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Of the Magnet Cove rocks this resembles most that of arkite (IV), especially as regards Al,O,, (FeO), MgO, and Na,O, though it is distinctly higher in SiO, and CaO and lower in K,O. Referring it to Diagram 3, its position established by means of SiO, is shown at X, and the points where this vertical is cut by the oxide curves are the "molecular ratios calc." of the table. The small crosses along the vertical indicate the positions of the various oxides as found. They can be identified by the values in the table.

It will be observed by reference to the diagram or to the last two columns of the table, that in the case of oxides whose curves are approximately straight lines, as Al,O, and Na, O, the found and calculated values coincide, while in the case of oxides yielding decided curves the value found is below that calculated.

This is in accordance with the demonstration of Harker1 that if a series be linear the admixture of two or more members will produce a rock having the composition of a possible member of the series, while in a curvilinear series the mixture will not correspond to a possible member.

Another method for arriving at the composition of the magma as a whole would seem to be furnished by the determination of the mean point of each of the curves, thus giving the average composition. If the equations of the various curves were known, these could be calculated mathematically. But for practical purposes it can be done by determining, for each I HARKER, JOUR. GEOL., Vol. VIII, p, 394, 1900.

oxide, the ordinal value for each successive tenth of an inch, and taking the mean. The result of this process is given in II below, that given by the previous process being given in I.

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The two agree fairly well, and are of the same general character, though there are marked discrepancies, II being decidedly more basic in all respects than I. What may be the explanation of this, I am not mathematician enough to say. But the general agreement would indicate that one of the two, or their mean, cannot be far from the truth, i. e., as near as the data at hand permit of approximation.

It is of interest to note that I have been unable to find the analysis of any rock which agrees at all closely with either of these two results. Those which are as high in alkalis being lower in bivalent oxides, while those which agree in this respect are lower in alkalis and alumina. Whether this indicates that there are serious sources of error in the method employed, or else that some undifferentiated magmas may possess chemical compositions not corresponding to those of rocks as yet known, is a question which cannot be decided here. It would seem as if there were nothing a priori contrary to the latter hypothesis.

In this connection Harker's' remark may be cited: “Given a series such that its diagram has markedly curved lines, the result of the admixture of two members may be something not only foreign to the series, but highly peculiar by comparison with igneous rocks in general." It is true that Harker was discussing the case of the mixture of two members of a series, but HARKER, op. cit., p. 395.

differentiation and admixture (of two members of a series) may to a certain extent be regarded as inverse processes, so that the occurrence of a magma of this anomalous composition need not occasion surprise. Being rich in both of the generally antagonistic groups of oxides, it would be especially liable to differentiation. The general lability of the monzonitic magmas as regards the conditions controlling crystallization has been pointed out elsewhere.1

The general chemical composition can also be calculated by the relative volumes of the various phases, which has been the only method heretofore available. This would seem to be far more uncertain than the new method, which is based on the mathematical course of differentiation, since the ignorance of certain data may affect the result very seriously. Thus we cannot tell where the boundaries between two zones really fall, and (beneath the hornstone ridge especially) whether there may not be a zone of transitional material.

Assuming that the limits come half way between zones, and that they are of uniform thickness in all directions, we can easily

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'F. L. RANSOME, Am. Jour. Sci., Vol. V, p. 370, 1898. H. S. WASHINGTON,

JOUR. GEOL., Vol. V, p. 376, 1897.

calculate the volumes of the several spherical shells, which must also be assumed to represent the true ellipsoidal ones. The results are given below, including the relative volumes and weights (obtained by correction of the former for specific gravity), and the average composition deduced from this latter.

This result is notably less basic than the former calculated from the curves, and approaches somewhat closely to the compositions of the foyaite and the arkite, though in a general way intermediate between the two. This is so, since these two form (on this basis) 90 per cent. of the whole. It must be remembered, however, that this method is not based on curves, but on a succession of steps, and that the influence of the greater width of the more acid phases is intensified by their greater distance from the center. At the same time both methods indicate a magma rich in Al,О3, CaO and alkalis, low in SiO2 and MgO, and with moderate iron.

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Inasmuch as there must be a (probably rather large) correction made for the greater mass of foyaite, on the analogy of the Shonkin Sag laccolith, all these figures can, for the present, be regarded as only suggestive and illustrative of the method of investigation proposed, than representing exactly the actual state of affairs.

It is of course hazardous to theorize on such limited data as are yet available, but the methods indicated in Pirsson's paper and the present one would seem to be of not uncommon applicability, and well worth further trial in the investigation of other favorable localities. Indeed, as Pirsson has remarked, "it would seem as if this should be the point of departure in the study of other series." The methods indicated certainly put the study of rock differentiation upon a purely mathematical basis, which in the hands of a competently mathematical petrographer, should surely lead to an exact quantitative knowledge of the laws which control this, and very probably, with the aid of physical chemistry, to a knowledge of the rationale of the process.

I PIRSSON, op. cit., p. 576.

In my former paper I suggested as an explanation of the exceptional character of the Magnet Cove and Umptek laccoliths, in having the borders more acid than the centers, that the arrangement depended on the general chemical character of the undifferentiated magma. The process of differentiation was conceived to be, at least for such small bodies, in great part, a sort of fractional crystallization, the magma being regarded as a solution, so that, in accordance with the laws of cooling solutions, the solvent (i. e., the portion present in excess) crystallizes out first around the borders on cooling of the mass.

From what has been learned of the composition of the magma, it is evident that, even though low in silica, it was originally of a decidedly leucocratic character. In other words, the potential feldspathic and feldspathoidal constituents predominated very largely over the calco-ferromagnesian. This is seen plainly from the relative weights of the spherical shells, but even the more basic composition derived from the curves shows the same thing. Thus the composition with 47.24 per cent. of SiO, may be obtained approximately by several different mixtures of all or some of the types analyzed, but in every case it necessitates taking from six-tenths to eight-tenths of foyaite, or foyaite and arkite. It seems scarcely necessary to give these calculations, which are purely empirical. The same composition may also be reduced to mineralogical composition in several ways, according to the assumptions made, but here, also, we get about two-thirds of leucocratic minerals.

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The original body of magma, then, at Magnet Cove was, notwithstanding its low silica, decidedly leucocratic, as demanded by the theory, so that the alumina and alkalis, with the proper amount of silica for the formation of feldspar and feldspathoids, playing the rôle of solvent, would crystallize first, and hence form the outer portion of the mass.

The latest paper by Weed and Pirrson, already cited, is of great interest in this connection. Here it is shown conclusively that in the well-dissected Shonkin Sag laccolith the outer melanocratic shonkinite is present in enormously greater quantity

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