Chemistry:Clarke number

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Short description: Relative abundance of elements in Earth's crust

Clarke number or clarke is the relative abundance of a chemical element, typically in Earth's crust. The technical definition of "Earth's crust" varies among authors, and the actual numbers also vary significantly.

History

In the 1930s, USSR geochemist Alexander Fersman defined the relative abundance of chemical elements in geological objects, denoted in percents, as Russian: кларки, lit. 'the clarkes'.[F 1]:141 This was in honor to the American geochemist Frank Wigglesworth Clarke, who pioneered in estimating the chemical composition of Earth's crust, based on Clarke and colleague's extensive chemical analysis of numerous rock samples, throughout 1889 to 1924([C 1][C 2][C 3][C 4][C 5][C 6][C 7][C 8][C 9]).

Examples based on Fersman's definition:

  • Russian: весовой кларк, lit. 'weight clarke': When the whole mass of a planet X is [math]\displaystyle{ Mx }[/math] [kg], and the mass of oxygen there is [math]\displaystyle{ Mo }[/math] [kg], then the weight clarke of oxygen in planet X is [math]\displaystyle{ Km=\frac{Mo}{Mx} }[/math] (dimensionless)
  • Russian: кларк числа атомов, lit. 'clarke of atom count': When the whole count of atoms in a rock Y is [math]\displaystyle{ Ay }[/math] [mol], and the atom count of silicon there is [math]\displaystyle{ As }[/math] [mol], then silicon's clarke of atom count in rock Y is [math]\displaystyle{ Ka=\frac{As}{Ay} }[/math] (dimensionless)
  • Fersman's "clarke of Earth's crust" is the Earth's surface including 16 km-thick lithosphere, hydrosphere and atmosphere.[F 1]:141

In Russian

Russian: кларки is synonymous to "the relative abundance of elements" in any object, either in weight ratio or in atomic (number of atoms) ratio, regardless of how "Earth's crust" is defined, and denotation is not restricted to percents.[x 1]

In English

In the English speaking world, the term "clarke" was not even used in Wells(1937)[U 1]:4 which introduced Fersman's proposal, nor in later USGS articles such as Fleischer(1953).[U 2] They used the term "relative abundance of the elements". Brian Mason also mentioned the term "clarke" in Mason(1952)[M 1]:42(mistakenly attributing it to Vladimir Vernadsky, later corrected to Fersman in Mason(1958)[M 2]:47), but the definition slightly differed from Fersman's, limiting it only to the average percentage in Earth's crust, but allowed to exclude hydrosphere and atmosphere. Besides for explaining the term, Mason himself did not use the term "clarke".[M 2]

A variant term "clarke value" is occasionally used (examples:[x 2][x 3]:778). However, "clarke value" can have a different meaning, the clarke of concentration (example:[x 4]:412).

Terms "clarke number" and "Clarke number" are found in articles written by Japanese authors (example:[x 5]:55).

Usage in Japan

In Japan, "clarke" is translated as kurākusū (クラーク数, clarke number). The word sū (数, number) is always added, which happens to make the term appear similar in form with scientific constants such as abogadorosū (アボガドロ数, the Avogadro constant). The term may have a narrower sense than Fersman's. Several of the following constraints may apply:

  • Only of Earth's crust[I 1]
  • Lithosphere approximated as a 10 mile-deep layer from sea level[I 1]
  • Must include all of three layers: lithosphere (93.06%), hydrosphere (0.91%) and atmosphere (0.03%)[I 1]
  • Only mass ratio[I 1])
  • Denote in percents[I 1]) (not in ppm or ppb)
  • (What the quoter believes to be) data from Clarke and Washington(1924)

Another peculiarity in Japan is the existence of a popular version of data, which was tabulated in reference books such as the annual "Chronological Scientific Tables" (RCST1939(1938)[R 1]:E46), the "Dictionary of Physics and Chemistry" (IDPC(1939)[I 1]:app.VI) and other prominent books on geochemistry and chemistry.[H 1]:(62) This version Kimura(1938)[K 1] was devised by chemist Kenjiro Kimura (ja).[K 2]:5 It was often quoted as The "Clarke numbers" (unsourced examples:[x 6]:443,[H 2]:429 t2). The numbers differed from any versions by Clarke / Clarke&Washington (1889–1924[C 1][C 2][C 3][C 4][C 5][C 6][C 7][C 8][C 9]), or anything listed in foreign (non-Japanese) articles such as the USGS compilation [U 2]:4 t2, thus unknown outside of Japan. Yet the numbers were sometimes quoted in English articles without citation (example:[x 5]:55).

As geological definition of "Earth's crust" evolved, the "10 mile-deep" approximation were deemed out-of-date, and some people considered the term "clarke number" obsolete too.[H 2] Yet other people may have meant broader senses, not limiting to Earth's crust, leading to confusion.[I 2]:355 RCST1961(1961) switched their "clarke number" table from Kimura(1938) to Mason(1958) based[R 2][R 3], and the label "clarke number" on table was removed in RCST1963(1962)[R 4]. IDPC(1971)[I 3] removed the "clarke number" table which was a Kimura(1938)'s variant[I 4][D 1]. IDPC(1981) said the term is mostly abandoned,[I 2] and the dictionary entry for "clarke number" itself was removed from IDPC(1998).[H 2]:431 So "clarke numbers" became associated almost solely with Kimura(1938)'s data, but Kimura's name forgotten. Incidentally, in major reference books, there was no data table titled "clarke numbers" which showed Clarke's original tables.

