ... , .. ·~· 

9915 10010 10015 

7 

• I 

1.5 

Summation 

10110 

ANALYSES OF THE GRANITE AND THE DJABASE, AS REPORTED BY COLLABORATING ANALYSTS 

I e 

010 

BULLETIN 980 PLATE 1 

DIABASE 

. . . .. . ... . . .... . I • • • f •••••• 

1.5 2.0 215 

.. .. .. 

. • . • 

.. .. . .. . .. . .. . ' . . . . . 

310 

o.o 0.5 1.0 1.5 

015 ' 

. . .. 

. 

• . • 

. . . . .. ... . . . . . . ' .... 1.0 1.5 

• 

. • 

• 

. • 

.. • 

. . . . . . . . . . . . . . . . 

• • ?t •• 

010 

. • 

• • 

. . 

.. • .. ... . .. 

•••• 

015 

0.0 015 

. . . . .. . .. . ... I e e e ' • 

010 015 

. . . • . •• . . .. . . .... . 

1.0 

e e • ., e e e e I e 

99.5 10010 10015 

I .5 

101,0 
•• 

SPECTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 43 

Orthoclase, albite, anorthite are reported as felds'par only, since the 

amount of K20 in plagioclase, and Na20 in orthocla.se, was not 

dete:t:mined. 

The second test is somewhat more positive. The histograms 

(figs. 1, 2) show a numberof determinations differmg so markedly from 

the main group as to leave a reasonable doubt in one's mind that they 

could be-attributed to normal experimental error. If a statistical 

device is used whereby measurements which differ from the mean by 

more than twice the standard deviation (X-x>2s) are discarded, it 

turns out that about 6 ·percent of them should be rejected altogether, 

and that an equal proportion are close to the discard threshold. Table 

12 lists the rejected 6 percent. · If the analyses are subjected to this 

test, less than h~lf of the laboratories pass for all determinations; if one 

reject is permitted, less than two-thirds pass. The 34 .rejected 

determinations are about equally divided between the two rocks and 

include every constituent except CaO in the diabase. The remaining 

histograms indicate for all except the Ti02 in the diabase sample 

(W- 1) a shift of the statistical mean in the direction of the consensus 

mean if the determinations listed in table 22 are omitted from the 

computation. This is shown by arrows in table 20, each directed 

toward the consensus-mean columns. Lest the reader suspect that 

in this test the "wish was father to the thought," it should be stated 

here that the consensus means were set up before there was any 

thought of applying this reject test. If therefore the premise is valid 

that the extremely low and extremely high determinations can be 

discarded, it would appear that a new statistic-al mean, closer to the 

consensus mean than now shown, should have preference. _ 

The third test is essentially a new investigation, using as analytic 

material a synthetic rock of approximately the same compo,sition as 

the natural granite or diabase already used. Since the composition 

of such a synthetic rock would be known within very definite and 

narrow limits, the work of a selected group of chemists could be closely 

controlled. If their determinations checked with the known composition of the synthetic standard, it might reasonably be assumed 

that their work on the two natural rock standards was equally significant and that their values should have preference over others. 

By this indirect approach a more reliable calibration for the spectrochemical working curves might be realized. This project, now under 

way, will be reported on at a later time. 

047705-51-4 
44 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

TABLE 22.-Compila~ion of rejected determinations in chemical analyses of standard 

rock samples 

Number of 

rejects 

[Based on X-.X>2s] 

Constituent 

Rock sample 

G-1 W-1 

o_ _ __ _ ___ __ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ __ _ _ _ _ _ 10 

2 

l

Ti02---- _ ----------------------- _ ------------------- ___ ----- ___ --- x Fc20a- ____ ------------------------- ____________________ ------- __ __ x 

,_---------- i~f:::~mm~= ~~ ~~ ~~=~ ~~= ~~~ ~~~~ =~ ~ ~ ~~~ ~ ~~ ~ ~ =mm ----r--- ~ ~ ~ ~ +~ ~: 

THE WORKING CURVES 

The need for the foregoing discussion lies in its application to the 

construction of accurate working curves. In figs. 4-10, showing these 

working curves, the ordinate is a ratio of line intensities, that of the 

analysis line to the internal-standard line, which varies directly and 

linearly with the concentration of the analysis element. If standards 

of known concentration are available a working curve can be established for each constituent. These curves can then be used for analysis 

of unknowns. 

In figs. 4-10 the degree of uncertainty is indicated by the form of 

ea.ch plotted point. For the diabase sarp.ple (W-1) and the granite 

sample (G-1) rectangles are employed in which the vertical side· 

represents the error in the spectrochemical analysis; the horizontal 

side gives the corresponding error in the chemical analyses. The 

center of each rectangle is the plot of the mean values of the intensity 

ratio .and of the chemical determination. The smaller the rectangle 

for a given constituent the more accurate is the working curve in the 

• 
•. 

SPECTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 4Q 

neighborhood of that point. The relative degree of error in the two 

nwthods of analysis may be determined by the shapes of the rectangles. 

For standards appearing in the working curves other than diabase 

(W-1) and granite (G-1), the degree of uncertainty is unknown and 

the elliptical symbol used indicates only spectrochemical uncertainty. 

The chemical values for G-1 and W-1 used in figw·es 4 to 10 are 

the c01nputed ones (table 14)-figures 8-10 are based on computed 

n1cans fr01n flame-photometer data only. Although some evidence 

was assembled in the previous section favorable to the concensus 

n1can, the dispersion of values about this mean (table 19) is greater 

in most cases than the computed errors .of table 5. Until fw·ther 

chemical investigation with a synthetic standard is carried out, 

therefore, the degree of uncertainty in the standards is most logically 

shown by the computed error of the mean. 

REFERENCES CITED 

Ahrens, L. H., 1950, Spectrochemical analysi~, Addison-Wesley Press, Cambridge, 

Mass. 

Ahrens, L. H., Dennen, W. H., Canney, F. C., and Gorfi.nkle, L., 1952?, Quantitative spectrochemical analysis of silicates. (In preparation.) · 

Kvalheim, A., 1947, Spectrochemical determination of the major consituents of 

minerals and rocks: Jour. Opt. Soc. America, vol. 37, p. 585. 

Larsen, E. S., 1938, Accuracy of chemical analyses, etc.: Am. Jour. ·sci., vol. 35, 

p. 94. 

Strock, L. W., 1948, Analysis of rock-forming minerals by spectrochemical methods 

in petrological research [abstract]: Geol. Soc. America Bull., vol. 59, pp. 

