Popular Science Monthly/Volume 16/January 1880/Why Do Springs and Wells Overflow? II
|WHY DO SPRINGS AND WELLS OVERFLOW?|
By JOSEPH J. SKINNER, Ph. D.
THE commonly accepted answer to the above question is that the water of springs and of flowing wells is forced out by the pressure of other water at some higher level, this pressure being transmitted to the water of the spring or well through continuous underground channels, either containing water alone or water filling the interstices of some porous material, these waters being the product of rainfall, dew, and snow. But this answer has sometimes been found not to satisfy a certain class of minds; and, as long ago as 1834, Arago thought it not beneath him to publish in the "Annuaire du Bureau des Longitudes" for 1835 a considerable essay, in which he shows conclusively that the rise and flow of water in springs and artesian wells are sufficiently explained by the cause assigned above. Further on will be found a translation of some passages from this elegant essay.
Arago was so certain of the correctness of his views, that from his knowledge of the geological formations of France he not only foretold that potable water would be found by boring an artesian well at Grenelle, near Paris, but that the water would rise and overflow the surface. In 1833 he succeeded in getting the French Government to undertake the boring of this well, and although about eight years were required to complete it and it was for some time in danger of being abandoned, his urgent representations prevailed in obtaining a further prosecution of the work, and in 1841 his foresight was rewarded with the splendid success familiar to the public. Modern engineers, in judging of the chances of getting flowing water from an artesian well in any particular locality are guided by the same general theory as that held by Arago.
But a writer in the November number of this magazine combats this theory, "not merely from speculative motives, but in the interest of public health," and offers an explanation of his own, involving a "newly discovered force" which "not only may, but which positively must, force waters out of springs at high elevations." This "new force" as it is called in another sentence, is "the resultant of the earth's centripetal and centrifugal forces," and it produces springs and flowing wells by acting "impulsively upon the subterranean water deposits," tending "to force them into and though the natural channels of the earth's crust." It is proposed here to examine Mr. Green's article in some detail, in connection with a consideration of the generally accepted theory of springs and flowing walls.
A peculiarity in one or two of Mr. Green's quotations led me to verify them in the works cited by him, and in doing so I could but notice that he had apparently made a number of slips of the pen, which, though perhaps unimportant in themselves, yet give indication of some carelessness. For instance, in quoting from "Littell's Living Age," he changes Colne to Coln, Watford to Wetford, Pole's Hole to Pales's Hole, Dickenson to Dickinson, Canstadt to Constadt, Bruckman (which should have been Bruckmann) to Buckmann, and predicted to discovered. Another of his quotations from the same source is this, "The artesian well at Tours rose with a jet that sustained a cannon." The original said, "An artesian well at Tours rose with a jet that sustained in the air a cannon-ball." As the account of Professor Buckland's address given in "Littell's Living Age" was not a verbatim report, even this statement seemed to me likely enough to have suffered a slight change at the hands of the reporter; so I went one step further back, to Professor Buckland's "Bridgewater Treatise," of which he spoke in his address, where I find this statement: "At Perpignan and Tours, M. Arago states that the water rushes u]) with so much force, that a cannon-ball placed in the pipe of an artesian well is violently ejected by the ascending stream." Something like this is probably what Professor Buckland said in his address; and the difference between the ejecting of a ball from a pipe and the sustaining of it in the air may have seemed to the reporter of the address of slight consequence; but when you go from ejecting a hall from a pipe to the sustaining of it in the air, and then to the sustaining of a cannon, one is reminded of the man who was said to have thrown up something as black as a crow, and as the story passed from mouth to mouth he was finally declared to have thrown up three black crows.
