3808803The Origin of Continents and Oceans — Chapter 8J. G. A. SkerlAlfred Wegener

III. ELUCIDATION AND CONCLUSIONS

CHAPTER VIII

THE VISCOSITY OF THE EARTH

After the compilation in the foregoing chapters of the chief arguments in favour of the displacement theory, we will henceforth assume them to be correct, and on this supposition we will deal with a series of problems which are linked so closely with the subject-matter of the displacement theory that a discussion of them seems to be desirable. A new light will thus be shed on many an old problem, and many things will be spoken of, in which can be seen a further confirmation of the displacement theory, even if they are not so convincing as the earlier proofs.

The question as to whether, and if so in how far, the earth is to be considered as a viscous or as a rigid body is now being much discussed by the geophysicists. We will consider the grounds of both views in turn, beginning with those of viscosity. They are especially the phenomena of isostasy, the continental displacements, the movement of the poles, and the flattening of the earth near the poles.

It is a well-known fact that isostasy, the equilibrium of adjoining portions of the earth's crust, is universally satisfied on a large scale. Just as indubitable is the occurrence of vertical movements of compensation tending to the restoration of isostasy wherever it has been disturbed over a great area. We have already discussed isostasy in Chapter II, and have also referred to Scandinavia and North America as examples of isostatic movements of compensation. They were submerged about 250 and 500 m. respectively in the Pleistocene by the load of the inland ice, but have been elevated these same amounts after the melting of the ice. Rudzki[1] has shown that it is not a matter of elastic deformations, for he calculated the very plausible thickness of 933 m. for the former ice-sheet from Airy’s theory of isostasy on the basis of the assumed elevation of Scandinavia of 280 m. (the figure for North America being 1667 m. with an elevation of 500 m.). The supposition of an elastic deformation, on the other hand, would lead to a wholly improbable thickness of ice of 6 to 7 km. The lag in the movement of elevation also testifies to the fact that flow-movements must be taken into account. Scandinavia is still rising about 1 m. in a century, although 10,000 years have passed since the maximum temperature, when the ice was removed. W. Köppen has recently made it seem probable that the area depressed by the burden of ice is surrounded by a zone with slight opposite vertical movement, and explains this by the lateral squeezing out of the sima beneath the depressed block.[2] All this naturally presupposes viscosity.

Not only do the vertical movements for the restoration of isostasy, but also the horizontal movements of the continents, positively demand that the earth be viscous. We need not consider this point any further, since it has been dealt with sufficiently in the preceding pages.

The third phenomenon belonging here is the displacement of the poles of rotation in the course of the earth’s history. In Chapter VI we have deduced the position of the poles in the Carboniferous period; it was essentially different from that of to-day. We certainly do not know whether the position is also altered in relation to the interior of the earth, or if, as many authors contend, the crust only has been displaced. Presumably both occur. But, whichever be true, we need in each case the assumption that the globe, or a part of it, is viscous. This is quite obvious in a shifting of the crust; but in the matter of the displacement of the pole relative to the interior of the earth, we also need a viscous earth. Laplace has shown that the axes in a rigid earth cannot be displaced. His idea indicates that in this case the axis of maximum inertia is firmly fixed through the protuberance at the equator, so that even the greatest displacement of continents and other geological phenomena could not move it to any marked extent. At the same time the axis of rotation also must be confined to this position, allowing for the small Euler perturbation. It is otherwise, when the earth is a viscous body. Lord Kelvin says about this assumption[3]: “We may not merely admit, but assert as highly probable, that the axis of maximum inertia and axis of rotation, always very near one another, may have been in ancient times very far from their present geographical position, and may have gradually shifted through 10, 20, 30, 40, or more degrees, without there being at any time any perceptible sudden disturbance of either land or water.” Rudzki[4] also says: “In case the palæontologists ever come to the conclusion that the distribution of climatic zones in one of the past geological epochs point to an axis of rotation totally different from the present axis, there will be nothing left for the geophysicists but to accept this contention.” Schiaparelli,[5] in particular, has examined the question of polar displacement for the three cases of an entirely rigid earth, an entirely liquid earth, and one with a retarded adjustment to the position of the poles for the time being (i.e., a viscous earth). In the first case he comes naturally to the conclusion of Laplace of the invariability of the axis of rotation. On the other hand, in the case of the completely liquid earth, the poles are very movable, since then the flattening follows immediately every alteration of the position of the poles, and can therefore no longer contribute to the stabilization of the axis of inertia. Exceedingly rapid wanderings of the pole are to be expected in this case, such as do not occur in the earth’s history. Finally, on the third supposition, that of retarded adjustment, the earth behaves as a rigid body so long as the forces moving the poles do not exceed a certain value. Then there only exists Euler’s perturbation such as is observed to-day. But as soon as this limit is exceeded (which happens as soon as the radius of the curve of the perturbations exceeds the critical limit), the poles, in some sort, run away. Extensive, even if slow, polar wanderings are then able to take place. Now, since wanderings of the poles of this kind are manifestly detectable in the earth’s history, the conclusion must be drawn that the earth behaves as a viscous body.

