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DEP~-~Jt~~~t.J;.·"OF ~~~-~~~,TE,~IOR •. >-. ·~~~:.\";.'·_.',: .,. ··_ jl.' -. ,1, ~ ·~~ ,: ; • 

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WATER-SUPPLY 

No. 67 

WASHINGTON 

GOVERNMENT PRINTING flFFICE 

1902 

UNITED STATES GEOLOGICAL SURVEY 

CHARLES D. WALCOTT, DIRECTOR 

THE 

MOTIONS OF UNDERGROUND W1\TERS 

BY 

CHARLES S. SLIGHTER 

WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1902 

CONTENTS. 

LETTER OF TRANSMITTAL _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ____________________________ _ 

CHAPTER I.-Origin and extent of underground waters __________________ _ 

Depth of ground water _____________________________________________ _ 

Total amount of underground water_ _ _ _ _ _ _ _ _ _ _ _____________________ _ 

Permeability of rocks _______________________________________________ _ 

Porosity of rocks and soils __________________________________________ _ 

Motion of the water _________________________________________________ _ 

Cause and rate of movement ____________________________________ _ 

The laws of flow_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _______________________ _ 

Mechanic~l analysis of S')ils _____________________________________ _ 

The author's formula for determining flow ______________________ _ 

Maximum flow _________________________________________________ _ 

CHAPTER H.-Surface zone of flow of ground waters _____________________ _ 

Underground drainage basins _______________________________________ _ 

Shape of the water table ____________________________________________ _ 

The underflow ______________________________________________ - - __ - - __ _ 

Rate of movement of the underflow_ _ _ _ _ _ _ _ _ _ _ _ _ _ ______ -________ _ 

Return waters from irriga~ion __________________________________ _ 

. Effect of tile drainage, etc ________________ ·- _ _ _ _ _ _ _ _ _ _ _ __________ _ 

Chlorine method of determining the rate of tho underflow _______ _ 

Tho author's method of determining the rate of the underflow ___ _ Conclusions _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __________________ . _______________ _ 

CHAPTER IlL-Deep zones of flow _______________________________________ _ 

Distinguishing features _____________________________________________ _ 

Percolation into deep :::ones _____________________ .. ___________________ _ 

Dakota formatimL _______________________________________________ - __ _ 

Potsdam formation ________________________ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ____ _ 

CHAPTER IV.-Recovery of un::lergrouncl water from the snc·face flows ___ _ Common open wells ____ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ______________________ _ 

Contamination of surface wells__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _____ _ 

Non uniformity of neighboring wells _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _____ .- ____ _ 

Fluctuations in the position of the water table and the effect mi 

wells and springs _____________________________________________ _ 

Available supply of wells and S)rings-------------------- ------- Collecting galleries and sn bcanals ___________________________________ _ 

Sn bsurface dams ____________________________________________________ _ 

Advantages of underground su~)ply _________________________________ _ 

CHAPTER V.-Artesian and deep we~ls __________________________________ _ 

· Yield or capacity of artesian wells _________________________________ _ 

Simple methods of measuring the yield of flowing wells _____________ _ 

Failure of artesian wells ____________________________________________ _ 

Mutual interference of artesian well:;_ _ _ _ _ _ _ _ _ _ _ _ ___________________ _ 

Artesian wells of Savannah, Ga ______________ . ______________________ _ 

INDEX - -- ---- - - -- -- - - - --- - - - - -- - -- - - ----- -- --- - ---- -

5 

Page. 

11 

13 

14: 

14 

15 

16 

17 

17 

18 

21 

24 

28 

31 

32 

33 

38 

41 

43 

46 

46 

48 

50 

52 

53 

54 

57 

59 

61 

62 

68 

69 

70 

73 

73 

76 

77 

79 

83 

90 

93 

95 

97 

103 

ILLUSTRATIONS. 

Page. 

PLATE I. Sections of Wisconsin sandstone: A, Red sandstone from 

Laville; B, Brown sandstone from Argyle__________________ 20 

II. A, Sink-hole connection with underground drainage system; B,. 

Underground channel. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 32 

III. Map showing the deltas or fans of disappearing streams as 

they leave their mountain canyons _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 38 

IV. A, Spring formed at outcrop of an impervious floor; B, Artesian well ______ .. ______ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 62 

V. A, View looking up the Pacoima Wash from the site of the 

subsurface dam; B, View of 50-foot section of subsurface 

dam on the Pacoima Wash, showing excavationandlagging_ 74 

VI. View from bottom of 50-foot section of Pacoima subsurface 

dam, showing lagging in place and construction of concrete 

wall _____ . ______________________________ _, _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 76 

VII. A, View of top of completed subsurface dam on the Pacoima 

Wash, showing wells on upper side of same; B, View of central 

portion of subsurface damon the Pacoima Washduring over- flow_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 78 

VIII. Lines of flow into a well in a region in which the ground water 

has a constant motion in a general direction _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 82 

FIG. 1. Ideal section across a river valley, showing the position of the ground 

water and the undulations of the water table with reference to 

the surface of the ground and bed rock _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 13 

2. Diagram illustrating Darcy's law of the flow of water through a column of soil _________________________________________ ~ _ _ _ _ _ _ _ 18 

3. Hazen's experimental filter for the determination of the laws of 

flow of water through sand and the evaluation of the transmission 

constant of the same _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 19 

4. Unit rhombohedron formed by passing planes through the centers 

of eight contiguous spheres in the most compact packing of a mass 

of spheres, and showing the shape of the pores in such a mass____ 20 

5. Unit element of the pore space in a mass of spheres packed in the 

most compact manner possible, being a plaster cast of the interior of the solid of fig. 4 ________________________ .. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 21 

6. Diagram illustrating Hazen's method of making mechanical analy- ses of soils _____ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 23 

7. Diagram illustrating various pressure gradients and the maximum 

flow _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ____________ .. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 28 

8. Diagram showing lines of flow into a drainage ditch and the shape 

of the water table in its neighborhood _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 29 

9. Contour map showing position of the water table, supposed lin<:>s 

of motion of ground water, and the thalwegs or drainage lines _ _ 33 

7 
8 ILLUSTRATIONS. 

Page. 

FIG. 10. Diagram illustrating Chalon's principle that the main core of the 

underground drainage, or subterranean thalweg, naturally lies 

nearer the steeper side of the valley than does the surface stream_ 34 

11. Diagram illustrating lines of flow of ground water over a series of 

monoclines, synclines, and anticlines _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 34 

12. Diagram illustrating lines of flow of ground water over a series of 

monoclines in an impervious bed _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 35 

13. Diagram illustrating lines of motion of ground water in an outcrop of a pervious bed underlain and overlain with impervious 

strata __________________ . ____________________ .. ____ .. _ _ _ _ _ _ _ _ _ _ _ _ 36 

14. Diagram showing seepage lines in a pervious bed resting upon an impervious floor ________________ . ___ . __ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 37 

15. Diagram showing direction and rate of seepage in a pervious bed 

resting upon an impervious floor _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 38 

16. Diagram showing growth of Cache la Poudre River__________ _ _ _ _ 44 

17. Curve obtained in determining the velocity of ground water by the 

chlorine method __________________________________ . _ _ _ _ _ _ _ _ _ _ _ 47 

18. Diagram illustrating the author's electrical method of determining 

the horizontal velocity of ground water__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 48 

19. Curve obtained by the author's electrical method of determining 

the velocity of ground water _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 49 

20. Cross section through South Dakota artesian basin, based upon published data of Darton, Todd, and others____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 55 

21. Diagram illustrating how gas and oil have been retained beneath 

anticlines of shale during protracted geologic intervals, thus proving the substantial imperviousness of the covering _ _ _ _ _ _ _ _ _ _ _ _ _ 56 

22. Darton's map of catchment area of the Dakotas and the Dakota 

artesian basin ____ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 57 

23. Section along the Missouri River near Great Falls, Mont_________ 58 

24. Wisconsin outcrop of Potsdam and St. Peter sandstones____ _ _ _ _ _ _ 59 

25. Diagram showing the formation of a stratum spring at an outcrop 

of an inclined impervious stratum_____________________________ 61 

26. Diagram showing the formation of overflow springs at the edges of a basin of impervious materiaL _______________ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 61 

27. Diagram showing the formation of chasm springs in a cut which 

extends below the natural level of ground waters _ _ _ _ _ _ _ _ _ _ _ _ _ _ 62 

28. Common dug well; shallow in water_________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 63 

29. Diagram illustrating the cha:o.ging position of the water table near 

a 3-inch well during ten consecutive hours of continuous pumping at an average rate of 2,313 gallons per day _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 64 

30. Diagram illustrating the varying position of the water table in a 

well due to pumping for various intervals and modified by rainfall and stops of various duration ____________ ,,________________ 65 

31. Hoadley's laboratory apparatus for the investigation of the phenomena of common open·and driven wells _____ ·- _ _ _____ _ _ _____ 66 

32. Combination dug and tubular welL___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 67 

33. Diagram showing rise of water in city well at Garden, Kans., after 

heavy pumping _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 68 

· 34. Curve showing rise of water surface in well at Garden, Kans.____ 68 

35. Diagram illustrating danger of contamination of surface wells from 

cesspools_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 69 

36. Diagram showing extreme irregularities of the water table and the 

depth of wells in east Schleswig-Holstein ____________________ -. _ 70 
ILLUSTRATIONS. 9 

Page. 

FIG. 37. Diagram showing fluctuation of the height of the ground water 

and associated phenomena as observed at Munich______________ 71 

38. Diagram showing fluctuation of the height of the ground water 

and associated phenomena as observed at Berlin ________ ~ _ _ _ _ _ _ _ 72 

39. Autograph record of simultaneous changes in flow of spring and 

atmospheric pressure. _ _ _ _ _ _ _ _ _ _ ___________________ . _ _ _ _ _ _ _ _ _ _ 73 

41l. Diagram illustrating Balbach's theory of the contamination of wells 

or collecting galleries by reversed flow from rivers _ _ _ _ _ _ _ _ _ _ _ _ _ 73 

41. Diagram illustrating principle involved in construction of infiltration galleries for gravity flow_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 7 4 

42. Plan of infiltration galleries proposed by Willard D. Johnson_____ 75 

43. Longitudinal section of infiltration galleries designed by Willard 

D. Johnson __________________________________________________ . _ 76 

44. Map showing location of springs in the vicinity of South Britain, 

Conn ________________________________ . _________ .. __________ .. _ _ _ 80 

45. Diagram illustrating the fall of pressure as water moves through a pervious material _________ .. _________________________ . _ _ _ _ _ _ _ _ 83 

46. Diagram illustrating the author's graphical solution of problems in 

the yield of artesian wells __________________________________ .. _ _ 87 

47. Diagram illustrating graphical solution of an artesian-well problem ________________ . ________________________________ .. _ _ _____ .. _ 88 

48. Graphical representation of the relations between Q and Qo in the 

equation on page 8.1_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 89 

49. Di~gram illustrating flow from vertical and horizontal pipes______ 91 

50. Map showing location of artesian wells at Savannah, Ga ___ , _ _ _ _ _ 98 

LETTER OF TRANSMITTAL. 

DEPARTMENT OF THE INTERIOR, 

UNITED STATES GEOLOGICAL SURVEY, 

DIVISION OF HYDROGRAPHY, 

TVashington, D. C., March 26, 1902. 

SIR: I have the honor to transmit herewith a manuscript by Prof. 

Charles S. Slichter on the motions of underground waters, and request 

that it be printed in the series of "\Vater-Supply and Irrigation Papers. 

Professor Slichter has been giving considerable time and attention to 

experimental and theoretical considerations of the movements of 

underground waters, the preliminary results of which were published 

in Part II of the Nineteenth Annual Report. The present paper 

treats of the simpler and more general topics connected with the 

movements of water underground, being intended to answer the more 

elementary questions which arise in a consideration of the subject. 

Examples are given of the various areas in which water occurs underground, the origin and extent of the waters are discussed, and methods 

of bringing them to the surface and making them available are 

touched upon. 

Very respectfully, F. H. NEWELL, 

Hydrographer ,in Charge. 

Hon. CHARLES D. WALCOTT, 

Director United States Geological Survey. 

11 

THE MOTIONS OF UNDERGROUND WATERS. 

By CHARLES S. SLICHTER. 

CHAPTER I. 

ORIGIN AND EXTENT OJi' UNDERGROUND 'WATERS. 

All underground waters have their origin in rainfall. A part of 

the rainfall immediately runs off the surface of the ground into the 

streams and rivers, just as the rain is diverted by the roof of a house 

into the gutters and spouts. Another portion of it is absorbed temporarily by the surface soil, but is again returned to the atmosphere 

by evaporation, either directly or through the agency of vegetation. 

A third portion penetrates the lower levels of the soil, there to become 

a part of the great mass of underground water and help to furnish · 

the perennial supply of streams and lakes, of springs and wells, and 

to take part in geologic work of the most profound importance. 

FIG.l.-Ideal section across a river valley, showing the position of the ground water and the 

undulations of the water table with reference to the surface of the ground and bed rock. 

In its downward course through the soil the rain water soon reaches 

a level at which the soil is completely saturated. rrhe surface of this 

saturated zone is known as the water table or water plane. It is the 

water existing in the soil or rocks below this water table which is 

usually included in the term underground water. Above the zone of 

saturat.ion the soil usually contains a large percentage of moisture, 

which plays a most important part in the growth of plants and in the 

physical, chemical, and biological phenomena of the soil. The consideration of the phenomena in this nonsaturated portion of the soil 

does not, however, come within the scope of this paper. 

The depth of the water table below the surface of the ground varies 

much in different localities. In regions of copious rainfall it is 

usually but a few feet below the surface. In arid regions its depth 

may be measured in hundreds of feet. In general the water table 

13 
14 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

follows contours very similar t,o those of the land surface, hut its 

undulations and slopes are of much less magnitude than those of the 

surface of the ground. This is shown in the ideal section forming 

fig. 1. A region in which the water table lies at great depth below the 

surface of the ground is, of course, a region of deep wells. A locality where the water t.able coincides with the surface of the ground is 

a swamp or marsh. 

DEPTH OF GROUND WATER. 

The lowest theoretical limit at which ground waters can exist is 

reached when. the pressure in the rocks, due to the weight of the 

superincumbent material, is so enormous that, all cavities and pores 

in the rock are completely closed. This limit has been shown by 

Professor VanHise to be at a depth of approximately 6 miles.a The 

region above this depth Van Hise has distinguished as the zone of fracture, for in it pressures and stresses result in the actual breaking and 

fracturing of the rock. The region below this depth has been called 

by Van Hise the zone of flowage, for in it the enormous pressures will 

not permit the formation of cracks and cavities, and the rocks, when 

transformed by stresses, must actually flow like clay under the pressure of the hand. Adopting, then, this fundamental classification of 

VanHise, we may say that the lower limit of the existence of ground 

water is found when we reach the lower boundary of the zone of fracture. This limit, however, refers primarily to the geologic work of 

ground waters and not to the practical limit of its occurrence in quantities sufficient for economic uses, for, as will be seen later, the principal zones from which underground water is actually recoverable in 

useful quantities are almost completely confined to the domain of sedimentary rocks and surface deposits. Even the mineral and thermal 

springs from beds of crystalline or metamorphic rocks are from a level 

much above the geologic limit of depth. 

TOTAL AMOUNT OF UNDERGROUND WATER. 

r_rhe amount of ground water within the crust of the earth is enormous. The writer estimates the entire amount to be about 565,000 

million million cubic yards, or about 430,000 million million cubic 

meters. He has arrived at this result by considering that the geologic 

limit of the existence of ground water is at an average depth of 6 

miles below the surface of the land and 5 miles below the floor of the 

ocean. The land surface and water surface he has assumed to be 

52,000,000 square miles and 144,700,000 square miles, respectively. 

The average pore space of .the surface rocks which is occupied by 

water or moisture he has taken as 10 per cent of their total volume. 

He believes that this estimate of 10 per cent is too large rather than 

too small. It forms, however, a convenient basis for the estimates. 

aPrinciples of North Amerit"an pre-Cambrian geology,_by C. R. Van Rise: Sixteenth Ann. 

Rept U. S. Geol. Survey, Pt. I, 1~96, p. 593. 
SI..ICHTER.] PERMEABILITY OF ROCKS. 15 

According to these estimat,es, the total amount of underground 

water is sufficient to cover the entire surface of the earth to a uniform depth of from 3,000 to 3,500 feet. Assuming a mean depth .of 

the ocean of 12,000 feet leads to the conclusion that the total amount 

of oceanic water is about 1,800,000 million million cubic yards, so 

that the total quantity of ground water is nearly one-third the amount 

of the oceanic water. 

Former estimates of the quantity of underground water the writer 

believes to be ent.irely too large. The most frequently q noted estimate 

is that of Achille Delesse.a He estimates that the average amount of 

water in the surface rocks is 5 per cent by weight or 12t per cent by volume. He supposes that the increase of temperature in the interior of 

the earth (1 o C. for 100 feet) would limit the existence of water in the 

liquid form to a dept,h of 3,300 meters if it were not for the increase 

of pressure due to this great depth. Allowing for this, Delesse estimates that liquid water may exist at a depth of 18,500 meters and at 

a temperature of 600° C. These considerations lead him to the enormous estimate of 1,530,000 million million cubic yards (1,175,089 million million cubic meters). This, he says, is one nine hundred and 

twenty-first of the volume of the globe, which is nearly equal to Beaumont's estimate of the volume of the sea, one eight hundred and 

twenty-seventh of the the earth's volume. 

The discovery of Van Rise that pores can not exist in the rocks at 

a depth much greater than 10,000 meters requires us to throw out 

these older estimates based upon the temperature gradient of the 

earth's crust. 

PERMEABILITY OF ROCKS. 

It has been tentatively assumed that all rocks are pervious to water. 

In a very general sense this may be said to be the case. Practically 

all rocks, even those of greatest strength, are not entirely solid masses 

of matter, but instead are collections of discret.e particles and crystals 

more or less perfect.ly cemented and compacted t.ogether. This fact 

is much better understood when it is remembered that all except 

igneous rocks were at one time deposits laid down on the bottom of 

the sea by rivers and currents. These sediments may in time be 

changed t,o sedimentary rocks, and the sedimentary rocks in turn be 

changed to harder and more compact metamorphic and crystalline 

rocks, yet the original granular character of the mass is rarely·completely lost, even in its changed condition, and the open texture persists, in some degree, forever. The small spaces or por-es between the 

rock particles are usually occupied by water. 

In building the St. Gothard tunnel the rocks encountered from the 

southern end were "principally mica-schist, hornblende rock and 

gneiss containing more hornblende and mica and quartzite," yet the 

aBull. Soc. geol. France, second series, Vol. XIX, 1861-62, p. 64. 
16 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

contained water was so great that the grade of the tunnel had to be 

changed from 1: 1,000 to 1: 500 in order to obtain proper drainage. a 

A portion of the underground water may be found in the larger 

cracks and crevices of the rocks, but by far the larger portion exists in 

the minute pores and openings between the rock particles themselves. 

or in the small interstices between the separate grains of the son. 

POROSITY OF ROCKS AND SOILS. 

The fractional part of a rock or of soil which is occupied by open 

spaces or voids determines its porosity. Thus, if a gallon of sand will 

hold, when saturated, three-tenths of a gallon of water, the -porosity 

of the sand is said to be 30 per cent, three-tenths of its volume being 

made up of pores between the grains of sand. Likewise, if a cubic 

foot ~f sandstone will hold, when saturated, one-quarter of a cubic 

foot of water, the sandstone is said to have a porosity of 25 per cent, 

for one-fourth of its volume is pore space or voids. 

The following table (I) contains several determinations of the 

porosities of Wisconsin building stones, made by Mr. E. R. Buckley, 

State geologist. They are probably the most carefully made determinations yet published. Special attention is called to the fact that 

all of the rocks listed in the table are building stones and that the 

important water-bearing rocks l!aturally show higher porosities than 

the more compact of these.. From the table it is seen that the amqunt 

of open or unoccupied space in these building stones varies from about 

1 part in 400 for the Montello granite to more than 1 part in 4 for the 

Dunnville sandstone. It is worthy of remark in this connection that 

the Montello granite was selected for the sarcophagus of the tomb of 

Gen. U.S. Grant, because comparative tests showed it to l)e the 

strongest granite in this country. Its porosity here given (about onefourth of 1 per cent) shows that even the strongest rocks are measurably porous. 

TABLE I. 

Porosities of Wisconsin building stones, as determined by E. R. Buckley, -State 

geologist. 

Kind of stone. Name of quarry. 

Granite.--· ____ -------- Berlin (Wis.) Granite Co .... -·--_--.-------- __ ----._----._---- Do ___ .·------------ Montello (Wis.) Granite Co _______________________________ ----

Niagara limestone ____ Marblehead (Wis.) Lime and Stone Co----------------------

L o ~~ r---Maiiiesla·n- ~~~~e~~~t :~~~~:~-~~ ~~~:: :: =: ::=:===:::: ~ = ::::::::::::: 

limestone. 

Sandstone _ _ _ _ _ _ _ _ _ _ _ _ _ Chicago and N C?rthwestern Railwa:y ., Ableman, Wis .. _. ___ _ 

Do-----------------~ Bass Island (Wis.) and Lake SuperiOr Sandstone Co.,Ash- 1 land, Wis. Do _________________ 

1 

Dunnville, Wis _____________________________ --.- ____________ ---· 

Average 

porosity 

of two specimens. 