On page 76 of the November "Popular Science Monthly," in discussing Mr. Howell's article on the "Subterranean Outlet" to the Upper Lake region, Mr. Green says of Mr. Howell that "having shown that Lake Superior at its surface is 600 feet above the Atlantic and at its bottom 573, and Ontario to be 235 feet above, with the same depth as Superior, he proceeds to make the following significant statement." This quotation would make Lakes Superior and Ontario each only twenty-seven feet deep, which is evidently a mistake; and on referring to Mr. Howell's article in "Scribner's Monthly" we find that he did not say that the bottom of Lake Superior is 573 above the Atlantic, but that "we find its bed descending 573 feet below the level of the Atlantic"; neither did he say that Ontario has the same depth as Superior, but that it "descends to an equal distance below the level of the Atlantic."
But let us begin at the beginning of Mr. Green's article, and see how he starts off. After a few words of introduction, he quotes from the account of Professor Buckland's address a few sentences ending as follows: "At Brentford, England, there were many wells that continually overflowed their orifice, which is a few feet only above the Thames. In the London wells the water rises to a less level than in those at Brentford." Mr. Green then says: "By hydrostatic pressure, the Professor, of course, means a head, i. e., that the water flowed to these wells from a higher point. If this rise were due to hydrostatic pressure, why did the water rise to a lower level at London than at Brentford among the hills?" Now, Professor Buckland's statement, just quoted, makes the orifice of the Brentford wells "a few feet only above the Thames," and Mr. Green makes his first imaginary difficulty by placing these wells "among the hills." He then quotes largely from Professor Buckland's address, and afterward exclaims: "Wells to supply London, the Professor thinks, must not be utilized to draw water from a depth of thirty or forty feet, because it would cut off the supply due to the rains which do not sink deeper than three feet!" But the Professor had not said that "rains do not sink deeper than three feet." He had, indeed, said that one intelligent manufacturer, Mr. Dickenson, had found by a rain-gauge that "except in December, January, and February, rain-water rarely descends more than three feet below the soil," etc. This statement apparently convinces Mr, Green that rain-waters never get deeper into the earth than three feet. But there are soils and soils. And Professor Buckland did not neglect to point out their differences. He said, "The rain that falls on the uncovered chalk within the area of these basins (like that of London) descends, by countless crevices, into the lower regions of the chalk strata," etc. And even Mr. Dickenson's observations during many years had shown him that, in spite of the fact that in the drier part of the year the rain-waters rarely sank into his soil more than three feet, yet the quantity of summer water in the river Colne varied with the rain in the preceding winter. He probably knew, therefore, that these winter rains must be largely absorbed by the sponge-like chalk formations in the neighborhood, and slowly work their way downward many feet, to issue gradually at lower points in the form of springs to feed the river in summer.
Mr. Green quotes further from Professor Buckland's address, showing the great value of artesian wells in Wurtemberg, and then goes on: "From which quotations it appears that the Professor is in a remarkable position. At Wetford" (sic) "these wells could not be utilized because the river-supply of the Coln" (sic) "would be exhausted; but in Germany they were a new and important source of supply to the rivers themselves." The Professor's position may be remarkable, but it is certainly reasonable. For it is a well-known fact that in some localities, that of Tours for one, as stated by Arago, artesian wells may be bored to any number hitherto tried without sensibly affecting the flow of those first sunk in the immediate neighborhood, while in other localities every new well either diminishes the flow of old wells or makes the level of the water in them sink. This last is the case near London. The "American Cyclopædia," article "Artesian Wells," says: "In the vicinity of London it is observed that the height to which the water rises diminishes as the number of wells is increased. In 1838 the supply of water from them was estimated at six million gallons daily, and in 1851 at nearly double the amount, and the average annual fall of the height of the water is about two feet." Professor Buckland had also stated that "Mr. Clutterbuck demonstrated, by a long-continued series of measurements of the water in the chalk-hills of Hertfordshire, near Watford, that every drop of water taken from that neighborhood would have been abstracted from the summer and autumn supplies of the river Colne." Hence, even if the wells in Germany were, as stated rather strongly by Mr, Green, "a new and important source of supply to the rivers themselves," it would not alter the fact, shown by experiment, that the proprietors of mills on the river Colne, and the owners of adjacent water-meadows, would have been robbed of rights which they had inherited from time immemorial, by drawing the water-supply of the great city of London from wells in the chalk formations of Hertfordshire.