1355-1356. 
46 CONTRIBUTIONS 'fO GEOCHEMISTRY, 19 50-51 

INTENSITY ANALYSIS LINE I INTENSITY _Sr 2931 

0.1 0.5 5.0 0.5 

, 

0 

<i "' 

c 

z 

<( 

Lt 

z 

0 

i= 

1.0 

~ 10 

tz 

w 

0 

z 

0 

u 

~Obsidian 

~ smceous limestone 

·Pyroxe~ Siliceous limestone 

• Granite tlandord 

-~1 1.~ . ~ <> Pyroxene 

:io:S, 

Olivine -

• . Hornblende ,~ ~ Obsidian ~ ~ Granite standard 

.:-.. -, Oia_ base standard 

Microcline - "\ 

FIGURE 4.-Working curves for Iron and aluminum. The aluminum point for microcline is unusually far 

off the working curve-perhaps because of a compositional effect. Obs, obsidian; W-1, standard diabase; 

Ls, limestone; G-1, standard granite; Py, pyroxene; 01, olivine; Hb, hornblende; Mic, microcline. These 

are the standards referred to in table 1. 

.• 

c· 
0 

c: 

~ 

~ 

z 

w 

(.) 

a: 

w 

a.. 

z 

0 

~ a: 

~ 

z 

w 

(.) 

z 

0 

(.) 

SPECTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 47 

INTENSITY ANALYSIS LINE I INTENSITY Sr 2931 

0.001°' 1 5.0· 

0.005 

0.01 

Granite standard I o Obsidian 

\.. Siliceous limestone 

0.05 

0.1 

c::> Pyroxene 

Diabase standard I . Hornblende 

\ 

0.5 

FIGURE 5.-Working curve for manganese. This curve is unusually fiat. Abbreviations as in figure'· 
48 

0.1 

0.05 

0.1 

0.5 

0 

0 

u 

~ 1.0 z 

L&J 

u. 

0:· 

L&J' 

a. 

z 

0 

~ <( 

0: 

~ 

z 5.0 L&J 

u 

z 

0 

u 

·CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

INTENSITY ANALYSIS LINE I INTENSITY Sr 2931 

0.5 1.0 5.0 10 

r---------------~------+-' ----------~- -"Jab~se standard • 10 

-

11 

~omblende \~ • 

~ ~~~roxene i\ - Siliceous ~ 

50 ' limestone \ 

100 

FIGURE 6.-Working curves for calcium. Because Ca 3158 begins to absorb above approximately 10 per 

cent CaO, Ca 3006 is employed at relatively high concentrations of calcium. Abbreviations as in figure 4. 
) 

,.. 

SPECTROCHEMICAL. ANALYSIS-MAJOR CONSTITUENTS 49 

INTENSITY ANALYSIS LINE I INTENSITY Sr 2931 

1.0 

0 

0' 

~ 

.... 

z 

LLJ 

u 

a::: 

LLJ 

a. 

z 

0 

~ 5.0 

a::: 

.... Diabase • • z 

LLJ 

Hornble~-- u 

z 

0 

u 10 

Pyro.,ne \ 

50 

l!~IOURE 7.-Working curves for magnesium. Both exhibit the effect of self-absorption at relatively high 

concentrations of magnesium. Abbreviations as in figure 4. 
/ 

50 

0 

z 

> 1-

u; 

z 

w 

1-

z 

CONTRIBUTIONS TO GEOCHEMISTRY, 19 50-51 

r---------~--~0~------~ 

~9 

-.~-~---7 --------1 

3 ~/6 I 

o'O 

I;>' 4 /0 2 

0.1~------L---~--L-~-L~~-L-------L--~---L~ 

1.0 5.0 10 50 

CONCENTRATION PERCENT Na20 

FIOURE 8.-Working curve for sodium. Plotted points closely spaced about tho working curve. 

1. W-1. 

2. K feldspar (U.S. Bur. Standards, No. 70). 

3. Two parts of W-1 and one part of G-1. 

4. One part of W-1 and one part of G-1. 

5. One part of G-1 and one part of K feldspar. 

6. G-1. 

7. One part of Na feldspar and one part of K feldspar. 

8. One part of G-1 and one part of Na feldspar. 

9. Na feldspar (U.S. Bur. Standards No. 99) 

( 
SPECTROCHEMICAL ANALYSIS-MAJOR CONSTITUENTS 51 

C\1 

~ 10.-----.--.--.--.-.-.-.-..-----.--~-.--, 

~ v 

.. 

~ 

>- 1-

u; 

z 

~ 1.0 L,._ ___ __J,_ __ ...~..-_..____J,_--I..--I..--1--L-1.....----.....,J---...L.---'----l 

z 

1.0 5.0 lO 50 

CONCENTRATION PERCENT K20 

FIGURE 9.-Worklng curve for potassium (direct method). Restricted to concentrations above about. 3 

percent. 

1. One part Na feldspar (U.S. Bur. Standards No. 99) and one part G-1. 

2. One part W-1 and one part G-1. 

3. G-1. 

4. One part Na feldspar and one part K feldspar. 

5. One part G-1 and one pi>rt K feldspar. 

6. K feldspar (U. S. Bur. Standards No. 70) . 
52 

>-

t-

(i) 

z 

w 

t-

~ 

>-

t-

(i) 

z 

w 

t-

~ 

CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

0.05L---~--~_u~~~L---~--~_L~~~~--~---L_L~~_LU 

0.01 0.05 0.1 0.5 1.0 5.0 10 

CONCENTRATION PERCENT K20 I CONCENTRATION PERCENT Na20 

FI,GURE 10.-Working curve for potassium (indirect method; sodium as variable internal standard). Applicable over a wide range of K/Na concentration ratios. 

1. Na feldspar (U.S. Bur. Standards No. 99). 

2. W-1. 

3. One part Na feldspar and one part G-1. 

4. One part Na feldspar and one part K feldspar. 

5. G-1. 

6. One part G-1 and one part K feldspar. 

7. K feldspar (U. S. Bur. Standards No. 70). 

( 

<. 

• 
A COOPERATIVE INVESTIGATION OF 

• PRECISION AND ACCURACY IN 

CHEMICAL, SPECTROCHEMICAL, AND MODAL ANALYSIS OF 

SILICATE ROCKS 

PART 4. SPECTROCHEMICAL ANALYSIS OF SOME OF THE 

RARER ELEMENTS IN THE GRANITE AND DIABASE 

SAMPLES. 

By L. H. AHRENS 4 

INTRODUCTION 

As sensitive and quantitative methods of analysis become available, 

increased attention is focussed on the abundance and distribution of 

the rarer eletnents in the earth's crust. Much of this information is 

based on spectrochen1ical methods of analysis, and in common rock 

types some 15 to 20 of the rarer eiements may be d~termined by these 

methods. For a list of such eletnents see Ahrens (1950) and table 23 

in this report. Several other elements may be determined providePthat novel and lengthy procedures, some of which necessitate chen1ical 

pre-enrichment, are used. Here, however, we will be concerned only 

with those elements which may be determined by direct procedures. 

There is little doubt that most published spectrochemical analyses 

are reasonably reliable insofar as they show the correct magnitude. 