Per cent. 

0.384 

0.237 

0.77 

6.4 

13.19 

5.6 

20.7 

28.26 

aTunneling, Explosive Compounds, and Rock Drills, by Henry S. Drinker, New York, 1878, 

p. 276. 
SLICHTER.] CAUSE .AND RATE OF MOVEMENT. 17 

The porosity of quartz sand will usually vary between 30 and 40 

per cent, and that of clay loams between 40 and 50 per cent, depending 

upon the variety of sizes in the mixtur~ and the manner of packing 

the particles. 

MOTION OF THE WATER. 

In general the water contained in the porous soils and rocks is not 

stationary, but possesses an exceedingly slow, although perfectly 

definite, motion. The best evidence of this is supplied by geology, 

which shows that nearly all of the rocks have been vastly changed by 

the work of underground wat,ers. Enormous amounts of material 

have been slowly deposited in the pores of loose sandstones and limestones, until they have been converted into strong and nearly impervious rocks. Professor Van Rise estimates t.hat thousands of cubic· 

miles of dissolved quartz have been deposited by the slowly moving 

ground waters in sands and sandstones, until in some instances the 

latter have been converted into solid quartzite. a Almost any specimen 

of rock, especially tf examined in thin sections under the microscope, 

will show some evidence of the work of moving ground waters. In 

many cases broken and worn fragments of crystals will be observed 

to have been pat,ched and mended and added t6 until this so-called 

"secondary growth" has become a most important part of the rock. 

In other cases cementing material and minerals .not originally present 

are found distributed t.hroughout the rock in great abundance. 

Indeed the solution, transportation, and redepositing of material 

through the agency of ground waters is a geologic fact of profoundest 

importance, and is in evidence everywhere within the surface rocks of 

the earth. 

CAUSE AND RATE OF MOVEMENT. 

The cause of the motion of water through a porous medium is the 

same as the cause of the water movement through the pipes and conduits of a water-supply plant of a city-the difference of pressure 

from point to point. The difference in pressure in. the case of ground 

waters is nearly always due to gravity alone. The water 1p.oves in 

the undergrol.1nd current for the same reason that water moves in the 

surface streams--it flows from a higher to a lower level. 

The rate of the movement of water through a porous soil or rock 

depends upon several important elements, which may be enumerated 

as follows: (1) The size of the pores in the water-bearing medium, the 

capacity to transmit water being enormously greater for large pores 

than for small pores; {2) t.he porosity of the material, the flow being 

much greater for high porosity tha_n for low porosity, other things 

being equal; (3) the pressure gradient, or the change in the pressure, 

or bead, per unit of length measured in the direction of the motion, 

aEarth movements; presidential address of C. R. Van Rise: Trans. Wisconsin Acad. Sci., Vol. 

XI, 1896, p. 511. . 

IRR 67-02--2 
18 MOTIONS 0]' UNDERGROUND WATERS. [NO. 67. 

the flow being greater, of course, for high gradients than for 'low 

gradients; and ( 4) the temperature of the water, the flow being noticeably greater for high temperatures than for low temperatures. 

THE LAWS OF FLOW. 

:Many experimenters have attempted to discover the exact law followed by water when traversing a porous medium, and to express 

that law by means of a mathematical formula. The earliest attempt 

to deduce such a law was made in 1856 by a Frenchman named 

Darcy, a who announced that the flow of water in a certain direction 

through a column of soil is proportional to the difference in pressure 

at the ends of t.he column and inversely proportional to the length of 

the column. According to this law, doubling the length of the soil 

a. b c 

Fro. 2.-Diagram illustrating Darcy's law of the flow of water through a column of soil. The 

length of the soil column in case a is CD, and the difference in pressure at the ends of the column is A B. In case b the length of the soil column (C' D') is one-half of CD of case a, while the 

pressure difference (A'B') is the same as A B of case a. Therefore, according to Darcy's law, 

the flow in case b is twice that in case a. Likewise the flow in case c is twice that in case a, since 

the soil column is of the same length as in case a, while the pressure difference (A" B") is twice 

A B of case a. The amounts of the flows incases band care equal t~ each other, for the length 

of the column of soil and the pressure difference are each double those of case b, which, according to Darcy's law, makes the flows equal. 

column and keeping the water pressure the same at the ends will 

result in halving the flow, while doubling the pressure differences at 

the ends of the column and keeping the length of the column the 

same will result in doubling the flow. These facts are illustrated in 

fig. 2. Darcy expressed his conclusions by the following formula: 

'O=kl!_ .. h' (1) 

in which 1-' stands for the velocity of the moving ground water, p the 

difference in pressure at the ends of the column of soil (measured 

usually by the height of the water column, as in fig. 2), h the length 

of the column, and k a constant depending upon the character of 

aLes fontaines publiques de la ville de Dijon, by H. Darcy, Paris, 1856. 
SLIC.HTER.] THE L.A WS OF FLOW. 19 

the soil, especially upon the size of the soil grains, which must be 

experimentally determined in each case by the use of apparatus shn.: 

ilat· to that shown in fig. 2. 

Numerous other experimenters have investigated the same problem, 

with results substantially the same. Among the most important of 

these is the result of an American engineer, :Mr. Allen Hazen, a whose 

conclusions are expressed by the folloiring formula: 

l'=C(l2 ~ (0. 70+0. 03t), (2) 

in which v is velocity of the water, in meters daily, in a solid column 

of the same area as that of t,he sand, c is a constant factor which 

Inlet 

-., 

·Loss of ___ t head 

FIG. 3.-Hazen's experimental filter for the determination of the laws of flow of water through 

_ sand and the evaluation of the transmission constant of the same. The length of the soil column 

must be measured between the points at which the pressure gages enter the large cylinder filled 

with sand or other :material subject to experimentation. 

Hazen's experiments indicate to be approximately 1,000, d is the 

"effective size" of sand grain (measured in millimeters), which is such 

that 10 per cent of the material is of smaller grains and 90 per cent 

of larger grains than the size given, his the loss of head, l is the 

thickness of sand through which water passes, and tis the temperature on the centigrade scale. Hazen states that the loss of head 

should be measured from points just inside the ends of the soil column, 

as is shown in the accompanying illustration of his apparatus, fig. 3. 

a Some physical properties of sands and gravels, by Allen Hazen: Rept. Massachusetts State 

Board of Health, 1892, p. 541. 
20 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

Hazen's work has been the basis on which the estimates of American 

tmgineers have been founded and has become standard. 

Prof. F. H. King, in a long series of carefully conducted experiments, showed that the flow of water may increase ~mew hat faster 

than the pressure.a The formulas given herewith, however, are 

quite accurate enough for all engineering purposes to which they 

properly apply, although the refinement of a second approximation 

may restilt in a slight modification. 

In another paperb the writer has given an expression for the flow ot 

water or other fluid through a column of soil made up of uncemented 

grains of nearly uniform size and of a well-rounded or approximately 

spherical form. It was there shown that a mass of spheres thrown 

together in a haphazard way will present great variety in the amount 

FIG. 4.-Unit rhombohedron formed by passing planes through the centers of eight contiguous 

spheres in the most compact p::~.ckin3' of a mass of spheres, and showing the shape of the pores 

in: such a mass. 

of open space or porosity within the mass. The value of the porosity 

is shown to be independent of the size of the grains but dependent 

merely upon the manner of packing. The minimum porosity of a 

mass of spheres, or t,he porosity when th8 spheres are packed in the 

most compact manner possible, was shown· to be 25. 9'5· per cent of the 

whole space occupied by the spheres. The maximum porosity that is 

probable in a mass of spheres was shown to be 47.64 per cent of the 

whole space occupied. 

If a quantity of common shot be poured into a glass and the amount 

of ope.n space between the shot be determined by measuring the 

aPrinciples and conditions of the moven:ents of ground water. by F. H. King: N:neteenth 

Ann. Rept. U. S. Geol. Survey, Pt. II, 1899, p. 5J. 

bTheoretical investigation of the motion of r:round waters, by C. S. Sl.:.chter: N.'.neteenth Ann. 

Rept. U.S. Geol. Survey, Pt. II, 1899, p. 2£5. 
U. S. GEOLOGICAL. SURVEY WATER-SUPPLY PAPER NO. 87 PL. I 

SECTION S OF WISCONS I N SANDSTONE. 

A, Red s3.nd:;tor.e from L a'li lle; JJ, brcwn sandstone from o). rgyle 
SLICHTER.] THE J,AWS OF FLOW. 21 

quantit.y of water required to fill the pores between the shot, it will 

be found that the re~nlti.ri.g porosity will bewell:'Within the limits just 

given. It will also be found that the porosity will vary greatly if 

different methods be used in filling the glass, but that it is possible 

to obtain the same porosity with small shot as with large shot. Th-0 

pores between the shot will be seen to be somewhat triangular in 

form, as shown in figs. 4 and 5, and they are both larger in diameter 

and shorter in length for a packing of spheres having a large porosity 

than they are for a packing of low porosity. This very important element in the transmission capacity of a soil the writer has attempted to 

take proper account of in the derivation of the formula given on page 

24. The individual grains in a mass of sand are not, of course, 

FIG. 5.-Unit element of the pore space in a mass of spheres packed in the most compact manner possible, being a plaster cast of the interior of the solid of fig. 4. By piling up a number of 

solids like this, with their similar faces in contact, the continuous pores in a mass of spheres 

would be represented. 

exactly spherica·l in form, but it is true that the length, shape, and 

number of the pores, and other factors affecting the transmission 

capacity, are quite similar in a waterworn sand to those found in a 

mass of shot of proper size. Small variations in the shape of the 

particles have little or no effeet on the result. 

MECHANICAL ANALYSIS OF SOILS. 

A water-washed quartz sand when viewed under the microscope 

looks very like a mass of common gravel or a heap of cobblestones. 

Pl. I, taken from the report of E. R. Buckley, State geologist of 

Wisconsin, on Wisconsin building stones, illw~trates the general 

appearance very well. Soils and sands which have been deposited by 
22 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

running water are often well sorted as to size, but in general a naturally occurring deposit is to be regarded as a mixture of grains of a 

great variety of sizes. It therefore becomes necessary to determine 

the extent to which grains of the various sizes are present in any 

sample and to be· able to express the results in a convenient way. 

The determination of the structure of the soil is known as soil 

analysis, or, more properly, as the mechanical analysis of soils. In 

order to compare one soil with another as to its capacity to transmit 

water, it is necessary to have some way of arriving at a mean or average-sized grain which it is appropriate to associate with each sample. 

This mean diameter is known as the e.ffecti'l'e size, and is such that if 

all grains were of t,hat diameter .the soil would have the same transmission capacity that it actually has. Hazen's method of determining the effective size consists in first separating or analyzing the sand 

or soil into several grades by use of sieves of known mesh. The 

effective size is determined from the dimensions of the mesh of a 

sieve which will permit 10 per cent of the sample to pass through it, 

but will retain the other 90 per cent. r_rhat is, in any soil, 10 per cent 

of the grains are smaller than the effecUve size and 90 per cent are 

larger. 

In order to give expression t.o the variety of sizes present in a sample, Hazen introduces a number known as the un1jormity coefficient. 

To determine this magnitude, first find the size of sand grain which 

is such that 60 per cent of the mat,erial is of smaller grains and 40 per 

cent of larger grains. This result, when divided by the effective 

size of soil grain of the entire sample, gives the uniformity coefficient. Thus, if 60 per cent of a sample be finer than 0.62 mm. and 

10 per cent be finer than 0.25 mm., the uniformity coefficient is~~~!, 

or 2t. Hazen concludes from his experimental work that the 10 per 

cent of small grains in a sample of a natural sand or soil has the same 

influence on the rate of flow of water as the 90 per cent of large grains, 

provided the uniformity coefficient does not exceed 5. 

To illustrate Hazen's method, t,he analysis and diagram {fig. 6) on the 

next page are reprinted from his paper in the report of the Massachusetts State board of health for 18D2, page 547. A curve similar to the 

one here reproduced (fig. 6) should be dravn1 for each analysis, so that 

the points of crossing of the 10 per cent and the 60 per cent lines can 

be determined; from the ordinates of these the effective size and the 

uniformity coefficient are derived. 

Weight [of sample], dry, 110.9 grams. It was put into a series of sieves in a 

mechanical shaker and given 100 turns (equal to about 700 single shakes). The 

sieves were then taken apart, and the portion passing the finest sieve weighed. 

After noting the weight, the sand remaining on the finest sieve but passing all the 

coarser sieves was added to the first and again weighed, this process being repeated 
SLICHTER.) MECHANICAL ANALYSIS OF SOILS. 23 

until all the sample was upon the scale, weighing 110.7 grams, showing a loss by 

handling of only 0.2 gram. The figures were as follows: 

I 

Sieve I Size of 'ep- I Quantity Per cent of 

marked. aration of of sand total 

this sieve. passing. weight. 

' 

~~fillimete rs. Grams. 190 _________ 0.105 0.5 0.5 14() _________ 0.135 1.3 1.2 

• 

100 _________ 0.182 4.1 3. 7 6() __________ 0. 3'20 23.2 21.0 40 __________ 0.46 56.7 51.2 20 __________ 0.93 89.1 80.5 10 __________ 2.04 104.6 94.3 

I 

6 ___________ 3.90 110.7 100.0 

Plotting the figures [in columns 2 and 4], we find from the curve that 10 and 

()0 per cent respectively are finer than .25 and .62 millimeter, and we have for the 

.effective size, as described above, .25 and for the uniformity coefficient 2.5. 

The most promising method of soil analysis for the purpose of determining its transmission capacity is that devised by Professor King. 

70 

.93 .6Z------- 60 

~ I 40.... I ~ ~ r-3~0:-"------~ I ~ ~ q, c .3~ 

1-:~,...,0~----v~ 

.zs 

10 .;a/: 0 .10~ i I 

I 

I 

D11M£T£R 111( MILLIMETERS 

FIG. 6.-Diagram illustrating Hazen's method of making mechanical analyses of soils. 

The analysis is accomplished without the use of sieves, by means of 

an apparatus known as King's aspirator. In this method the effective 

size is determined by measuring the time required for the flow of a 

known amount of air through the sample, the measurements being 

made under a known pressure. It seems that the . results yielded by 

this method are much more concordant than those given by other 

1nethods, and the apparatus desPrves a thorough test by engineers 

interested in soil analysis. a 

a A new method for the mechanical analysis of soils, by F. H. King: Fifteenth Ann. Rept . 

.Agr. Exp. Station Univ. Wisconsin, Madison, 1898, p.123. 
24 MOTIONS OF UNDERGROUND W .ATERS. [NO. 67, 

THE AUTHOR'S FORMULA FOR DETERMINING FLOW. 

The formula which the writer has devised for determining the flow 

of water through a column of sand is as follows: 

l2 

q=0.2012 :~;cubic feet per minute. (3) 

In this formula q stands for the quantity of water transmitted by 

the column of sand in one minute; p is the difference in pressure at 

· the ends of the columns, or the head under which the flow takes place, 

measured in feet of water; sis the area of the cross section of the 

sand column, measured in square feet; his the length of the column, 

in feet; dis the mean diameter of the soil grains, measured in millimeters, or the so-called "effective size;" fl is the number which takes 

account of the friction between the particles of water, and is known 

as the coafficient of viscosity (it is defined as the amount of force necessary to maintain unit difference in velocity between two layers of 

water unit distance apart; its value, which decreases rapidly with an 

increase in the temperature of the water, for temperatures from 32° 

to 100° is given in Table II, below); K is a constant which depends 

upon the porosity of the sand, and its value for porosities, vary~ng 

from 26 to 47 per cent, has been computed and is given in ~rable III, 

on the opposite page. 

TABLE II. 

Variation of the viscosity of water, with temperature, and the relative flow of 

water of various temperatures through a soil, 50° F. being taken as the standard 

temperature. 

Tempera- 1 Coefficient Relative 

t of vis- flow.a ure. cosity p.. 

Degrees F. 

32 

35 

40 

45 

50 

55 

60 

65 

70 

75 

. 80 

85 

90 

95 

100 

0.0178 

0.0168 

0.0154 

0.0142 

0.0131 

0.0121 

0.0113 

O • .DW5\ • ,0.098 

! 8:r:~ \ f 0.081 ' 0.077 1

\ 0.073 

\,Q:~~/ 

! 

0. 74 

0. 78 

0.85 

0.92 

1.00 

1.08 

1.16. 

1.25 

1.34 

1.42 

1.51 

1.62 

1. 70 1.80 

1.90 

a"' Relative flow" means flow at given tempf,rature compared with flow at 50° F. It is 

expressed as a percentage. ! 

I 
SLICHTER.] AUTHOR'S lfORMULA FOR DETERMINING FLOW. 25 

TABLE III. 

Constants for various porosities of an ideal soil. 

Porosity 1 Log.K. Diff. Colog.K. m. K. -----

Per cent. 

0.26 0.001187 1. 9258 563 8.0742 

0.27 0.001350 1.8695 504 8.1005 0.28 0.001517 1.8191 490 8.1809 0.29 0.001694 1. 7701 502 8.2299 0.00 0.001905 1. 7199 467 8.2801 0.31 0.002122 1.6732 455 8.3268 0.32 0.002356 1.6277 400 8.3723 0.33 0.002601 1.5847 4.'38 8.4152 0.34 0.002878 1.5409 410 8.4591 0.35 0.003163 1.4999 407 8.5001 

0.36 0.003473 1.459'2 400 8.5408 0.37 0.003808 1.4193 377 8.5807 0.38 0.004154 1.3816 371 8.6184 

0.39 0.004524 1. 344.') 367 8.6555 0.40 0.004922 1.3078 35.'3 8.692'2 0.41 0.00.5339 1.2725 351 8. 7275 

0.42 0.005789 1.2374 345 8. 7626 0.43 0.006267 1.2029 339 8. 7971 0.44 0.006776 1.1690 320 8.8310 0.45 0.007295 1.1370 312 8.8600 0.46 0.007838 1.1058 329 8.8942 0.47 0.008455 1.0729 _.,.,....,._,..,._ 8.9271 

If t stands for temperature of the water Fahrenheit, the author's formula, in which the coefficient of viscosity has been replaced by an 

expression varying wUh t.he temperature similar to that given in the 

formula of Hazen, may be written.as follows: 

q=11.3 ~~a:;;_ [1+0.0187(t-32)] cubic feet per minute. (4) 

It is seen from the above formula that the quantity of water transmitted by a column of sand not only depends upon the length of the column and the head of water as expressed by Darcy's law, but varies in 

a most remarkable way with the effective size of the soil grain, with 

the temperature of the water, 3nd with the porosity. Since the flow 

varies as the square of the size of the soil grain this element in the 

formula has a most important effect, as doubling the size of the soil 

grain will quadruple the flow of water. Thus the flow through a sand 

whose effective size of grain is 1 mm. is 10,000 times the flow through 

a soil whose effective size of grain is 0.01 mm. The variation of flow 

with temperature is also important, as the flow at 70° F. is about 

double that at 32° F. The variation in porosity is quite as importa-nt 

as the variation in temperature. 

From Table III it appears that if two samples of the same sand are 

packed, one sample so that its porosity is 26 per cent and the other· 

sample so that its porosity is 47 per cent, the flow through the latter 

sample will be more than seven times the flow through the former 

sample. If the two samples of the sa:me sand are packed so that their· 

porosities are 30 per cent and 40 per cent, the flow through the latter 
26 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

sample will be about 2. 6 times the flow through the former sample. 

These facts should make clear the enormous influence of porosity on 

flow, and the inadequacy of a formula of flow which does not take it 

in to account. 

Part of the expression on the right side of formula (3) or (+)depends 

only upon the character of the soil through which the water is passing. Representing this by k we have: 

(12 

k=o.2o12 flx=JJ£d2

, 

and the formula for the flow becomes 

(5) 

(6) 

which is essentially Darcy's formula. The constant k is the quantity 

of water that is transmitted in unit time through a cylinder of the 

soil of unit length and unit cross section under unit difference in head 

at the ends. We shall frequently refer to k as the transmission constant, or merely as the constant of a soil. 

It should be especially noted that the velocity of flow through a soil 

for the pressure gradients and size of grain that commonly occur is 

exceedingly slow, and much less than might at first be supposed. 

Darton states that tho rate of flow in the sands of the Dakota formation, from which the remarkable artesian wells of South Dakota draw 

their supply, does not exceed a mile or two a year. a Mr. E. L. Rogers 

Teported to the Denver society of civil engineers b that American estimates agree with careful and exhaustive studies of French engineers, 

which show the average velocity in sands to be about a mile a year, 

tOr about an eighth of an inch a minute. In Arizona the rate has been 

:figured out as between one-fourth and one-third of an inch per minllte, while on Arkansas River above Dodge, Kans., a ditch a mile 

long and 5 feet below the water table in the sand developed a flow of 

about three-eighths inch per minute. 

a New developments in .;-ell boring and irrigation in eastern South Dakota, by N.H. Darton: 

Eighteenth Ann. Rept. U.S. Geol. Survey, Part IV, l89'i, p. 600. 

b Engineering Record, Vol. XXV, p. 4351. 
SLICHTER.) SIZES OF SOIL GRAIN AND .PRESSURE. 27 

TABLE IV. 

