BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF 189X AM.3.m , l.9./.U(l?-^-- Cornell University Library GB 1003.A89 Waters within the earth and laws of rain 3 1924 005 012 699 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924005012699 WATERS WITHIN THE EARTH AND LAWS OF RAINFLOW BY W. S. AUCHINCLOSS, C.E. AUTHOR OF " LINK AND VALVE MOTIONS "—(Gcrmaji Editi(»i, "Sch£iber-U7id CouHssensteurungen ") AI^O OF "NINETY DAYS IN THE TEOPICS" FELLOW AMEKICAN ASSOCIATION FOB THE ADVANCEMENT OF SQENCE MEMBER INSTITUTO POLYTECHNICO BEAZILIEEO PHILADELPHIA Copyrigbt W. S. AiicIiiaclo9S 1897 «P A.i w^^H WATERS WITHIN THE EARTH. An abundant supply of fresh water is so essential to all the activities of life, that everywhere the question of rainfall is regarded with the keenest interest, and stations have been established through- out the world for keeping accurate records of the times and amounts of downpour. These observations, however, go no further than the surface of the ground. They tell us nothing about the subse- quent history of the water as it journeys onward through the dark recesses of the earth ! How much of it is taken up by evaporation ? How much is needed to satisfy the demands of plant-life? Much less do they give the faintest idea of what quantity reappears in lake or stream after months of unseen flow ? Our research has the twofold object of supplying the missing history and developing the laws of subterranean flow, or, more con- cisely, rainflow. The standard for measure and comparison will be the household well, because it is found in every country and affords a ready access for underground study. Let us trace the progress of a summer storm ! — The first drops that fall simply moisten the ground. Gradually the surface becomes saturated, after which water can no longer enter the soil as fast as the rain falls. The excess, therefore, must glide away over the surface to the lowlands. When the storm ceases a portion of the water will evaporate, but a larger portion will be taken up by vegetation. It is generally conceded among agricul- tural authorities that grasses and herbs require for perfect growth a daily supply of water equal to their own weight. Possessed of so great capacity, we can readily understand how the midsummer demand seizes all that escapes evaporation, and for the time being stops all further descent of the water. With the disappearance of vegetation during the winter months this demand ceases and the (3) water continues its descent as rapidly as the nature of the soil per- mits. Finally, it falls into what may properly be called the great subterranean lake, or, more concisely, the subldke. This body of diffused water underlies the earth's surface and is almost coextensive with its area. Its universal character is evidenced by the fact that wherever a well is sunk to a sufficient depth one is sure to fiud the sublake, and its water will fill the cavity only to the level of the sub- lake. We have described it as a body of diffused water, because its globules fill the interstices of the soil, sand, or disintegrated rock among whose particles it exists. Furthermore, it fills all fissures and openings in subjacent rock to which it has access. Most rocks are wholly impervious to water, but their extensive fissures store it in vast quantities. When, therefore, a well pierces one of these fissures an abundant supply is fully guaranteed. Evidently in sinking a well through solid rock the result is always a matter of chance, and depends upon whether the drill encounters a fissure large enough to give the needed supply without going to some extra- ordinary depth. Occasionally a hillside fissure is not perfectly enclosed, but has a minute opening at the surface of the ground. In such case the water bubbles forth as a refreshing spring. Artesian wells count their depth by hundreds of feet, and finally pierce water- bearing strata whose surface outcrop is likely to be found many mile? distant. These storage strata are filled with water of the great sublake. When the lake surface stands at a greater elevation than the mouth of the well, the discharge takes place under pressure and the water rises like a fountain. In making a comparison between the sublake and lakes found on the earth's surface, we observe : \st. The sublake is not affected by storms. Id. It has no tide. Zd. Its surface is never frozen. 49Eni>-riE«iaESIi9E9KSE ,|8^;EE;E=i;M|E:: mii\l\ 1 1 I 1 1 1 II - . • -.