The presence of a significant systematic error (see pt. 3) cannot, however, be overlooked. The presence of such an error makes it difficult 

to c01npare the analyses of a suite of 1ninerals and rocks made by one 

analyst with the analyses of another suite made by another analyst. 

For exatnple, the abundance of gallium in the igneous rocks fr01n many . \. . areas of the earth's crust rs about 0.0015 percent, accordrng to spectrochemical analyses made by Goldschmidt and Peters (1931) and others. 

Van 1'ongeren (1938) also ·employed spectrochemical .analysis for a 

study of the distribution of gallium and other elements in the East 

Indian Archipelago and obtained an abundance value for gallium 

three times that of Goldschmidt and Peters. Some geologists may 

conclude that the East Indian Archipelago as a w}lole is enriched in 

gallium. This is possible, but it seems unlikely when one takes into 

.consideration the geochemical properties of gallium. Gallium is very 

uniforn1ly distributed throughout the main mass of igneous rocks, and 

it would indeed be surprising for such an element to have enriched 

4 Massachusetts Institute of Technology. 

53 
54 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

TABLE 23.-Comparison of spectrographic and chemical methods of 'analysis for rarer elements in the granite and diabase samples 

Granite standard 1 Diabase standard 

Spectrographic Chemical Spectrographic Chemical 

Constituents 

~ ·(L:bo- (Ficld ratory test) test) 

2 3 

4 5 

(F. ld (Labo- 10 ratory tC':;t) test) 

-------1-----------------------

BaO...... .. . . . . .. . 0. 34 0. 15 0. 15 ... .. ... . .. . .. .. 0. 028 0. 043 0. 030 ............... . BcO ..•..•......... 0 .00056 ........................ 0 0 ............•........... B20s ....................... 0 ........................ -------- .003 -------- ....•... -------- CoO .....• _........ 0 . 00038 0 0. 0001 0. 00038 . 0044 . 0032 . 0038 0. 002 0. 0052 Cr20a.............. .0015 .0044 .0037 -------- ........ .018 .019 .016 ....•... _______ _ CuO ................ 001 .0019 .00062 .001 .0025 .016 .011 .0055 .01 .016 Ga20s.............. .0027 .0024 .0026 ________ -------- .002 .0016 .0026 -------- -------- La20s.............. .050 .022 .015 -------- -------- .Oo.18 0 0 -------- _______ _ LhO............... .004 -------- .005 ________ -------- .002 .002 -------- -------- MoOs.............. . 00082 . 00082 ________ . 002 -------- 0 0 -------- . 0007 -------- ( 

Nd20a-------------- -------- -------- .0093 -------- ........ ----···· ......•. 0 -------- -------- NiO................ . 0006 0 ........ . 008 0 . 006 . 01 .....•.. . 02 . 010 PbO .. ~------------ .0027 .0024 .0025 .002 .0015 0 0 .00078 .0006 .0006 Rb20.............. .065 ________ 2.06 ........ ........ .0016 2.007 ....•... -------- Sc20s .....•......... 0 . 00031 . 0006 ________ ........ . 0023 . 0052 •. 0078 -------- _______ _ 

SrO ................. 11 .014 .03 ........ -------- .05 .017· .030 ---------------- V20s............... . 0025 . ooa8 . 0027 ........ ________ . 032 . 0.'32 . 050 _______________ _ 

Y20s............... . 0038 . 0032 . 0030 -------- -------- 0 -------- 0 -------- -------- ZnO ...•........... ····--·- -------- -------- -------- .0067 .......• ......•. .....•.. .•..•... .011 Zr02. -------------- . 027 . 026 . 038 -------- ________ . 0068 . 013 . 013 -------- _______ _ Mno______________ ________ .019 .031 ________________ .... c... .18 . 20 _______________ _ 

1 Fluorine was determined spectrochemically (granite only) at Massachusetts Institute of Technology by R. H. Seraphim and L. H. Ahrens who obtained a value of 0.055 percent. For this analysis, use was made 

of standards prepared from analyzed phosphate rock (U. S. Bureau of Standards, No. 120) and diabase. 

Two analysts determined fluorine chemically; one gave a value of 0.04 percent and the other 0.09 percent. 2 Rubidium analyses determined in three different ways. sA value of 0.00_55 percent Sc20s is given by A. Kvalheim. 

by a factor of three over such a large area. The _literature contains 

several statements about the enrichment, or impoverishment, of certain 

of the rarer elements in different areas; some of these statements are 

probably valid, but it seems that many merely reflect analytical 

variation. 

In order to reduce systematic analytical error to a minimum, use 

may be made of the granite and diabase provisional standards. With 

each bate~ of specimens the analyst could analyze the standard diabase and granite samples, and in this way all results could be calibrated in terms of these two standards. Naturally, the standards 

themselves should be reliable; with this in mind, several spectrochemists are undertaking determinations of the rarer elements that 

they are able to handle, and from their determinations it should be 

possible to assign recommended values for each constituent. 

In this paper (part 4) the available analytical data are presented, 

but recommended values for each constituent are not given because 

thus far only three complete sets of data are at hand. This paper is,· 

therefore, much in the nature of a preliminary report, and a detailed 

account will appear later as a separate publication in which recOin-
SPECTROCHEMICAL ANALYSIS-SOME RARER ELEMENTS 55 

· mended values will be given and where details of each spectrochemical 

method used will be provided. 

At the time of writing, analytical data had been received from Dr. 

R. L. Mitchell, Macaulay Institute of Soils Research, Aberdeen, 

K. J. Murata, United States Geological Survey, Washington, D. C., 

and A. Kvalheim (scandium only; thus far) of Statem Rastoff Laboratorium, Oslo. The cooperation of these persons in spending much 

time in making complete analyses of each specimen is gratefully 

acknowledged. A third set of data, by Lorraine G. Garfinkle and 

L. H. Ahrens, of the Cabot Spectrographic Laboratory, Department 

of Geology, Massachusetts Institute of Technology, also is available. 

In addition to the spectrochemical analyses, some chemical determinations of certain of the constituents have been made by chemists 

at the United States Geological Survey, and very grateful· acknowledgment is made for their cooperation. These analyses serve as 

useful checks for the spectrochemical determinations, and the chemical 

determinations are themselves checked by the spectrochemical 

determinations. · 

RESULTS AND DISCUSSION 

Table 23 gives the spectrochemical determinations by R. L. Mitchell 

(column 1), K. J. Murata (column 2), and L. G. Garfinkle and L. H. 

Ahrens (column 3), together with chemical determinations ·by field 

methods by Hubert W. Lakin, Hy Almond, Fred Ward, and Laura 

Reichen (column '4), and by laboratory methods by Harold Bloom 

(column 5). 

No attempt is made in this chapter to draw any conclusions about 

spectrochemical precision and accuracy from the data given in table 23. 