Velocity of water in sands of 'Oarious effecfi1'e sizes of soil g1·ain and the maximum 

flow or transmission constant fm· each soil. 

[Porosity, 32 per cent; temperature, 50° F. Results for other porosities can be found by the use 

of Table V, and for other temperatures by the use of Table II.] 

1. I 2. I 3. 4. 5. I 6. I 7. 

Diameter I Velocity, Velocity, V13locity, Maximum Logarithm I 

of soil pressure pressure pressure tra~~~~~ion ?f numbers I Kind of soil. grain. gradient 1:1. gradient 1:1. gro.dient 100 constant, k. In column 5. feet to 1 mile. 

Miles pe1· Miles per Ou.jt.per 

Mm.. Ins. per min. yea1·. year. twin. 

0.01 [ 0.0014 0.0113 0.00026 0.000036 5. 5.569 )sm. 0. O"Z 0. 0054 0.0452 O.OOHrZ 0.00014! 6.1590 0.03 0.0122 0.1016 0.00230 0.000324 6.5111 0.04 0.0218 0.1807 0.00408 0.000577 6. 7610 0.05 0.0340 0.2823 0.00638 0.000901 6. 9548 0.06 0.0490 0.4065 0.00918 0.001298 7.1132 }Very fine 0.07 0.0667 0.5534 0.01250 0.001766 7.2471 0.08 0.0871 0. 7223 0.01633 0.002308 7.3631 sand. 

0.09 0.1103 0.9147 0.02066 O.OOZ920 7.4654 0.10 0.1361 1.129 O.O'Z551 0.003605 7.5569 

lFffie~nd 0.12 0.1961 1.627 0.03674 0.005192 7. 7153 0.14 0.2668 2.213 0.05011 0.007065 7.8491 0.15 0.3063 2.541 0.05753 0.008112 7. 9091 0.16 0.3485 2. 89'Z 0.06382 0.009'Z28 7. 9651 0.18 0.4412 3.659 0.08266 0.01168 8.0675 0.20 0.5446 4.518 0.1021 0. 01442 8.1590 0.25 0.8509 7.058 0.1594 0.0'2253 8.3528 0.30 1.225 10.16 0.22£6 0.03244 8.5111 }Medium 0.35 1.668 13.84 0.3125 0.04417 8. 6451 0.40 2.178 18.07 0.4081 0.05768 8. 7610 sand. 

0.45 2. 757 22.87 0.5165 0.07300 8.8633 0.50 3.403 28.23 0.6377 0.09012 8.9548 0.55 4.119 34.17 0. 7718 0.1090 9.0377 0.60 4.901 40.65 0. 9183 0.1298 9.1132 0.65 5. 751 47.81 1.077 0.1523 9.1827 0.70 6.671 55.34 1. 250 0.1766 9.2471 Coarse 0. 75 7.660 63.53 1.435 0.2028 9.8l71

1 

~nd. · 0.80 8. 714 72.28 1.633 0.2308 9.3631 0.85 9.835 81.57 1. 843 0.2604 9.4157 0.90 11.03 91.47 2.066 0.2920 9.4654 0.95 12.28 101.9 2.302 0.3253 1.00 

2.00 13.61 54.46 112.9 451.8 10.21 

2.551 1.442 

0.3605 0.1590 ~:~} 3.00 122.5 1,016 22.96 3.244 0.5111 Finegravel. 4.00 217.8 1,807 40.81 5. 768 . 0. 7610 5.00 340.3 2,823 63.77 9.012 0.9548 

Table IV, above, gives the velocity of movement of water .in sands 

of various grades for different pressure gradients. Column 1 gives 

the effective size of the soil grains in millimeters. As already stated, 

this size is such that if all grains were of that diameter the soil would 

have the same transmission capacity that it actually has. Column 2 

gives the velocity of flow, or the rate at which the water moves through 

the ground in inches per minut,e under a pressure gradient of 1 foot 

difference in head to each foot of distance. Column 3 gives the velocity of flow reduced to miles per year, the pressure gradient being the 

same as in column 2. Column 4 gives the velocity of flow in miles 

per year under a -pressure gradient of 100 feet to the mile. The 

velocity for a pressure gradient of 10 feet to the mile would be onetenth of the numbers in this (fourth) column, and so on for other 

gradients. Column 5 gives the actual discharge in cubic feet per 

minute for each square foot of cross section if the pressure gradient 

be 1 foot difference in head for each foot of distance. For a pressure 
28 MOTIONS OF UNDERGROUND W .ATERS. [NO. 67. 

gradient of 1 foot difference in head for each 100 feet of distance, the 

flow per square foot will be 0.01 of the tabulated numbers, and so on 

for other gradients. The numbers in this {fifth) column have also 

been called the "transmission constants," and have been represented 

in the formulas by k. 

TABLE V. 

Rclati'L·e flow of water through sands of same effective size grain, but packed so 

as to possess different porosities. 

p~~~t~l ;r~1J's~r Relative 

flow." 

30 0.81 

32 1.00 

34 1. 2'~ 

36 1. 47 

38 1. 76 

40 2.09 

a "Relative flow" means flow for the given porosity compared with flow for porosity 32 per cent as standard. It is expressed in the table as a percentage of the flow for a sample having a porosity of 32 per cent. 

MAXIMUM FLOW. 

Inasmuch as the flow of ground water is nearly always caused by a 

difference in head due to gravity only, the maximum flow t.hat is posA/ 

I 

I 

I 

I 

I 

I 

I 

-¥ 

GAADlEtfTJa 

Maximum flow 

tRAOJENT t:l.4 

flow.'o/ .... maximun) 

GRADIENT t:2 

Flow Yz maximum 

FIG. 7.-Diagram illustrating various pressure gradients and the maximum flow. In these three 

cases the upper portions of the soil columns are supposed to be supplied with water as fast 

as it can flow through the columns. The escape at X, Y, Z is supposed to be perfectly free. 

The head under which the flow takes place is h, in each case, as shown at the left of the figure. 

The various lengths of the soil columns, lh 12, and 13 produce the pressure gradients h/11 = 1; 

hjl2 = 1\; and hjl3 = i, respectively, with the resulting flows in proportion if the material in 

the various columns be the same. 

sible is found in the case in which the ground water is free to move 

in a vertical direction, as in a perfectly underdrained sand-filter bed. 

The motion in this case is due to the weight of the water of saturation, and the flow is of course greater than would be the case if the 

water were obliged to flow in a direction inclined to the vertical, instead of in the vertical direction as supposed. These facts are illus-

. tratetl in fig. 7. The flow in the case of pressure gradient 1:1 forms 

a most convenient basis for calculation, and it is frequently called, 

as suggested by Hazen, the maximum flow. The flow for any other 

gradient is immediately calculable from the maximum flow-for a. 
SLICHTER.] MAXIMUM FLOW. 29 

gradient 1:100 the flow being, of course, one one-hundredth of the 

maximum flow. 

The appropriateness of the term maximum flow is illustrated by 

fig. 8, which shows the original water table and the depressed water 

table due to the construction of a drainag~ ditch. It is plain that the 

pressure gradient for all of the streams of flow marked by arrow 

heads is less than the gradient 1:1. If the wetted area of the ditch 

be multiplied by the maximum flow for the kind of material in which 

the ditch has been excavated the flow thus computed will in every 

case exceed the flow actually determined by measurements of the 

yield of the ditch. 

FIG. 8.-Diagram showing lines of flow into a drainage ditch and the shape of the water table 

in its neighborhood. The head under which the flow takes place is the difference in height of 

the original water table and the level of the surface of the water in the ditch. This is much 

less than the lengths of the curved lines of the flow into the ditch, hence the rate of flow 

must be much less than the so-called maximum flow. 

There is not uniformity in the use of the term velocity as applied to 

the motion of ground waters. We use the term to express the rate 

(measured as so many feet a day, etc.) at which the water advances 

through the porous medium, irrespective of the amount of water thus 

advancing. The amount of ground water (measured in cubic feet per 

minute, etc.) passing through a given cross section the writer has 

called the flow or the discharge. It is equal to the velocity multiplied by the porosity. Some measure velocity as a rate of motion in a 

solid column of same area as the cross section of the porous medium. 

This is the same magnitude which we have called flow. 

In using Table IV one should use the numbers in columns 2, 3, or 4 

if the velocity of ground water is wanted, but should pass to column 

5 if the flow or yield is required. Thus, suppose it is desired to find 

the rate of motion of ground water through a bed of sand which slopes 

10 feet to the mile. The results can be found for various materials 

and grades of matedal by dividing the numbers in column 4 by 10, 

since a slope of 10 feet to a mile will cause but one-tenth of the velocity 

existing for a slope of 100 feet to a mile. For materials of various 

grad~s we obtain the following results: 

Velocity of ground water 1'n rnaterials of different grades, pressure gradient 10 

feet per mi~e. 
30 MOTIONS OF UNDERGROUND W ATERR. (NO. 67. 

Suppose that it is desired to ascertain the amount, of water that will 

pass t.hrough a bed 200 feet deep and 1,000 feet wide, having the same 

slope as that just mentioned. This problem requires us to find the 

flow, and the numbers used in the computation should t.herefore be 

taken from column 5 of Table IV. The flow for 1. square foot of 

cross section of the bed will be -d-lo of the maximum flow given in 

that column for material of various grades, and the total flow is found 

by multiplying t.he maximum flow by -d-lo X 200 X 1,000, which gives 

the following results for the same materials described in the preceding 

table: 

Flow of grot1:nd wate1· in rnaterials of different grades through a bed of vertical 

cross section 200 by 1,000 feet, sloping 10 feet per rnile. 

Cu. ft. per miu. 

Fine sand__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5. 5 

Medium sand ______ . ____________________________ . ____________ . _ _ _ 22.0 

Coarse sand ________________________ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 87. 0 

Fine graveL _____________________________________________________ 546. 0 

The estimates in Table IV were based upon a porosity of 32 per 

cent. For other porosities the results must be changed by the percentages shown in Table V. Thus all of the results just found must 

be increased by about 37 per cent if the porosity of the material be 

35 inst,ead of 32 per cent. 
CHAPTER II. 

SUR~,ACE ZONE OF FLOW OF GROUND WATERS. 

)'lost people obtain their ideas of underground streams of water 

from the descriptions of the underground torrents in the Mammoth 

and other caves. Such notions, however, are erroneous. The rivers 

found in caverns are almost exclusively peculiar to limestone or 

calcareous formations and are not typical of subterranean streams. 

The underground drainage of calcareous rocks is, nevertheless, of 

great interest. The well-known solvent action of rain water percolating through limestone has no more beautiful demonstration than the 

existence of caverns like the :Mammoth Cave, with its scores of miles 

of ramifying passages and its enormous vaulted chambers. As is 

well known, these galleries and passages represent the channels of 

former subterranean streams which for the most part have now found 

escape at lower levels. Maps of such caves show that the passages are 

arranged somewhat like the branches of a tree-very similar, indeed, 

to the divisions and subdivisions of surface drainage as represented 

by the main river, the lesser rivers, and the tributaries. 

As a rule, the running streams of limestone caverns, as well as those 

found in the seams, joints, fissures, etc., of crystalline and other rocks, 

join the surface-drainage system before they have attained any considerable size. Therefore large cavern streams are very rare, and 

when discovered they have attracted wide attention. The Echo 

River of the Mammoth Cave, one of the largest and best known of 

this type, is from 20 to 200 feet wide and from 10 to 40 feet deep. 

Sometimes little can be directly observed of a subterranean stream 

except the enormous spring which marks its mouth. The famous 

Wyandot Spring, near Columbus, Ohio, representing the drainage of 

a considerable area collected into ramifying passages in the Corniferous limestone, is a good example of this type, as are also the enormous 

fresh-water springs in the ocean off the coast of Florida. 

Pl. II shows a sink hole connecting with an underground drainage 

system, and an underground channel, as observed by Mr. Willard D. 

Johnson on the southwestern plains. The writer is indebted to Mr. 

Johnson for the photographs. 

Putting the subterranean streams of the limestone type into a class 

by themselves, there remain the great systems of underground drainage represented by the slowly percolating waters of sand and gravel 

deposits, sandstones, and other porous materials. It is this class of 

31 
32 MOTIONS OF UNDERGROUND W .ATERS. [No.67. 

subsurface drainage that we must regard as the important one, both 

because of its actual areal extent and because of its economic importance as a possible source of water supply. It is the water of this 

type of underground drainage that is properly designated ground 

water or underground water, the running water of crevices and caverns rarely being uppermost in mind when this term is used. 

Underground waters may be divided into three principal zones: (1) 

The unsaturated zone; (2) the surface zone of flow; and (3) the deeper 

·zones of flow. 

The motion of water in the unsaturated zone is essentially in a verti-_ 

cal direction, downward, supplying the saturated sheet below it in times 

of rainfall, and upward supplying the surface evaporation and the 

r(':quirements of vegetation by means of the capillary action of the 

soil during rainless periods. A special discussion of this zone of 

ground waters does not come within the scope of this paper, and is 

therefore omitted. 

The surface or upper zone of flow extends from the level of the 

water table to the first impervious material of general extent reached 

by the underground water in its downward percolation. 

The deeper zones of flow are those that lie below the first impervious 

stratum. rrhere may be several zones falling within this class. In 

these zones the direction and character of the flow are usually quite. 

independent of surface topography and are almost entirely controlled 

by large regional and geologic conditions. Special consideration of 

the deeper zones of flow will" be postponed to a later chapter of this 

paper. 

UNDERGROUND DRAINAGE BASINS. 

The unit of the surface zone of flow of ground waters is the river 

valley. In the surface zone t,he rate and direction of motion of the 

underground water conforms primarily to the slopes and grades of the 

land surface. The effective principle in the surface zone is that underground flow follows the trend and direction of the surface drainage. 

The direction taken by the surface waters in their course into 

streams and drainage channels is in general the same as that taken 

by the see-~ waters of the upper zone of flow. As previously 

pointed out, actual determinations usually show that the water table 

has a slope which is essentially similar to the slope of the surface 

of the ground, differing from the latter principally in being less 

steep. The surface divide or watershed usually coincides with the line 

of the underground water divide or watershed, and the motion of the 

underground seepage into the streams and rivers is similar to the 

lines followed by the surface·drainage into the same streams. 

The lowest line of drainage of the valley is known technically as 

the thalweg. Topographically it is a line upon a contour map which 

is a natural water course. Beneath the thalweg there is usually a similar drainage line for the underground current, in general·coincident 
U. S. GEOLOGICAL SURVEY WATER·SUPPLY PAPER NO. 67 Pl. II 

A. SINK-HOL E CONNECTION WITH UNDERGROUND DRA INAG E SYSTEM. 

B. UNDERGROUND CHANN EL, 
SLICHTER.] UNDERGROUND DRAINAGE BASINS. 33 

with the thalweg. For other parts of the valley the actual lines of 

motion of the underground water are represented by a set of curves 

which cut the contour lines of the water table at right angles, as shown 

in fig. 9. The similarity of the contours of the water table to those of 

the land surface enables one to sketch approximately the lines of 

underground seepage from a contour map of the su1·face. 

For the most part tlie lines of flow run into the surface streams or 

thalwegs, but between A and B and X and Y there is indication of 

an underflow or general movement in the direction of the surface 

streams and independent of the same. 

FIG. 9.-Contour map showing position of water table (continuous lines), supposed lines of 

motion of ground water (arrowed lines), and the thalwegs or drainage lines (heavy lines). 

It is claimed by Chalon, a a. French engineer, that the subterranean 

thalweg. on the main line of underground drainage is usually nearer 

the steeper side of the valley than is the surface stream. (See fig. 10.) 

Such principles are emphasized in foreign treatises, but American 

experience has not found them of great value. 

SHAPE OF THE WATER TABLE. 

The similarity between the contours of the land surface and the 

contours of the water table just explained must not be taken too 

literally. The coincidence of the surface and subterranean thalwegs and of the surface and subterranean watersheds is a common 

occurrence, but is not a geologic necessity. In itself the surface topoga Sur la recherche des eaux souterraines: Mem. Soc. ingeniem"S civils de France, 1897, Vol. II, 

p. 38. See also L'Art de decouvrir les sources, by L'Abbe Paramelle, fourth ed., Paris, 1896, 

p.138. . . 

IRR 67-02--3 
34 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

raphy is only one, and often not the most important, element in the 

control of the underground current. 

FIG. 10.-Diagram illustrating Chalon's principle that the main core of the underground 

drainage, or subterranean thalweg, naturally lies nearer the steeper side of the valley than 

dqes the surface stream. The surface stream is at Tv and the subterranean thalweg at T8 • 

The horizont,al distribution and motion of the ground water is influenced first of all by the form of the surface of t,he impervious layer. 

FIG. H.-Diagram illustrating lines of flow of ground water over a series of monoclines, synclines, and anticlines, as at M, S, and A, respectively. 

It is also influenced in a 1narked degree by the varying altitude of the 

surface or receiving area, by the character of the pervious layer, by the 
SLICHTER.] SHAPE OF THE WATER TABLE. 35 

altitude and distance of the nearest thalweg or drainage channel, and 

finally by the amount of the rainfall. These elements acting together 

in a region determine the depth of the water table below the surface and 

the direction and rate of motion of the underground current,. They 

form a complicated system, and it is not easy to describe t,he precise 

part which each plays in a given case. Fine material and large rainfall tend to make the ground water Rtand high within the hills and 

elevat,ed places and to give steep gradients to the water table. I...~ikewise coarse material and light rainfall tend to a low water t,able and 

to light gradients. From these considerations it is obvious that the 

form of the impervious stratum affects the water table much less in 

humid climates t,han in semiarid or ariel climates. 

It is also important to remember that synclines in the impervious 

material (as at S, fig. 11) crossed by the lines of motion of the ground 

FIG. 12.-Diagram illustrating lines of flow of ground water over a series of monoclines i:u an 

impervious bed. 

water ,have no effect on the form of the water table. Hmvever, if the 

lines of motion follow a syncline instead of ·crossing it, the water 

table also will probably have a synclinal form, although less pronounced than that of the impervious layer. :Monoclines in an impervious floor crossed by moving ground water will give a similar form 

to the water table, as shown in fig. 12. We may normally expect, 

then, that the water table in the direction of' the lines of motion will 

be a series of monoclines, as shown in figs. 1, 11, and 12, with only occasional deviations during periods of rainfall. 

rrhe motion of the ground water as a whole is somewhat like the 

slow motion of a very viscous sirup or the slowly creeping ice of a 

glacier. These comparisons, however, are likely to be misleading. 

In the slow motion of a viscous liquid the bounding layer sticks fast 

to the walls of the vessel containing the liquid, so that motion nearly 
36 MOTIONS OF UNDERGROUND WATERS. [N0.67. 

ceases in the neighborhood of the boundary. This is not the case, however, 

in the movements of ground waters, 

as the frictional resistance which the 

water meets is present in each individual pore between the soil particles, 

and is not transmitted from layer· to 

layer through the water itself, as in 

the case of a viscous liquid. If the 

material is no finer near the impervious layer or boundary the resistance to motion per unit length is no 

greater at the boundary of the region 

than in its interior. This uniform distribution of the resistance to motion 

throughout the mass of the ground 

water, and the separation of each individual stream in a capillary pore 

from every other similar stream in the 

neighboring pores makes t,he character of the motion difficult to understand. The motion of water in pipes, 

canals, and surface stream·s is an exceedingly poor and a very misleading 

analogy. If it were not for the everpresent controlling influence of gravit,y 

the motion would be entirely analogous to the flow of heat or electricity 

in a conducting medium, as the writer 

has shown in another paper. a 

A remarkable conclusion from the 

paper just cited is that ground-water motions resemble in general character the motions of a "perfect" or 

frictionless liquid under similar conditions but with the porous medium 

entirely absent. The chief difference 

lies in the fact that in the case of 

a perfect liquid gravity produces a 

rapidly accelerated motion, the energy 

represented by the increase in the motion being the equivalent of the work 

done by the external forces (gravity), 

while in the case of the motion of the 

water in the pores of the medium 

a See Chapter r:: of Theoretical investigation of the motion of ground waters: Nineteenth Ann. 

Rept. U.S. Geol. Survey, Pt. II, 1899, p. 295. 
SLICHTER.] COMPARISON WITH FJ ... OW OF HEAT. 37 

most of the energy contributed by the work of the e~ternal forces 

is transformed into heat by the enormous friction in the capillary 

spaces. Thus in fig. 12 the velocity along the various lines of flow, 

represented by the continuous curves with arrowheads on them, 

is substantially_ the same for each line, since they are of practically 

the same length. The water flows along them just as heat would flow 

along a conducting material of the same shape. Likewise in fig. 11 

the velocity along the lower lines of flow is somewhat less than along 

the upper lines, for the lower linet:; have the greater length. Again 

we may imagine that the ground water flows along them just as heat 

would flow along a conductor of similar shape, unless the ground 

water is about to escape to the surface drainage, as at s· in figs. 25 

and 26; in this case the effect of gravity is to give relat.ively high 

velocities to the water lying next to the impervious floor. The writer 

has shown that the velocities and lines of motion can be calculated for 

such cases, some results being shown in figs. 14 and 15. 

The contention of some German hydrographers that there can b~ 

no motion a in a region like ASB in fig. 11 must be entirely a ban· 

doned. The water must circulate in all parts of the enlargements in 

the porous medium, f0rthe same reasons that heatwo~ld be conducted 

. . ~ 

FIG. 14.-Diagram showing seepage lines in a pervious bed resting upon an impervious floor. 