But Mr. Green's two propositions that differ most essentially from the commonly accepted theory of artesian wells are—1. That the flow of water from them is not due to pressure transmitted from water at a higher level, but to "some force not yet identified"; and, 2. That the supply of water for such wells, and indeed for ordinary springs, comes from "subterranean waters, seldom if ever influenced by rains" (p. 75, line one). Mr. Green identifies the required force as "the resultant of the earth's centripetal and centrifugal forces," and, having found that the tendency of this resultant is to force water up, wherever there is an opening upward in the earth's crust, of course it is necessary to suppose that there is a plenty of subterranean water already down. He seems to think it entirely unnecessary to suggest any means of replenishing the supply of this subterranean water, or even to imagine that it could ever need replenishing.
Listen to Mr. Green: "Imagine the 'majestic column' at Grenelle rising thirty feet high, and the overflow in the other cases being due to hydrostatic pressure—i. e., due to the fact that all these immense floods were the result of a flow from some other higher bodies of water." Ordinary people will find it as easy to imagine this as to suppose that these floods are the result of flow from lower bodies of water unconnected with higher ones. But he goes on: "Why did it not occur to Professor Buckland that, however high and abundant the source, such drains must of necessity have sooner or later exhausted the supply, if no equivalent streams were flowing into that also? But suppose this" (sic) "to be so, whence could come the higher head to flow into and supply that in turn? Carry this on until a flow is secured from the highest land on the earth, and then whence comes the flow to supply that?" This is beautiful. Why did it not occur to Mr. Green that, however low and abundant the source, such drains must of necessity have sooner or later exhausted the supply if no equivalent streams were flowing into that also? But suppose this to be so, whence could come the lower head to flow into and supply that in turn? Carry this on until a flow is secured from the center of the earth, and then where are you?
In another place (p. 81) Mr. Green says: "Suppose it had been fully proved that a particular overflowing spring was caused by hydrostatic pressure, it would still remain to be accounted for how the water got to that higher point. This can best be done by the force demonstrated," etc. But supposing, if you can suppose, that a particular overflowing spring were caused by Mr. Green's "newly discovered force" acting on a lower body of water, it would still be for him to show how, according to his theory, the water got to that lower point. His position plainly is (see p. 81), that if any openings exist between bodies of water imprisoned in the earth's crust and the surface of the earth, these waters, unless entirely isolated bodies, would as a rule flow upward. If there were millions of cubic miles of water in accessible subterranean reservoirs, and no drain on them but that caused by the wells made by man, the supply might be considered "ample for all practical purposes," no matter how it got there or what forced the water up; but Mr. Green argues that not only flowing springs but the bulk of the waters of the rivers St. Lawrence, "Ganges, Nile, Indus, Senegal, Rhine, Rhône, Vistula, Elbe, Loire, Gaudiana, Po, Adige, Swale, Tay, Severn, Don, Monongahela, Platte, Missouri, and numerous others" must be derived from a subterranean water-supply, which, he says (p. 77), "is known to be constant, and has always been so." One would think that rivers like those mentioned, flowing for centuries, if fed by a subterranean water-supply, would ultimately make a serious drain on the subterranean reservoirs; but, although Mr. Green's theory does not admit the possibility of any water getting back into these reservoirs, rivers and wells still flow.