When developing a method, a spectrochemist frequently makes replicate determinations from which he is able to compute the relative 

deviation-as a measure of precision. Rarely, however, is he able 

to evaluate the accuracy, unless the investigation involves a major 

constituent which may be analyzed chemically with a high degree 

of accuracy. . 

In general, the comments made in part 3 about the precision and 

accuracy of spectrochemical analysis apply also to the minorconstituent elements. Under ideal conditions the relative deviation 

may be 3 percent and values of. 5 to 10 percent are not uncommon. 

However, as the concentration of an element approaches a level at 

which its most sensitive usable line begins to fade into background, 

precision deteriorates. In order to cover a relatively large number of 

elements in a relatively few operations~ general spectrochemical 
56 CONTRIBU'fiONS TO GEOCHEMISTRY, 19 50-51 

methods are often employed and these have been used in this investigation for the standard granite and diabase. The use of relatively 

general methods usually means a loss of precision, for although it is 

often possible to develop a precision method for a limited number of 

elements which have similar properties, this method is not really 

suited to the precise an.alysis of other elements. Usually a com- -

promise -between speed and,, precision is sought, because if many 

methods have to be employed to retain precision, the excessive time 

required would detract from the desirability of using a spectrochemical 

method. There are definite indications, however, that serious loss 

in precision need not be introduced by employing general methods 

and it is only a matter of time before really precise general methods 

will be available. One might compare the present state of affairs in 

the spectrochemical analysis of minerals and rocks with that of 

chemical analysis during the Berzelius era. 

One encouraging feature about the results given in table 23 is 

that in general each analyst has reported on the same elements and 

no obvious errors are apparent. This may -appear a silly statement, 

but "obvious" errors-mainly ones of reporting an element that is 

undoubtedly present at a concentration. far below its detection limitstill appear in the literature. Factors such as type of instrument 

and technique employed do influence the number of elements an 

analyst js capable of handling, but in general each analyst should 

be able to analyze approximately the same number of elements. In the 

main, the agreement between the analysts is satisf~ctory: agreement 

on some constituentR is very good, on some reasonable, and on a few, 

poor. Better agreement was not expected ·for several reasons. 

First, the reproducibility of the methods, expressed as relative deviation, varied from about 5 to 10 percent to 30 to 40 percent, and as 

the concentrations of some constituents border on concentrations 

~t the limit of detection, still larger deviations would be expected 

for them; secondly, each analyst has employed an entirely different 

procedure; thirdly, the presence of significant systematic error is 

probable; and fourthly, some sampling error may have been introduced for the granite standard, particularly for Mo and Zr. The 

granite standard is a little coarser than is desirable, and for those 

methods which employ very small quantities of specimen-a couple 

of milligrams, as in cathode-layer excitation-a sampling error 

appears significant. The. colorimetric determinations tally reasonably 

well with the spectrochemical determinations where the concentration 

of the element is sufficiently high to permit easy analysis for both 

spectrochemical and colorimetric methods; for example, cobalt in 

( 
SPECTROCHEMICAL ANALYSIS-SOME RARER ELEMENTS 57 

diabase. In granite, where the concentration of cobalt is much 

lower, disagreement is more marked. 

A fuller discussion on the r.esults wili be published later. 

REFEHENCES CITED 

Ahrens, L. H., 1950, What to expect from a standard spectroc?omical analysis 

of common silicate rock typos: Am. Jour. Sci., vol. 248, pp. 142-145. 

Goldschmidt, V. M., and Peters, Cl., 1931, Zur Geochemic des Galliums: Nachr. 

Gesell. Wiss., Gottingen, Math.-Phys. Kl., 1, 165. 

Van Tongeren, W., 1938, Contributions to the knowledge of the chemical com-

. position of the earth's crust in the East Indian Archipelago, I, II, D. B. 

Centens, Amsterdam. 

A COOPERATIVE INVESTIGATION OF 

PRECISION AND ACCURACY IN 

CHEMICAL, SPECTROCHEMICAL, AND MODAL ANALYSIS OF 

SILICATE ROCKS 

PART 5. MODAL ANALYSES OF THE GRANITE AND 

DIABASE TEST ROCKS 

BY FELIX 0HA YES 5 

MINERALS OF THE TEST ROCKS 

As both test specimens are typical examples of extremely common 

rocks, an extended petrographic description is unnecessary. The 

diabase consists of augite and plagioclase (labradorite) with smaller 

amounts of quartz, potash feld~par, biotite, and opaque minerals. 

Although quartz is nowhere abundant it was noted in every thin 

section; no olivine was detected. Quartz is generally associated 

with potash feldspar in micropegmatitic intergrowth. Most, if not 

all, of the opaque material is oxide; sulfides were not found in a search 

of several thin sections under reflected light. 

The granite contains quartz, microcline, plagioclase (oligoclase), 

small amounts of biotite and muscovite, almost 1 percent of opaque 

and about l;lalf of 1 percent of nonopaque accessories. As in the 

diabase, sulfides have not been detected. Nonopaque accessories 

include apatite, carbonate, fluorite, and tourmaline as well as occasional grains of sphene. The first three of these occur in every 

thin section, but apatite is easily the most abundant. Carbonate and 

muscovite are largely restricted to plagioclase, which is-usually slightlyclouded from alteration. As in almost all New England granites, 

biotite is sometimes replaced by chlorite; the replacement is rarely 

complete, and partially replaced flakes may occur in the same microscopic fiel9 with others that are entirely unaffected. A more complete 

description of the gra.nite bas been published elsewhere (Chayes, 

1950). 

-~qcophysical Laboratory, Carn~gic Institution o JWae_l_Ungton (D. 0.). 

59 

947795-51-5 
60 CONTRIBUTIONS TO ~EOCHEMISTRY, 19 50-51 

MODAL ANALYSES 

Preparation of the test materials is described in part 1 of this 

report. It will be remembered that 8 small, evenly spaced blocks 

were broken out of the granite strip before the bulk of the sample 

was crushed. Thin sections were cut from both ends of each block 

so that there are in all 16 parallel thin sections spaced at alternate 

4- and 6-inch intervals along the length of the strip. Thin sections 

were also prepared from 12 chips of the diabase, but the relation of 

these chips to each other in the original sample is not known. All 

slides were etched with HF and stained with sodium cobaltinitrite 

before covering. On each covered slide a continuous area of 500 

1run.2 was outlined, and in this area a_point-counter analysis was run 

with a horizontal intercept distance of 0.3 mm. and an interval of ( 

1 mm. between traverses. 

Both rocks are fine-grained and well suited for mod~J analysis. 

In<Jividual analyses are recorded in tables 24 and 25. Mean values 

and standard deviations are shown in table 26. No specific-gravity 

corrections have been used for the granite. For the diabase the 

following factors were applied to the volume percentages: Quartz, 

2.66; potash feldspar, 2.56; plagioclase, 2.71; pyroxene, 3.30; biotite, 

3.12; opaque accessories, 5.2; nonopaque accessories, 3.2. Application of these factors, of course, shifts mean values slightly for all 

constituents and considerably for plagioclase and pyroxene. Unless 

the factor is very large and applies to a major constituent, its effect 

on dispersion is negligible. 

