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It is no doubt a somewhat difficult problem to determine accurately the total amount of force exercised by gravity on the ocean; but for our present purpose this is not necessary. All that we require at present is a very rough estimate indeed. And this can be attained by very simple considerations. Suppose we assume the mean depth of the sea to be, say, three miles. The mean depth may yet be found to be somewhat less than this, or it may be found to be somewhat greater; a slight mistake, however, in regard to the mass of the ocean will not materially affect our conclusions. Taking the depth at 3 miles, the force or direct pull of gravity on the entire waters of the ocean tending to the production of the general circulation will not amount to more than that of gravity, or only about that of the attraction of the moon in the production of the tides. Let it be observed that I am referring to the force or pull of gravity, and not to hydrostatic pressure.
The moon, by raising the waters of the ocean, will produce a slope of 2 feet in a quadrant; and because the raised water sinks and the level is restored, Mr. Ferrel concludes that a similar slope of 2 feet produced by difference of temperature will therefore be sufficient to produce motion and restore level. But it is overlooked that the restoration of level in the case of the tides is as truly the work of the moon as the disturbance of that level is. For the water raised by the attraction of the moon at one time is again, six hours afterwards, pulled down by the moon when the earth has turned round a quadrant.
No doubt the earth's gravity alone would in course of time restore the level; but this does not follow as a logical consequence from Mr. Ferrel's premises. If we suppose a slope to be produced in the ocean by the moon and the moon's attraction withdrawn so as to allow the water to sink to its original level, the raised side will be the heaviest and the depressed side the lightest; consequently the raised side will tend to sink and the depressed side will tend to rise, in order that the ocean may regain its static equilibrium. But when a difference of level is produced by difference of temperature, the raised side is always the lightest and the depressed side is always the heaviest; consequently the very effort which the ocean makes to maintain its equilibrium tends to prevent the level being restored. The moon produces the tides chiefly by means of a simple yielding of the entire ocean considered as a mass; whereas in the case of a general oceanic circulation the level is restored by a flow of water at or near the surface. Consequently the amount of friction and molecular resistance to be overcome in the restoration of level in the latter case is much greater than in the former. The moon, as the researches of Sir William Thomson
show, will produce a tide in a globe composed of a substance where no currents or general flow of the materials could possibly take place.
Pressure as a Cause of circulation.-We shall now briefly refer to the influence of pressure (the indirect effects of gravity) in the production of the circulation under consideration. That which causes the polar column C to descend and the equatorial column W to ascend, as has repeatedly been remarked, is the difference in the weight of the two columns. The efficient cause in the production of the movement is, properly speaking, gravity; cold at the poles and heat at the equator, or, what is the same thing, the excess of heat received by the equator over that received by the poles is what maintains the difference of temperature between the two columns, and consequently is that also which maintains the difference of weight between them. In other words, difference of temperature is the cause which maintains the state of disturbed equilibrium. But the efficient cause of the circulation in question is gravity. Gravity, however, could not act without this state of disturbed equilibrium; and difference of temperature may therefore be called, in relation to the circulation, a necessary condition, while gravity may be termed the cause. Gravity sinks column C directly, but it raises column W indirectly by means of pressure. The same holds true in regard to the motion of the bottom-waters from C to W, which is likewise due to pressure. The pressure of the excess of the weight of column C over that of column W impels the bottom-water equatorwards and lifts the equatorial column. But on this point I need not at present dwell, as I have in my last paper entered into a full discussion as to how this takes place*.
We come now to the most important part of the inquiry, viz. how is the surface-water impelled from the equator to the poles? Is pressure from behind the impelling force here as in the case of the bottom-water of the ocean? It seems to me that, in attempting to account for the surface-flow from the equator to the poles, Dr. Carpenter's theory signally fails. The force to which he appeals appears to be wholly inadequate to produce the required effect.
The experiments of M. Dubuat, as already noticed, prove that any slope which can possibly result from the difference of temperature between the equator and the poles is wholly insufficient to enable gravity to move the waters; but it does not necessarily prove that the pressure resulting from the raised water at the equator may not be sufficient to produce motion. This point will be better understood from the following figure, where, as
* Phil. Mag. for October 1871.
before, PC represents the polar column and E W the equatorial column.
It will be observed that the water in that wedge-shaped portion W CW' forming the incline cannot be in a state of static equilibrium. A molecule of water at O, for example, will be pressed more in the direction of C than in the direction of W', and the amount of this excess of pressure towards C will depend upon the height of W above the line C W'. It is evident that the pressure tending to move the molecule at O towards C will be far greater than the direct pull of gravity tending to draw a molecule at O' lying on the surface of the incline towards C. The experiments of M. Dubuat prove that the direct force of gravity will not move the molecule at O'—that is, cause it to roll down the incline W C; but they do not prove that it may not yield to pressure from above, or that the pressure of the column W W' will not move the molecule at O. The pressure is caused by gravity, and cannot, of course, enable gravity to perform more work than what is derived from the energy of gravity; it will enable gravity, however, to overcome resistance, which it could not do by direct action. But whether the pressure_resulting from the greater height of the water at the equator due to its higher temperature be actually sufficient to produce displacement of the water is a question which I am wholly unable to answer.