The last phenomenon to be quoted as evidence of the viscosity of the earth is its oblateness. So far as the accuracy of our measurements permits us to form an opinion, the amount and orientation of the polar flattening are in agreement with its rotation, a state of affairs which can only be attained by flow. But we can examine this question geologically by comparing the alternate advance (transgression) and withdrawal (regression) of the sea with the wandering of the poles. That a simple connection exists between these phenomena has already been suspected by numerous authors as, for example, Reibisch, Kreichgauer, Semper, Heil, Köppen, amongst others.
Fig. 21.—Transgressions and regressions caused by the wandering of the poles.
Fig. 21 explains this. If during a wandering of the poles the earth lags behind in the alteration of its shape whilst the ocean adjusts itself immediately, then regression must prevail, in front of the wandering pole and transgression behind it. The reconstructed map of the displacement theory places us in a position to verify this already long-asserted, but never proved, law. We select for this the period from the Devonian to the Permian, because the poles during this time wandered rapidly,[6] as was shown in Chapter VI. If we introduce into our Carboniferous map of the earth the coast-lines of the Lower Devonian and Lower Carboniferous according to the customary palæogeographic descriptions, for example, of Koszmat or L. Waagen, the areas submerged and emerged are obtained as shown in Fig. 22. But in this period the South Pole advanced from Cape Colony towards Loanda, that is, in the direction of South America, and the North Pole departed from North America. We thus see the rule confirmed that in front of the pole regression occurs, behind it transgression. In the succeeding period, from the Lower Carboniferous to the uppermost Permian, the poles, according to our earlier representation, nearly reverse their direction


Fig. 22.—Transgression (dotted), regression (shaded), and wandering of the poles between the Lower Devonian and Lower Carboniferous.

of movement: the South Pole wanders from Loanda towards the interior of Australia, and the North Pole approaches North America. The transgressions and regressions shown for this lapse of time are shown in Fig. 23, and the rule is again confirmed. It seems the more significant since the relations in North as well as South America are absolutely reversed. To my knowledge this is the first proof of the correctness of the long postulated law, and the clarity of this result appears to me to be not only a sign of the truth of the displacement theory, but also of the position and movement of the poles assumed by us for this period.

We can make a second similar trial of the transgression rule if we no longer consider the history of the whole earth, but confine ourselves to a limited space. It can be seen on the latitude curve of Central Europe (Fig. 19, on page 110) that Europe approached the pole from the Carboniferous to the beginning of the Jurassic (in front of the pole), from this to the Eocene it departed from it (behind the pole), and thence to the Quaternary approached it very closely again (in front of the pole). The European transgressions and regressions completely correspond throughout.


Fig.23.—Transgression (dotted), regression (shaded), and wandering of the poles between the Lower Carboniferous and Upper Permian.

Regression universally prevailed from the Carboniferous to the beginning of the Jurassic, but then great transgressions set in which created the Jurassic and Cretaceous seas, and which laid a great portion of Europe under water until the Eocene. From this period commenced a striking regression, which led to the complete emergence of Europe. It certainly can be no accident that the rule thus holds so well.[7]