Despite being removed from major reference books, data from Kimura(1938) and phrases such as "the Clarke number of iron is 4.70", unsourced, continue to circulate, even in the 2010s (example:[x 7]:799).

Example data

This section lists only historical data. For recent data, see Abundance of elements in Earth's crust.

Technical definition of "clarke", "Earth's crust" and "lithosphere" differ among authors, and the actual numbers vary accordingly, sometimes by several times. Even the same author presents multiple versions, with various estimation parameters or knowledge refinements. Yet they are often quoted without source, rendering the data unverifiable. Clarke & Washington[C 7]:114[C 8]:34 t17 presented estimations of the average composition of outer part of Earth with four variants:

  1. 10-mile crust, hydrosphere and atmosphere.
  2. 20-mile crust, hydrosphere and atmosphere.
  3. 10-mile crust, only igneous rocks and sedimentary rocks. (i.e. exclude hydrosphere and atmosphere)
  4. 10-mile crust, only igneous rocks. (i.e. exclude hydrosphere and atmosphere)

"The earth's crust" in Clarke and Washington works can mean two different things: (a) The whole outer part of Earth, ie. lithosphere, hydrosphere and atmosphere; (b) Only the lithosphere, which in their works just meant "the rocky crust of the earth". "Crust" here means (b).

  • Following tables do not cover all elements. Some elements not on the table may have larger abundance. Some minor elements are listed here to aid identifying the origin of unsourced documents.
  • Some entries contain data for the disputed element 43 masurium.
  • Precision (number of digits) may be adjusted to improve legibility.

Of the mass of 10 mile-thick lithosphere plus hydrosphere and atmosphere

Tables of historical data for some elements of their relative abundance in Earth's crust.