If we suppose 9 feet to be the height of the equatorial surface above the polar required to make the two columns balance each other, the actual difference of level between the two columns will certainly not be more than one half that amount, because, if a circulation exist, the weight of the polar column must always be in excess of that of the equatorial. But this excess can only be obtained at the expense of the surface-slope, as was shown at length in my last paper. The surface-slope probably will not exceed more than 4 feet or 4 feet. Suppose the ocean to be of equal density from the poles to the equator, and that by some means or other the surface of the ocean at the equator is raised, say, 4 feet above that of the poles, then there can be little
doubt that in such a case the water would soon regain its level; for the ocean at the equator being heavier than at the poles by the weight of a layer 4 feet in thickness, it would sink at the former place and rise at the latter until equilibrium was restored, producing, of course, a very slight displacement of the bottom-waters towards the poles. It will be observed, however, that restoration of level in this case takes place by a simple yielding, as it were, of the entire mass of the ocean without displacement of the molecules of the water over each other to any great extent. In the case of a slope produced by difference of temperature, however, the raised portion of the ocean is not heavier but lighter than the depressed portion, and consequently has no tendency to sink. Any movement which the ocean as a mass makes in order to regain equilibrium tends, as we have seen, rather to increase the difference of level than to reduce it. Restoration of level can only be produced by the forces which are in operation in the wedge-shaped mass W C W', constituting the slope itself. But it will be observed by a glance at the figure that, in order to the restoration of level, a large portion of the water W W' at the equator will require to flow to C, the pole.
According to the general vertical oceanic circulation theory, pressure from behind is not one of the forces employed in the production of the flow from the equator to the poles. This is evident; for there can be no pressure from behind acting on the water if there be no slope existing between the equator and the poles. Dr. Carpenter not only denies the actual existence of a slope, but denies the necessity for its existence. But to deny the existence of a slope is to deny the existence of pressure, and to deny the necessity for a slope is to deny the necessity for pressure. That in Dr. Carpenter's theory the surface-water is supposed to be drawn from the equator to the poles, and not pressed forward by a force from behind, is further evident from the fact that he maintains that the force employed is not vis a tergo but vis a fronte (Proc. Roy. Geog. Soc. Jan. 9, 1871, § 29). [To be continued.]
XV. On Quartz, Ice, and Karstenite. By W. H. MILLER, M.A., F.R.S., Professor of Mineralogy in the University of Cambridge*.
AMONG the minerals presented to the University by H. W.
Elphinstone, Esq., are two crystals of quartz associated with chlorite, apparently from the same, but unknown, locality.
* Communicated by the Author.
Each of these crystals exhibits one face of a rhombohedron, having angles which differ too widely from those of the forms described by Des Cloizeaux in his Manuel de Minéralogie to admit of identification with any of them, and therefore has probably never been observed before.
The larger of the two crystals, besides the supposed new face, which will be denoted by the letter 5, has the forms 2 II, 100, 122, 8īī, 1011, 142, a41 2. The faces 5, 100 are rather uneven, the bisection of the images of the bright signal being uncertain to the extent of about 2' in the former and rather less in the latter. Three observations of the angle between these faces gave 30° 23'5, 30° 23'-5, 30° 24' respectively.
The other crystal has the forms 2 Īī, 100, 122, a412, a 41 2 in addition to 5. This last face is very even and bright; but 100 is rather imperfect. The observed angle between these faces lies between 30° 22'2 and 30° 28'4.
Of the faces given by Des Cloizeaux, those which most nearly approach the position of 5 make with 100 angles of 29° 26', 30° 4, 30° 44', having for their symbols 1144, 833, 1355 respectively. In order to obtain more probable values of the indices of 5, let us suppose the angle between 100 and 5 to be 30° 24', hk k the symbol of 5, and D, T the angles which the axis of the rhombohedron makes with normals to the faces 100, hkk. Then, since D=51° 47' and T-D=30° 24', we have T=82° 11'.
The converging fractions approximating to this number are:—
5 6 17 23 86
The first two fractions give the faces 11 44, 135 5 already noticed; the third a face 37 14 14, making an angle of 30° 18' with 100, and therefore not very probable; the fourth a face making with 100 an angle of 30° 25', which, taking into account the imperfections of the faces of the crystal, agrees sufficiently well with the observations. The resulting symbol is
50 19 19.
The fraction obtained by adding the numerators and denominators of the third and fourth fractions, leads to the symbol 29 11 11. The face of which this is the symbol makes with 100 an angle of 30° 22', and is therefore hardly so probable as