On account of the novelty of the principles involved, we have entered somewhat more fully into the connection between wandering of the pole and transgression than the train of ideas of this book immediately required. What can we now conclude from these facts about the viscosity of the earth? The variations of level, which are produced by these transgressions and regressions, are of the order of magnitude of some hundreds of metres. Thus the crust of the earth may lie by this amount above its position of equilibrium in front of the pole; below it, behind the pole. All these transgressions have the character of shallow seas similar to the North Sea or the Baltic. But the equatorial radius of the earth is about 21 km. greater than the polar. Therefore the wandering of the pole between the Carboniferous and Quaternary, amounting to nearly 90° of arc, must, if the earth had behaved as a rigid body, have elevated Spitsbergen about 21 km. and depressed Central Africa a similar amount beneath the level of the sea. In place of this, as already said, we have only transitory elevations and submergences of some hundred metres. The earth has thus largely adjusted itself to this new position of its axis of rotation; the radius has become about 21 km. shorter beneath Spitsbergen, and 21 km. longer in Central Africa. This obviously can only take place because of flow.

But however clearly these facts testify to the viscosity of the earth, this is doubted by many geophysicists, because they can prove that the earth is about two to three times as rigid at room-temperature as steel (which possesses a viscosity coefficient of 8 × 1011 c.g.s. units). We must consider this in a little more detail. The result is arrived at in three different ways. From the observations of Geiger and Gutenberg on the velocity of earthquake-waves in the core of the earth, it follows that the coefficient of viscosity at a depth of 0.4 radius of the earth is 36 × 1011 c.g.s., whilst for the zone of silicate rocks about 7 × 1011 c.g.s. is obtained. On the other hand, Schweydar[8] found from the elastic tides of the solid earth, which were measured by the horizontal pendulum, the value of the effective tidal rigidity of the earth 18 × 1011, for the centre of the earth 31 × 1011. Thirdly, a viscosity coefficient may also be calculated from the oscillations of the poles. These can be split into two overlapping periods, namely, a forced oscillation of the length of a year, which can be traced, according to Spitaler and Schweydar, to the action of the annual shifting of the atmospheric masses on the axis of inertia, with the chief phenomenon of a free swing of 14 months, which corresponds to a revolution of the rotation pole around the pole of inertia. Assuming a rigid earth, the period of this oscillation should only amount to ten months according to Euler’s theoretical calculations. Newcomb suspected that it may be extended by the yielding of the earth, which permits a partial adjustment of the form of the ellipsoid on the new direction of rotation. Hough and Schweydar calculated from this a coefficient of viscosity of 18 × 1011 in agreement with the result of the tidal observations. Schweydar found, in accordance with the results of seismic research, the value of 7 × 1011 for the zone of silicate rocks of the earth, originally estimated as 1500 km. in thickness,[9] and for the core, probably made of iron, according to Wiechert’s observations on earthquakes, a value of about 20 to 24 × 1011. The difference between these figures is of little importance. It is quite sufficient for our purpose to know that the earth as a whole is more rigid than steel.

Schweydar has also examined the question suggested by the earthquake observations as to whether a fluid magmatic layer exists beneath the earth’s crust: “It appears that a magmatic layer the fluidity of which is only to be compared with that of sealing-wax at room-temperature, and the thickness of which is only 100 km., cannot be present. By calculation, it is seen that the assumption of a liquid layer approximately 600 km. thick, the viscosity coefficient of which is of the order 1013 to 1014, beneath a crust of the earth of thickness 120 km., is in closest agreement with the observed facts.” The viscosity coefficient of sealing-wax at ordinary temperature is of the order of 109, or, in other words, Schweydar finds that the sima beneath the continental blocks is about 10,000 times as rigid as sealing-wax at room temperature.

It is certainly not to be wondered at if these quite reliable results are felt to contradict the ideas developed above on the viscosity of the earth.

The solution of this apparent contradiction lies in the great dimensions of the earth and in the long periods of time which are at disposal for geological changes. This is a point which has been quite insufficiently appreciated in the previous literature, but which is of the greatest importance in geophysics. In the laboratory a small steel model of a sphere behaves in every way as a rigid body. But a steel sphere of the magnitude of the earth flows under the influence of its own attraction, at least if the necessary thousands of years are allowed for it to do so. It is the transition from the prevalence of molecular forces (degree of rigidity) to that of the molar forces (gravity), which is the factor here.[10] Isostasy signifies the predominance of the molar forces, absence of isostasy that of the molecular forces. For this reason, very small heavenly bodies, as many planetary moons, some of the small planets, and, more naturally still, the meteorites, do not possess the spherical shape; for that betokens isostasy. Isostasy prevails on the moon, taken as a whole; the great inequalities of its surface show, however, that the molar forces are there considerably less than on the earth, so that the molecular forces are more prominent. In fact, even the altitude of the mountains is no accidental magnitude, but is essentially determined by the relation of these two forces, a fact indicated by the similar heights of the Alpine peaks, to which A. Penck[11] has drawn attention. The mountain systems thus indicate the extent to which molecular forces could maintain themselves against gravity.