~ A, B, C, Dis a vertical section. Rain falls upon the surface AB and finds free escape at the surface AD. The curved lines show the paths along which the seepage takes place. The effect of 

gravity is to draw these lines close together near the impervious floor. 

over similar enlargements in a conductor. A~l lines of motion must 

begin and end in the· boundaries of the water-bearing medium, and 

must entirely traverse and completely occupy all enlargem~nts in the 

porous strata. 

As already indicated, the general trend of the moving underground 

water, under the influence of gravity, is into the neighboring streams 

and lakes. This motion must be materially modified by many causes, 

which frequently present most complex combinations. While the 

return flow of ground water to the water courses by means of dif· 

fused and almost imperceptible seepage is the rule, yet we must 

remember that geologic conditions may be such-for example, the 

outcropping of an impervious stratura-as to force the water table 

above the surface of the ground and converge and concentrate the 

lines of flow into a strong current. In the latter case we have 

the phenomenon of the flowing spring. Ground wat.er returning to 

the surface in the form of springs so quickly attracts observation 

a Otto Lueger, Wasserversorgung der Stadte, p. 127. 
38 MOTIONS OF UNDERGROUND WATERS .• [NO. 67, 

that the more important but less obvious return in the form of diffused seepage almost entirely escapes attention. 

FlO. 15.-Diagram showing direction and rate of seepage in a pervious bed resting upon an 

impervious floor. The directions and lengths of the arrows show, respectively, the direction 

and the velocity of motion at various points in the pervious bed. Rain falls upon AB and 

escapes at AD, as in fig. 14. 

THE UNDERFLOW. 

The ground water after starting on its journey toward the river 

valley may not after all find its way immediately into t11e channel. 

Sometimes it takes a general course down the thalweg and toward the 

sea within the porous medium itself. This movement may be so great 

as to constitute a large underground stream, scores of feet in depth 

and miles in breadth. 

The moving sheet of water beneath the bed and banks of a stream 

is the underflow, properly so called. This term is also extensively 

used in the West to designate the nearly stationary ground water of 

the Great Plains. It originated with those who formerly believed 

that there was a great sheet of water beneath the surface of the Plains, 

originating in the melting snows of the R.ocky Mountains and flowing 

rapi.9-ly through the subsoil toward J\ilissouri R.iver and the sea. 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 67 PL. Ill 

• 

< 

.,.. 

(' 

< 

~ 

,.I- ! IZ I! 

- MAP SHOWING THE DELTAS OR FANS OF DISAPPEARING STREAMS AS THEY LEAVE 

THEIR MOUNTAIN CANYONS. 
SLICHTER.] THE UNDERFLOW. 39 

It is evident that a considerable underflow is impossible with 

material as fine as is sometimes found filling the valleys of rivers. 

Such material may playa very important part in the·storage of water, 

but it can not be an important element in its tritnsportation over 

great distances. An entirely different condition may exist where the 

sands and gravel beneath the stream are sufficiently coarse, as is likely 

to be the case near the source of streams in the mountains. Here the 

material deposited by the stream is the coarser sands, gravel, and 

bowlders brought down by the ri1ountain torrents. The running 

water will no.t deposit the finer material until the stream bed reaches 

a gentle slope and the current has lost its high velocity. The periodic 

floods sweeping down the mountain sides during the heavy rains soon 

fill the river canyons with coarse debris, on the surface of which the 

perennial stream has its bed. Below the bed of the stream there is a 

vast body of water slowly percolat,ing through the coarse material. 

Occasionally as we pass down the stream we may find the rock walls 

of the canyon nearer together, or perhaps the bed rock beneath the 

debris is closer to the surface, the result in either ease being a marked 

augmentation of the amount of water in the river, because the percolating waters of the underflow are forced to the surface and mingle 

with the waters of the surface stream. 

At the mouth of the canyon the valley broadens out and the bed 

rock sinks more deeply beneath the surface of the land, while the 

stream deposits more and more of its suspended matter. The underflow may also broaden and deepen to fill the greatly enlarged channel, 

· the finer material and lesser slope decreasing the speed with which 

it flows down the valley. The valley may be now so broad that if the 

rainfall be copious the constant increments to the underflow from 

seepage of the rainfall from the higher land must give rise to regular · 

flow of the subsurface waters into the perennial stream itself,. causing 

its constant growth during its course toward the sea. On the other 

hand, if the stream issues from its mountain canyon in an arid region 

the surface stream may gradually disappear, until a dry wash through 

the valley, only occasionally swept with floods- from the mountains, 

marks the general course pursued by the silent underflow. 

Numerous instances of the disappearance of mountain streams 

occur in the arid regions of the West. There are many interesting 

cases along the Coast Range in California, two of which are shown 

on the ~Cucamonga topographic atlas sheet of the Geological 

Survey. From that map will be seen the way in which the disappearing streams fan out into numerous branches, which are very appropriately called, from analogy, the deltas of the rivers. In Pl. III 

are shown the distributing deltas of King, Kaweah, and Kern rivers, 

California, as they enter San Joaquin Valley from their canyons in 

the western edge of the Sierra Nevada. There can be no question 

that the underflow in this case follows the gene1·al trend indicated by 

the surface branches. 
40 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

It has been pointed out how the broadening of the valley, as a 

stream flows out of its mountain canyon, will have effects entirely 

opposite, depending upon whether the climate of the valley be arid 

or humid. If t.he climate be arid the broadening of the valley will 

expose the underflow to increasing evaporation during its slow movement in a broad belt, while if the limate be humid the bro~dening 

of the valley will greatly increase the collecting area of the rainfall 

and constantly contribute a part o the underflow to the water of the 

river itself. In one case the broac ening of the valley is t.he oc~asion 

of the constant diminution of th volume of the river; in the other 

case it is the occasion of the const nt growth of the river. 

The relation of the underflow t the waters of the river channel 

presents many interesting phenom na and variations. In some cases 

silt may have rendered the chan el of the river so impervious that 

for considerable distances little i terchange can take place between 

the river waters and the underfl w waters. This sealing effect of 

river silt is illustrated in an att mpt by Nettleton to measure the 

velocity of the underflow of the io Grande. a The plan was to sink 

holes in a sandbar a little below t e water line, with the expectation 

that the water would rise in the1 to the level of the river surface. 

It was then proposed to note the ti 1e it took a colored liquid to travel 

from one hole to the next one dow stream. But even on this island, 

surrounded by water and still u der water a few days prior to the 

experiment, and to all appearance composed of the same material as 

the river bed and its banks, the~ did not succeed in finding water 

3 feet below the surface. The h les were within a foot of the river 

and yet no water came into them ithin twenty-four hours. 

1.,hat underflow wat.ers are so etimes quite independent of the 

water flowing in the surface strea is abundantly shown by the experience of German water-supply engineers. B. Salbach cited some 

interesting examples before the engineering congress at the Chicago 

World's Fair in 1893. b In 1867 Sal bach was called to report upon the 

preliminary works then under way for testing the sources of supply 

.of the city of Halle. These works consisted of borings in the Aue, 

near Beesen, above the junction of the Elster and the Saale, in a 

thick and widely extended bed of gravel, and in pumping large quantities of water from a well which a chemical analysis had shown to be 

suit.able for the proposed supply. 

It had been assumed, before undertaking the examinations, that 

the water from the neighboring rivers had penetrated this bed of 

gravel. That this assumption was erroneous was speedily proved. 

In the first place, the water taken from the gravel was shown to have 

a See Final Report of Chief Engineer E. S. Nettleton: Ex. Doc. 41, Pt. II, Fifty-second Congress, first session, p. 35. 

bExperiences had during the last twenty-five years with waterworks having an underground 

source of supply. by B. Balbach, Baurath at Dresden, Saxony: Trans. Am. Soc. Civil Eng., Vol. 

XXX, 1893, pp. 293-329. 
SLICHTER.] RATE OF MOVEMENT OF THE UNDERFLOW. 41 

an entirely different chemical composition from that of the river -

water, the water from the gravel being harder than that taken from 

the river, while the water of the Saale gravel was still harder than 

the water of the Elster gravel. In the next place, it was shown by a 

series of experiments that a natural filtration of the river water was 

wholly impossible. To prove this several wells were dug along the 

shore of the river, and 1,he ground-water level in them was reduced, 

by pumping, about 4 feet lower than the river level. When this was 

done the earth over the whole water level on the river side was 

entirely dry. Extending the well laterally until within about 14 

inches of the bank of the river caused no flow of water from the bed 

of the river into the well, this last 14 inches of soil being dense and 

impervious. These examinations proved that in this case at least 

there was no flow of water from the river into the bed of gravel of the 

valley, and that the water drawn from the wells was au independent 

underground source of supply which flowed parallel to the river 

through the gravel anrl followed the general slope of the valley. 

Salbach also gave an account, of t,he water-bearing gravels of the 

valley of the Elbe. Several bore holes put down on the right bank of 

the Elbe showed a steep slope of the water table at right angles to the 

river. The ground water taken from these holes was found to be 

exceedingly pure and of an appreciably less degree of hardness than 

the water of the river. Borings on the left bank showed a less slope 

of the water table at right angles to the river, while the samples of 

water taken from the borings were pure, but somewhat harder than 

the water of the Elbe. Borings put down in the river itself to a depth 

of from 23 to 26 feet showed that the ground water rose in the bore 

holes 6 inches above the level of the river, while the water was softer 

than the river water. It is a remarkable fact that the ground water in 

almost the entire valley of the Elbe is softer than that of the river. 

RATE OF MOVEMENT OF THE UNDERFLOW. 

The magnitude of the underflow depends, obviously, upon many 

important factors. One of these is the average gradient of the river 

valleys. Others are the depth, width, and composition of the beds 

which constitute the alluvial deposits of the stream. The fineness of 

this alluvium is of special importance. An inspection of Table IV 

(p. 27) will show that a coarse sand or gravel will permit an underflow 

of considerable magnitude. On the other hand, a fine material will · 

render the underflow quite insignificant. 

Direct observations of the rate of motion of the underflow are almost 

completely lacking in this country. A number of indirect observations of various kinds enable us, however, to form an idea of the possible rates under special circumstances. One of the highest determinations of the rate of underflow is that made by Hicks for Loup 
42 MOTIONS O:F' UNDERGROUND WATERS. (NO. 67. 

River in Nebraska. a In the region considered September is a relatively dry month, much drier than August. The maximum rainfall 

usually occurs about the middle of July. N otwithstandin~ the marked 

decline in precipitation, and quite independent of the state of the 

weather at the time, the Loup rivers generally rise in September. 

The increase in volume is slight, yet perceptible, and, occurring in a 

dry month, can not be explained by contemporary causes. Hicks 

believes the rise to be due to the July rainfall upon the neighboring 

undrained areas, which amount to about one-third of the entire basin. 

~,he percolating waters reach the rivers about two months after they 

have fallen as rain, and estimating the average distance traversed by 

the subterranean water as 20 Iniles, Hicks computes the rate of flow 

to be about one-third of a mile per day. This rate of flow is so enormous, as can be seen by reference to the fourth column of Table IV, 

·that the explanation must be defeetive. Possibly the phenomena 

may be explained by t,he lesser evaporation of September. 

More satisfactory conclusions as to the rate of the underflow may 

be deduced from the measurements of s~page reported by Professor 

Carpenter. 0 Estimates basell upon the seepage from the Fort Morgan 

canal and a new section of the same canal gave for the first a velocity 

of about 3 feet a day and for the second a \~elocity of about 15 feet a 

day. Water Commissioner J. ~r. Hurley reports to Carpenter that the 

seepage from the Weldon Valley canal has progressed 1f miles in five 

years. N. C. Alford reports that in one case, under the I.Jarimer 

County canal, it was five years before seepage showed at a distance 

of 40 rods from the canal, though the slope was considerable. In one 

case, near Greeley, according to Mr. S. A. Bradfield, it seems to have 

taken about ten years foi.· the water to move 2f miles.c 

C. E. Grunsky has measured the seepage loss in King River and 

the Fresno canal, California, ct and found that the losses for various 

sections of the canal were 3. 77, 3.48, and 1.25 second-feet per mile. 

The average velocities of seepage through the canal bed, calculated 

on a basis of average width of 40 feet and a porosity of 33 per cent, 

are, respectively, 4.8, 4.3, and 1.6 feet per day. According to the same 

authority the losses on various portions of the Fresno canal were 8.49, 

0. 7 4, and 0. 95 second-feet per mile. The average velocities of seepage, 

calculated on a basis of width.of canal bed of 50 feet, are, respectively,. 

8.4, 0. 7, and 0.1 feet per day. The average losses on a 6-mile and a 

1-mile section of the Centerville Rnd Kingsbury canal were, respectively, 15.63 and 52.35 second-feet per mile. These figures lead, on a 

basis of canal width of 50 feet,, to the enormous seepage velocities 

of 16 and 52 feet per day, respeetively. For a number of miles this 

a On the underflow and sheet water, etc., by L E. Hicks: Ex. Doc. 41, Pt. III, Fifty-second Congress, first session, Washington, 1892, p. 187. 

~·Seepage or return waters from irrigation: Bull. Colorado Agr. Exp. Sta. No. 33, p. 45 et seq. 

cOp. cit. · 

dirrigation near Fresno, Cal., by C. E. Grunsky: Water-Supply and Irrigation Paper U. S. 

Geol. Survey No. 18,1898, pp. 76, 77. 
SLICHTER.) RATE OF MOVEMENT OF THE UNDERFLOW. 43 

canal is within several hundred yards of the edge of the descent 

to the bottoms, which lie from 20 to 30 feet below the surface of the 

upland. This location in porous soils and subsoils causes great loss 

of water by percolation. 

The writer has made determinations by the chlorine and other methods (see pp. 48-50) of the rate of movement of the underflow beneath 

the channel of Arkansas River in western Kansas. Six miles below 

Garden, at a level of 10 feet below the river bed, the velocity was found 

to be 2t feet per day. The fall or gradient of the river ·bed is about 7 

feet to the mile. The material below the 10-foot leYel is coarser than 

that above, and the velocity in it is undoubtedly higher, although 

the determined rate must be considered rather high for a gradient 

of 7 feet to the mile. South of tHe island, near Garden, the rate was 

found to be very high, a motion as great as 12 feet per day being 

determined. The motion at these points seemed to be entirely in the 

direction of the thalweg, it being impossible to detect any side or cross 

motion at the particular point,s where the experiments were made. 

Determinations of the rate of underflow in the narrows of the 

Hondo and San Gabriel rivers, in southern California, by the author's 

electrical method, gave rates of 3f, 4, 5f, and 7 feet per day. This 

work is in progress as this paper goes to press. 

Gilbert reports that the underflow sands of the Arkansas River 

Valley in eastern Colorado have a breadth approximately as great as 

the bottom lands of the river, and range in depth from~ to 20 and 30 

feet. a The slope of the water table is from 7 to 15 feet to the mile. 

The sands are exceedingly variable in texture. One of the coarser of 

two samples gave a. porosity of 29 per cent. The effective size of the 

grains is not given by Gilbert, but he states that a saturated sample, 

if freely drained, would part with about one-third of its water in several days. These data, however, are not sufficient to estimate the 

effective size of grain very closely, but the writer believes that they 

indicate that the effective size was between 0.05 and 0.1 mm. If the 

former, the magnitude of the underflow in the river valley, if the sand 

be assumed to be 20 feet thick and 50 miles wide, with a slope of 10 

feet to the mile, is barely 10 cubic feet per minute. If the effective 

size· be assumed to be 0.1 mm., the underflow would be about 36 

cubic feet per minute. A sand as coarse as 1 mm. would, under the 

same conditions, furnish an underflow of 3,600 cubic feet per minute. 

RETURN WATERS FROM IRRIGATION. 

Some remarkable instances of changes from the condition of diminishing rivers of arid valleys to the condition of growing rivers of 

humid valleys have been noted in various parts of the West, these 

being the results of the irrigation of considerable portions of river 

lands. Data relating to these changes have been given in various 

a The underground waters of the Arkansas Valley, by G. K. Gilbert: Seventeenth Ann. Rept. 

U.S. Geol. Survey, Pt. II, 1896, p. 557. 
44 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

annual reports of the United St,ates Geological Survey, in connection 

with the results of river measurements, notably on the Gila, Boise, 

C!:. 

() 

),. 

~ 

<( 

0 

.... 

IZO SEC.FT. 

1/0 

100 

~ 

e 

so "'( 

loJ 

"Cl 

"'( 

1\J loJ 

(JO ti :t: 

c: 

Cl Cl 

~ "'( "'( 

\oJ loJ 

70 ~ :t: :t. ..j 

Cl 

"'( 

loJ 

60 :t: 

so 

It 

~~-------+-----h~--~~----~~~~~--~~~~~~--~~~4-----~ 40 

a: 

1<.1 

Q: 