cited as Clarke (1889) Clarke (1891) Clarke (1908) Clarke (1911) Clarke (1916) Clarke (1920) Clarke & Washington (1922) Clarke & Washington (1924) Clarke (1924) Berg (1929) Berg (1932) Fersman (1923) Fersman (1934) RCST1937 (1936) RCST1939 (1938) Kimura (1939)
cited in [C 1]:138 c.3 [C 2]:39 c.3 [C 3]:32 c.3 [C 4]:34-35 c.3 [C 5]:34 c.3 [C 6]:35 c.3 [C 7]:114 c.1 [C 8]:34 t.17 c.1 [C 9]:36 c.3 [B 1]:11 [B 2]:113 t.15 [F 2]:18 t.VI c.5 [F 1]:148 t.XV c.X [F 3]:174 t.15 c.X [R 5]:316 [R 1]:E46 [K 2]:5 t.4
titled "clarke"? - - - - - - - - - - Yes Yes Yes Yes
elements 19 19 20 20 20 20 31 27 20 28 87 89 89 89
lithosphere 93% 93% 93% 93% 93% 93% 93% 93% 93% 13.5/14.5 Yes Yes Yes Yes Yes
definition 10 miles 10 miles 10 miles 10 miles 10 miles 10 miles 10 miles 10 miles 10 miles 16 km 16 km 16 km 16 km 16 km 10 miles
rock types All All All All All All All All All All All All All All All
hydrosphere ocean 7% ocean 7% ocean 7% ocean 7% ocean 7% ocean 7% 7% 7% 7% 1/14.5 Yes Yes Yes Yes Yes
atmosphere N 0.02% N 0.02% N 0.02% N 0.02% N 0.02% N 0.02% 0.03% 0.03% Yes Yes Yes Yes Yes Yes
remarks often mentioned often cited. >100% >100% >100% popular in Japan
Z element (mass%) (mass%) (mass%) (mass%) (mass%) (mass%) (mass%) (mass%) (mass%) (mass%) (mass%) (mass%) (mass%) (mass%) (weight%) (weight%)
8 O Chemistry:oxygen 49.98 49.98 49.78 49.85 50.02 50.02 49.190 49.520 49.20 49.5000 49.500 49.70 49.130 49.500 49.500 49.500
14 Si Chemistry:silicon 25.30 25.30 26.08 26.03 25.80 25.80 25.710 25.750 25.67 25.7000 25.300 26.00 26.000 25.300 25.800 25.800
13 Al Chemistry:aluminium 7.26 7.26 7.34 7.28 7.30 7.30 7.500 7.510 7.50 7.5000 7.500 7.45 7.450 7.500 7.560 7.560
26 Fe Chemistry:iron 5.08 5.08 4.11 4.12 4.18 4.18 4.680 4.700 4.71 4.7000 5.080 4.20 4.200 5.040 4.700 4.700
20 Ca Chemistry:calcium 3.51 3.51 3.19 3.18 3.22 3.22 3.370 3.390 3.39 3.3900 3.390 3.25 3.250 3.390 3.390 3.390
11 Na Chemistry:sodium 2.28 2.28 2.33 2.33 2.36 2.36 2.610 2.640 2.63 2.6300 2.630 2.40 2.400 2.630 2.630 2.630
19 K Chemistry:potassium 2.23 2.23 2.28 2.33 2.28 2.28 2.380 2.400 2.40 2.4000 2.400 2.35 2.350 2.400 2.400 2.400
12 Mg Chemistry:magnesium 2.50 2.50 2.24 2.11 2.08 2.08 1.940 1.940 1.93 1.9300 1.930 2.35 2.350 1.930 1.930 1.930
1 H Chemistry:hydrogen 0.94 0.94 0.95 0.97 0.95 0.95 0.872 0.880 0.87 0.8700 0.870 1.00 1.000 0.870 0.870 0.870
22 Ti Chemistry:titanium 0.30 0.30 0.37 0.41 0.43 0.43 0.648 0.580 0.58 0.5800 0.630 0.50 0.610 0.630 0.460 0.460
17 Cl Chemistry:chlorine 0.15 (Cl+Br) 0.15 (Cl+Br) 0.21 0.20 0.20 0.20 0.228 0.188 0.19 0.1900 0.190 0.20 0.200 0.190 0.190 0.190
25 Mn Chemistry:manganese 0.07 0.07 0.07 0.08 0.08 0.08 0.108 0.080 0.09 0.0900 0.090 0.09 0.100 0.090 0.090 0.090
15 P Chemistry:phosphorus 0.09 0.09 0.11 0.10 0.11 0.11 0.142 0.120 0.11 0.1200 0.120 0.10 0.120 0.120 0.080 0.080
6 C Chemistry:carbon 0.21 0.21 0.19 0.19 0.18 0.18 0.139 0.087 0.08 0.0800 0.080 0.35 0.350 0.080 0.080 0.080
16 S Chemistry:sulfur 0.04 0.04 0.11 0.10 0.11 0.11 0.093 0.048 0.06 0.0600 0.060 0.10 0.100 0.060 0.060 0.060
7 N Chemistry:nitrogen 0.02 0.02 0.02 0.03 0.03 0.03 0.030 0.030 0.03 0.0300 0.030 0.04 0.040 0.030 0.030 0.030
9 F Chemistry:fluorine - - 0.02 0.10 0.10 0.10 0.030 0.027 0.03 0.0270 0.026 0.08 0.080 0.026 0.030 0.030
37 Rb Chemistry:rubidium - - - - - - - - - 0.0033 3.50E-03 - 0.008 3.50E-03 0.030 0.030
56 Ba Chemistry:barium 0.03 0.03 0.09 0.09 0.08 0.08 0.075 0.047 0.04 0.0400 0.040 0.04 0.050 0.040 0.023 0.023
40 Zr Chemistry:zirconium - - - - - - 0.048 0.023 - 0.0230 0.023 - 0.025 0.023 0.020 0.020
24 Cr Chemistry:chromium 0.01 0.01 - - - - 0.062 0.033 - 0.0330 0.038 0.02 0.030 0.033 0.020 0.020
38 Sr Chemistry:strontium - - 0.03 0.03 0.02 0.02 0.032 0.017 0.02 0.0200 0.020 0.02 0.040 0.020 0.020 0.020
23 V Chemistry:vanadium - - - - - - 0.038 0.016 - 0.0160 0.018 0.02 0.020 0.013 0.015 0.015
28 Ni Chemistry:nickel - - - - - - 0.030 0.018 - 0.0180 0.018 0.02 0.020 0.018 0.010 0.010
29 Cu Chemistry:copper - - - - - - 0.010 0.010 - 0.0100 0.010 0.02 0.010 0.010 0.010 0.010
58 Ce Chemistry:cerium - - - - - - 0.019 (Ce+Y) 0.014 (Ce+Y) - 0.0022 2.00E-03 - 2.90E-03 2.00E-03 4.50E-03 4.50E-03
30 Zn Chemistry:zinc - - - - - - 0.004 - - 0.0045 0.017 - 0.020 0.017 4.00E-03 4.00E-03
32 Ge Chemistry:germanium - - - - - - - - - 2.00E-08 1.00E-04 - 4.00E-04 1.00E-04 6.50E-04 6.50E-04
43 Ma masurium - - - - - - - - - - - - 1.00E-07 1.00E-07 1.00E-07 1.00E-07
others 0.00 0.00 0.48 0.47 0.47 0.47 0.00 0.032 0.47

Other variants

Some authors call these "clarkes" too, some do not.