After giving Professor Buckland's illustration of the theory of artesian wells, in which he likens the case in nature to a layer of sand and water between two saucers, Mr. Green says, "Should these exceptional and assumed conditions occur in nature, the result would be substantially as indicated." But we know that similar conditions do occur, and not very rarely either. He continues, "But, as will be seen at a glance, the flow from a well sunk under such circumstances would be limited to the amount of water between the two saucers, and this will be limited to the quantity of rainfall." This is very true. He adds, "Since flowing wells and springs are seldom if ever thus limited, we infer that the case supposed does not occur." On the contrary, we have every reason to believe that flowing wells and springs are almost always thus limited. Mr. Dickenson's observations, already quoted by Mr. Green, proved that the quantity of summer water in the river Colne varied with the rain in the preceding winter. In every particularly dry summer springs by the thousand are entirely dried up, and the flow from the majority of others is greatly diminished. On the other hand, in wet seasons all but the most extraordinary springs have their flow increased. In some geological formations increase of flow occurs very soon after the beginning of rains. Arago states as the uniform observation of miners, especially those of Cornwall, that in mines situated in the midst of certain limestones water increases in the deepest drifts a very few hours after it has begun to rain on the surface of the earth. He also refers to springs on the coast which gush out from vertical cliffs of chalky limestone, which in the same way increase largely in strength immediately after rain.
That artesian wells are not sensibly affected by particular rainstorms is no proof that they are not ultimately supplied by rains, but only shows that the quantity of water furnished by the wells is exceedingly small compared with the total quantity at any time in the layer of porous material tapped by the wells. Such layers, between two saucer-like formations of impermeable matter, would generally have some points of their outcrop at a lower level than others. At these low points of the outcrop natural springs would occur, which would have a flow more or less constant in proportion to the extent and height of the porous layer above them, and their flowing would continually tend to draw the level of the water in the porous layer down to their own altitude. Rains, falling on the exposed edges of the porous layer, would in great part be absorbed, and, gradually trickling through the pores, be slowly discharged by these natural springs. If an artesian well had its opening into the porous layer far below the lowest of these natural outlets, no ordinary rain would sensibly change the effective head of water that supplied it; but, if rains should cease entirely, the springs and the well would ultimately stop flowing. In a work on "Water-Supply Engineering," which contains much valuable information, Mr. J. T. Fanning says of such a geological formation as the common theory of artesian wells assumes, that when first discovered it "is invariably full to its lip or point of overflow. Its extent may be comparatively large, and its watershed comparatively small, yet it will be full, and many centuries may have elapsed since it was molded and first began to store the precious showers of heaven. A few drops accumulated from each of the thousand showers of each decade may have filled it to its brim many generations since; yet this is no evidence that it is inexhaustible. If the perennial draught exceeds the amount the storms give to its replenishment, it will surely cease, in time, to yield the surplus." (Compare with this the extract given above from "The American Cyclopædia," showing an annual sinking of two feet in the level of the water in the artesian wells near London.)
Mr. Green can not account for the flow of streams from the mountain-region of Pennsylvania and from Lake Chautauqua without the intervention of his "newly discovered force." He quotes approvingly a statement that "it is a wonder to the unpracticed observer where the water-supply of Chautauqua Lake comes from." "Unpracticed observer," indeed! But the practiced observer will tell you without hesitation that the water-supply comes from the clouds. Mr. Fanning (op. cit.) states, as the estimate from experiments, that "in the Eastern and Middle United States the evaporation from storage reservoirs, having an average depth of at least ten feet, will rarely exceed sixty per cent, of the rainfall upon their surface." It follows that any natural exposed basin, under these circumstances, would surely fill up, just from the rains on its surface, if there were not some outlet for the water. Mr. Fanning gives the mean annual rainfall at Fredonia, New York, a few miles from Lake Chautauqua, as 36·55 inches. If we assume that the lake has an area of forty square miles, and take the annual rainfall on its surface at three feet in depth, the total volume of this rainfall would be 3,345,408,000 cubic feet. Supposing that sixty per cent, of this is lost by evaporation, there will yet remain in average years 1,338,163,200 cubic feet of water to be somehow disposed of, which is more than would supply a stream eight feet wide and one foot deep, running for a year at the rate of three and a half miles per hour. Besides the rain falling directly on the surface of the lake, a calculation of the area of the land around it, at a higher elevation than its water-level, would undoubtedly show, no matter what unpracticed observers might anticipate, that the rain-water known to fall on this area would be ample to supply all the springs that flow into the lake, and leave a good margin of surplus to evaporate from plants and soil, and to filter away into the earth.