The question, in what manner the mere dimensions of the earth can exert such an influence on the behaviour of its materials need not, therefore, remain unanswered. We know that steel loses its rigidity under such pressures as we can mechanically produce, and becomes plastic. We cannot erect an indefinitely high column of steel without reaching a limit at which the foot of this column begins to flow. If we imagine an entire continental margin of steel, its uppermost portion would certainly remain rigid, but the lower layers would become plastic under the pressure of the mass lying above it, and would flow out laterally. Thus steel is no longer a solid body in such large dimensions as that of the earth. Indeed, it may be said that for such dimensions no solid body exists, and that all bodies have the property of viscid fluidity, but that the times needed for deformation will be different, according to their coefficients of viscosity. On this last point it is very instructive to note that Schweydar arrived at the result that the simasphere is about 10,000 times as rigid as sealing-wax at the temperature of a room. If a stick of sealing-wax be thrown on the floor, it breaks into splintery fragments; but if it be left supported only at two points, a bending can be noticed after some weeks; and after some months the unsupported portions will hang practically vertical. Geologically speaking, sealing-wax is thus of such mobility at ordinary temperatures that we cannot use it at all for the explanation of geological phenomena. If the sima has a viscosity coefficient 10,000 times as large as that of sealing-wax, then a month for the sealing-wax is equivalent to a thousand years for the sima. And this is a period of time which corresponds more with geological changes. We need not therefore draw the conclusion from Schweydar’s figures that the earth, because it has the same viscosity as steel, behaves as if it were a rigid body. This is only the case with impulses of short duration, as with the quickly alternating tides, or still more earthquake-waves, and perhaps also the oscillations of the poles. But as soon as we have to deal with thousands or millions of years instead of seconds, days or years, we must say: “the earth has only the viscosity of steel; it behaves, therefore, as a viscous, fluid body.”

It cannot be in any way denied that these ideas are somewhat paradoxical. But it must not be forgotten that even experiments in the laboratory with viscous, fluid substances appear paradoxical, because they are contrary to usual experience. Pitch, for example, behaves as an absolutely solid body when subjected to blows and percussion, but, given time, it begins to flow under the influence of gravity; a piece of cork cannot be forced through a sheet of pitch, but after a lengthy period its slight buoyancy is sufficient to allow it to rise slowly through the pitch from the bottom of a vessel. Because these things appear paradoxical, the explanation of the flow of glaciers at first presented difficulties, so that special causes, as, for example, regelation (secondary freezing), were thought to be necessary, until the recent observation on the similar flowing polar glaciers, with their low internal temperatures, gave a more correct idea of the viscous fluidity of these objects.

There remains to be mentioned the fact that there are a great number of differently defined coefficients of viscosity, solidity and rigidity. Without going into the matter further, only one example will be given to show what properties of bodies are concerned.

Maxwell calls a body soft if it reacts quickly to an impulse, but only after a certain limit of force has been exceeded; on the other hand, he calls it “a viscous fluid” when it reacts to an infinitely small impulse, although infinitely slowly. “When this continuous alteration of form is only produced by stresses exceeding a certain value, the substance is called a solid, however soft it may be. When the very smallest stress, if continued long enough, will cause a constantly increasing change of form, the body must be regarded as a viscous fluid, however hard it may be. Thus a tallow candle is much softer than a stick of sealing-wax; but if the candle and the stick of sealing-wax are laid horizontally between two supports, the sealing-wax will in a few weeks in summer bend with its own weight, while the candle remains straight. The candle is therefore a soft solid, and the sealing-wax a very viscous fluid.”[12]

Wax behaves in a similar manner to tallow. A wax figure can exist for a century without collapsing, if only the temperature does not attain the melting-point, whilst the same figure worked in sealing-wax would gradually flow away.