TABLE 24.-Diabase modes converted to percent by_ weight 

Slide No. 

1 ____ ----------.-----.--------- 2.-----------------------------

3 •• -----·---------------------- 4.-------------.--------------- 5.----------------------------- 6.--------------------.-------- 7------------------------------ 8.-----------------------------

9 ______ ------------------------ 10 ••• --------------------------- 11.------------------------_._ --- 12.-----------------------------

Average _________________ _ 

Quartz 

0.8 

1. 7 

1.6 

2.0 

1.8 

2. 7 

2. 7 

1.7 

1.3 

1.5 

1.9 

2.0 ---1.8 

Potash Plagio- feldspar clase 

---

2.3 46.8 

2. 7 45. i 

2.5 ·45.6 

2.6 46.4 

3. 7 43.6 

3.3 40.9 

3.4 44.6 

4.2 43.6 

1.8 48.3 

2.5 46.8 

3.6 44.2 

3.0 43.1 

------ 3.0 45.0 

Accessories 

Pyroxene Biotite 

Opaque Nonopaque 

------------ 45.9 1.4 2.6 0.1 

45.0 1.4 3.1 .3 

·45.9 ;9 3.5 .0 

44.4 2.0 2.6 .1 

44.9 1.8 4.0 .2 

48.6 1.1 3.1 .2 44.0 2.0 3.1 .2 

43.9 2.0 4.5 .1 

43.0 2. 7 2.8 .1 

-u.o 2.3 3.0 .o 

44.2 1.9 3.8 .4 

46.0 2.1 3.6 .1 ------------ 45.0 1.8 3.3 .2 
) 

.I 

MODAL ANALYSis-GRANITE AND DIABASE 

TABLE 25.-Granite modes, percent by volume 

Slide No. 

13 .............................. . 

14.-----------------------------

15.-----------------------------

16.-----------------------------

17------------------------------

18.-----------------------------

19.-----------------------------

20.---------.------••••.• -... ---

21 .... -.-------·---·------------ 22.-------·--------------------- 23.-----------------------------

24.-----------------------------

25.-----------------------------

26.----------------------.------

27------------------------------

28.-----------------------------

Average. _________ --------

Quartz 

27.8 

25.5 

29.6 

29.2 

27.5 

28.8 

28.4 

26.2 

27.8 

25.7 

27.3 

29:1 

25.7 

27.9 

25.6 

28.2 

---27.5 

Potash 

feldspar 

---

35.6 

35.4 

34.4 

33.6 

36.3 

35.1 

33.6 

36.2 

34.6 

37.0 

31\.1 

36.3 

36.8 

32.0 

37.1 

36.6 

---35.4 

Plagioclase Muscovite Biotite 

---------

30.2 1.7 2. 7 33.0 1.7 3.1 

30.6 .8 3. 7 32.2 1.5 2.3 

31.8 1.2 2. 2 29.9 .9 3.8 

30.9 1.9 3.5 

31.8 1.3 3. 2 31.7 1.5 3.0 

30.6 1.6 4. 2 31.9 .7 3. 2 29.1 1.4 2. 7 32.7 .9 3.4 

34.2 1.2 3.8 

32.4 . 7 3.3 

29.3 1.2 2.8 --------- 31.4 1.3 3. 2 

TABLE 26.-Average modes for the test rocks 

61 

Accessories 

Opaque Nonopaque 

------

1.1 0.9 .6 .7 .5 .3 

.9 .3 .6 .3 . 7 .8 

1.4 .2 

1.0 .3 

1.1 .4 

.8 .2 

.4 .5 

1.2 .2 

.4 .1 . 7 .2 

.5 .4 

1.1 .6 ------

.8 .4 

Diabase (12 sections) Granite (16 sections) 

Mineral 

Mean Standard 

dev. _Mean Standard dev. 

Quartz •• ----------------------------------------------- 1. 8 0. 5 27.5 1. 4 Potash feldspar ___ ------------------------------------- 3. 0 . 7 35.4 1. 4 Plagioclase _______ -------------------------------------- 45. 0 2. 0 31.4 1. 4 

~r~~~:~~--~============================================= 4t g 1

: g --------3~2- ----------:& 

Muscovite .... ----------------------------------------- ------- _____ ----------- _ 1. 3 . 4 

Opaque accessories. ___ --------------------------------- 3. 3 . 6 . 8 ------------ Nonopaque accessories.------------·------------------- . 2 ------------ . 4 ---------·--

Average length of count.·-----------------·------ 1345 1502 

The results provide a useful check on the homogeneity of the samples prior to crushing. The analytical, or precision, error of point 

counting has been shown to be essentially binomial (Chayes, 1949), 

and it may be shown that the observed dispersions for major and 

minor minerals in the granite are not significantly larger than analytical error alone. That each of them is in fact a little larger than 

the corresponding theoretical estimate suggests some,source of variation other than analytical error. But this source contributes so 

modestly, if at all, to the dispersion of each mineral that its presence 

could not be established without a much larger group of analyses. 

Scatter comparable to that observed might easily have resulted if a 
62 CONTRIBUTIONS TO GEOCHEMISTRY, 19.5 0-51 

single thin section had been analyzed 16 times instead of each of the 

16 sections being analyzed once.6 For the diabase the situation is not 

quite the same .. Pyroxene variation is suitably small, but plagioclase 

~ispersion is a little large-as is the variation for both quartz and 

potash feldspar. This may be inherent in the sample but is more 

probably attributable to an unfortunate coincidence of inferior 

sections and inadequate staining. The slides were ground too 

thin and contained occasional holes. If these were sometimes not 

detected, they would be recorded as plagioclase or. quartz. Similarly, incompletely stained potash feldspar might be tabulated sometimes as quartz and sometimes as plagioclaf3e. Errors of either type 

would tend to enlarge the observed sca~ter for all three minerals, 

and this is probably what has happened. For reasons which will ( 

become apparent shortly, there seemed little need to repeat the analyses on a new set of slides. 

COMPARISON OF MODES AND CHEMICAL ANALYSES 

~Chemical and spectrographic results are for the most part estimates 

of the sa~e quant.ities and wherever this is true they may be directly 

compared with each other; in the absence of systematic bias the pro-

~edure w~ich yields the smaller dispersion is preferable for a particular constituent. No such direct comparison of modes with either 

chemical or spectrographic analyses is possible. yet some reasonable 

comparison of modes with analyses, particularly chemical, would be 

very useful to the petrographer, who is often compelled to rest content with thin sectio.ns whe:o he would like to have analyses and 

almost as frequently tries to obtain from analyses information that 

could just as well be gotten from. sec~ions. 