^ - ^ V- - *-6^ : : :: ! h; EE E ; IE i ": n\\\\]l\\\\\\\m\\ ^ ! Ttrni 1 1 1 1 1 1 1 1 i^'S-H ^Xi a ■ ..iU CD |zi H N r/l l>« -«l Nl >< ^ H rh pt] |zi M g Q 1-1 P, ^ F- CQ << H W M fcl = depth of saturated rock. 24 g2 = depth of water recovered ; but these depths are equal, ■ B + 1 ^ E 24 24' It is, however, a fact that the flow producing the depth E does not cease when the height E has been reached, but will run for many hours before it spends itself, or all the interstices of the depth —^2 — have emptied themselves, so as to restore the equilibrium. The total value is therefore equal to H X E 24 and we have the relation of R + 1 = E.H. or R = (E XH) — 1. . . . (1) 32 The investigation of vortex-flow also furnished a means for ex- pressing the relation between the terms E and F. Thus: 60 % F = E X 11.1. or F = 18.5 X E (2) Example : For Hill Crest the efflux E = 0.78, and the total hours required for recovery H = 84 ; substituting these values, we have : R = (0.78 X 84) — 1. Hence R == 65 = Number units rock-section to each unit of water. Shrinkage of Sublake. When the surrounding country is quite level and the sublake area of great extent, the remov^al of 1000 gallons by pumping will produce no more impression upon the sublake than would result from taking a bucket of water out of a pond. Such effect, however, would not be the case when the sublake underlies an undulating country, for the elevation of the ground naturally limits the lake area, so that a depression (say, one or more inches) would result from pumping out 1000 gallons. In the following investigation this depression will be spoken of as inches of shrinkage. To properly determine shrinkage involves a series of observations extending over a couple of weeks. With the sublake in repose, as in Fig. 7, each observation for the first four days will have one and the same reading. On the fifth day the pumping takes place, and in consequence the lake falls D inches. Recovery follows on the succeeding days, until at last the return ceases. The sublake surface will now be found at C, short of its former level AB by a distance S. The readings taken on the next five days will show that the shrinkage S is permanent. The second case of shrinkage is that where the sublake is steadily rising and should be plotted as shown in Fig. 8. Here the pump- ing interrupts the natural ascent of the water along the path AB. The recovery ceases at the point C, a distance, CN, actually higher than the fifth-day reading, but falls short of the normal by a dis- tance S. The third case of shrinkage is developed when the sublake is steadily falling, and should be plotted as shown in Fig. 9. Here the total shrinkage seems equal to NC, but in reality BN is due Pig. 7. // /i 13 IV MSS. ',UJ^- !tJ>'tj/s. wholly to natural decline of the waters, while S is the shrinkage due to pumping. "Whence we learn that the difference between readings (takeu before and after recovery) only expresses true shrinkage when the lake is in repose. Also that this difference is of questionable magnitude when the sublake is steadily rising and excessive when the sublake is steadily falling. At times combinations of two cases occur and require careful consideration. 34 Velocity of Flow. A soil or disintegrated rock may have a uaiform texture, but if it is traversed by water-bearing fissures they will develop a more rapid flow than the discharge due to texture per se. For this reason one may calculate the absorbent power of a rocli specimen without in reality determining the resultant flow, as the latter depends on the presence or absence of fissures. The Hill Crest experiments give evidence that its flow was due alone to porosity of soil. The well, therefore, is a good one for the purpose of investigating the question of velocity. But whatever may be the final result, we should con- sider it more in the light of an approximation than an exact measurement. On general principles we have : ! Original volume i f Mean area of ^ t Velocity i f Total ) occupied by \^\ water-bearing [ X -^ per hour >■ X "^ hours of V water and soil. ) Uurface in sq. in. J (.in inches. J ( Eecovery. ) Notation. D = Depth, in inches of Q gallons. H = Total hours required for recovery. R = Number of units of rock-section to each unit of water. E -j- 1 = Eock- and water-sections combined. Q = Number of gallons in a well of D depth. V = Average velocity of horizontal flow in inches per hour. Embodying same in general formula, we have : 231 Q (E -j- 1) = 144 (0.23 D X 1.57 X 0.75) X V X H . . (3) = 144 (0.27 D)V.H Since Q n , Example: In the case of Hill Crest E = 65 and H = 84. Sub- stituting the values of E, and H in equation No. 4, we have : V = 52.6 inches per hour, which gives us the average velocity of flow in a horizontal direction during the lime of recovery. 