In nature there are all transitions between these two extremes of Maxwell, and even the examples given do not really form these extremes. Thus an infinitely small impulse is certainly not sufficient to cause deformation of sealing-wax, but the limit is so low that it begins to flow “of itself,” that is, under its own weight. In any case composite bodies such as form the silicate mantle of the earth must show characters of both kinds. If, therefore, neither sima nor sial can be compared with one of Maxwell’s prototypes, yet in my opinion a comparison with these throws much light on the processes of displacement which are so difficult for our imagination to grasp. A considerable difference is shown between both these substances, which we cannot explain better than by comparing the sima with sealing-wax and the sial with wax or tallow. Sima is the harder material (basalt is the best paving stone!), but nevertheless the most fluid. Sial preserves its form (as continental blocks) so long as the forces remain under the limit, but becomes folded or fractured when this is exceeded.

We have not in the foregoing pages considered the temperature relationships in the body of the earth. These also are of importance with regard to the question of the possibility of displacement. The composite silicate rocks have no sharp melting-points, as the researches of Doelter and Day have shown, but only a range, occasionally very great, of melting temperature. It can be said that diabase melts at 1100° C. and Vesuvian lava at about 1400° to 1500° C. These temperatures apply to atmospheric pressure, so that some 100° C. must certainly be added for a depth of 100 km.[13] On the other hand, the deepest boreholes to-day of Czuchov II. and Paruschowitz V. in Upper Silesia give an increase of temperature of 3.1° C. for each 100 m. depth for the uppermost 2 km. of the earth’s crust.[14] These measurements were carried out in sedimentary rocks which possess a smaller thermal conductivity than igneous rocks, in consequence of which the isotherms therein are closer together. In the primitive rocks of the tunnels of St. Gotthard, Mönch and Simplon the temperature gradient is only 2.2, 2.2 and 2.4° C. for each 100 m. Since here, again, an abnormally slight gradient may be assumed on account of the convex form of the mountain, 2.5° C. per 100 m. can be considered as a good average value for the continental blocks. Corresponding measurements cannot naturally be carried out in the sima. If Friedländer’s[15] statement is correct, which finds for hypabyssal igneous rocks, a smaller thermal conductivity and a temperature gradient of 6° C. for 100 m., then, by rectilinear extrapolation, at 9 km. depth in the continental block (beneath the sea-level), the same temperature (about 230° C.) would prevail as under the ocean. Beneath this level, however, the rocks below the ocean would be hotter than the strata at the same depth on the continental block. Friedländer’s figures are, of course, reliable only to a small extent. But a slight difference of thermal conductivity of this character is sufficient to compensate for the fact that on the floor of the ocean at 5 km. below sea-level a temperature of 0° C. prevails, whilst the continental blocks at the same depth have already a temperature of about 135° C.[16]

By the use of linear extrapolation at a depth of 100 km. in the continental block, a temperature of 2500° C. is reached, a figure far above the melting-point of igneous rocks. It is universally agreed, however, that such a rectilinear extrapolation is inadmissible. But unfortunately we do not know the law by which the temperature alters with depth. Probably in the first place it is dependent on the distribution of radium in the earth’s crust. For the temperature of the centre of the earth, which, in contrast to the earlier much higher estimates, is assumed to be about 3000° to 5000° C., we consequently possess only very scanty fundamental information. Still it is probable that temperatures between 1000° and 2000° C. are to be expected at 100 km. depth, so that the assumption that a temperature of about the melting-point is reached on the under-margin of the continental blocks is not contradictory to our previous ideas.

It must certainly not be thought that this melting temperature is at the same depth all over the world, and that the depth is constant at all times. On both these questions the phenomenon of “granite fusion” is very instructive. The observations by Cloos in South Africa has freed its significance from previous doubts, and shown that the fusion-isotherms can at times penetrate up to the surface of the earth. It is probable that to these places with an abnormally high position of the fusion isotherm are opposed others with an abnormally deep position. We do not know the causes of the variations in the course of time. In this case also the radio-active transformations perhaps play a part.

In any case, the mobility of the sima must be increased by high temperature. We do not know, yet, however, how these relations vary with the depth, and whether there is especially a zone of greatest mobility at the under surface of the continental blocks.

But in any case the separation of the blocks of sial will be favoured by the fact that, according to Doelter,[17] the melting-point of sial rocks is in general 200° to 300° higher than that of the sima, so that magmatic sima and solid sial could exist side by side at the same temperature. The fact that the molten sial is more viscous than molten sima also favours it.