It seems as if Mr. Green must be somewhat imaginative when he says that, "from the highest mountains in the world—the Himalayas—out of their highest points, great cataracts and streams have poured and still do pour," etc. Has any man ever been anywhere near the highest points of the Himalayas to verify such a statement? I translate the following from Arago's work already mentioned:
"The argument chiefly depended upon by those who felt obliged to seek the origin of subterranean waters in the precipitation which intensely hot aqueous vapors, coming from central regions, had experienced at the moment of their contact with the cold, earthy layers near the surface, was drawn from a fact well worthy of examination: I mean the pretended existence of tolerably abundant springs at the summit, at the culminating point, of some mountains. Our little Montmartre itself figured in this polemic. There was, indeed, upon this hillock, a spring (perhaps it still exists) which was hardly sixteen metres (fifty feet) below its highest part. No water, it was said, could constantly feed a spring thus placed, without coming from beneath in the state of vapor. Upon examination, however, it was found that the portion of Montmartre above the spring, and which could consequently transmit its waters by the method of simple interior draining, was about five hundred and eighty-five metres long and one hundred and ninety-five metres wide. Now, the mean volume of rain which falls in Paris upon such an extent of ground, between the 1st of January and the 31st of December, much exceeds the quantity of water which the little spring in question annually yielded.
"It was necessary, then, to seek for the difficulty at another point.
"This was believed to have been found in a locality not far from Dijon; but there as well, in spite of appearances, the rain-waters received on the portion of land overlooking the spring could amply suffice for its supply."
After referring to the former ignorance of people concerning the quantity of rain, of dew, and of snow, falling in different regions, Arago continues: "For example, people did not believe that the basin of the Seine. . . . received annually by rain a quantity of water equal to the tribute which the Seine bears to the sea in the same space of time. Perrault and Mariotte first studied the question experimentally, and they found, as is usual in such cases, that the vague conceptions of their predecessors were precisely the opposite of the truth. . . . The volume of water which passes yearly under the bridges of Paris is hardly the third of that which falls in rain into the basin of the Seine. Two thirds of that rain either return into the atmosphere by evaporation, or sustain vegetation and the life of animals, or drain into the sea by subterranean passages,"
Without insisting further on the fact that the rain-waters, dews, and snows falling on higher grounds must be sufficient to account for all flowing springs and wells (except, possibly, such cases as the geysers), let us see how Mr. Green's subterranean water-deposits are to be driven to the surface of the earth by his "newly discovered force." Why, by making the earth's centrifugal force act in the direction of the tangent to the earth's surface, and then getting the resultant of this force and of gravity! Further, since the question of the relative intensities of these two forces "does not enter into the problem," you may assume that they are equal, and thus you will find that "the direction of the resultant itself is, say, 45° from the direction of the force of gravity. . . . Moreover, since the resultant has been shown" (by saying that the diagonal either of a square or of a parallelogram is longer than either of its sides) "to be greater under all circumstances than gravity, certainly the vast aggregations must also be greater than the aggregated gravity, and will be able to overcome it under the conditions stated. . . . The intensity of the centrifugal force will increase with the distance from the center of the earth, while gravity will decrease; the resultant will also increase. Thus we find the strongest and most abundant overflows at the tops of mountains or on high plateaus."
As a specimen of mechanical exposition this is almost unique, but it is too ludicrous to mislead. In point of fact, as every schoolboy ought to know, the centrifugal force due to the earth's rotation, on a particle at any place on the earth, does not act in the direction of the tangent to the earth's surface, but in the outward direction of the radius of the circle of latitude of the place; a diagonal of a parallelogram is frequently shorter than either of its sides; the centrifugal force acting on a particle, due to the rotation of the earth, is never more than about the 289 part of the force of gravity; the direction of the resultant of this centrifugal force and of gravity is always very nearly that of gravity; the intensity of this resultant is always less than that of gravity; and instead of increasing with the distance from the center of the earth it decreases. Perhaps these are points that make no difference in the value of Mr. Green's theory; but still they are worth the consideration of any one who proposes by contraries to upset the doctrines of such men as Arago, Faraday, Garnier, and Halley.