cited as Clarke (1889) Clarke & Washington (1924) Clarke & Washington (1924) Clarke & Washington (1924) Clarke (1924) Goldschmidt (1937) Goldschmidt (1937) Mason (1952) Mason (1958) RCST1961 (1961) Mason (1966) Mason & Moore (1982)
cited in [C 1]:138 c.1 [C 8]:34 t.17 c.2 [C 8]:34 t.17 c.3 [C 8]:20 t.11 c.1 [C 9]:36 c.1 [G 1]:99-100 [U 2]:4 t.2 [M 1]:41 t.8 [M 2]:44 t.9 [R 2] [M 3]:45 t.3.3 [M 4]:46 t.3.5
titled "clarke"? - - - - - - - - Yes - -
elements 19 27 27 35 20 80 80 85 78 78
lithosphere 100% Yes 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%
definition 10 miles 20miles 10 miles 10 miles 10 miles 10 miles 10 miles 10 miles
rock types All All igneous + sedimentary igneous All igneous igneous All All All All All
hydrosphere (no) Yes (no) (no) (no) (no) (no) (no) (no) Yes (no) (no)
atmosphere (no) Yes (no) (no) (no) (no) (no) (no) (no) Yes (no) (no)
remarks wrong composition
Z element (mass%) (mass%) (mass%) (mass%) (mass%) (mass ppm) (weight%) (mass ppm) (mass ppm) (weight%) (mass ppm) (mass ppm)
8 O Chemistry:oxygen 47.29 48.080 46.710 46.590 46.46 46.600 466,000 466,000 46.600 466,000 466,000
14 Si Chemistry:silicon 27.21 26.720 27.690 27.720 27.61 277,200 27.720 277,200 277,200 27.720 277,200 277,200
15 Al Chemistry:aluminium 7.81 7.790 8.070 8.130 8.07 81,300 8.130 81,300 81,300 8.130 81,300 81,300
26 Fe Chemistry:iron 5.46 4.870 5.050 5.010 5.06 50,000 5.000 50,000 50,000 5.000 50,000 50,000
20 Ca Chemistry:calcium 3.77 3.520 3.650 3.630 3.64 36,300 3.630 36,300 36,300 3.630 36,300 36,300
11 Na Chemistry:sodium 2.36 2.690 2.750 2.850 2.75 28,300 2.830 28,300 28,300 2.830 28,300 28,300
19 K Chemistry:potassium 2.40 2.490 2.580 2.600 2.58 25,900 2.590 25,900 25,900 2.590 25,900 25,900
12 Mg Chemistry:magnesium 2.68 2.010 2.080 2.090 2.07 20,900 2.090 20,900 20,900 2.090 20,900 20,900
1 H Chemistry:hydrogen 0.21 0.510 0.140 0.130 0.14 nicht ber. - 1,400 1,400 0.140 1,400 1,400
22 Ti Chemistry:titanium 0.33 0.600 0.620 0.630 0.62 4,400 0.440 4,400 4,400 0.440 4,400 4,400
17 Cl Chemistry:chlorine 0.01 0.101 0.045 0.048 0.05 480 0.048 314 200 0.020 130 130
25 Mn Chemistry:manganese 0.08 0.090 0.090 0.100 0.09 1,000 0.100 1,000 1,000 0.100 950 950
15 P Chemistry:phosphorus 0.10 0.130 0.130 0.130 0.12 800 0.118 1,180 1,180 0.118 1,050 1,050
6 C Chemistry:carbon 0.22 0.091 0.094 0.032 0.09 0.032 320 320 0.032 200 200
16 S Chemistry:sulfur 0.03 0.050 0.052 0.052 0.06 520 0.052 520 520 0.052 260 260
7 N Chemistry:nitrogen - 0.016 - - - - 46 46 0.0046 20 20
9 F Chemistry:fluorine - 0.028 0.029 0.030 0.03 0.030 300 700 0.070 625 625
37 Rb Chemistry:rubidium - - - - - 310 0.031 310 120 0.012 90 90
56 Ba Chemistry:barium 0.03 0.048 0.050 0.050 0.04 250 0.025 250 400 0.040 425 425
40 Zr Chemistry:zirconium - 0.024 0.025 0.026 - 220 0.022 220 160 0.016 165 165
24 Cr Chemistry:chromium 0.01 0.034 0.035 0.037 - 200 0.020 200 200 0.020 100 100
38 Sr Chemistry:strontium - 0.017 0.018 0.019 0.02 150 0.015 300 450 0.045 375 375
23 V Chemistry:vanadium - 0.016 0.016 0.017 - 150 0.015 150 110 0.011 135 135
28 Ni Chemistry:nickel - 0.018 0.019 0.020 - 100 0.010 80 80 0.008 75 75
29 Cu Chemistry:copper - 0.010 0.010 0.010 - 100 0.010 70 45 0.0045 55 55
58 Ce Chemistry:cerium - 0.014 (Ce+Y) 0.014 (Ce+Y) 0.015 (Ce+Y) - 46.1 0.0046 46 46 0.0046 60 60
30 Zn Chemistry:zinc - - - 0.004 - 40 0.004 132 65 0.0065 70 70
32 Ge Chemistry:germanium - - - n*E-11 - 7 0.0007 7 2 2.00E-04 1.5 1.5
43 Ma masurium - - - - - - - - - - - -
others 0.033 0.033 0.500

Clarke of concentration

A related term "clarke of concentration" or "concentration clarke", synonym: "concentration factor (mineralogy)", is a measure to see how rich a particular ore is. That is, the ratio between the concentrations of a chemical element in the ore, and its concentration in the whole Earth's crust (i.e. "clarke") [M 1]:42[x 8]:43.

If the concentration of a commodity in an ore X is [math]\displaystyle{ Kx }[/math] [ppm], and the "clarke" of that commodity is [math]\displaystyle{ Ke }[/math] [ppm], then "the clarke of concentration" of that commodity X is [math]\displaystyle{ Kk=\frac{Kx}{Ke} }[/math] (dimensionless).

The value represents the degree to which the commodity is concentrated from crustal abundances to the ore by natural geochemical processes; a clue for whether the commodity could be mined economically.[1]

References

Footnotes

  1. ↑ Nassar, Nedal T.; Lederer, Graham W.; Brainard, Jamie L.; Padilla, Abraham J.; Lessard, Joseph D. (2022-05-17). "Rock-to-Metal Ratio: A Foundational Metric for Understanding Mine Wastes". Environmental Science & Technology 56 (10): 6710–6721 (p6718 equation 2). doi:10.1021/acs.est.1c07875. ISSN 0013-936X. PMID 35467345. Bibcode: 2022EnST...56.6710N. 