As neither rock is weathered and none of the major minerals is 

markedly abnormative, the CIPW norm provides a ready means of 

q~mparmg. modes with chemical analyses. Norms have been com- '-

puted by mineralogists of the Trace ~lements Section, Geochemistry 

and Petrology ·Branch, United States Geological Survey, and are 

shown with the analyses in tables· 1 and 2. The average norms are 

s,hown in ~able 27, and agree quite well with the average modes. The 

o Since this was writt~>n a detailed test of the point counter has been undertaken by members of the geology 

department of the Massachusetts Institute of Technology. Five operators analyzed each of five of the slides 

whose ail.aly;es are shown in tabies 24 and 25, each operator running the group i~ a different order. Agree· 

ment between mean values is admirable throughout and analytical error is not significantly larger than the 

theoretical precision error of the method except for biotite and muscovite. In this particular rock identification and tabulation conventions for the micas have proved difficult to standardize. Even for the micas, 

however, the excess of observed over expected analytical euor, though clearly significant, is not large by 

standards usually applied to this type of work. The study was completed too late for inclusion here, and 

·its results will therefore be published separately. 
MODAL ANALYSIS-GRANITE AND DIABASE 63 

coincidence is not exact but the differences are readily explained.7 . 

The largest discrepancy is between rnodal and normative pyroxene. 

Normative pyroxene contains neither alumina nor titania; all alumina, 

including that present in pyroxene, is calculated as feldspar, yielding an excess of normative over modal plagioclase. Titania is calculated as ilmenite, and quite appropriately there is a considerable 

excess of normative over modal opaque constituents. In the diabase 

the principal divergences between norm and mode may thus be 

reasonably attributed to simplifications in the calculation of pyroxene, 

v simplifications inevitable if the actual composition of the pyroxene 

is unknown. 

) 

TARLE 27.-Comparison of norms and modes of test rocks 

Means 

Mineral 

Norm 

Diabase (W-1) 

Quartz-------------------------------------------------

Orthoclase ___ ------------------------------------------ Plagioclase ______ ---_-_-_-_-_-----_-----------_--------- Pyroxene ______________________________________________ _ 

Opaque accessories _____________________________ -------_ 

Granite G-1 

Quartz _____ . ___________________________________________ _ 

Orthoclase ______ -------- __ ---- __ -- __ ---- ___ ---_-------- Plagioclase _____________________ ----_-_----------------- Opaque accessories_-- ___________________________ -------

4.1 

4. 0 47.6 

38.8 

4.6 

28.6 

32 5 33.7 

1.8 

Mode 

1.8 

13.0 

45.0 

45.0 

3.3 

27.5 

I 35.4 

31.4 

.8 

Standard deviations 

Norm 

1.7 

1.2 

2.3 

2. 9 

1.4 

Mode 

0.5 

I, 7 

2.0 

1.5 

.6 

2. (\ 1. 4 2. 8 I 1. 4 

2. 0 1. 4 

.3 ------------

1 l'otnsh feldspar-feldspar stained yellow on immersion in sodium cobaltinitrite solution after HF etch. 

In the granite the principal discrepancies bet,yeen norm and mode 

are in the feldspars and probably may be laid to the convention 

by which N a20 present in potash feldspar is calculated as albite, 

increasing normative plagioclase at the expense of normative orthoclase. This is strongly indicated by the fact that the excess of 

normative over modal plagioclase (2.3 percent) is so nearly matched 

by the excess of potash feldspar over normative orthoclase (2.9 percent). Again, it is hard to see how such oversimplification can be 

avoided unless the composition of the potash feldspar is known. 

It will be noted that each ilorm is richer in quartz than its corresponding n1ode. In the rnilling of such large quantities of rock there 

7 'I' he discussion of this section is intended to apply only to the subject matter of this paper. '!'he problem 

is a very old one, however, and was admirably described in the original presentation of the CIP'W system 

(A Quantitative Classification of Igneous Rocks, W. Cross, J. Iddings, L. Pirsson, and H. S. Washington, 

1903, University of Chicago Press, pp, 112-113, and particularly pp. 146-153), in which all the explanations 

of discrepancies between mode and norm used here were first advanced. 
64 ·CONTRIBUTIONS TO GEOCHEMISTRY, 19 50-51 

is abundant opportunity for contamination by the grinding medium; 

flint pebbles were used in grinding the granite but the grinding medium 

used in preparation of the diabase is not known. 'Some of the excess 

of normative quartz in diabase may be due to the CIPW convention 

regarding titania, since in the calculation it not only takes up no silica 

itself but also ties up an equivalent amount of ferrous oxide which 

would otherwise be combined with silica. 

Even in such simple rocks as these, however, exact coincidence of 

norm and mode is hardly to be anticipated. The important matter 

is that tb.e agreement is quite fair as it stands, and this can mean only -....· 

that by and large each major mineral is well represented by its normative analogue. With this in mind we may pass to a consi~eration 

of the columns headed "standard deviations" in table 24. Without ( 

exception the normative standard deviations are larger than those 

for the mode: Of course, widely discrepant chemical analyses are 

partly responsible for this curious situation, but the fault is not entirely theirs by any means; oDly by throwing away at least 25 percent of the analyses of each rock can normative dispersion be brought 

down to the same level as modal. Nor may the excessive variation 

of norms be attributed entirely, or even largely; to the conventions of 

c-alculation. The conventional or and px molecules vary less than 

would more complex normative parameters which attempted to represent the minerals more closely. 

There is no escaping the fact that normative variation would be 

reduced far below the level of modal variation, if the interlaboratory 

reproducibility of chemical analysis justified results carried to hundreths of percents, as the standard statement encourages one to 

suppose. Actually the comparison of standard deviations in table 

27 probably would face the other way even if agreement among the 

test analyses wer~ ordinarily to a few tenths instead of to several 

tenths of a percent for certain key elements: alkalis and alumina 

in granite and alkaline earths, iron, and alumina in diabase. 

For immediate purposes the modal results are important not because they look well alongside the norms, but because they provide 

direct assurance of the homogeneity of the test rocks. Judging by 

agreement between duplicates submitted by many analysts, the same 

assurance could have been obtained if ·any one of the analysts had 

been called on for replicate analyses. This procedure, however 1 

would have been far more expensive, even supposing that an analyst 

could have been persuaded to run 12 or 16 entirely independent analyses of the same material. 

From the viewpoint of the· analytical chemist the results of the 

testing program afford no more than a description of the current 

state of affairs in rock analysis. They do not contain information 
MODAL ANALYSIS-GRANITE AND DIABASE 65 

about biases in any of the determinations; except in a very crude 

fashion they do not gage the consistency of any analyst's work; and, 

unless one is prepared to regard agreement as a measure of accuracy, 

they afford no means of judging analyses or analytical procedures. 