Cl 

~~~-----.A-~~~4---~~--~~~~~-~--------+---~~--4-----~ < 30 

Q: ~ i;j 

~ 

"'( 

.... 

~~---+~~~~~~~--~--~~-4--------------r---~---+----~ zo 0 

0 ~~~~-=~5======== to~======~I5MILES 

~ 

\&. 

(:) 

FIG. 16.-Diagram showing growth of Cache la Poudre River. The horizontal distances or 

abscissre give the distances in miles from the first weir at the canyon to the point of measurement. The vertical distances or ordinates represent the amount of return waters in cubic feet 

per second. The distances were measured not along the curves of the river but on the map, 

taking generally a straight course across the bottoms, because it was thought that the amount 

of inflow will not be increased by the curves of the river, but, instead, will depend upon the 

straight course of the stream, other things being equal. It is evident that there is a general 

agreement between the various lines, notwithstanding certain irregularities, such as the small 

inflow in the first section in March and August, 1894, and actual losses recorded in the fifth or 

adjacent sections in 1891, 1893, and 1894. 

Platte, and other rivers. One of the most complete series of measurements is that made by Prof. L. G. Carpenter in the valley of Cache 
SLICHTER.) RETURN WATERS FROM IRRIGATION. 45 

la Pondre River, a tributary of South Platte River, Colorado. As the 

lands of the valley were gradually brought under cultivation one of 

the effects first noticed was the gradual saturation of the subsoil and 

the rise of t·lle w~ter table, a phenomenon very common in all irrigated countries, and usually evidenced by a decided rising of the 

waters in the wells. In many places in the Cache la Poudre Valley 

the rise iu the water table was from 20 to 40 feet. This addition to 

the water table and increase in the pressure gradient brought about a 

gradual seepage toward the river and even the creation of flowing 

springs and marshy areas. The river was changed from a diminishing stream to an increasing one, so th~t waters used for irrigation 

upstream returned as seepage waters to the river and were again withdraWn for irrigation farther downstream, until the same water was 

used several times. A summary of the measurements of this river 

down to 1896 is presented graphically in fig. 16. 

TABLE VI. 

Rer;~trn waters of Cache la Poudre River, Colorado, from measurements made in 

1895.a 

[There are no tributaries between stations, and all measurements were made in October, when water in stream is as low as it usually gets.] 

Station. Water in 

river. 

Drawn out by canals. 

Water in G{e~ui~<ii:.;- Total 

ri;;:~J~ts between sta- gro~nd-wa- diverted. tions. ter mflow · 

No. 1 ___________________________ cu.ft.l27."oo~· ~-~-~~-~-~~~~~~~ ~~!t::_e:_~~~: ~~!t:~-~~~ ~~~: ~-~!.~·~-e-~~~~: -------------- 5.498 -------------- -------------- -------------- No.2--------------------------- 133.973 -------------- 139.471 11.862 11.862 -------------- 9.4~ ------------------------------------------ No.3___________________________ 149.985 -------------- 159.470 25.497 37.359 

-------------- 7.453 -------------- -------------- -------------- No.4.__________________________ 161.863 -------------- 169.316 19.331 56.690 

-------------- &i.IJ55 -------------- -------------- -------------- No.5-------_-----_-----________ 153.117 ______ __ _ _ ____ 192.072 30.209 86.899 

The following are Professor Carpenter's conclusions: b 

(1) There is a real increase in the volume of the streams as they pass through 

the irrigated sections. 

(2) There is no such increase in the streams as they pass through the unirri-

- gated sections. On the contrary, there is an actual loss, even when the drainage 

of a large area enters. 

(3) The increase is more as the irrigated area is greater. 

( 4) The increase is approximately proportional to the irrigated area, and it seems 

probable that with more intimate knowledge of the amount of water applied and 

the features of the drainage the proportions would be found to be close. 

(5) The amount of the in~rease depends very slightly, if at all, upon the rainf~Lll, and so far as it does it is influenced principally by the rainfall on the irrigated lands. Only where the lands are already saturated is the rainfall sufficient 

to cause seepage. . 

(6) There is no perceptible underflow from the side channels even where they 

drain several thousand square miles. 

a From Engineering Recor.d, Vol. XIV, p. 48. 

bTenth Biennial Report State Engineer of Colorado, 1901, p. 210. 
46 MOTIONS OF UNDERGROUND WATERS. (NO. 67. 

(7) The inflow is practically the same throughout the year. It is more in 

summer, less in winter, principally because of the effect of the temperature of 

the soil. 

(8) The passage of the seepage water through the soil is very slow, s~ th~t it 

.may take years for the seepage from the outlying lands to reach the river. 

(9) The amount of seepage is slowly but constantly increasing. 

(10) It may be expected to increase for some years to come. 

(11) .An increased amount of land may be brought under cultivation with time, 

more especially on the lower portions of the·streams. 

(12) The seepage being nearly eonstant throughout the year, whiie the needs 

are greatest in summer, the use of storage will best utilize the water from inflow. 

* * * * * * * 

(15) On the Poudre River about 30 per cent of the water applied in irrigation· 

returned to the river. 

(16) The use of water on the upper portions of a stream, when water is not 

immediately needed by prior appropriations, will increase the flow of the stream 

late in summer and .Prevent such low stages as it would have without this 

resulting action. 

(17) The seepage water is already an important factor in the water supply for 

the agriculture of the State. The capital value of the water thus received in the 

valley of the Cache la Poudre alone is not less than$300,000, and perhaps $500,000, 

and for the Platte is from $2,000,000 to $3,000,000. It is large for the other 

streams, but of unknown amount. 

(18) An actual loss is ineurred in carrying a stream like the Platte through, 

sandy beds. 

(19) IDtimately the returns from seepage will make the lower portions of such 

valleys as the Platte more certain of water and probably enable a larger aereage 

to be grown. 

EFFECT OF TILE DRAINAGE, ETC. 

The effect of the return waters from irrigation in increasing the 

dry-months flow of a strean1 and making the available supply of water 

more constant finds its exact counterpart in the effect of the deforest~ 

ing and cultivation of the land upon the perennial flow of rivers. 

The changed condition of the streams and the influence of the light 

flow in tho dry months upon the smaller water powers which have 

usually followed the settlement of the country are too well known to 

need special comment. Another striking example of the same kind 

is observed in river valleys in which ·large portions of the marshes and 

lowlands have been reclaimed by tile drainage. The tiling of the 

land permits the percolating waters from the rains to find almost 

immediate passage into the streams, while under natural conditions 

the return seepage would require weeks or months to reach the rivers. 

Part of the falling off in the reliability ~f th~ water power at Aurora,_ . 

Ill., and other points on Fox. River must be attributed to the reclamation of thousands of acres of lowlands in the upper part of its valley. 

CHLORINE METHOD OF DETERMINING THE RATE OF THE UNDERFLOW. 

Continental engineers formerly attempted to determine the rate of 

movement of ground water by experimental pumping from a number 

of test wells, deriving the velocity of flow from computations based 
SLICHTER.] CHLORINE .METHOD OF DETERMINING VELOCITY. 4 7 

upon these data. A .chemica} method of tracing the moving ground 

water was occasionally used with success. The earliest instance of 

this nature was probably· the successful attempt to trace the origin 

of an underground vein of water encountered in building a tunnel in 

Switzerland by charging the ground water with common salt. 

A. Thiem introduced a similar method in his investigations of 

ground-water movements near Leipzig. His method is as follows: In 

line with the probable direction of motion he digs two test wells at a 

known distance apart. In the upper well he places a substance which 

is readily dissolved by water and can easily be tested by chemical 

analysis. He then takes samples of the water at suitable intervals 

from the lower well, from the analysis of which he is able to draw 

eoncl nsions as to the rate of flow. The dissolved chemical penetrates 

40 

K ~ ------ t ---!V I 

I 

I v 

--

I () t 

() I' 

1~30 I v I 

~ . I 

t 

t Jl II. A 

~zo· If II: 

~ 

~ 

~ I 010 I ~ 

!c- ------ ------ ------ ----- ------W- ------ __ JJ 

~to~. 12 •I'< ';"' Tl/11£ 9. 30 10 II z 3 4 5 . 6 7 8 9 10 I 

FIG. 17.-Curve obtained in determining the velocity of ground water by the chlorine method. 

The distance A B represents the time of passage of the ground water between two wells. B is 

the point of inflection of the curve. The dotted line L J K P is the form that the curve would 

take if there were no diffusion of the salt. The rounded parts M and N are due to diffusion. 

German hydrographers have incorrectly used the maximum point P for the determination of 

the velocity instead of the point of inflection B. 

in all directions radially from the place of its introduction in the 

water-bearing strata, with greater or less v~locity, according to the 

permeability of. the ground, and in concentrically decreasing strength 

of solution ... Since the entire body of water during the distribution 

of the solution moves at the same time in the direction of the second · 

well, the movement of the chemical is greater in half of the circuit of 

the charged water than in the other half, according as the diffusion 

takes place with or against the natural current of the ground water. 

The shorter the distance between the test wells the greater the degree 

of concentration. The velocity of the ground-water stream is determined by plottin~ the results of simultaneous analyses from both 

wells. {See fig. 17.) 

Thiem used common salt in his experiments, be.cause it is rapidly 

IRR 67-02--4 
48 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

soluble and is easily determined chemically; and it has the further 

advantages of neither poisoning nordiseoloringthe ground water. He 

used this method in the new water-supply systems at Greiswald and 

Stralsund with good result~.a 

B A 

..----..-~l I ltl't-------i I nnn~n i 

R 

~·. = ~:· . -.-I 

~.·:-·· ... · ·· .. ~~·-· ·.·.~ 

~ 

}:--.---,--- . . r.--'---'-'- •. 

\--'-:----:----. 

~·­

~--· 

~· ~: 

r-'-7-'- ~.· 

·.·~ . .__,....., ·~ 

·~ 

., ···-~ 

. . ·-:--:--t 

·---=-----~ 

~-....,...--·:__. ·~ 

~·.-·.-:-·-.· -==~7""-- ....... : -:"-: ~......,-~~··~ 

.. ····))~~)·.· -·~·-··.·: 

. '----' .. , 

·:.:~ 

~~·~ 

.··.·~.~ 

:·:·.··.·.·.~ 

·.·:: ..... ~:------~ 

.·~ 

~ ... 

FIG. 18.-Diagram illustrating the author's electrical method of determining the horizontal 

velocity of ground water. The ground water is supposed to be moving in the direction of 

the arrow. The upstream drive well is charged with an electrolyte. The gra.dual motion 

of the ground water toward the lower well and its final arrival at that well are registered by 

the ammeter A. B is the battery and R a suitable resistance. 

THE AUTHOR'S METHOD OF DETERMINING THE RATE OF THE 

UNDERFLOW. 

A more rapid and less laborious method of surveying underground 

currents of ground waters than the chlorine method becomes almost 

imperative when extensive surveys are undertaken. Since July, l!lOl, 

the writer has given much attention to the dev~lopment of a new 

aVe::."fahren fur Messung nattirlicher Grundwassergeschwindigkeiten, by A. Thiem: Polyt. 

Notizblatt, Vol. XLII, 1887, p. 229. 
SLICBTER.] AUTHOR'S METHOD OF DETERMINING VELOCITY. 49 

method intended to be especially applicable to the survey of the underflow streams of the Plains. Acting under the authority of the chief 

hydrographer of the United States Geological Survey, he made preliminary field tests along the valley of Arkansas River in western Kansas 

during the month of August, 1901, and has continued the work in 

the lab(}ratory and fie.ld since that time. The experip.tents seem to 

leave little to be desired either in the certainty of the results or in the 

rapidity with which work can be prosecuted. The method is an electrical one. A double row of It-inch drive wells is sunk across the 

channel of the river whose underflow is to be tested. The upstream 

wells are then charged with a strong electrolyte, which dissolves and 

passes downstream with the moving water. (~ee fig 18.) 

The passage of the electrolyte toward the lower well is shown by 

the gradual movement} of the needle of an electrical instrument, and 

.ZB 

.Z4 

.zo 

~ .16 

!t 

~ .12 

~ . "Loa ~ 

.04 ...--" T-

.oo I 

21 3 4 5 p,ol, 

A. 

I-f... 

'{ I". 

t. 

il' I 

I 

..... I 

I 

I 

I 

I 

s 7: e s I 

I 

B. 

I" I'-

1'\ 

" ........ 

I'-

~--- r---

10 II IZ I Z 3 4 5 s 7 a A.M. 

T/ME 

FIG. 19.-Curve obtained by the author's electrical method of determining the velocity of ground 

water. The distance A B represents the time of passage of the ground water from the upper 

to the lower well. The sudden deflection at B shows the final arrival of the electrolyte at the 

lower well. The point B should l:::e taken at the point of inflection of the curve and not at the 

highest or maximum point. If the point of inflection be taken the effect of the diffusion of 

the electrolyte will be nullified. 

the final arrival at the well is shown by a sudden and strong deflection 

of the needle. (See fig. 19.) It is exceedingly interesting to watch 

the gradual movement of the water in this indirect way. In an hour 

or two a very good indication of the rate can be obtained ·by noting 

the slope of the current curve obtained. If several of a row of wells 

are being used sirnult.aneously, the main stem of the underground 

current will show itself by the rapidly rising electrical currents 

corresponding to certain of the wells. Thus not only are the tedious 

chemical analyses of the chlorine method obviated, but the actual 

movement of the water is traced from the beginning of the experiment, which is impossible in the older methods. 

Numerous electrolytes have been tried, both in the laboratory and 

in the field. It is obvious that the electrolyte must possess the following properties: (1) It must be readily soluble in water; (2) it must 
50 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

be chemically inactive to the dissolved matter in natural waters or to 

the material of the pervious medium; (3) it must possess a low coefficient of diffusion; (4) it must possess a high conductivity; and (5) 

its cost must be low. Of the numerous salts tried up to the present 

time ammonium chloride has given the best results. With this salt 

a current of sufficient intensity to throw the needle of a recording 

ammeter can be obtained by the use of a few dry cells. 

The electric circuit to the wells can be made in various ways. A 

brass rod insulated from the well tube and lowered into the downstream well by means of a rubber-covered wire may serve as one electrode, the casing of the same well constituting the other electrode. 

In this case the indic~tion of the movement of the ground water will 

not be noted until the electrolyte has reached the lower well, where 

its presence will be shown by a sharp rise in the current curve. 

Instead of this the two wells themselves may be used as electrodes, in 

which case the gradual passage of the electrolyte downstream can be 

observed from the beginning, but the final indications of its arrival 

at the lower well are less pronounced. The best method is a combination of these two: Run the wire from the casing of the lower well 

to one pole of the battery, with the ammeter in circuit, and connect the other pole of the battery both to the internal electrode of 

the lower well and to the casing of the upper well. In this case the 

gradual movement of the ground water from one well to tpe other is 

shown on the ammeter chart, and an abrupt indication of the arrival 

of the electrolyte at the lower well is also recorded. 

The drive wells may be made of perforated sections from 4 to 8 feet 

long, so that a well will offer free passage to the water throughout its 

entire length. The internal electrode may be made in several insulated links with separate external wires, so that varying velocities at 

different depths can readily be determined. 

While making tests in the underflow of Hondo River, California, 

the author was able to determine the different velocities in three different strata of gravel penetrated by the wells by a -single settirig of 

the wells. The curve developed three well-marked points of inflection, corresponding to the velocities in the several strata, and the 

brass screens on the well point and well-point extension were bh:tckened by the electrolyte at depths corresponding to the three strata. 

Underflow measurements were made by the author on Mohave River 

at the site of the proposed dam near Victorville, CaL At this point 

the river passes through a narrow gorge, barely 120 feet wide at the 

river surface. Here the greatest depth to bed rock is 4 7 feet, and, 

the material is a very coarse granite sand or fine gravel. A double 

row of test wells across the narrows, with extra downstream wells for 

the determination of the direction of flow, gave velocities at various 

points of 6, 8, 20, 35, 48, and 64 feet per day. Notwithstanding these 

high rates the total volume of underflow is quite small on account of 
SLICBTER.] CONCLUSIONS CONCERNING UNDERFLOW OF RIVERS. 51 

the li~ited cross section (4,160 square feet). For a cross section at the 

dam site see Eighteenth Ann. Rept. U. S. Geol. Survey, Part IV, page 

709. Estimating a porosity of 33 per cent and an average velocity of 

50 feet per day gives a total underflow of 0.8 second-foot, or 520,000 

gallons per twenty-four hours. 

The velocities at this point were so high t.hat the electrolyte passed 

between wells only 18 inches apart without touching them, and a 

small quantity of caust~c potash had to be added to spread the electrolyte into a broad stream. 

CONCLUSIONS. 

The important facts concerning the underflow of rivers are brought 

together in the following summary: 

(I) In the mountainous portions of streams, where the river slope 

is great, and the material deposited in the river channel is coarse, the 

underflow in the direction of the tha~weg may be relatively very large. 

(2) The seepage in the steeper slopes and terraces of a river valley 

is primarily in a direction toward the thalweg and not along it. 

(3) The underflow in the alluvium beneath the surface of the bottom 

lands of the valley is greater in the direction toward the channel than 

in the direction of the thalweg, except (a) where the water table has a 

greater slope downstream than toward the channel, and (b) where the 

fine silt of the river channel covers deeper deposits of coarser material, 

rendering seepage into the channel difficult and underground passage 

downstream easy. 

(4) The velocity of the underflow is very small and the total amount 

is commonly gre~tly exaggerated. 

( 5) The rate of the underflow is especially small in t~e beds of 

overloaded, silt-depositing st.reams, although the storage capacity in 

such cases may be correspondingly great. 
CHAPTER III. 

DEEP ZONES OF FLOW. 

The sedimentary rocks usually occur in alternating layers of sandstone, shale, and limestone, or in alternating successions of sandstone 

and shale. These classes of 1·ocks represent the various kinds of 

deposit,s which are laid d_,wn on the floor of the sea. Originally the 

sandstone was sand, deposited near shore in the more rapidly moving 

water. The shale was mud, deposited in the belt of sluggish currents 

in shallow water. The limestone was limy ooze, the remains of limesecreting organisms upon the deeper and quiescent floor of the sea. 

Sand and mud are therefore called mechanical sediments and the calcareous ooze is called an organic sediment. 

Water is, then, not only the transporter of the material worn from 

the shore and the surface of the land, but it is also the sorter of that 

material. '"rhe gradual change in the shore line by erosion and by 

alternating elevation and subsidence of the land has caused rocks of 

these various classes to be deposited above one another in a more or 

less regular threefold succession, shale above sandstone and limestone above shale. The various st,rata are usually not arranged, 

therefore, like the leaves of a book, in perfectly horizontal and coextensive ]ayers, but the arrangement is better likened to the overlapping of the shingles on the roof of a house, sediments of one class 

being imbricated with those of the other classes. The higher ends of 

the strata correspond to the deposits laid down near the shore, unless 

earth movements have inverted the direction of the original dip. 

The common alternation of sandstone, shale, and limestone found 

in the sedimentary rocks is a fact of the greatest importance in the 

consideration of the motion of underground waters. The sandstones 

are in general the most pervious of all water-bearing rocks, and the 

shales are usually the most impervious. Generally limestone is to be 

·classed as an impervious rock, although frequently it is a water-bearing rock of great importance. 

Important classes of pervious limestones. are the following: (1) 

Chalk and partially consolidated shelly limestone, such as coquina, 

etc.; (2) limestone that has at one time been exposed in the belt of 

52 
SLICHTER.] DISTINGUISHING FEATURES OF DEEP ZONES or FLOW. 53 

weathering ~The solvent action of surface waters upon limestones and 

the readiness with which they are rendered cavernous and prolific 

bearers of water are too wetf·known to require special comment.); and 

(3) deeply buried limestone in which a portion of the carbonate of 

. lime has been replaced by dolQmite or carbonate of magnesium. The 

dolomite being less bulky than the chemical equivalent of calcium carbonate, the substitution may render the limestone sufficiently porous 

to become an important water-bearing rock. A well-known example 

is the Trenton limestone in Ohio, which bears enormous quantities of 

water, oil, and natural gas in its upper dolomite layers. a The substitution of basal magnesium for calcium may in itself account for a 

porosity of from 10 to 12-! per cent. 

The sandstones are not only confined by impervious material 

above them and often below them, but their exposures above the 

surface of the land are normally covered with a very pervious, coarse, 

sandy 'soil which readily imbibes the rainfall. Thus all of the elements 

are present for the storage and circulation of underground waters in 

the zones of the sedimentary rocks far below the surface zone of flow. 

DISTINGUISHING FEATURES.I 

The pervious and water-bearing sandstones and limestones beneath 

the surface zone of flow constitute what we have called the deeper 

zones of flow. There may be several of these deeper zones, or they 

may be absent altogether. When present, they are distinguished from 

the surface zone of flow by the following characteristics: 

(1) The surface zone of flow has a free, unconfined upper boundary 

(the water table) and an impervious lower boundary. rrhe deep zone 

of flow has an impervious upper boundary as well as an impervious 

lower boundary. · 

(2) The unit of the upper zone of flow is the drainage area or river 

valley. The unit of the deep zone of flow is regional and geolpgic 

and not dependent upon surface contours. However, it must not be 

forgotten that the deeper geologic structure is frequently the principal determining factor controlling the surface drainage, so that the 

deep zones of flow do not ~ommonly run counter to t.he direction of 

the surface flow. 

(3) The surface zone of flow is dependent upon the local rainfall of 

the immediate region. The deeper zones of flow receive their waters 

from distant areas. 

( 4) The surface zone of flow is in part above the level of surfacedrainage channels, while the deeper zones are entirely below the local 

drainage level. 

aFor more complete discussion see Rock waters of Ohio, by Edward Orton; Nineteenth 

1!\.nn. Rept. U.S. Geol. Survey, Pt. IV, 1899, p. 640. 
54 MOTIONS O:B' UNDERGROUND WATERS. [NO. 67, 

(5) There is commonly a difference in the chemical composition of 

the waters from the two zones. It is difficult in our present state of 

knowledge to make valuable generalizations. The waters of the surface zones are usually less mineralized than those of deep strata, but 

in arid regions this general rule is frequently reversed. The carbonates are the predominant salts of the ;nrface waters. The deeper 

waters are usually characterized by rather high amounts of dissolved 

chlorides. Waters of the surface zone contain dis~olved oxygen gas, 

which is almost entirely absent from the deep waters. 

Some of these distinctions (1, 2, and 4 above) are illustrated by the 

accompanying ideal cross section through South Dakota (fig. 20). 

This section is along a line from Sioux Falls to Chamberlain and 

thence along the thalweg of White River to the Black Hills. rrhe 

diagram is based upon similar drawings published by Darton, Todd, 

and others, but without attempt to show with absolute accuracy the 

geologic details. The deep zone of flow is approximately from west 

to east, through the porous strata marked Dakot~ sandstone, the water 

entering at an elevation of more than 3,000 f~et, at B. The impervious upper layer is the Benton shale or clay. This cross section presents considerable variety in the surface zones of flow. Between C 

and· D the upper zone of ground water drains from east and west into 

Cheyenne River, which here flows north. From D toE the surface 

ground waters drain from north and south into White River. From 

E to F is the valley of the Missouri. East of this river the surface of 

the land is covered with glacial drift, represented by the light surface 

shading in the diagram. At G is James River; at Hand I are the 

forks of Vermilion River, and at J is Big Sioux River. 1,hese streams 

flow to the south, so that the surface ground-water seepage is substantially east and west. 

PERCOLATION INTO DEEP ZONES. 

The rainfall finds it.s way into the deeper zones of flow in various 

ways, either directly by percolation into the exposed ends of the pervious strata, or indirectly by the seepage from streams and rivers 

which have cut their valleys through the outcrops. The water must 

leave the deep zone at a lower level than that at which it enters, and 

hence the outlets· for the water must be sought in the lower outcrops 

of the rock, where, perhaps, a river has eroded a channel through it, 

or where the impervious cover is locally absent. There is also always ~ 

the possibility of the escape of water through joints and faults, and 

even by seepage through the covering strata, for imperviousness as 

applied to rocks is merely a relative term. The covering layer of 

shale or hard rock has an enormously greater area than the vertical 

transmitting section of the pervious rock, so what the covering rock 

lacks in permeability it can make up in area. 
LQ 

lQ 

rn 

~ 

< lXI 

z 

~ 

~ 

~ ~ 

~ 

H 

0 

~ 

~ 

A 

~ p 

0 

rn 

III 

r;!) 

l:J 

~ I:II 

H Fw. 20.-Cross section through South Dakota artesian basin, based upon published data of Darton, Todd, and others. The section is along a line through 

z Sioux Falls and Chamberlain and thence along the thalweg of White River. All of the wells shown are within a few miles of this line, excepting the 

0 Rosebud well, which is 25 or 30 miles from the line and on much higher land. The base of altitudes is the sea level. The height to which the water would 

~ rise in a closed tube at the various wells is shown by the heavy black lines. In studying the drawing one should remember that it has been necessary to 

~ use a scale which greatly exaggerates vertical, in comparison with horizontal, distances. 

rn 

~ 

&; 

s 

~ 
56 MOTIONS OF UNDERGROUND WATERS. (NO. 67. 

·1'he ratio of the cross section of the Potsdam sandstone to the area 

of the covering stra-t& i§ e~fettinly no less than 1: 3,000, f01' thtntv~rage thickness of the Pot~dam is about 700 feet, while the formation 

is known to exist as a water-bearing rock for at least 400 miles south 

of the catchment area. The average thickness of the Dakota sandstone is approximately 200 feet, while the distance from the catchment 

area in the Black Hills to the eastern outcrop at Yankton is about 350 

miles, so that the ratio of the area of the transmitting cross section of 

the porous strata to the area of the covering strata is about 1: 9,000. 

Thu~ if, on the avera~e, the covering material had in the one case only 

30100 and in the other only 9 t(00 of the transmission capacity of the 

water-bearing stone, there would still be as great opportunity for 

the upward escape of the water as for its onward movement. This 

upward seepage would cause motion of the water in the porous strata, 

so that motion is possible even if there be no actual outcrop of the 

transmitting rock. 

FIG. 21.-Diagram illustrating how gas and oil have been retained beneath anticlines of shale 

during protracted geologic intervals, thus proving the substantial imperviousness of the 

covering. 

Local upward seepage may explain, perhaps, some of the anomalous 

variations in pressure of underground water in artesian basins. It is 

certain, however, that upward leakage is entirely absent over large 

areas. In the Ohio oil regions, for example, all of the oil and natural 

gas, not being continually supplied to the rock as water is, would have 

escaped ages ago if we suppose the most minute permeability to the 

overlying strata of shale. The gas and oil·are held under the anticline of shale as shown in fig. 21, just as air may be held under a 

basin inverted in a tub of water. It would seem equally reasonable. 

to suppose that the briny water which underlies the petroleum has 

occupied its present position during the same geologic interval as that 

in which t,he petroleum has been impounded. While this may be true 

in special instances, it is far from being the necessary conclusion, for 

the water on which the 'oil floats is a continuous body, and is free to 

flow toward an outlet in a distant portion of the formation, while the 

oil and gas, confined by their low density to a particular anticline, can 

not escape so long as their own covering holds, even though a neighboring anticline be pervious and leaky. 
SLICHTER.] DAKOTA AND OTHER FORMATIONS. 57 

The following water-bearing formations of wide extent and of high 

economic impm~tanc6>may be specially mentioned as good illustrations 

of deep zones of flow: 

(1) The Dakota formation, commonly referred to as the Dakota 

sandstone, outcropping in the Black Hills and in the foothills of the 

Rocky Mountains, and underlying the Dakotas, Nebraska, and Kansas, and of unknown extent northward. 

( 2) The Potsdam sandstone, outcropping in a V -shaped area in 

central Wisconsin, dipping southward under Illinois, Iowa, Indiana, 

and Ohio at great depths, and outcropping again in the great uplift 

which has formed the Rocky Mountains. 

! ··-··-··--·-··-··-

I 

··, 

- :U~:Jrt..f:/;"st:,:;;::ec~s;!d'::.;,~" $edlmt'nfBr,Y ITJr"'lii'IOHS 

~~~ ::::~;,~:;';;:J:,::nO:,';.':~oS:'""::,~tl •nd 

l:,B E.llp!D~d porl'on qf OaJrDff!l 8r;t~5iiln f!l~ _ ·--··-·· -·· _ 

- CB$Nirn ol#crop '"O.lrota S6ndsl'on~ 

FIG. 22.-Darton's map of catchment area of the Dakota and the Dakota artesian basin. 