Cited works

  • C: Frank Wigglesworth Clarke of USGS and Henry Stephens Washington
  1. ↑ 1.0 1.1 1.2 1.3 Clarke, Frank Wiggleworths (1889-10-26). "The relative abundance of the chemical elements" (PDF). Bulletin of the Philosophical Society of Washington (Philosophical Society of Washington) 11: 131–142. 1892. https://www.dropbox.com/s/eiwvh6yurwuj6il/Volume%2011.pdf?dl=0&page=168. Retrieved 2020-03-28. 
    • Based on 880 igneous rock samples.
    • Chlorine and bromine data are summed.
  2. ↑ 2.0 2.1 2.2 Clarke, Frank Wiggleworths (1891). "Relative abundance of the chemical elements" (PDF). Report of Work Done in the Division of Chemistry and Physics Mainly During the Fiscal Year 1889-'90 (United States Geological Survey) Bulletin 78: 39. doi:10.3133/b78. https://pubs.usgs.gov/bul/78/report.pdf. Retrieved 2020-04-01. 
    • Numbers identical to (Clarke 1889).
  3. ↑ 3.0 3.1 3.2 Clarke, Frank Wiggleworths (1908). "The data of geochemistry" (PDF). Bulletin (United States Geological Survey) 330. doi:10.3133/b330. https://pubs.usgs.gov/bul/0330/report.pdf. Retrieved 2020-03-19. 
  4. ↑ 4.0 4.1 4.2 Clarke, Frank Wiggleworths (1911). "The data of geochemistry" (PDF). Bulletin (United States Geological Survey) 491. doi:10.3133/b491. https://pubs.usgs.gov/bul/0491/report.pdf. Retrieved 2020-03-19. 
  5. ↑ 5.0 5.1 5.2 Clarke, Frank Wiggleworths (1916). "The data of geochemistry" (PDF). Bulletin (United States Geological Survey) 616. doi:10.3133/b616. https://pubs.usgs.gov/bul/0616/report.pdf. Retrieved 2020-03-19. 
  6. ↑ 6.0 6.1 6.2 Clarke, Frank Wiggleworths (1920). "The data of geochemistry" (PDF). Bulletin (United States Geological Survey) 695. doi:10.3133/b695. https://pubs.usgs.gov/bul/0695/report.pdf. Retrieved 2020-03-19. 
    • Numbers identical to (Clarke 1916)
  7. ↑ 7.0 7.1 7.2 7.3 Clarke, Frank Wiggleworths; Washington, Henry Stephens (1922-05-01). "The Average Chemical Composition of Igneous Rocks". Proceedings of the National Academy of Sciences of the United States of America (National Academy of Sciences) 8 (5): 108–115. doi:10.1073/pnas.8.5.108. PMID 16586858. Bibcode: 1922PNAS....8..108C. 
    • Based on 5159 igneous rock samples.
    • Table contains data for 31 elements, most comprehensive among Clarke's publications. Amount of cerium and yttrium are summed.
  8. ↑ 8.0 8.1 8.2 8.3 8.4 8.5 8.6 Clarke, Frank Wiggleworths; Washington, Henry Stephens (1924). "The composition of the earth's crust" (PDF). Professional Paper (United States Geological Survey) 127. doi:10.3133/pp127. https://pubs.usgs.gov/pp/0127/report.pdf. Retrieved 2020-03-19. 
    • Often cited. Beware there is another article in the same year (Clarke 1924) reporting different results.
    • Based on 5159 igneous rock samples.
    • p17 mentions that the 10miles crust consist of lithosphere:93.06%; hydrosphere:6.91%; atmosphere:0.03%, but p34 explains that table 17 is calculated using approximations ie. lithosphere:93%; hydrosphere:7%; atmosphere:0.03%. No mention of the exact calculation process.
    • Table 17 contains data for 27 elements. Amount of cerium and yttrium are summed.
  9. ↑ 9.0 9.1 9.2 9.3 Clarke, Frank Wiggleworths (1924). "The data of geochemistry" (PDF). Bulletin (United States Geological Survey) 770. doi:10.3133/b770. https://pubs.usgs.gov/bul/0770/report.pdf. Retrieved 2020-03-19. 
    • p.27 mentions (Clarke Washington), numbers differ. Data for only 20 elements, lesser than previous works such as (Clarke Washington).
    • Based on 5159 igneous rock samples.
    • Amount of cerium and yttrium are summed.
  • U: United States Geological Survey (USGS)
  1. ↑ Wells, Roger Clark (1937). "Analyses of rocks and minerals from the laboratory of the United States Geological Survey, 1914–36" (PDF). Bulletin (United States Geological Survey) 878: 4. doi:10.3133/b878. https://pubs.er.usgs.gov/publication/b878. Retrieved 2020-03-21. 
  2. ↑ 2.0 2.1 2.2 Fleischer, Michael (1953). "Recent estimates of the abundances of the elements in the earth's crust" (PDF). Circular (United States Geological Survey) 285. doi:10.3133/cir285. https://pubs.er.usgs.gov/publication/cir285. Retrieved 2020-03-21.  (a review)
  • B: Georg Ernst Wilhelm Berg (de)
  1. ↑ Berg, Georg Ernst Wilhelm (1929) (in de). Vorkommen und Geochemie der mineralischen Rohstoffe: Einführung in die Geochemie und Lagerstättenlehre, besonders für Chemiker und Studierende der allgemeinen Naturwissenschaften. Leipzig: Akademische Verlagsgesellschaft. OCLC 595448842. https://books.google.com/books?id=lFRUAAAAMAAJ. 
  2. ↑ Berg, Georg Ernst Wilhelm (1932) (in de). Das Vorkommen der chemischen Elemente auf der Erde. Johann Ambrosius Barth Verlag (de). https://books.google.com/books?id=XuFDAAAAIAAJ. 
  • F: Alexander Fersman