The situation revealed by the test is probably more serious than many 

analysts realized, and it will certainly come as a shock to most geologists. But the only way chemists can take full advantage of the 

information is by obtaining more. 

Although the comparison in table 27 is not very informative to 

the chemist, it is of immense value to petrographers. It should 

encourage us to place more reliance on adequately planned and carefully executed micrometric analysis for the accumulation of quantita0 tive information about the mineralogical composition and variation 

of many common rocks. It should warn us against placing much 

assurance in comparisons of rocks or inferences about their variations 

based on collections of analyses culled from the literature. These 

are both matters of sufficient importance to warrant further discussion. 

.. 

BEARING OF THE RESULTS ON PETROGRAPHIC PRACTICE 

While theories about the origin and formation of rocks have multiplied and anastomosed at an alarming rate, the techniques of descriptive petrography have changed very little in the past half century. 

The continual interaction between hypothesis and observation which 

ought to characterize every healthy descriptive science is conspicuously lacking in petrography. This paralysis of the descriptive 

faculty, which finds us so often opposing theories to each other instead 

of testing them against observations, is no doubt the product of many 

and complex causes, some of which may be forever beyond our control. A large part of the difliqulty, however, stems from the fact 

that resolution of many petrographic controversies requires abundant 

quantitative data, and we simply do not have the numbers. This 

unfortunate situation is a direct consequence of the hallowed tradition that the petrographer is willing to spend unlimited amounts of 

time in the examination, description, and interpretation of microtextures and structures which have been well-known since the days 

of Roscnbusch and Zirkel, but ordinarily feels no compunctions 

whatever about dumping on the shoulders of the chemist all responsibility for quantitative data about rock composition. Even the work 

of geologists who do their own analyses often reflects this sharp dichotomy between qualitative petrography and quantitive chemical 

analysis. By any standards, and certainly by standards the world 

usually applies to petrographic research, chemical analyses are expensive. Few petrographic projects can justify more than a handful 

of them, and this is simply not enough. 
66 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

It is certainly fair to infer from table 27 that for the purpose of 

estimating the mineralogical composition of either test rock a single 

thin-section analysis contains about as much and about as reliable 

information as a single chemical analysis. Yet even for a comparative 

novice the thin-section analysis-by point counter-should not require 

more than a half hour if only 1,600 points are tallied, and for the 

experienced worker it is a matter of 15 minutes. For such exceedingly common rocks as the test samples and for many others as 

well, conscientious application of techniques now available would 

soon produce enough reliable quantitative information so that we 

could proceed to the long overdue task of separating the theoretical 

wheat from the chaff. Many rocks, of course, cannot be handled 

aaequately by present techniques. Glasses and shales probably will 

always resist, but the point counter could easily be modified for use 

on large polished slabs to permit analysis of coarse-grained rocks. 

Where even this will not suffice, recourse to fragment analysis may 

be advisable. Special techniques will have to be developed for use 

on highly oriented rocks, of course, but in general there seems to be 

no reason why useful quantitative measurements should not be ob-

_tainable from any rock containing mineral grains of moderate size. 

This is not to suggest that fewer rock analyses be made, for in fact 

we ought to have many more and far better chemical analyses. Even 

·under optimum circumstances, boweve'r, the petrographer doing a de-

_tailed field study will rarely be able to afford more than a few analyses 

of any particular rock, and financial considerations usually oblige him 

to stop far short of this goal. Economy and speed are the real advantages of modal analysis, and together they offer the possibility of 

an enormous extension and amplification of our knowledge of rock 

variation. Provision of numerous reliable quantitative modes of each 

of the important petrographic units involved in his work ought to be 

regarded as a major responsibility by anyone working in eucrystalline 

rocks. 

In another and equally important respect the test raises a problem 

for which there seems tq be no solution. Except that all the chemical 

analyses listed in tables 1 and 2 are of the san1e two rock samples, 

their accumulation and tabulation parallels a very common petrographic practice. Toward the close of many petrographic reports 

there appears a section devoted to a comparison of the rocks in question with similar rocks ·exposed elsewhere and described, usually, by 

other workers. The qualitative aspects of such comparisons are generally admirable, and the stability of our descriptive techniques often 

!llakes it possible for us to take full advantage of work dating almost 

from the earliest development of the subject. The only quantitative 

comparison, however, is usually not of petrographic data at all; it is 

( 
MODAL ANALYSIS-GRANITE AND DIABASE 67 

in nearly every case a tabulation and discussion of chemical analyses 

culled from the literature. 

Viewed in this light the scatter of the chemical results, whether as 

direct oxide percentages or as norms, must profoundly disturb every 

petrologist. The dispersion of oxide percentages is well shown in the 

histograms of figure I, part 2. Normative variation is so extreme 

that in the absence of direct evidence to that effect there would be 

little reason to suppose all these analyses were of the same two rocks. 

Most of the diabase norms carry a few percent of quartz, but one 

shows 8.8 percent of that mineral and in another olivine is present to 

the extent of 5 percent. Normative plagioclase ranges from 43 to 

56 percent in amount and from An46 to An73 in composition. 

In the granite normative quartz varies all the way from 24 to 40 

percent, a range wide enough to include almost all the granites in the 

world, yet many granites can easily be distinguished from each other 

on the basis of modal quartz alone. Most of the granite norms contain a little corundum, as they should since the rock contains a little 

muscovite. In 5 of the 33 analyses, however, the norms show more 

than a percent of corundum; in one of these there is 3 percent and 

in another 5 percent; in 5 other norms there is an actual deficiency 

of alumina so· that some of the lime appears as diopside. In most 

granites-including the Westerly granite-the ratio of modal orthoclase to plagioclase is remarkably stable, and this ratio, or its normative analogue, is widely applied in rock classification. In the 

norms of the test analyses the ratio or:pl varies from 0.74 to 1.32. 

Normative plagioclase ranges in composition from An5 to An24• 

Given the information that only two homogeneous samples are involved, we can make some attempt to separate the sheep from the 

goats and almost any reasonable ranking scheme brings the same analyses into question. But what could we do abo.ut these variations 

if we were told that the sample for each analysis was geographically 

distinct and the collection was of interest to us as a means of estimating 

the range of composition commonly exhibited by rocks of these two 

types? 

The answer is dishearteningly clear; we could do absolutely nothing. 

A collection of individual analyses of each of a large number of rocks 

of the sa1ne type is bound to overestimate grossly the variability of 

the type, and collections of analyses of more than one rock type will 

necessarily underestimate the differences between types. Under these 

circumstances "transitions," "gradations," "gradual passages," etc., 

are demonstrated easily from almost any extended table, and we quickly 

come to feel.that all divisions between rock types are arbitrary. It is 

easy to say that compilations of this sort exaggerate dispersion, but 

it is impossible to estimate the size of the exaggeration. Variation 
68 CONTRIBUTIONS TO GEOCHEMISTRY, 1950-51 

among the test analyses is certainly very much larger than the internal 

variation of either rock and probably larger than differences between 

many related but reasonably distinct rock species. Providing rock 

types are defined independently of chemical composition, mean values 

computed from tables of analyses are probably quite good, though 

there is no way to find out just how good. But any approach which 

attempts to establish a difference between two or more rock types by 

means of comparisons which place much weight on individual analyses 

by different chemists is immediately suspect. 