35 Area or Flow. "When a large quantity of water has been removed from a well by pumping, the question arises as to what area of sublake will be disturbed by the process of recovery. In other words, how far-reaching is the influence of the vacancy caused by pumping? The answer is that in some cases the area can be determined ap- proximately, while in others it is practically unlimited, and those instances which show shrinkage at time of recovery are the only ones susceptible of calculation. The estimate for area of flow can be made on the general prin- ciple of cubic volumes of soil, viz. : Total vol. of soil ] f That portion which i r That portion which "j from which the f ^^ ) supplies inflow [ + \ supplies inflow >• water is drawn. ■' ' during pumping. • (. during recovery. J Notation. T = Total number of square feet in area of flow. 8 ^ " " of inches sublake is lowered by shrinkage. h ■ = Portion of a day occupied in pumping. W = Influx (in gallons) during pumping. Then Total volume of soil from which the water is drawn = T X -r- That portion which supplies inflow during pumping = op (R- + 1) 1728 But r Mean area i ( Daily \ r Time W = ^ laid bare I X 60 % } max. flow I X | of ( by pumping. J (. per sq. ft. J i pumping. or W = l:5p^ X 0.6 F X A 2 24 Introducing the value of F from equation 2, we have : W= 0.363 D.E.h (5) Substituting, we have : J That portion which I supplies inflow during pumping=0.0486 D.E.h. (E+1). And equation 2 expressed in cubic feet gives us : I That portion which I. supplies inflow during recovery = 0.27 D Jl H, After assembling the terms we find : ?| = 0.0486 D.E.h. (E + 1) + 0.27 D. ^ H. 12 1^ Therefore ; T =Sr0.27 V.H. + 0.58 E.h. (R + l).l (6) Example: In the case of the Hill Crest experiment of Feb. 1893, D = 132i E = 0.78 8 = 1.25 h = 3 H = 84 E = 65 V = 52.6 Required the area of flow, from which the well gathered its water at time of recovery ? It is only necessary to substitute the above values in equation 6, to find : Area of flow = 135,680 square feet = SA Acres. Although this investigation shows that in cases of shrinkage it is quite possible to determine the acreage covered by the sublake, still its contour line can never be fixed, for that depends wholly on the characteristics of the soil or bed-rock. For a given locality it may be either a circle, an oblong, or any irregular figure. 37 POPULAR MISAPPREHENSION. It is a great mistake to imagine that rain- Slow Penetration fall penetrates rapidly to the lake. This is of Rainfall. rarely the case, and in many soils it takes months to accomplish the journey. In- stances have occurred at Hill Crest wherein the ground-water steadily lessened in months of heavy rainfall; also instances in which the water steadily rose ia times of severe drought. For example, the surface of sublake lowered 52 inches during July and August, 1891, regardless of the fact that the rain fell in exceptionally large quantities, amounting to 10 inches. Again, the surface of the lake 7-ose 42 inches between April 12 and May 3, 1891, notwithstauding the fact that not a drop of rain fell, while the water was rising ! These facts show that no investigator is able to predicate the condition of ground-water from the data of a rainfall record, nor can he use the latter for the former under any circumstances. The theory of rainflow introduces a new Typhoid Fever view as to the healthfulness of grouud- and Ground-Waters, waters, when considered in their relation to the increase or decrease of typhoid fever. For more than thirty years the German theory has found many advocates. The leading idea has been that a very close relationship exists between the annual rise and fall of ground-water and the increase or the decrease of typhoid fever. The ratio being an inverse one, viz., as water subsides typhoid increases, as water rises typhoid diminishes. In our own country the subject has been care- fully investigated by the Board of Health of the State of Michigan. (See Annual Report for fiscal year 1894.) It is a notorious fact that many household wells are constructed with little regard to sanitary conditions. Some wells are exposed to 38 the'^ir and sun, so that grasses and weeds grow during the summer months and fringe their border; while strong winds deposit dust and leaves over the surface of the water ; also various forms of animal life enter and die. Then, too, many wells are concave at the mouth, so that surface-water finds ready entrance during heavy storms. Worse still, many wells are sunk in porous soils in close proximity to cesspools or leaky drain-pipes. As all like con- ditions can be discovered and remedied, such wells form no part of our investigation, but must be ruled out of the question. Examin- ing the reports, we observe : First, that taking the health records given from 1889 to 1893 we are able to construct the following diagram : Table XVI. — Typhoid Reported in Michigan. /S8f. -1893. JAN. FEB. mi m. MAY M. M m. SEP. OCT. M MC. P^HCENTofTYPHOIb. 