  1. ↑ 1.0 1.1 1.2 Fersman, A.E. (1934) (in ru) (djvu). Geochemistry. Том 1. Leningrad. http://www.geokniga.org/bookfiles/geokniga-geohimiya-tom-1-fersman-ae-1934.djvu. Retrieved 2020-03-21. 
    • p141: definitions of "clarke".
    • p146 table 15 column 1 quotes (Clarke 1889) in (Fersman 1934)) but actual data is on p138, and the numbers on Fersman's are different from anything in (Clarke 1889).
    • p161 fig.18 "clarkes of meteorites": An example of applying the term "clarke" to objects other than geospheres.
  2. ↑ Fersman, A.E. (1923) (in ru) (pdf). Chemical elements of earth and space. Peterburg: Науч. хим.-техн. изд-во Науч.-техн. отд. ВСНХ. http://www.geokniga.org/bookfiles/geokniga-himicheskie-elementy-zemli-i-kosmosa.pdf. Retrieved 2020-03-21. 
  3. ↑ Fersman, A.E. (1955). "Geochemistry Vol1" (in ru). Selected Works of Academician A.E. Fersman. Том 3. Moscow: Publishing House of the Academy of Sciences of the USSR. http://www.geokniga.org/books/5120. Retrieved 2020-03-30.  (Posthumous revision. Data in p174 table 15 seems identical to (Fersman 1934))
  • G: Victor Goldschmidt
  1. ↑ Goldschmidt, V.M. (1938). "Geochemische Verteilungsgesetze der Elemente. ix: Die Mengenverhältnisse der Elemente und der Atomarten" (in de). Skrifter Utgitt av Det Norske Videnskaps-akademi I Oslo. I. Mat-Naturv. Klasse (Oslo: J. Dybwad) 1937 n.4.. OCLC 762456670. https://books.google.com/books?id=mbooAQAAMAAJ. Retrieved 2020-04-21. 
  1. ↑ 1.0 1.1 1.2 Mason, Brian Harold (1955). Principles of Geochemistry (1st ed.). John Wiley & Sons. p. 42. https://books.google.com/books?id=43Q1AAAAMAAJ&q=%22term+clarke%22. 
    • Attributing the term "clarke" to Vladimir Vernadsky. The numbers he gave as examples ("the clarke of oxygene is 46.60, of silicon, 27.72") was his own data (based on Clarke&Washington(1924) and Goldschmidt) for rocky crust excluding hydrosphere and atmosphere.
    • p.42 Attributing the term "clarke of concentration" to Vladimir Vernadsky, but without specifying location in source. Mason himself used the term "concentration clarke" instead.
  2. ↑ 2.0 2.1 2.2 Mason, Brian Harold (1958). Principles of Geochemistry (2nd ed.). John Wiley & Sons. p. 47. OCLC 614731481. https://archive.org/details/principlesofgeoc00maso. 
    • p.47 Corrected the term "clarke" originator to Fersman. He maintained "Clarke of concentration" come from Vernadsky.
    • p.45 Table 9 "The Average Amount of Elements in the Earth's Crust": Mason claims data for major elements are taken from Clarke and Washington but they are not. Most data for major elements are identical to (Goldschmidt 1938), which were only about igneous rocks. Mason argues that the average of igneous rocks can reasonably represent the whole crust.
  3. ↑ Mason, Brian Harold (1966). Principles of Geochemistry (3rd ed.). John Wiley & Sons. ISBN 9780471575214. OCLC 570774645. https://books.google.com/books?id=KkBRAAAAMAAJ. 
  4. ↑ Mason, Brian Harold; Moore, Carleton B. (1982). Principles of Geochemistry (4th ed.). John Wiley & Sons. p. 49. ISBN 978-0-471-08642-0.  (other format ISBN 978-0-471-57522-1)
    • pp.46-47 Table 3.5 "The Average Amounts of the Elements in Crustal Rocks in Grams per Ton or Parts per Million"
  • K: Kenjiro Kimura (ja)
  1. ↑ Kimura(1938) = (RCST1939 1938)
  2. ↑ 2.0 2.1 Kimura, Kenjiro (1939). (in ja)The Journal of the Japanese Society of Balneology, Climatology (日本温泉気候物理医学会) 5: 1–11. doi:10.11390/onki1935.5.1. "(p.11 footnote 8) table 3(sic) is a clarke number table based on data in recent literature and my recalculations".  (p.5 table 4 is the clarke number table. Identical to (Kimura 1938))
  • H: Research on the history of chemistry
  1. ↑ Onishi, Hiroshi (2001). "[Transition of Clarke Number as Seen in Rikagaku Jiten and Rika Nenpyo"] (in ja). The Journal of the Japanese Society for the History of Chemistry (Japanese Society for the History of Chemistry) 28 (4): 265–268. https://ci.nii.ac.jp/naid/10007418243. 
    • An essay.
    • p.(62) denotes "Unfortunately, Rikanenpyō edition 34((RCST1961 1961)) and edition 35((RCST1962 1962a))'s usage of clarke numbers are erratic", but doesn't mention how.
  2. ↑ 2.0 2.1 2.2 Ebihara, Mitsuru (1998). "[Clarke numbers — doomed data?"] (in ja) (PDF). Kagaku to kyoiku (The Chemical Society of Japan) 46 (7): 428–431. doi:10.20665/kakyoshi.46.7_428. https://www.jstage.jst.go.jp/article/kakyoshi/46/7/46_KJ00003520487/_article/-char/en. 
    • An essay.
    • p429: translation of quote: "today our knowledge have sub-ppb level accuracy. Clarke numbers, which are defined as percent-based, became inconvenient."
    • table 2 "clarke numbers": Lack citation. Values identical to (Kimura 1938).
    • table 1 "average composition of igneous rocks": mis-cited as Clarke&Washington's are not. They are actually Mason's heavily modified version (Mason 1958).