LITERATURE CITED 

Chayes, F., 1949, A simple point counter for thin-section analysis: Am. Mineralogist, vol. 34, pp. 1-11. ( 

Chayes, J!.:., 1950, Composition of the granites of Westerly and Bradford, Rhode 

Island: Am. Jour. Sci., vol. 248, pp. 378-407. 

{. 
A COOPERATIVE INVESTIGATION OF 

PRECISION AND ACCURACY IN 

CHEMICAL, SPECTROCHEMICAL, AND MODAL ANALYSIS OF 

SILICATE ROCKS 

PART 6. SUMMARY OF RESULTS 

BY H. w. FAIRBAIRN 7 

It is the hope of the authors that readers of this bulletin will be both 

disturbed and encouraged by its contents. It is notorious that the 

twin themes of precision and accuracy have not been accorded their 

proper rank in many branches of quantitative geological work, partly 

through lack of data but in part also through disregard· of the signifi~ 

cance of these problems. In the fields of petrology and geochemistry 

at least, the present report is an emphatic reminder that evaluation of 

quantitative methods cannot be neglected. 

To petrologists the discrepancies in many of the chemical analyses 

will be the most disturbing feature of this report, even if certain 

determinations are eliminated as gr.ossly in error. The likelihood of 

occurrence of many of these discrepancies is of course commonplace to 

chemists and causes no surprise if the conditions of analysis are 

appreciated. Since, however, few petrologists are practicing chemists, 

the strong probability that analytical error is responsible for a large 

part of the total variation shown by a group of analyses is usually 

ignored. To make matters worse, the chemical data are in many cases 

obtained in such a way that it is impossible to separate the total 

variation into portions attributable to analytical error and true sampling 

variation. In the long run this lack of planning usually leads to gross 

overestimates of sampling variation. Furthermore, the common 

assumption that the same chemical precision can be realized for any 

constituent regardless of its relative concentration is thoroughly 

fallacious, so that interpretations of rock and mineral analyses which 

do not take this into account are of little value. Chemists know 

better, but as they are not usually interested in what petrologists do 

with their analyses, liaison is seldom established. 

On the analytical side, the need for further interlaboratory collaboration by chemists is clearly indicated. With an adequate stock of 

'Massachusetts Institute of Technology. 

69 
'/0 ·CONTRIBUTIONS TO GEOCHEMISTRY, 19 50-51 

homogeneous test materia] this could now be clone. As outlined in. 

part 3 an additional aim of the present investigation is to obtain, 

by means of a synthetic rock standard, better agreement on the two 

original standards. If this is possible, chemists will in the future have 

a more reliable base for checking their work. The results of the 

present investigation may serve as a guide in evaluating previously 

published work; they indicate that analyses by the sam.e chemist, or 

by different chemists from the same laboratory-assun1ing fixed 

operating conditions-can probably be used for comparative work in 

petrology; on the other hand, comparisons of analyses made in different 

laboratories had best be used with extreme caution. As Chayes 

points out (pt. 5) ranges reported in the granite and diabase standards 

are greater than compositional limits for related but distinctly different 

rock types. Discrepancies in determination of alkali metals are 

particularly critical in this regard, since to a large extent feldspar 

composition controls rock classification. It would appear that more 

widespread use· of flame photometric and spectrochemical methods 

would improve the quality of alkali metal determinations. (See pt. 3.) 

Average analyses of rock types might profit by reappraisal of certain 

details. As far as silica (Si02) is concerned the variation from one 

rock to another related one is large enough that chemical discrepancies 

are negligible. This is not true for many of the other constituents, 

particularly if their concentration is low. The retention of two 

figures beyond the decimal point, except for very minor constituents, 

becomes ridiculous for most petrologic purposes. The chemist 1s 

justified in presenting his results in this way since addition to lOU 

percent is a test of his work. Petrologists, however, should ruthlessly 

discard unnecessary detail beyond the decimal point. · 

Compared with chemical procedures, spectrochmnical methods are 

in their infancy. Nevertheless, present evidence shows, for spectrochemical determination of the major elements, precision comparable ~ 

·with that of chemical methods (pt. 3, table 18) and they have as 

added advantages the saving of time and money, the use of a small 

sample, a permanent record of the spectrum. Although few spectrographic laboratories are at present in a position to do work of this 

kind, there is every reason to believe that their numbers will grow. 

The chemical laboratory will never be displaced, since a chemist will 

always be required t.o determine water (H20) and iron oxide (FeO) and, 

in ordinary silicate rocks, silica (Si02), because of its high concentration. At present, also, phosphorus pentoxide (P20 5) remains within 

. the province of the chemist. It would appear then that a happy 

marriage of chemical and spectrochemical procedures would do much 

·for the petrologist and geochemist. Both techniques require skilled 
RELIABILITY. OF. THE ROCK ANALYSES 71 

analysts and adequate interlaboratory standardization. From now 

on it is not too much to expect that these requirements will be Inet. 

Passing down the scale to concentrations of elements beyond the 

scope of chemical procedures, it is obvious that for the spectrachemist much interlaboratory calibration remains to be done. Methods then1selves are inadequately standardized. As in any form of 

analysis, procedures giving high precision and accuracy are timeconsuming. However, as is pointed out in part 4, lower orders of. 

precision and accuracy are often adequate and can be obtained in 

much shorter time. Published abundance values for minor elements 

in the earth's crust need critical review, since they are based on work 

in a few laboratories only, with no interlaboratory standardization 

'J whatever. As already noted in part 3 this standardization, using the 

granite and diabase provisional standards, should not be difficult to 

achieve. 

Precision in modal analysis of thin sections has now been carried 

to a n1uch higher level than heretofore and the method emerges as a 

more potent weapon for petrographers than was formerly thought 

possible. Here, as in chemical and spectrochemical work, interlaboratory checking is advisable, and in fact it is now in progress. 

Modal analysis is a pw·ely petrographic tool, developed by petrographers for petrographers, and deserves nwre prominence in their 

work than it has· received. The method involves neither costly 

apparatus nor great expenditure of time and gives results obtainable 

in no other practicable way. 

It is the hope of the authors that critical evaluation of analytical 

data will in future be the rule rather than the exception. Such 

evaluation should have been commonplace a generation ago. It is 

ow· hope that the work described in these pages will initiate similar, 

more extensive, and better designed studies of the accuracy and 

) precision of analytical methods used by petrologists, geochemists, 

and mineralogists. 

o·