(3) The Atlantic Coastal Plain deposits, extending along the eastern 

margin of the Alantic slope from Long Island to Texas, and about IOO 

miles in width. These consist. of a succession of unconsolidated deposits 

consisting mainly of sands, clays, and marls, instead of sandstone, 

shale, and limestone, which lie on the east-sloping floor of the ct·ystalline rocks. The western edge has an altitude of from 300 to 400 feet 

&bove the sea. 

DAKOTA FORMATION. 

Darton's map (fig. 22) of the outcrop of this formation in the Black 

Hills and in the foothills of the Rockies shows the source of the 

supply of water to the formation so far as known. The map shows not 

only the surface outcrop, but also the drainage area that is tributary 
58 

pnossy111 

8fl.l~O Sf/E'd/f?<J./,9 

MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

to it. Darton gives the approximate area of these outcrops of permeable beds as follows: Black 

Hills, 2,400 square miles; Bighorn 

Mountains, 7,000 square miles; 

Rocky .Mountain foothills in Mon~ 

tan a, more than 3, 000 square miles; 

Rocky Mountain foothills in W yoming, about 1, 500 square miles; 

total, 13,900 square miles. 

The Dakota sandstone in the 

Black Hills receives water as follows: 

(1) Of the rain which falls on the 

Dakota sandstone probably onefourth is directly absorbed by this 

rock. 

(2) All the drainage of the Hills 

crosses the Dakota sandstone, 

which therefore receives a second 

accession. 

(3) A probable third accession 

is from the Carboniferous group 

which underlies the Dakota sandstone. Many streams of the Hills 

either sink or lose considerable 

·water in the lower beds of the 

Carboniferous. Inasmuch as this 

group thins out and is apparently 

absent in the eastern part of the 

basin, it is probable that a portiou 

of this water is passed along to the 

Dakota sandstone. 

Missouri River flows over the 

outcrop of the Dakota sandstone 

in passing from Great Falls to Fort 

Benton, Mont., as can be seen from 

consulting Darton's map (fig. 22) 

and the accompanying section (fig .. 

23). In this part of its course the 

river is believed to lose a considerable volume of water. 

The elevation of the outcrop of 

the Dakota sandstone in the Black 

Hills is from 3,100 to 3,800 feet 

above sea level. The outcrop far-
SLICHTER.] DAKOTA AND POTSDAM FORMATIONS. 59 

ther west, in the foothills, reaches an elevation much higher, as can 

be seen by consulting fig . .22. The sandstone comes to the surface 

again in southeastern Dakota, near Yankton, and along Missouri and 

Big Sioux rivers, at an elevation of about 1,200 feet. In this area 

there is evidence of leakage from the sandstone, probably greatest in 

the neighborhood of Yankton. At Chamberlain, Running Water, 

·"'· ; 

• ~Potsdam formation 

- StPeter sandstone 

FIG. 24.-Wisconsin outcrop of Potsdam and St. Peter sandstones. Figures indicate height, in 

feet, above mean sea level. 

and Randall, springs are· seen rising from the bed of Missouri River. 

Through extensive areas in Dakota this subterranean wat.er is under 

enorm,ous pressure and constitutes one of the most remarkable artesian areas in the world. More will be said of this area later. 

POTSDAM FORMATION. 

The Wisconsin outcrop of this water-bearing series is shown in 

fig. 24. The altitude of the V -shaped outcrop is in the neighborhood 
60 MOTIONS OF UNDERGROUND WATERS. fNo. 67. 

of from 900 to 1,000 feet above sea level. The soil above the outcrop 

is sandy and porous over extensive areas, making the .catchment area 

especially favorable for the imbibition of water. The area of the outcrop is nearly 12,000 square miles, and the thickness of t.he formation 

reaches a maximum of nearly 1,000 feet. The strata of the series are 

mostly porous sandstones, with occasional layers of shale and some 

beds of limestone. The Potsdam is overlain by the Lower Magnesian 

limestone, varying in thickness from 65 to 250 feet. Overlying the 

Lower J\!Iagnesian is another water-bearing sandstone of great importance, known as the St. Peter. It varies in thickness from 212 feet 

to a fraction of a foot, the average being probably between 80 and 100 

feet. The rock is of an exceedingly friable character, being, as a rule, 

hardly compact enough to permit handling. Overlying the St. Peter 

is the Trenton limestone. The Potsdam and its overlying strata dip 

gently away from the V-shap€d outcrop. 

The water-bearing sandstones of these formations supply artesian 

water of· exceptional purity to large areas in southern Wisconsin, 

northern Illinois, and northeastern Iowa. ~rhe head of the flowing 

wells is not high anywhere within the area, and at many places the 

wells have to be pumped. This artesian basin is remarkable on 

account of its large areal extent and the excellent quality of the water 

rather than the large flow of individual wells. The usual yield of 

earefully constructed wells varies from 50 to 300 gallons a minute. a 

a A tabulation of the data from wells in Illinois will be found on page 810 of the Nineteenth 

Annual Report of the United States Geological Survey, Part II; see also Vol VI, Iowa Geological Survey. 
CHAPTER IV. 

RECOvERY OF UNDERGROUND WATER FROM THE SURFACE FLOWS. 

It has already been explained that underground water comes to the 

surface and joins the surface waters by diffused seepage into rivers, 

lakes, and marshes, and into the bed of the sea. It has also been pointed 

FIG. 25.-Diagram showing the formation of a stratum spring at an outcrop of an inclined impervious stratum, as at S. 

out that if the return seepage, owing to unusual geologic conditions, 

is stron~ly concentrated in special areas, the returning water constitutes a spring or a natural fountain. A surface spring is usually 

FIG. 2tt-Diagram showing the formation (at SS) of overflow springs at the edges of a basin of 

impervious material. 

associated with an outcrop of an impervious stratum. The simplest 

form is shown at S, fig. 25, which, if we follow the classification of 

. Haas, may be called a stratum spring. A fault in the bed rock may 

61 
62 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

force the ground water to the surface, forming a so-called fault spring, 

as at "Spring B," fig. 1, page 13. Other forms are overflow springs;-

as at SS, fig. 26; chasm springs, as in fig. 27, or valley springs, as at 

"Spring A," fig. 1, page 13. A stratum spring is shown in Pl. IV, A. 

COMMON OPEN WELLS. 

Besides these natural processes which are constantly returning 

underground waters to the surface waters, there are several wellknown ways of artifically restoring ground waters to the surface. 

The most common of all methods is, of course, the construction of an 

open well and the raising of the water to the surface by appropriate 

mechanical means, as shown in fig. 28. This is so universal a practice that it requires but little discussion. The well is simply excavated to a suitable depth below the water table, so that the ground 

water of the surface zone of flow is free to flow into the excavation. 

FiG. 27.-Diagram showing the formation of chasm springs in a cut which extends below the 

natural level of ground waters. 

The result of the regular removal of water from the well is the lowering of the water table in its neighborhood, the water table assuming 

the very regular curve shown in figs. 28, 29, and 31. The form of 

this surface can be worked out from theoretical considerations, and 

the results seem to agree substantially with experiment. These figures (29, 30, and 31) are taken from the rept>rt- of a v&ry carefully 

conducted series of experiments by J. C. Hoadley, C. E., of Boston, 

Mass. a The investigations are known as the Melrose or Malden 

experiments, because the first series was carried out in the town of 

Melrose, near the boundary of Malden, and on the border of the uncultivated tract known as Middlesex Fells. 

Fig. 29 shows the varying posit.ion of the water table on May 24, 

1882, near a 3-inch pipe, during ten hours of continuous pumping at 

a See Sanitary Engineer, Vol. XI, 1884, pp. 11, 31), 60, 84, and Proc. Soc. Arts, Boston, 1882-83, 

p.l15. 
U. S. GEGLOGICAL SURVEY WATER-SUPPLY PAPER NO. 67 PL. IV 

A. SPRING FORMED AT OUTCROP OF AN IMP ER VIOUS FLOOR. 

B. ART ES IAN W ELL. 
SLICHTER.] COMMON OPEN WELLS. 63 

a mean and nearly uniform rate of 2,313 gallons an hour. The pumping was from a It-inch suction pipe dropped loosely into the well. 

There had been no pumping from the well for seventy-five hours preceding the experiment. The head required to force the water into the 

It-inch pipe with open end (no holes) and to overcome bends and 

friction in pipe was 29.5-20.75=8.75 feet .. The barometer stood at 

FIG. 28.-Common dug well; shallow in water. 

50.015 inches, the thermometer at 67.6° F'. The height of partial 

vacuum in suction pipe, as indicated by vacuum gage, was 20.75 feet 

above base; height of absolute vacuum, as indicated by vacuum gage 

above the base line, was 6. 75 feet; height of valve seat of steam pump 

above base, 40.80 feet. Fig. 30 shows the effect of pumping, of stopping the pump, and of rain, upon the height of ground water in one of 

IRR 67-02--5 
64 MOTIONS OF UNDERGROUND WATERS. (NO. 67. 

the wells. The pumping was at the rate of 2,010 gallons an hour, 

except for several stops indicated on the diagram. 

Fig. 31 illustrates a very excellent apparatus designed by Hoadley 

for the experimental study of well phenomena in the laboratory. The 

Fig. 29.-Diagram illustrating the changing position of the water table near a 3·inch well 

during ten consecutive hours of continuous pumping at an average rate of 2.,313 gallons an hour. 

(After Hoadley.) 

sand is held within a 48-inch cylindrical curb of wire cloth, so placed 

in'a larger tank as to leave a l-inch space all round, which can be 

kept filled with water to supply the sand during experimental pumping from a well at the center of the cylinder. Numerous brass tubes 

drilled with fine holes occupy positions in the sand at various dis-
SLICHTER.] COMMON OPEN WELLS. 65 

tances from the central well and communicate with appropriate gages 

of glass tubes, from which the position of the ground-water surface in 

the sand can be determined at any time, as shown in the lower part 

of fig. 31. 

The capacity of surface wells depends upon several factors. Perha.ps the most important is the degree of fineness of the material of the 

water-bearing stratum. The size of the soil grains not only controls 

the rate at which water can be transmitted to the well, but also determines the proportion of the contained water which the soil will freely 

part with. The fine-grained soils retain a considerable proportion of 

the water of saturation as capillary water, even after free means of 

!>_Z_F_E_E;_"C~~f!~~ ~~-£-':.lfY!_ •• _ ----------------- _________ . ______ ----------------- _ --- _____ --------

.3Z FEET ABOVE 8"5£ LINE ----- ----------------------------- ;:--:-=--- ~------ ----------- ---- -------- -----

1 : : : ! : : ~: : : : : I : : I : I ~! : :~ I 1 1 

31 I I I I I I I I I I I ~I I ·~ I I • I '• 

-• +-~- t- -rtl.t-:- ;-~~ r-r-~-~ ;-~-~ -f- +_;!,;;;R~~~ ;-~-:-~-I I ~- --.. ----.. -11 -; .. 1-~ .. :- 1 -j•-

: : : :~~: 1 : ;~:; , : 1 , 1 : : : ~~z~~uHs ~ I : , : : : :l:~: .. + .. ;;!~~~T!:::~~: ! ! :: : 1 , 

: I I :~\.: : I :~: ! ! : : : : I : 1 0:.-u:'P/N~:Ir) 1 I : t : : :e:~f : :HAY£ 8££N ~ : : '.1 I ~ : : 

30 : : : :~~ : : :~: ! : : : : : : ! : ~: ~ -;:: P~M~I,.;G ~R~M: ~~~: : :::g~~~~~:~~~~~ : : ~:: : I : 

- _ .. -t- -:- -;.~ r_;-~--~:-:--r- ~-,-1----r -i -:-~~- :-- -~:-~~L~-1!~~-+- ~-~~~-t -:- ~-~- ;--:- -l!t-:-~ ~-~- "t- -:--

: : : :~q, : : lvt~: I 1 I : : : I I~~ ~ ~: :apqo:= 1 1 ~;:: I I : 1 1 : ~ : :~:: : I : 

I ' I I ·~!': I I ~· I : I I I I I : I ~I I (I I : I I l : :~t;,, : ~ ' I I I ~ I I ~·1 • I ' 

z_~l.LU~_j _ _i_ J~ l_i_j __ i _ _i __ U __ ~_i_L_L. JLJ_j_U _Ll_~ __ U_J_l_L ~-LU~lJ_i_l_ S 10 II IZ I Z 3 4 5 6 7 8 9 10 II IZ I Z 3 8 9 10 II ll I Z 3 4 5 § 7 8 9 10 II rz I Z 3 4 5 

M. MIDNIGHT F:M.MA~JI$.MIDNJ61rT M. 

FIG. 30.-Diagram illustrating the varying position of the water table in a well due to pumping for 

various intervals and modified by rainfall and stops of various duration. ({\.fter Hoadley.) 

drainage are established, so that fine-grained material will not only 

deliver water slowly but will furnish only a small total amount. The 

yield of the well also depends upon the amount that the water table 

is lowered by the withdrawal of water, or the head under which the 

flow takes place, and upon the size and shape of the excavation and the 

character of the walls and casing. Theoretical considerations seem to 

show that the yield of a well is direct,ly proportional to the transmission constant (k of formula on page 26 of this paper) of the porous 

material, and nearly proportional to the head, or the distance the 

water table is lowered. If the well is deep and relatively small in 

diameter (say from 6 to 12 inches), increasing the diameter seems to 
66 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

have little effect on the volume, doubling the diameter adding barely 

8 or 10 per cent to the theoret,ical yield; while if the well is shallow 

and porportionately large in diameter the yield seems to be proportional to the diameter·, so that doubling the diameter would double 

the flow. This dependence of yield upon diameter is only true when 

the well is being used to nearly its full capacity. \Vhen the well is 

drawn upon for but a small percentage of its full capacity the indica-

.. ~~~ ::-~~ ::: :~ I ~= F:: .. == : .. -= .. -:-~ ~f:-r 

,, , II'!,..JI-1~·-1~-11--1'" ,~: ~.::. ;} 

... ,: ~:. >~ ~;. ·. .· . ' ' i : , ,, \ : 

't 

~ ... 

~ ~ Iii : 

tions are that doubling the diameter will have a greater effect no 

the capacity of the well than these 

figures indicate. a 

As already stated, the flow of 

ground water into a well, if it be 

not too shallow, varies directly as 

the distance the surface of the 

water in the well is lowered by 

pumping. Thus, if the water in 

a well is lowered 2 feet below the 

natural level by pumping from it 

at the rate of 20 gallons a minute, 

the same well may be expected to 

yield approximat,ely 40 gallons a 

minute if the water is lowered 4 

feet below the natural level. For 

shallow wells the yield will not 

increase in this direct ratio, but 

will be considerably less, on account of the decrease in percolat,ing surface, due to the lowering 

of the water table in t,he neighborhood of t,he well. Besides the 

advantages just mentioned, tubular wells, owing to their greater 

depth, are much more likely to 

FIG. 31.-Hoadley's laboratory apparatus for strike a vein Of COarse material, 

the investigation of the phenomena of com- a small stratum of which may be mon open and driven wells. expect,ed to furnish much more 

water than a considerable depth of fine material. This accounts 

for the well-known superiority of deep tubular wells over common 

dug wells. \Vhen a large supply of water is required, as for irrigation or for village supply, it is a common practice to sink several 

tubular wells in the bottom of a large dug well (see fig. 32). In this 

way not only is a large supply obtained, but the large well acts as 

a See the author's theoretical investigation of the motion of ground wate1s: Nineteenth Ann. 

Rept. U.S. Geol. Survey, Pt. II, 1899, pp. 358,362,364. 
SLICHTER.] COMMON OPEN WELLS. 67 

a storage reservoir, equalizing the load upon the pumps and permitting temporary overdrafts of the capacity of the wells. Some careful 

meaurements of the rate of rise of the water surface in a well after 

pumping has ceased have been made by Mr. Willard D. Johnson. 

Data from the city well at Garden, Kans., as obtained by him, are 

shown in figs. 33 and 34. The curve in fig. 34 agrees very closely with 

FIG. 3".3.-Combination dug and tubular well. • 

estimates based on theoretical considerations, which indicate t.hat 

if at the end of· a certain period of time (say fifteen minutes) the 

depression is half of the original amount, then at the end of twice 

that period of time (thirty minutes) the depression will be one-fourth 

of the original amount; at the end of thrice the period of time (fortyfive minutes) it will he one-eighth of the original amount, etc. 
\ 

/ 

68 MOTIONS OF UNDERGROUND W .ATERS. [NO. 67. 

CONTAMINATION OF SURFACE WELLS. 

Since the upper surface of the ground water in the surface zone of 

flow is everywhere exposed to contamination by seepage of impurities 

FIG. 33.-Diagram showing rise of water in city well at Garden, Kans., after heavy pumping. 

from the surface of the ground, wells in this zone of ground waters 

are especially subject to pollution. 

The organic impurities-such as decaying vegetable and animal 

matter, and the products of their decomposition, animal excreta, 

Minutes. 0 ~ ~ g :;: ~ 8 ;:; ~ ~ ~ ~ 8 :=; ~ ;s ~ ::5 8 ;:; ~ ~ ~ ~ 8 S ~ ~ s; ~ 8 ;:; ~ ~ ~ 

Hours. 0 1 2 3 4 5 

FIG. 34.-Curve_showing rise of water surface in well at Garden, Kans. 

especially disease germs common to such matter, etc.-constitute the 

most dangerous elements in drinking water. The possibility of such 

contamination can frequently be avoided by a proper location of the 

well. The slope of the ground will usually give an indication of the 
SLlCHTER.] CONTAMINATION 0.1!' SURF ACE WELLS. 69 

direction in which the ground water is moving, and sources· of contamination above the well can therefore be foreseen. It is true, however, that the depression of the water table in the immediate vicinity 

of the well will permit it to draw impurities from all directions, 

especially in the dry months, when the depression extends considerable distances. In the thickly settled districts of cities and villages it 

is extremely difficult to locate surface wells so that they will not be 

polluted to a greater or less extent,. 

Contamination from cesspools is much more dangerous than contamination from surface filth, for the upper few feet of the soil contain living organisms which purify and destroy organic impurities 

slowly seeping downward, while the organic matter in cesspools is 

immediately contributed to the subsoil without the action of the 

nitrifying organisms. The author has noted 18 cases of typhoid fever 

in one district of a city, the families drawing their water from 18 

FIG. 35.-Diagram illustrating danger of contamination of surface wells from cesspool~. 

neighboring wells. The city was built upon the slope of a river terrace, and the alternation of we1ls and cesspools was essentially as 

illustrated in fig. 35. In this particular case pure artesian water from 

flowing wells could have been had by drilling about 1,000 feet,. 