Examples of usage

  • R: Chronological Scientific Tables (理科年表, Rikanenpyō)(:ja:理科年表): An (mostly) annual reference book published in Japan since 1925CE. Note that the actual published year is typically one year earlier than the nominal (book title) year.
  1. ↑ 1.0 1.1 東京天文台 (1938). Tokyo Astronomical Observatory. ed (in ja) (15 (S14(1939)) ed.). Tokyo Imperial University. E46. doi:10.11501/1223113. https://dl.ndl.go.jp/info:ndljp/pid/1223113/179. Retrieved 2020-03-22. "Based on F.W.Clarke and H.S.Washington(1922). With slight correction by G.Berg(1934), Kenjiro Kimura(1938) et al.". 
    • Edition 1939 was the first edition to adopt (Kimura 1938). Same data on edition 1939–1961.
  2. ↑ 2.0 2.1 Tokyo Astronomical Observatory, ed (1961) (in ja) (34 (S36(1961)) ed.). Tokyo Imperial University. 地87. "Numbers on this table represents the lithosphere, 10 miles thick from sea level, based mainly on Mason(1958).". 
    • Switched from (Kimura 1938) to (Mason 1958) based. Table's column title is "clarke number" on edition 1961–1962. Lists 85 elements, which is more than Mason(1958). Same data on edition 1961–1966.
  3. ↑ Tokyo Astronomical Observatory, ed (1962-01-20) (in ja) (35 (S37(1962)) ed.). Tokyo Imperial University. "Numbers on this table represents the lithosphere, 10 miles thick from sea level, based mainly on Mason(1958). Weight percentage of elements in lithosphere+hydrosphere+atmosphere are called clarke numbers.". 
    • (Mason 1958) based. Table's column title is "clarke number", which conflicts with the definition on the same page (see quote). Lists 85 elements which is more than Mason(1958). Same data on edition 1961–1966.
  4. ↑ Tokyo Astronomical Observatory, ed (1962-12-25) (in ja) (36 (S38(1963)) ed.). Tokyo Imperial University. "Numbers on this table represents the lithosphere, 10 miles thick from sea level, based mainly on Mason(1958). Weight percentage of elements in lithosphere+hydrosphere+atmosphere are called clarke numbers.". 
    • (Mason 1958) based. Table's column title changed to "weight percent ratio". Lists 85 elements which is more than Mason(1958). Same data on edition 1961–1966.
  5. ↑ 東京天文台 (1936). Tokyo Astronomical Observatory. ed (in ja) (Edition 13 (S12(1937)) ed.). Tokyo Imperial University. 316. doi:10.11501/1223097. https://dl.ndl.go.jp/info:ndljp/pid/1223097/187. Retrieved 2020-03-22. "Based on F.W.Clarke and H.S.Washington(1922). With slight correction by G.Berg(1934), et al.". 
    • Edition 1937 was the first edition to use the term "clarke number (クラーク数)". Same data on edition 1937–1938.
  • I: Iwanami Dictionary of Physics and Chemistry (岩波理化学辞典, Iwanami rikagaku jiten): Revised roughly by each decade. First edition 1935CE.
  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 石原, 純, 1881-1947 (1939-12-10) (in ja). Rikagaku jiten (1st Ed., Rev.2 ed.). Tokyo: Iwanami Shoten, Publishers. p. appendix VI. doi:10.11501/1161076. JPNO 49012036. 
    • First revision of IDPC where term "clarke number" and data table appeared. Unsourced. Data identical to (Kimura 1938).
    • Translation of quote from dictionary entry "clarke number": "F.W. Clarke assumed that rocks downto 10 miles (approx 16 km) below sea level should be quite similar to rocks on the surface of Earth. He determined a portion consisting of this, the hydrosphere and atmosphere as the outer part of the earth which is directly accessible to our observation, that is in weight percentage ratio of 93.06% lithosphere, 0.91% hydrosphere and 0.03% atmosphere. This portion is about 0.3% of the whole Earth. He calculated the weight percentage of elements in this portion. Thus, in accordance to A.Fersmann[sic]'s proposal, the abundance of elements in this range, denoted in weight percentage, are called clarke numbers." This differs from (Fersman1934 {{{2}}})'s "clarke", is rather similar to his "clarke of Earth's crust", but further binding to just one of Clarke's variants through a vague phrase "in this range".
  2. ↑ 2.0 2.1 (in ja) Iwanami rikagaku jiten (3rd ed.,amended ed.). Tokyo: Iwanami Shoten, Publishers. 1982. p. 355. JPNO 81020460. 
    • Have no data table titled "clarke number".
  3. ↑ (in ja) Iwanami rikagaku jiten (3rd ed.). Tokyo: Iwanami Shoten, Publishers. 1971. JPNO 69004765. 