6. ^. 3. 3. 3. s. 6. /3. // :^^. //. //. 2ri jdfTfn /g' /"^ J --' '^r- ,' [\ o ^ i [^ '' /" \ / „.. ' \] k DRnn. .A f I't e' 1 Iljfl l]1"l"f Till \\V From which we learn that typhoid became alarming about the middle of August and attained its maximum virulence about the 1st of November ; also that a small percentage existed during the first seven months in the year. Second. The annual rainfall in Michigan for the same period was about -| the rainfall in Philadelphia. Third. The "representative well" in the Capitol grounds at Lansing had an annual oscillation similar to that shown in Table II., only the zero occurred in February, and the July 39 elevation averaged 13 inches, tiie extremes being 11 and 24. Surely this record does not favor the ground-water theory because typhoid reached its worse stage three months before the lowest water-mark was touched, and the epidemic completely disappeared by the time that mark was reached. According to such a showing, subsidence would be chargeable with causing an epidemic, both to rage and to abate. Let us now examine the data given in the same report for " many wells scattered throughout the State of Michigan," whose waters were carefully watched between 1878 and 1883. We see at once that the average soil was more porous than that around the Lansing well, for the greatest rise in any one year was 96 inches and the least 40. Constructing a- table like No. II. we find : Table XVII.— Average Rise of Michigan Scjblake. At first glance this table seems to favor the popular maxim : high ground-water, little typhoid; low ground-water, typhoid an epi- demic ! It must be remembered, however, that the process of averaging a six-years' record throws characteristic points into the shade and only 40 makes note of general features. For example, the 22 per cent, typhoid average came from a group whose extremes were 18 and 37 ; in like manner the May 1st high-water-day, had for extremes April 1st and July 1st. Whenever, therefore, we aim to establish a true relation between two events occurring in a given year, manifestly we must not vitiate our data by diluting it with the diverse records of five other years. But, on the contrary, we should strengthen it by finding two consecutive years which have characteristic features as near alihe as possible, and use them as a basis for comparison. Let us take 1879 and 1880, because in those years the epidemics were of equal virulence ; also the ground-water rose and fell almost equal distances. The most important events are given in the accompany- ing diagrams : The ground-water stood in each year at its highest level May 1st. Typhoid attained the alarming stage of 10 per cent., say, August 1st to 15th, and the maximum amounted to 25 per cent. Now note that the typhoid in one case became alarming sixteen days before low water, and in the other sixty day?. The difference of forty-five days shows that the precise moment of low water had nothing to do with the origin of the disease. Also note that in 1880 typhoid reached its most virulent stage on the same day as low water, but in 41 1 879 it took ninety days after low water-mark was passed before it attained tlie same stage, showing that the precise moment of low water had nothing to do with the development of the disease. Incidentally the water rose in 1879, 20 inches. In harmony with the " low- water theory " such a rise ought to have put a decided check upon tlie disease, but nothing of the kind occurred. It in fact had no influence wliatsoever ! And why ? Simply because these phenomena were not related to each other as cause is to effect. The two diagrams flatly contradict each other. In 1879 the epidemic must be credited to 20 inches of rising water, while in 1880 an epidemic of equal violence raged with 20 inches of falling water. We might compare other years, but would find like inequalities and divergences. It is evident, therefore, that the Michigan data fail to establish any