NONUNIFORMITY OF NEIGHBORING WELLS. 

It is a not uncommon experience to find that water can not be 

obtained a short distance from a good well. Such a discovery always 

causes considerable comment, while the large regions in which ground . 

water is found at very uniform depths call forth no comment whatever. Irregularities in the strata, especially in the deposits of clay 

in the glacial drift, account for most of the observed diversity of 

supply. Fig. 36 illustrates an extreme form of irregularity which was 

observed in East Schleswig~Holstein. By the action of the ice and 

drift in Glacial times this formatio:1 was so thrown together that there 

were formed in the soil a number of trough-shaped and irregular 
70 MOTIONS OF UNDERGROUND W .ATERS. [No.67. 

cavities which have been filled with permeable glacial sand. These 

troughs or cavities have collected ground water at various depths 

into masses which are only in partial communication with one another. 

In fact: the ground water is for the most part separated into distinct 

streams of greater or less size, which are in communication with one 

another only during high water. A-G, fig. 36, represent wells whose 

water levels, on account of these conditions, show a great variety of 

height, and some of which, as at G, have no water in dry weather. 

Another cause of irregularity in the depth and supply of wells is 

found in localities where gravelly beds of ancient streams or the 

beaches of former lakes lie buried beneath a later formation of surface material. These lines of f_!;ravel are usually very narrow, but 

may extend for miles in a sinuous course, or in a gently curving 

course, as the case may be that of a buried stream oi· a buried lake. 

FIG. Sf).-Diagram showing extreme irregularities of the water table and the depth of wells 

(A, B, C, etc.) in East Schleswig-Holstein. (After Haas.) 

FLUCTUATIONS IN THE POSITION OF THE WATER TABLE AND THE 

EFFECT ON 'VELLS AND SPRINGS. 

The height of the water table is constantly subject to variation. 

Its position at any time is dependent upon the varying relations 

between rainfall and evaporation. ~.rhe influence of the formet· upon 

the position of the wat,er table can readily be ascertained by actual 

measurement. There will be observed, of course, not only variations 

corresponding to single rainstorms, but variations from the rainy 

months to the dry months and from rainy years to dry years, etc. The 

average position of the water table at Munich, determined from 

observations made in three wells and extending over a period of thirt,y 

years, is shown in fig. 37.(t A similar diagram for the city of Berlin, 

made from observations in thirty-seven wells and extending over sixteen years, is shown in fig. 38. Everyone is familiar with the common 

experience of the low stage of water in wells during dry monthR or 

a The diagrams are taken from the article by I. P. Gerhardt inDer Wasserbau, Leipsic, Vol. I, 

Pt. I, p 47. 
SLICHTER.] FLUCTUATIONS OF THE WATER TABLE. 71 

exceptionally dry years, which is caused by fluctuations in the water 

table like those represented graphically in these diagrams. 

Changes in the barometer produce interesting changes in the posi·· 

tion of the water table and still greater changes in the flow of springs 

and wells. 

Observations show that the flow of springs and wells increases with 

a lowering of the barometer. This phenomenon has been carefully 

noted from early times, accurate descriptions dating from the eighteenth century. Baldwin Latham, in 1881, gave the results of some 

very interesting observations in England. He reports that some of 

45.8 

3.').0 

0.18 0.22 

515.402 

51.').352 

FIG. 37.-Diagram showing fluctuation of the height of the ground water and associated phenomena as observed at Munich. Averages are for thirty years and from observations in three 

wells. Ground water and rainfall are in centimeters, saturation deficit in millimeters, The 

saturation deficit indicates the amount of water lackin~ for the complete saturation of the air 

at the prevailing temperature. 

the long-established millers on the chalk streams claimed that they 

were able to foretell the approach of a rainstorm by a sensible increase 

in the flow of the river before any rain had fallen. He undertook a 

series of observations to investigate t.he phenomenon, and found, by 

setting up gages in the spring of 1881, on the Bourne, in the Caterham 

Valley, near Croydon, and selecting periods when there was no rain to 

vitiate the results, that whenever there was a rapid fall in the barometer there was a corresponding increase in the volume of water flowing, and that with a rise in the barometer there was a diminution in 

the flow. The fluctuations in the flow of the Croydon Bourne, due 

t.o barometric pressure, at one period exceeded 500,000 gallons a day. 
72 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

Observations upon the yield of wells and springs and upon percolation gages gave similar evidence. In 1883 Latham made observations 

on the effect of barometric pressure upon the flow of water from 

artesian wells, with results in accordance with the other observations. a 

Similar results were later observed in Germany and in America.b 

(See fig. 39.) 