Not even the wonderful fact mentioned by Mr. Green, that "by inclosing an overflowing spring tightly, and allowing the inclosure to be terminated by a tube with an opening carried to a level below the fountain, the flow was increased"—not even this will overthrow the principles of mechanics, as any one who ever understood a siphon would know. Mr. Green says, "the flow was increased because the channel was increased, and the resultant of the natural forces with it." But if the resultant increases with the distance from the center of the earth, then why could he not increase the flow still more by running the tube to a great height above the fountain instead of below it? But even Mr. Green would hardly expect to increase the flow by such means. For it is well known that by confining the water of an artesian well to a tube in which it must rise above the ground, the natural flow is rapidly diminished as the height of the tube increases. The "American Cyclopædia" says: "The flow from this well (at Passy, two miles from Grenelle) began slowly, but on September 27th (three days after striking the water) had reached over 5,500,000 gallons per day. The yield at the mouth was greatly decreased when raised through a tube twenty-five feet high; a like result followed at Grenelle, where the yield was 440 gallons per minute at the surface, but decreased to 135 gallons when forced through a tube thirty-three feet high." Mr. Green will have to charge this great decrease of flow to something besides increase of friction; for it is easy to see that, if the tube were extended up just to the point to which the water would rise without flowing out, there would then be no friction. In fact, the laws of hydraulics and hydrostatics have something to do with the subject of artesian wells.
I have already mentioned some inaccuracies of statement in Mr. Green's discussion of Mr. Howell's article in "Scribner's Magazine." Mr. Green, finding that the difference of level between the surfaces of the water in Lakes Superior and Ontario is three hundred and sixtyfive feet, becomes certain that there can be no subterranean water connection between these lakes; for, he says, "If this channel exists as supposed, the surfaces of these lakes would find a common level, instead of a difference of three hundred and sixty-five feet"! Here is where Mr. Green should have brought in his ideas on friction, and have studied Professor Buckland's address more closely. In that address it is stated that "the surface-line of any subterranean sheet of water may be ascertained by measuring a series of wells at distant intervals along the dip of the stratum under examination. . . . Mr. Clutterbuck had further observed that the surface-line of subterranean sheets of water was not horizontal, like the surface of a lake, but inclined at a rate varying from fourteen to twenty feet per mile, in consequence of friction caused by the particles of the strata through which those sheets of rain-water descended with retarded motion to be discharged by springs. This inclination of the subterranean waterline in the chalk of Hertfordshire had been found, by Mr. Clutterbuck, to be nearly at the rate of twenty feet per mile in the chalk between Sir John Sebright's park at Beechwood and the town of Watford; and fourteen feet per mile in the chalk under tertiary strata in some parts of the basin of London. The engineers of the Southampton Railway had found a similar fall of about sixteen or seventeen feet per mile in the wells at the railway-stations between Basingstoke and Southampton." Without expressing an opinion of my own as to whether there really is or is not a subterranean water-channel between Lakes Superior and Ontario, it is evident enough that, even if there is, its size and character, as being more or less obstructed by solid or porous materials, together with its length, would have some influence in determining the quantity of water which could flow through it, even with a difference of water-level over its extremities equal to three hundred and sixty-five feet. Unless, therefore, Mr. Green's "newly discovered force" should suddenly cease to make Lake Superior an "overflowing spring of subterranean water," or, rather, unless the region from which Lake Superior gets its water should be deprived of its yearly rains, we need not immediately look for a common level of the water in Lakes Superior and Ontario.
- Arago said—but he apparently lived too early—"Every one knows that in many places the upper ground is of sand, and that sand lets water through it like a sieve.
- Mr. Green is not quite the first writer who, in undertaking to overthrow a well-established mechanical explanation of natural phenomena, has assumed that the earth's centrifugal force acts in the direction of the tangent to its surface. (See discussions on "The Tides," in vols. xi. and xii. of this magazine.)