Meanwhile, as I myself think, one cannot yet attach any decisive importance to the whole question of temperature, especially since Schweydar’s results show that the sima possesses a viscosity, even under the continents, which is 10,000 times greater than that of sealing-wax at room-temperature. Probably all processes would play a very similar rôle, even if the melting temperature of the silicates were never reached.

  1. Rudzki, Physik der Erde, p. 229. Leipzig, 1911.
  2. W. Köppen, “Das System in den Klimawechseln und Bodenbewegungen des Quartärs im Ostseegebiet,” Zeitschr. f. Gletscherkunde, 1922.
  3. Sir William Thompson, Report of Section of Mathematics and Physics, p. 11. Report of British Association, 1876.
  4. Rudzki, loc. cit., p. 209.
  5. Schiaparelli, “De la rotation de la terre sous l’influence des actions géologiques” (Mém. près à l’observatoire de Poulkova à l’occasion de sa fête semiséculaire), pp. 1–32. Petrograd, 1889.
  6. The similarly very rapid polar wandering in the Tertiary is less suitable for the purpose, because then the continents had already emerged to a greater extent; the area of continental shelf has become so small that the alterations of its boundary are not so striking as in more ancient periods, when much greater portions of the continental blocks lay beneath the water.
  7. Of course, not all fluctuations of level will be explained in this manner. Another cause, the depression through the loading with inland ice, has already been described. Moreover, the formation of great polar ice-caps must have as a consequence a marked general depression of the surface of the ocean, and the melting will correspond to an elevation of the ocean. Since periods have been detected in the earth’s history where at one pole at least no ice-sheet existed (because it lay in the middle of the Pacific), there must have been on these grounds not insignificant fluctuations of sea-level. Nevertheless, all the great features in the variation of transgressions must be traced back directly to the wanderings of the poles.
  8. W. Schweydar, Lotschwankung und Deformation der Erde durch Flutkräfte gemessen mit zwei Horizontalpendeln im Bergwerk in 189 m. Tiefe bei Freiberg i. Sa., Zentralbureau d. Internat. Erdmess., N.F., Nr. 38. Berlin, 1921.
  9. The school of Wiechert (B. Gutenberg, “Über Erdbebenwellen,” Nachr. d. Ges. Wiss. zu Göttingen, 1914) finally found from the propagation of earthquake-waves four surfaces of discontinuity, namely, at the depths of 1200 km., 1700 km., 2450 km., and 2900 km., of which the first and last appear most marked, so that the best assumptions at present are an approximately 1200 km. thick silicate covering, a median layer about 1700 km. thick, and a core of the earth measuring 3500 km. in radius.
  10. “Les forces molaires l’emportent sur les forces moléculaires” (Loukaschewitsch, Sur le mécanisme de l’écorce terrestre et l’origine des Continents, p. 7. Petrograd, 1910).
  11. A. Penck, “Die Gipfelflur der Alpen,” Sitz.-Ber. d. Pr. Ak. d. Wiss., pp. 256–268. Berlin, 1919.
  12. J. C. Maxwell, Theory of Heat, 2nd edition, p. 274, 1872.
  13. In all substances which become of greater density on solidification, and therefore sink in their own liquid, the melting-point rises a little with great increase of pressure. Probably most rocks belong to this category. The melting-point of diabase is elevated, according to Barus, about 0.025° for each atmospheric pressure, a result which Vogt corrects to 0.005°. On the other hand, the melting-point is depressed a little by greatly increasing pressure in the case of all substances that become specifically lighter on solidification and thus float on their own liquids. Ice, in particular, belongs to this group as well as also iron and probably all other metals.
  14. Michael and Quitzow, “Die Temperaturverhältnisse im Tiefbohrloch Czuchow in Oberschlesien,” Jahrb. d. Kgl. Preusz. Geol. Reichsanstalt, 1910.
  15. J. Friedländer, Beitr. z. Geophys., 11, Kl. Mitt., pp. 85–94, 1912.
  16. In this manner all hypotheses which would trace back the depression of the oceanic basins to cooling by the cold abyssal water would fall to the ground, together with the objection that the oceanic floor must be more solid than the continental block on account of the lower temperature.
  17. C. Doelter, “Petrogenesis,” Die Wissenschaft, 13. Brunswick, 1906.