useful relation between the prevalence of typhoid and the height of the ground-water; whether we consider the data of the " represen- tative well " at Lansing, or whether we take the figures given for the " many wells throughout the entire State," the result is one and the same. According to the principles of rainflow, the lake is not a body of water that becomes more and more polluted as summer advances. Its surface is not lowered materially by evaporation ; it does not change in temperature, nor is it productive of either animal or vege- table life. On the contrary, its surface is lowered by natural over- flow; when fresh accessions arrive they come only through the superincumbent soil, so that every globule of the water is not only perfectly filtered, but in a rightly conditioned well it is both potable and healthful. These considerations convince us that the typhoid ground-water theory is not supported by facts ; also that whatever relation or synchronism does exist, it is merely a coincidence, and jiossesses no special significance. Many property-owners have an idea they Household Wells can secure a satisfactory well by digging far Should Never Fail, enough to find water; they then deepen the cavity, whatever may be necessary to hold the daily supply, and finally wall up the interior. The idea is an erroneous one and at variance with the principles of rainflow, for it 42 ignores the question of periodic fluctuations. The chances are that such a well will fail in times of great drought. Fortunately the remedy is always at hand, and tedious observa- tions are not necessary to solve the question. The right way is to search the neighborhood for some Resident of twenty or thirty years' settlement, whose well has never failed, and learn from him the least depth of water his experience can recall. If perchance that depth would be sufficient for your daily wants, measure the present depth of water in his well, and dig your own well deep enough to secure preeisely the same present depth. For example : If the resi- dent remembers one season in twenty years during which he had only 3 feet of water in his well, ask yourself the question : Would 3 feet as a minimum satisfy my wants ? Afterwards measure his present supply. Suppose it amounts to 15 feet. Then dig your own well to whatever depth may be necessary to secure 15 feet of water. If, however, your wants exceed those of your neighbor, you should continue digging and deepen your own well enough to secure the excess also. Careful observance of this precaution is sure to give a never-failing supply. 43 RECAPITULATION^. It has been shown that a very large part of the annual rainfall passes away over the surface of the ground. Hence the importance of using every means to preserve our forests. For wherever the country is thickly wooded the undergrowth, ferns, leaves, and mosses arrest the flow of water, to the great benefit of the land; freshets seldom occur, also protracted periods of drought and failure of springs are scarcely known. It has been demonstrated that the withdrawal of a thousand gallons from any well, located in a compact soil disturbs the sublake over many acres of ground. Therefore it is the part of wisdom always to anticipate the encroachments of a growing population by providing an independent water-supply, located far beyond the reach of contaminating influences. The study has served the good purpose of clearing away certain popular misapprehensions with regard to the relations between rain- fall and rainflow ; between ground-water and typhoid fever ; it has also suggested what precautions are necessary to insure a never- failing supply of health-giving water. Our investigation has taught us to recognize the world-wide exist- ence of the great subterranean lake, its characteristic features, its periodic fluctuations, and how to measure both volume and velocity of its unseen flow. The most strilcing features discovered are equa- tions Nos. 1 and 2— showing the relation between rock- and water- sections ; also the analogy existing between the laws of subterranean flow and the laws governing the discharge of water through a weir ; the nature and process of recovery , likewise the relation between uniform flow and fading flow. Attention has also been directed to the fact that the daily temperature of ground water is equal to the yearly average temperature of the atmosphere. We believe that the present research has developed an outline of the general laws of rainflow, which for the first time places the sub- ject in its true light.