    • Have no data table titled "clarke number". The table titled "abundance of elements" was credited "based mostly on Taylor(1964) and Mason(1966)".
  4. ↑ 井上, 敏, 1894-1967 (1953) (in ja). Iwanami rikagaku jiten (2nd ed.). Tokyo: Iwanami Shoten, Publishers. p. appendix XI. doi:10.11501/2421663. JPNO 54000017. 
    • p365 dictionary entry "clarke number": Author of this entry is not mentioned. Text identical with (IDPC 1939) except spelling "A.Fersmann"(sic) changed to "A.Fersman".
    • p1379 Appendix XI clarke number data table: Unsourced. Data almost identical to (IDPC 1939), except masurium been removed, and footnotes added: "Recently, following updates are reported: Zn:8x10-3, Cu:7x10-3, Nb:2.4x10-3, Co:2.3x10-3, Tl:3x10-4, Ta:2.1x10-4, Cd:1.5x10-5 ... 93 Np: 1x10-18 (abundance rank 89 90), 94 Pu: 1x10-18 (abundance rank 89 90)". Data in these footnotes are not incorporated into the main table. Identical table is in "Kyoritsu Great Dictionary of Chemistry" (Concise edition (KGDC 1963)).
    • From 2nd edition, "Iwanami" was added to the title of the book.
  • D: Kyoritsu Great Dictionary of Chemistry
  1. ↑ Sugawara, Ken (1982-08-15) (in ja). Kyoritsu Great Dictionary of Chemistry, Concise Edition. 3 (Concise rev.32 ed.). Tokyo: Kyoritsu Shuppan. p. 67. ISBN 4-320-04017-1. 
    • Publication date of 1st non-concise edition is 1960
    • Entry's author is Ken Sugawara. Cited source is Miyake, Yasuo (1954) (in ja). . Table content identical to (IDPC 1953), with the same footnotes.
    • Extra quotes: "In addition to the typical mass/mass% table, Miyake recently proposed a novel table re-written in mol/kg (Miyake,1954)"
  • X: Other usage examples
  1. ↑ Template:GSEn
    • Example data given (A.P.Vinogradov(1962), K.H.Wedepohl(1967)) are of igneous rocks in Earth's crust, excluding both hydrosphere and atmosphere.
    • Mistaken :de:Karl Hans Wedepohl's first name with "Clarke".
  2. ↑ (in en) Economic Geology U.S.S.R. 1. Pergamon Press. OCLC 5304168.  (translation of several Russian academic papers to English)
  3. ↑ Lee, Tan; Yao, Chi-lung (1970). "Abundance of chemical elements in the earth's crust and its major tectonic units". International Geology Review 12 (7): 778–786. doi:10.1080/00206817009475289. Bibcode: 1970IGRv...12..778T.  (reprint from ACTA GEOLOGICA SINICA 1965, v.45 no.1 p.82-91. (PRC))
    • "Clarke values" in introduction. Chinese abstract Chinese: 克拉克值; literally: 'clarke value'
  4. ↑ Treatise on Geochemistry: The Crust. 3 (4 ed.). Elsevier. 2005. p. 412. ISBN 0-08-044847-X. https://books.google.com/books?id=QT52UZxDFwgC&pg=PR3. 
  5. ↑ 5.0 5.1 Miyake, Yasuo (1939). "Chemical Studies of the Western Pacific Ocean. II. The Chemical Composition of the Oceanic Salt. Part 2" (in en). Bulletin of the Chemical Society of Japan (The Chemical Society of Japan) 14 (3): 55–58. doi:10.1246/bcsj.14.55. 
    • Presenting only the ratio of Clarke numbers between strontium and calcium as 0.0059, without showing individual numbers nor source. "Clarke" is capitalized.
  6. ↑ Ito (1942). (in ja) (PDF)Journal of the Japan Institute of Metals (The Japan Institute of Metals) 6 (12): A443–A446. doi:10.2320/jinstmet1937.6.12_A443. https://www.jstage.jst.go.jp/article/jinstmet1937/6/12/6_12_A443/_article/-char/ja. Retrieved 2020-03-21. 
    • quote table with numbers identical to (Kimura 1938) without mentioning source
  7. ↑ Takada, Jun; Nakanishi, Makoto (2017). "Development of Novel Reddish Iron Oxide Based on Traditional Pigment "Bengala"" (in ja) (PDF). Journal of the Society of Materials Science, Japan (The Society of Materials Science, Japan) 66 (11): 799–803. doi:10.2472/jsms.66.799. https://www.jstage.jst.go.jp/article/jsms/66/11/66_799/_article/-char/ja. "the clarke number of iron is 4.70". 
    • Using clarke numbers without citation
  8. ↑ Laznicka, Peter (2010). Giant metallic deposits. Future sources of industrial metals (2 ed.). Berlin: Springer. doi:10.1007/978-3-642-12405-1. ISBN 978-3-642-12404-4. https://books.google.com/books?id=1tWllDxMkEYC&q=%22clarke+of+concentration%22. 
    • p43 says the originator of term "clarke of concentration" is Fersman(1933) but reference in p774 actually refers to (Fersman 1955)

See also



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