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(Read April 20, 1912.)

More than twenty years ago, in a paper on the relative abun dance of the chemical elements, the present writer compared a number of averages of analyses of igneous rocks, representing different regions, and showed that they were essentially identical. From these averages, combined into a general average, the mean composition of the igneous part of the lithosphere was computed, and the result obtained has since been confirmed by the study of much larger masses of data than were originally attainable. Other estimates, made by other computers upon similar lines, have since served to check my own, thereby giving to my conclusions a high degree of probability. The figures obtained have received a fairly general acceptance, and have served as a basis for other computations of a fundamental character.

This acceptance, however, has not been universal. The process of averaging analyses is criticized by several writers, who urge that it is unphilosophical. An analysis of a dike rock is given the same weight as that of a widespread and important formation, whereas each rock should be weighted in accordance with its volume. But we do not and probably cannot know these volumes, partly because detailed surveys are lacking, and partly because a surface outcrop fails to tell us what bulk of rock may lie below. If we try to estimate the volumes of the many rocks represented in the average, or

* Published by permission of the Director of the U. S. Geological Survey.

* Bull. Phil. Soc. Washington, 1889, Vol. II, p. 131. Also in Bull. 78, U. S. Geological Survey, 1891, p. 34.

See Bull. 491, U. S. Geological Survey, “The Data of Geochemistry," pp. 22–27.

* See, for example, Daly, Proc. Amer. Acad., 1910, Vol. 45, p. 211; Loewinson-Lessing, Geol. Mag., 1911, p. 248; and Mennell, Geol. Mag., 1904, p. 263, and 1909, p. 212.

even the areas exposed, we shall find ourselves relying in great part upon arbitrary assumptions, a procedure fully as unphilosophical as that which it would supplant. Estimates of that and similar kinds have been made, most recently by Loewinson-Lessing, whose figures give essentially the same result as that obtained by the method he has criticized. The method by volumes is doubtless ideal, but impracticable; and the true, philosophical procedure is to do the best we can with the available data. It is highly probable that the rocks of minor importance will balance one another, the persilicic and subsilicic varieties occurring in something like equal proportions. This supposition is sustained by the groups of average analyses which will presently be given. If we trust to individual judgments, different observers will reach widely different conclusions. Loewinson-Lessing supposes that the average rock may be about the mean of an average granite and an average basalt; Dalys argues in favor of a fundamental basaltic magma; Mennell, whose experience has been gained in a granitic region, regards granite as the dominant rock with all else of minor importance. Mennell makes a strong argument in favor of his contention; but there is weighty evidence against it. If we study recent lavas, that is, the rocks which issue from unknown depths far below the surface, we shall see that rhyolite, the effusive equivalent of granite, is much rarer than andesite or basalt. The Deccan trap, the Columbia River basalt, the andesites of South America, the lavas of Iceland and the Hawaiian Islands are good illustrations of this statement. Moreover, the river waters which originate in areas of crystalline rocks contain almost invariably an excess of lime over soda, which would hardly be the case were granite predominant. Much socalled granite is really either quartz diorite or quartz monzonite, rocks which are probably far more abundant than has been commonly supposed.

In order to test the method of averaging analyses we may now compare the averages so far obtained by different computers, and then pass on to averages of rocks from distinct and widely separated areas. In these averages only the more important constitu

* Bull. U. S. Geol. Survey, No. 209, 1903, p. 110.


ents of the rocks are considered, for the reason that the less con-
spicuous components have not been generally determined. They
will be separately discussed later. All the means have been recalcu-
lated to 100 per cent., and water, for obvious reasons, is excluded.
The methods for the determination of water are far from being
uniform, and the variations are so great as to obscure the essential
agreements between the other figures. The first table contains the
following averages.
(A) The average of 248 “superior” analyses of igneous rocks

selected by Washington from Roth's tables. See U. S.
Geol. Survey, Prof. Paper No. 28. Average computed by

the present writer, (B) The average of 536 British rocks, computed by Harker.

“Tertiary Igneous Rocks of the Isle of Skye,” Mem. Geol.

Survey United Kingdom, 1904, p. 416. (C) Washington's average of 1,811 rocks from all parts of the

world. U. S. Geol. Survey, Prof. Paper No. 14, p. 106. (D) Loewinson-Lessing's estimate of a mean between an average

granite and an average basalt. Inserted here for compari

son with the other columns. (E) The average of all the data relating to the composition of

igneous rocks contained in the laboratory records of the U. S. Geological Survey. Computation by F. W. C.

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The general agreement is striking, and Loewinson-Lessing's estimate fits well in with the others. The next table is devoted to the

igneous rocks of North America, and the analyses are nearly all taken from the Survey records. (F) Average of 250 analyses of rocks from the Atlantic slope,

Maine to Georgia. 78 of these are taken from Washington's tables, the others were made in the Geological

Survey. (G) Average of 113 analyses of rocks from the Yellowstone Park. (H) Average of 137 analyses of rocks from Colorado. (1) Average of 195 analyses of rocks from California. (J) Average for all North America. The figures of column E

combined with those of 398 analyses given in Washington's tables.

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For Europe the following data are sufficient, all the figures, except Harker's, having been taken from Washington's tables. (K) Harker's average for British rocks, as previously cited. (L) Average of 231 analyses of rocks from Norway, Sweden and

Finland. (M) Average of 420 analyses of rocks from the German and Aus

tro-Hungarian Empires. (N) Average of 250 analyses of Italian rocks. (0) General mean of the foregoing 1,427 analyses, plus 122 of

rocks from parts of Europe not otherwise covered. Good analyses of rocks from Asia, Africa and Australia, at least as given by Washington, are too few for satisfactory combination. In the next table I give a general average for North

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America, South America and Europe, South America being represented by the average of 82 analyses cited by Washington. The weights assigned are stated under each column.

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The last column may be taken as probably representing, with certain obvious limitations, the average igneous rock of the entire visible position of the lithosphere. The agreement between the preceding columns is so close as to suggest that similar averages from other parts of the world are likely to be of the same general order. It is hardly conceivable that analysts, dealing with rocks from such diverse regions as Colorado, South America, Germany, Great Britain, etc., should select subsilicic and persilicic rocks or salic and ferric rocks, in nearly identical proportions. The selection has been made by nature itself, and although there are differences indicating the existence of petrographic provinces, they are so slight as to leave

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