The phenomenon is usually explained by the expansibility of the 

air confined in the porous medium in the neighborhood of the ground 

water and of the air dissolved in the ground water itself. Even the 

air in the soil above the water table meets more or less resistance to 

its escape when the barometer falls, and consequently a differential 

40.3 

32.72 

O.il 

1=1 ..0 ~ i5. ~ ~ ~ ~~13 ~ g 1=1 ..0 ,_; :-: ~ ~ ~ 1J!,-i .p ~:., 

~~~~~~~~~oZA~~~~~~~~~8ZA 

46.2 

32.5 

0.59 

FIG. 38.-Diagram showing fluctuation of the height of ground water and associated phenomena as observed at Berlin. Averages are for sixteen years and from observations in thirty 

seven wells. Ground water and rainfall are in centimeters, saturation deficit in millimeters. 

pressure must exist over the surface of the water table and the surface exposed at the well or spring. 

A change of an inch in the height of the barometer corresponds to 

a change of pressure of about 1 foot of water. It is evident that such 

a differential pressure exerted over the surface of the water table is 

sufficient to materially affect the flow into wells and springs. 

A very unique and not uncommon phenomenon, due to the same 

cause, is the "blowing" of wells just before a storm, as has been 

observed in the West. The low barometer before a storm causes 

a See British Association Reports, 1881, p.614; 1883, p.495. 

b Einfluss des Atmospharendrucks auf die Ergiebigkeit von Brunnen und Quellen, by Otto 

Lueger: Centralblatt d. Bauverw., 1882, p. 8. F. H. King, U. S. Dept. Agr. Weather Bulletin 

No. 5, 189'2, p. 50. 
'SLICHTER.] COLI~ECTING GALLERIES AND SUBCANALS. 73 

large quantities of air to be forced from the well with a loud, roaring 

noise. 

AVAILABLE SUPPLY OF WELLS AND SPRINGS. 

We may summarize the conditions affecting the amount of ground 

water available for the supply of wells and springs as follows: (1) 

IV· 

H-t+H+I-H-+-1-H+I-1-f-F:j-H..H-l+I-H-+-H-14+1++-H-14+1+++-H+I-1-H .I HK+H++H++H~H+~~K+H++HK+H4+H~H++H++HH2 

H4+.H+I-H-++H+I-H++H~4+H-++H4+1++-H-14+1++++~+1-I-H.3 

H-t~~H++H+rH++H+H+I-H-++H+I-H++H+I-H++H+I-HH.4 

~+H~H+~~H+~+HM+H++H~~~~H+~~+~.5 

HH~~+H~4+H-+·~4+~+H+I-H+~+I-~~~~~-6 

HH~~H+~+I-H++H+H~H-++H~H+-H-I+I-H4-I-H~HHj 

~~HT+H+H4+H++H~H*+H+I-H+H4+1-H+~~~~.8 

~+H~~~+I-H-++H~~+H~~H4+1-~~~~~~ 

HH+HHH-foi4+H+I-H-+-l.-H:!H-l~.!+++l-lf-l+l-+-l-...j...h..~Y-l-..j.:.,H+I-RI!I. 

~+H~~-1-H++~~+H~~+!-1~1-+-1-~~HW~~~-1 

HH+H~H-++H++~~+H~~~H+I-+-I-~Y+~+H~~2 

HH+H~H-++H++~+H+HH+~+ffiH+HH+HH+H-+~4+~3 

~+H~H++H++H++H~~+H~H+~+MH+H4~~HH4 

HH+H++H-++H~H++H4+~H+~+H~~+I-~~~4+~.5 

~+H+*H-++H~H+-1-H+HH+~+I-I~I-+-I-+1-~~~+1-~.6 

~+H~H+~++H++H~H+~+H~H4+MH+H4+H++HH.7 

MH+H~H++H+I-H+-1-H+HH+~~H+I-+-I-+H~H-++H+I-HH-8 

~+H+I-H-+~+1-H+-1-H+HH+~~H+I-+-I-+H~H-+~+1-~.9 

HH+H+I-~~+1-H+-1-H+HH+~+HH+I-+-I-+H~~+H+I-~2~ ., 6 Z 6 126 f1 IS 1Z I 6 I • Z 6 Ill. fiiZ. 6 I 6 IZ ~ 

MAv 4 5 6 7 8 9 10 II 12 13 14 16 ~ 

FIG. 39.-Autograph record of simultaneous changes in flow of spring and atmospheric pres· 

sure. Upper curve is air pressure, lower curve flow of spring. (After F. H. King.) 

:Magnitude of the area contributory to the wells; (2) amount of the 

rainfall upon this area; (3) geologic structure, such as (a) the arrangement or stratification of the material, (b) the breadth and depth of 

the water-bearing medium, and (c) the character or composition of 

this material, such as its fineness and porosity; and(±) physiographic 

features of the land surface, such as moui1tains, plateaus, hills, valleys, plains, forests, prairies, cultivated areas, etc. 

COLLECTING GALLERIES AND SUBCANALS. 

Another method of obtaining water from the surface underflow of 

ground water is by excavating a ditch or tunnel, with its bottom 

!"10. 40.-Diagram illustrating Salbach's theory of the contamination of wells or collecting galleries by reversed flow from rivers. Liability of contamination begins, according to Salbach 

when the water table falls so as to intersect the bed of the stream, as it does at B B B B. 

below the water table, and running as nearly as possible at right 

angles to the direction of the underflow. A ditch so constructed is 
74 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

nothing but a very elongated surface well. Its 

great length often makes it possible to bring the 

water to the surface of the ground without pumping~ by simply extending the ditch with a slope 

less than that of the surface of the ground until 

the flow comes to the surface. When such a channel is excavated for the purpose of furnishing a 

city water supply, it is usually called a collecting 

or infiltration gallery. Such excavations may be 

either open and unwalled or covered and walled. 

~ A variety of terms have been applied by various 

~ authors to similar devices constructed for obtain- a 

~ ing water for irrigation. The open ditches are 

~ c.allecl gravity ClltA, folintains, ancl tlnderflow ca- ~ . 

51 nals, the first term applying especially when the 

.£ recovery is made without pumping. If the water 

~ is secured by tunneling or "mining" for water, 

~ ·the excavation is frequently called a subsurface 

"" canal or underflow tunnel. 1=1 :3 Several gravity cuts and tunnels made in the por-

~ ous gravels so common in California have yielded 

~ water in abundance. Fountains constructed in 

material having a relatively low transmission constant, while not furnishing water for irrigation 

works of great magnitude, have, nevertheless, been 

important factors in many localities. 'rhe yield 

of a fountain or infiltration gallery, like the capacity of a well, must depend very largely upon rO 

~ the character of the water-bearing material in 

0 

~ 'vhich the excavation is made, the yield being pro- .S 

~ portionate to t,he transmission constant. Other 

]' things being equal, the yield must be nearly pro- l portional to the length of the canal. The depth is 

tlll likewise an important factor. Theoretical consid-

~ erations indicate that the flow should be propor-

~ tional to the square of the depth of the water sur- ::s 

S face in the canal below the natural water table. 

~ This conclusion seems to be borne out by experi- ::.. 

fi~!~J%ll~im\~:iti~t~~~~ .~ ence. f!l;J!II;~::-;::;;.:;ji?(lt~~ ~ The usual practice in recovering underflow by - :;;l means of gravity works is to follow a grade much 

ci 

f::~J;_f:'.'J('::::;:::~::::~:..:-:::::~~~ ~ less than the slope of the ground surface until the 

floor of the canal is about 6 feet below the level 

of ground water, and then to follow, in the further excavation from that point, the same slope 

as the surface of the ground. It is obvious thaL 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 67 PL. V 

A. VI EW LOOKING UP THE PACOIMA WASH FROM TH E SITE OF THE 

SUBSURFAC~. DAM . 

B. VIEW OF 50-FOOT SECTION OF SUBSURFACE DAM ON THE PACOIMA WASH . 

SHOW ING EXCAVATION AND LAGGING. 
SLICHTER.] COLLECTING GALLERIES AND SUBCANALS. 75 

gravity works are impracticable where the ground water is at great 

depths or where there is an insignificant slope to the water table. 

The effect of the removal of ground water from the soil by means of 

an infiltration gallery is, of course, the lowering of the water table in 

the immediate vicinity of the excavation. The curved form assumed 

by the water table is approximately that shown in figs. 8 (p. 29) and 

40 (p. 73), and is similar to the form of the water table in the neighbor-

~1 o o 0 0 0 0 0 0 0 0 0 

0 

GATHERING GAI..LERIE:S 

0 

rl------------------J~~----------------~ ~ o o o o o o ~) o o o o o o 1 

~----------------~ 

1,., 

FIG. 42.-Plan of infiltration galleries proposed by Willard D. Johnson. 

hood of a well. If the infiltration gallery is constructed in close proximity to the bank of the river, and if the water collected is used for 

a city water supply, it is important, to know under what circumstances 

pollution may take place by seepage of river water into the gallery. 

According to Salbach such pollution will not take place unless the 

curved water table actually intersects the bed of the stream, as shown 

by B B B B in fig. 40. 

Disappointment has sometimes followed the construction of infiltra-
76 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

tion works of the types described, especially in regions of low rainfall 

or where the underflow had not previously been subjected to careful 

survey. The underflow cut above Dodge, Kans., is now entirely 

abandoned. The supply of water was disappointing and the river 

floods have filled the exca\Tation, which was dredged at great expense, 

with silt and sand. 

Mr. Willard D. Johnson has made important sugge.stions for the 

construction of infiltration galleries for gravity works, as shown in 

the accompanying figures ( 41, 42, and 43). He would use .one or 

more batteries of tubular wells to reach the best portions of the 

water-bearing medium, as shown by a careful survey made prior to 

the construction of the works. The best flow of water is usually 

FIG. 43.-Longitudinal section of infiltration galleries designed by Willard D. Johnson. 

found at a considerble depth below the water table, and Mr. Johnson's plan offers a simple way of reaching it without expensive excavation. 

SUBSURFACE DAMS. 

Another method of recovering the underflow of a stream is by ·means 

of a subsurface dam. Such a dam is constructed by .excavating a 

trench at right angles to the direction of the underflow and extending 

in depth to the impervious stratum, and then filling the trench with 

impervious material. If the underflow is confined within an impervious trough or canyon, it is obvious that such a construction must 

result in bringing it to the surface. An example of this is found 

on Pacoima <;:;reek, Los Angeles County, Cal., where a subsurface 

dam ~as constructed in 1887-1890. It is claimed that by means of 

this dam the owners have been enabled to use the bed-rock flow of 

water for the three dry years, 1898-1900, and thereby to successfully 

carry through the orange, lemon, and olive growing in Fernando 

Valley. This dam is described in the Eighteenth Annual Report of 

the United States Geological Survey, Part IV, pages 693 to 695; also 

in Reservoirs for Irrigation, Water Power, etc., by James D. Schuyler, 

1901, page 205. 

A view of the wash up the canyon from the site of the dam is shown 

in Pl. V, A. An underflow was known to exist, as the stream had a 

good perennial flow back in the hills, shown in the background of 
U. S. GE'OLOGICAL SURVEY WATER-SUPPLY PAPER NO. 67 PL. VI 

VIEW FROM BOTTOM OF 50-FOOT SECTION OF PACOIMA SIJBSURFACE DAM, SHOWII\lG LAGGING IN PLACE AND 

CONSTRi.JCfiON OF CONCRETE WALL. 
SLICHTER.] SUBSURFACE DAMS. 77 

Pl. V, A, which was observed to gradually sink into the deep gravel 

wash before reaching the plains. At the site of the dam the canyon 

walls are about 600 feet apart, and the rock floor is at irregular depths, 

generally from 25 t.o 50 feet below the surface of the gravel. 

In constructing the dam, a trench was excavated in successive sections at right angles to the course of the wash. Each section was 50 

feet long and 5 feet wide, as shown in Pl. V, B. The excavation 

extended to bed rock and was boarded up with 2-inch by 8-inch by 

8-foot timbers and lagged with 3-inch by 4-inch by 5--foot timbers, as 

shown in Pl. V, B, and Pl. VI. 'Vhen bed rock was reached, a small 

trench about 12 inches deep and 10 inches wide was excavated in it, 

and the construction of the eement and gravel dam was begun. The 

wall is about 2 feet thick, and was built up to the surface in the usual 

manner, loose surface material being replaced around the dam as 

built, completely inclosing and supporting it. Centrifugal pumps 

kept the trenches free from water while working at bed rock, except 

at the closing section. Two masonry collecting wells were built in 

the wall of the dam, as a part of the same structure and extending to 

bed rock. The wells are 4 feet in internal diameter, and are built 

heavy on the downstream side, but lighter and with a number of open~ 

ings to admit water on the upstream side. 

As constructed, the dam shuts off the underflow, with the exception 

of some leakage which developed in places, the dam not being completely water-tight. The underground reservoir formed in the 

upstream gravel can not be definitely outlined, but its surface area 

is about 300 acres. The water is collected by means of four lines of 

10-inch t,o 12-inch concrete tile pipes laid above one another in horizontal rows from 8 to 10 feet apart on the upper side of the dam, 

beginning within a few feet of the bed rock. The tiles are in 3-foot 

lengths, laid with open joints, and discharge into the collecting wells 

described. 

A distributing main is laid into each well about 10 feet below the 

surface, and is bent down inside of the well so as to take water about 

30 feet below the surface. These mains are 14 and 20 inches in diameter, and extend underground to the towns of San Fernando and 

Pacoima, furnishing water for irrigation and domestic use. 

The end sections of the dam were carried up about 2 feet higher 

than the central portion, so as to prevent an overflow of water cutting 

out the banks of the wash. The total cost of the structure was about 

$40,000, cement costing $5 a barrel and labor from $2 to $4 a day. 

The top of the completed dam is shown in Pl. VII, A, and a portion 

of the central section in Pl. VII, B. 

ADVANTAGES OF UNDERGROUND SUPPLY. 

The recovery of ground water for irrigation by pumping from wells 

or by means of gravity cuts, infiltration galleries, or submerged dams 

is, considering the amount of water recovered, more complicated and 
78 MOTIONS OF UNDERGROUND WATERS. (NO. 67. 

expensive than the common practice of using the perennial flow of 

surface streams. But as the waters of the streams become more and 

more appropriated other sources of supply must be sought. The 

principal alternatives are the storage of storm waters and the utilization of the underflow. The appropriat,ion of the perennial flow of the 

rivers by the mountain States l~aves the settlers along the valleys of 

the Great Plains dependent upon the underground waters for irrigation. Fortunately portions of western Kansas and Nebraska are 

supplietl with underground water wit,hin a reasonable distance from 

the surface. 'Vhile the size of underflow works must be small in comparison with the usual works of stream diversion or reservoir storage, 

yet there are compensating advantages associated with ·them which 

make their development especially worthy of encouragement where 

conditions are favorable. In the first place, the utilization of the 

underflow is making use of water which in most cases would otherwise go to waste. Frequently the underflow drawn from the alluvium 

of a river is completely replaced by return seepag_e of river water 

during flood stages of the stream, so that the sands and gravels are 

really being used as inexpensive and indestructible reservoirs for the 

storage of storm waters. In the second place, there is usually greater 

1;egularity and uniformity in the quantity of ground water than th(jre 

is in the perennial flow of rivers, although the former is by no means 

free from the influence of dry months and dry seasons, as has already 

been shown. Furthermore, irrigation by the use of windmills or 

other power along the river valleys of the Plains, even if practiced 

on a small percentage of the area, must have an appreciable effect in 

raising the level of the water table, in turn augmenting the acreage 

which can be cuhivated and irrigated, and increasing the percentage 

of the rainfall which will enter the soil. The combination of intensive farming on small irrigated tracts with cattle raising on adjoining 

natur-al grass lands would seem to indicate a most attractive future 

for vast portions of the Great Plains and to contain possibilities of 

unique economic and social interest. 

The fundamental disadvantage in the utilization of underground 

sources of water is the danger of overdrawing the natural supply. In 

regions in which the rainfall is light and catchment areas are small, 

as in parts of southern .California, it is easy to extend development of 

underground sources so as to greatly exceed the natural rate of annual 

replenishment. In this way underground reservoirs are depleted 

which have been ages in filling; principal as well as interest is drawn 

upon, and much disappointment must inevitably follow. 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 67 PL. VII 

A. VI EW OF TOP OF COMPLET E D SUBSURFACE DAM ON THE PACO IMA WASH , 

SHOWING WELLS ON UP PER SIDE O F SAM E. 

H. VIEW OF C E NTRAL PORTION OF SUBSURFACE DAM ON THE PACOIMA 

WASH DU R ING OV ERF LOW. 
UHAP'rER Y. 

ARTESIAN AND DEEP WELLS. 

In Chapter III several ways in which the water from the deep zones 

may again reach the surface have been pointed out. If outcrops of the 

porous stratum exist at lower levels than the exposures which constitute the receiving or catchment area, we may expect to find associated 

with them numerous springs and diffused return seepage. In places 

the covering rock may be defective or locally pervious, so that, if the 

pressure be great enough, wat,er from the deep zone may reach the 

surface, or at least pass into a higher zone of flow. Occasionally 

joint.s and faults in the overlying rocks give opportunity for deep 

springs to show themselves. In some places the association of deep 

springs with the faulting system of the covering rocks is a phenomenon of great persistency. Dr. Peale, in his report on the mineral 

waters of the United States, remarks the almost universal association 

of mineral and thermal springs with the faulting of rocks. a Prof. 

vV. H. Hobbs, who has made a study of the faulting system of the 

Pomperaug Valley, Connecticut, has kindly furnished a map (fig. 44, 

on next page) showing the association of springs and faults in that 

region. By referring to the map it will be noticed that the springs 

not only occur along the line of faults, but usually occur where two, 

three, or more faults intersect. "The Triangle" shown on the map 

is a swampy area caused by the dropping of a triangular block of 

surface rock left unsupported by three lines of faults. It is undoubtedly supplied by seepage around its margin. It is described in Professor Hobbs's paper in the Twenty-first Annual Report of the United 

States Geological Survey, Part II. 

The springs arising from the deep zones of flow are usually distinguished from surface springs by a great,er constancy of flow from 

season to season and by a greater uniformity in the summer and winter temperatures of the water. Many surface springs are found to 

dry up and permanently disappear with the settlement and deforesting of the country, but this phenomenon is much less common with 

deep springs. The deep springs are· also much less liable to co~­

tamination than surface springs, for reasons which are very obvious. 

Even if the source of the deep zone of flow be polluted, the time 

required for the water to reach the outlet at the spring is usually so 

great that all organic impurities are effectually broken down and 

oxidized. 

a Fourteenth Ann. Rept. U.S. Geol. Survey, Pt. II, 1894, p. 49. 

IRR 67 -02--o 79 
80 MOTIONS OF UNDERGROUND W .ATERS. (NO. 67. 

In order to artificially recover water from the deep zone of flow, it 

is obvious that it must first be reached by drilling through the overlying material, the practicability of which depends upon the character and thickness of the covering rock and the expense which it is 

feasible to incur for the purpose. If the water in the water-bearing 

stratum is found under high pressure, it will rise in the drill hole 

until the pressure head due to the weight of the water column just 

balances the pressure in the water-bearing rock, or, if the pressure be 

I .... 

_ '~ QMitchell's Spring 

I'\ 'I' 

N 

l 

' ' I ' I \ 

' ' '\ 

RATTLESNAKE. 

HILL 

\ 

PINE. HILL 

Y4 hmile 

-7?- •• Favlf.s Cold springs 

FIG. 44.-Map showing location of springs in the vicmity of South Britain, Conn. 

great enough, until the water actually overflows above the surface. 

In order, however, that the water may rise as high as possible, it is 

necessary that the drill hole he properly cased with suitable well 

tubing, so that there will be no opportunity for the escape of water 

into pervious beds above the water-bearing rock; otherwise the drill 

hole may serve merely as a passage way from a lower to a higher 

stratum. 

If the water actually overflows at the surface of the ground, we 

have an artesian well, properly so called. If the water does not rise 
SLICHTER.] .ARTESIAN .AND DEEP WELLS .• 81 

to the surface, we have a nonflowing or deep well. This distinction is 

an important one to the owner of the wells, for in one case water is 

obtained without the constant expenditure of work and the wear and 

tear of pumping machinery, while in the other case a continual expenditure of work and money is required to bring the water to the 

surface. In the explanation of the phenomena and of the difficulties 

to be met with and overcome the distinction is one of little consequence and is entirely disregarded by many writers. The determination of the question whether or not a given well will overflow depends 

upon the altitude of the top of the well; so that of two wells exactly 

alike in all respects except that one is drilled on higher ground than 

the other, both tapping the same water-bearing rock, the one may 

overflow while the other may not. For this reason many writers call 

both wells artesian, and distinguish them as flowing and nonflowing 

wells. If the adjectives flowing and nonflowing are used, we may 

designate as artesian any well made into a deep zone of flow where 

the water is found under a static pressure so that it will rise in the 

well above the impervious covering stratum. The essential differences between such a well and a surface well are due to the existence 

of the upper impervious stratum, which is absent in the surface zone 

of flow. Owing to the presence of this impervious cover, we may 

emphasize the following distinguishing characteristics between surface wells and artesian wells: (1) rrhe water in the water-bearing veins 

of an artesian well is under a static pressure and will rise when the 

impervious cover is penetrated, while the ground water supplying 

a surface well has. a free upper surface which is lowered and changed 

in shape when water is removed from the well; and (2) an artesian 

well is supplied by the rainfall of districts not in the immediate 

vicinit,y of the well, but often distant hundreds of miles, while a surface well draws upon the rainfall of the immediate vicinity. ~ l 

The conditions upon which the existence of artesian wells depends 

presupposes a knowledge of the principles involved in the motion and 

storage of underground waters in the deep zones of flow. The essential facts involved in such flow have been discussed in Chapter III. 

The diagram of the cross section of t.he Dakota artesian basin (fig. 

20, p. 55) will serve to illustrate the conditions present in any artesian 

basin. In that diagram it will be noticed that the high elevation of 

the western exposure of the porous Dakota sandstone in the Black 

Hills tends to give a high pressure to the water in the sandstone in 

its eastern and nearly horizontal portion. If there were absolutely 

no escape for the water to the east of the catchment area, we should 

expect the water to rise in each well, if the casing were extended high 

enough, to the horizontal line L-L' (fig. 20}. The actual observed 

pressure, however, departs widely from that line, due undoubtedly 

to leakage from the eastern outcrop of the sandstone, especially along 
82 MOTIONS. OF UNDERGROUND WATERS. [NO. 67. 

~he Missouri and Great Sioux rivers in the southeastei·n part of South 

Dakota. At Running Water, Randall, and Chamberlain springs are 

seen rising from the bed of Missouri River, which probably accounts 

for the tendency to lower pressure in the neighborhood of the river. 

The high pressure at Kimball, Plankinton, and other places east of 

Chamberlain, probably reaches these points in part by a more northerly route, along which the loss by seepage is less than at Chamberlain and southerly points. This is verified by the high pressure of 

205 pounds at, Cheyenne Agency and by a pressure of more than 180 

pounds at Crow Creek Agency, the latter place being halfway between 

Chamberlain and Pierre, and the pressure higher than is found at 

either of those places. 

As already stated, the essential features of an artesian basin are 

well illustrated by this example of the Dakota area. r.rhe same ·principles are involved in the Potsdam and St. Peter artesian basin in 

southern Wisconsin and northern Illinois, and in the other large artesian basins in the count,ry, except that· the high pressure and large 

yield of the Dakota wells are in excess of those common in other 

basins. For a more extensive discussion of the general principles 

involved the reader is referred to Prof. T. C. Chamberlin's paper entitled, The Requisite and Qualifying Conditions of Artesian 'Veils. a 

The principal conditions on which artesian flows depend are summarized by Cham berlin as follows: 

I. A pervious stratum to permit the entrance and the passage of the water. 

II. A water-tight bed below to prevent the escape of the water downward. 

III. A like impervious bed above to prevent escape upward, for the water, 

being under pressure from the fountain-head, would otherwise find relief in that 

dir"ection. 

IV. An inclination of these beds, so that the edge at which the waters enter 

will be higher than the surface of the well. 

V. A suitable exposure of the edge of the porous stratum, so that it may ta 

in a sufficient supply of water. 

VI. An adequate rain-fall to furnish this supply. 

VII. An absence of any [easy] escape for the water at a lower level than the 

surface at the well. 

These seven prerequisites as stated by Chamberlin have been widely 

quoted by various writers and have become classic. The writer has 

made no change in the statements except the substitution of the word 

"easy" for "any" in VII, which is undoubtedly in accord with the 

meaning intended by Professor Chamberlin. Of course the less opportunity there is for the water of the water-bearing rock to escape at a 

level below that of the well the higher will be the head of pressure at the 

well, but the water-bearing stone is usually so fine that the frictional 

resistance offered by it, to the movement of the water is sufficient to 

establish considerable pressure a few miles back from an outcrop. 

As wat,er flows through a horizontal porous medium under a head at 

a Fifth Ann. Rept. U.S. Geol. Survey, 1885, pp. 131-li3. 
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 67 PL. VIII 

LINES OF FLOW INTO A WELL IN A REGION IN WHICH THE GROUND WATER 

HAS A CONSTANT MOTION IN A GENERAL DIRECTION. 
SLICHTER.] AR'l'ESIAN WELLS. 83 

one end, t,he pressure gradually drops from the maximum value at 

the end at which the water enters to nothing at the free end from 

which the water flows. This is illustrated by fig. 45. If we should 

prevent the escape of water at K7 G2, it would rise to corresponding 

heights (H', H", H"') in all of the tubes. In spite of the free escape 

at the right end of the sand column K7 G2, the pressure gradient 

H1 H2 H3 H4 H5 H6 is sufficient tQ produce a flow at any point along 

the tube K1 K6 if the wall of the tube be punctured. In this case we 

may imagine that the water-bearing sand and its confining tube 

represent, respectively, the water-bearing stratum and the upper and 

lower impervious strata of an artesian basin, the water column at the 

left of the figur~ corresponding to the higher outcrop of the pervious 

FIG. 45.-Diagram illustrating the fall of pressure as water moves through a pervious material. 

rock in the catchment area, while a puncture made in the t,ube anywhere between K1 and K7 represents an artesian well. 

The general character of the lines of flow in the neighborhood of an 

artesian well is shown in Pl. VIII. 

YIELD OR CAPACITY OF ARTESIAN WELLS. 

The yield of an artesian well, or the amount of water delivered in a 

given time, is usually measured in cubic feet per minute or per second, 

or in gallons per twenty-four hours. The yield depends upon the 

same factors as -noted in Chapter IV, on surface wells, but in addition to the causes there enumerated as affecting the flow in common wells, we must now consider the frictional resistance which the 
84 MOTIONS OF UNDERGROUND WATERS. [N0.67. 

water suffers in flowing through the casing and drill hole of the well. 

This resistance increases with the length of the casing, and also 

increases very rapidly with a decrease in the diameter of the casing. 

For long pipes the following formula will give the approximate discharge in cubic feet per minute: 

=3""8 /d5h 

q ' -v fl' 

in which cl is the diameter of the pipe in feet; l is the length of the 

pipe in feet; h is the head under which the flow takes place, measured 

in feet of water; f is the friction factor, which depends for its value 

upon the character of the surface of the pipe, and varies with the size 

of the pipe and the velocity of flow (for rough approximations its 

mean value 0.02 can be used). 

The foregoing formula states that the discharge from a long pipe 

varies directly as the 2t power of the diameter of the pipe, directly as 

the square root of the head, and inversely as the square root of the 

length of the pipe. The discharge of pipes, however, is ordinarily 

taken directly from hydraulic tables, thus saving the labor of eomputation.a If we attempt to estimate by the formula or by a hydraulic 

table the discharge from the well tubing of a flowing well, using as 

the head the observed static head when the mouth of the well is closed, 

and using the known size and depth of the well and tubing for the 

diameter and length of the pipe, a result will be obtained which will 

always be found to be in excess of t.he actual flow from the well. The 

reason for this is that no account is taken of the enormous resistance 

offered to the flow of water into the well through the pores of the 

water-bearing strata. The amount of water yielded by the porous 

strata to the well can also be expressed by a formula, as the writer has 

shown in another paper. b In order to estimate the amount of water 

delivered by the porous medium its transmission constant must be 

known. Suppose this constant to be given, the following is the 

formula which expresses the yield of the well, neglecting, as already 

stated, the resistance due to pipe friction: 

2 7t h k a b' f . t 

( 200~ cu 1c eet per m1nu e, 

loge ,1 + ---n) 

in which h is the observed static head, in feet, a is the thickness of 

the water-bearing stratum (of transmission capacity k), and Dis the 

diameter of the well in feet. The logarithm used here is the natural 

a See Tables Showing Loss of Head Due to Friction of WP.ter in Pipes, by E. B. Weston, Van 

Nostrand, N.Y., 1896; and Graphical Solution of Hydraultc Problems, by P. C. Coffin, Wiley & 

Sons, New York, 1897. 

bTheoretical investigation of the motion of ground waters: Nineteenth Ann. Rept. U. S. GeoL 

Survey, Pt. II, 1899, p. 360. 
SLICHTER.) YIELD 0]' ARTESIAN WELLS. 85 

or napierian logarithm. a The denominator of t,he fraction in this 

formula is the only part that depends for its value upon D, the diam-

'l'his part of the formula, namely, , 1 

1,

200) 

loge( 1+ --y;-

eter of the well. 

changes value but slightly as D is changed. This fact is readily 

understood when we remember that 2 inches and 12 inches are the 

practical limits of size of artesian wells. In Table VII are written 

the various values which this expression takes for certain common 

sizes of wells. It is seen that the values differ but slightly for the various sizes, so that if friction in the pores of the sandstone be the only 

resistance that need be considered the capacity of such wells would be 

but slightly dependent upon the diameter of the well. 

TABLE VII. 

Values for various diarneters of wells of the factor in artesian-well forrnnla which 

depends upon the diarneter of the well. 

-·--- -----~---

I Value of Compared Diameter 1 with value 

of well. log.( 1+ 1,:) for 6-inch 

well. . I 

Inches. 

2 0.1125 0.876 

3 0.1179 0.918 

4 0.12"20 0.951 

H 0.1238 0.964 

5 0.1254 0.977 

6 0.1283 1.000 8 0.1333 1.039 

9 0.1354 1.055 

10 0.1374 l.Oill 

12 0.1408 i 1.097 

The formula for the actual flow from the well must take account 

of both the resistance offered by the water-bearing medium and the 

resistance due to pipe friction. The writer finds that the following 

formula is the expression of the actual yield of the well, if both of 

these factors are taken into account: 

- 2 ~o) cubic feet per minute, 

in which q is the estimated free discharge of water through the well 

and casing under head h, including in the estimate the influence of 

all valves, bends, reduction in size of pipe, etc., and Qo is the theoretical yield of the well under head h, if friction in the well and pipe 

be neglected. In this expression Qo varies only slightly with a change 

in the diameter of the well, while q ~aries rapidly for such change. 

a This formula was obtained by the writer in 1892. While the paper referred to was in press 

he discovered that substantially the same formula had been previously worked out by a German hydrographer. 
86 MOTIONS OF UNDERGROUND WATERS. [NO. 61. 

Table VIII gives values of Qo, or the theoretical yield of an artesian 

well, computed for various effective sizes of grains of the water-bearing medium. The table is calculated on the basis of a 6-inch well and 

100 feet thickness of water-bearing strata. Other thicknesses of strata 

and other heads of pressure will give proportional results. Such a table 

may be found useful in estimating the yield of wells in unconsolidated 

sands of known character, but of course it must not be expected te 

give results of very grea~ refinement. A nicety of numerical results 

is impracticable in such a subject, and the table, to be of value, must 

be used with discretion. 

TABLE VIII. 

Theoretical capacity (no allowance for pipe friction) of 6-inch artesian well 

extending 100 feet in materials of various kinds for various heads of pressure. 

[Proportional yields for other heads and other thicknesses of material. Yields for wells of 

other diameters can be obtained by the use of the last column of Table VII. Porosity, 3"2 per 

cent; temperature, 50° F.] 

Effective I 

I 

I 

I I 

size of 4-foot 8-foot 

grain. head. head. 

Mrn. 

I Cu. ft. pe>· Ctt.f~.per 

11un. nun. 0.02 ' 0.047 0.093 

0.04 0.186 0.37~ 

0.06 0.419 0.837 

0.08 0. 744 1.488 

0.10 1.16.'3 2.326 

0.12 1.675 3.350 0.14 2.279 4.558 

0.16 2.977 5.954 

0.18 3.768 7.536 

0.20 4.651 9.302 

0.25 'i'.~ 14.53 

0.30 10.46 20.92 

0.40 18.60 37.20 

0.50 29.07 58.14 

0.60 41.86 83.72 

0. 70 56.96 113.9 

0.80 74.4~ 148.8 

0.90 94.19 188.4 

1.00 116.3 232.6 

2.00 465.1 930.~ 

3.00 1046.0 209'2.0 

I 

1()-foot 

head. 

12-foot 

head. head. head. 

Conventional 

names of 

size of 

grains. I 

Cu.f~.per I Ctt./~.pe ntzn. nun. 0.116 0.140 

0.465 0.558 

1

16-foot I' 25-foot 

-r I Cu.f~.per ~-C-u-.j-~-.p-e-1· ;-----I 

mtn. mtn. 

o. 186 o. 291 }snt ' 0. 7 44 1.163 . 1.047 l.tOO 

1.860 2.233 2.907 3.492 

4.186 5. 025 

5.697 6.837 

7.440 8.931 

9.419 11.30 

11.63 13.95 

18.17 21.80 

26.16 31.38 

46.51 55.80 

72.67 87.21 

104.7 125.6 

142.4 170.9 

186.0 223.3 

2:35.5 282.6 

290.7 349. ~ 

1163.0 1395.0 

2616.0 3138.0 

I 

1. 674 2. 6!6 }Very fine 

2. 977 4. 651 sand 

I ~:¥&3 l~:rso il . 9. 116 14. 24 I 

1

1 U: ~~ ~: ~ Fine sand. 

18. 60 29. 07 1 

29. oo 45. 47 I 

41. 84 65. 41 }M d . I 74.40 116.3 e lUll 

116. 3 181. 8 sand. 

167. 4 :&il. 6 27 8 35?· 1 lc o a r s e ~~: ~ ~8: ~ sand. 

465.2 726.7 

1860. 0 2907. 0 lFine 

4184. 0 6541. 0 J ( gravel. 

The writer has devised the following graphi\..~al method of solving 

problems connected with the capacity of artesi~.n wells, and has found 

it to be very useful. We will first apply the 1nethod to a problem in 

which it is supposed that we know the theoretical yield of the well when 

pipe friction is neglected (that is, the value of Qo from Table VIII), 

and the value of the theoretical discharge (q) of the well tube under 

the given static head, which last may be taken from a hydraulic table, 

as already suggested. In fig. 46, let AB and BC be each laid off 

equal to Qo, so that AC=2Q0 • Then lay off CD at right angles to 

AC and equal to q. Join AD and lay off DE= CD and draw CE. 

Also lay off AF=CD and draw FG parallel to OE and make 
SLICHTER.) YIELD OF ARTESIAN WELLS. 

AH=AG. Then AH=Q, the total actual yield of the well. The 

line HB represents the loss of flow due to friction in the well and 

casing. If t,he well and casing were larger, CD would be longer, and 

likewise AH and AG would be greater, so that the flow Q would be 

increased. 

As a numerical example of this graphical construction, suppose 

that the water-bearing stratum is 100 feet thick, of effective size grain 

0.2 mm., and that the static head is equal to a 50-foot column of 

water. Let us determine the yield of a ±-inch well1,000 feet deep. 

From Table VIII we find that Qo=55.3 cubic feet per minute. On 

page 98 of 'Veston's hydraulic tables the discharge of 1,000 feet of 

4-inch pipe under a head of 50 feet is found to be about 257 gallons 

per minute, or 34:.3 cubic feet per minute, so that q=34.3. Draw 

AB=B0=55.3 and also OD=34.3. lVlaking the construction indicated, we get AH or Q=24.6 cubic feet per minute, which is some8 

______ ...._ ____ Q 0::-------

FIG. 46.-Diagram illustrating the author's graphical solution of problems in the yield of 

artesian wells. 

what less than half of the theoretical yield, with pipe friction 

neglected. 

Uncertainty as to the value of k, or the transmission constant of 

the rock, makes the application of this graphical solution more or less 

uncertain so far as precision of results is concerned. Nevertheless, it 

' is capable of giving 1nuch valuable information concerning the relations of the two fundamental causes affecting the capacity of wells, 

pipe friction, and capillary friction in the pores of the rock. 

Perhaps the most useful application of the method is to the inverse 

problem of determining the value of Q .. , or the theoretical flow, when 

the static head and the actual discharge of the well have been measured. The value of Qo can be found graphically in the following 

manner, as is shown by the dotted lines in fig. 46: Lay off on any 

straight line, A C, the known yield of the well, or Q=AlL Draw the 

line AKLN perpendicular to AH, and from Has center describe 

an arc with radius equal to q, cutting AN in K. Then lay off 
88 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

AL=HK=q, and draw Lltf parallel to KH. Next lay off A1V=LM 

and draw NB parallel to HK. Then AB is Qo, or the theoretical 

flow of the well if pipe friction were entirely absent. 

The usefulness of the inverse solution lies chiefly in the fact that 

it enables us to determine the increased yield which results from enlarging the diameter of a flowing well. Thus let us suppose that a 

4-inch well1,000 feet deep yields 26.6 cubic feet per minute under a 

static head of 50 feet; what yield should we expect from a 6-inch well, 

all other things being similar? 'Ve first lay off AH=24.6 in fig. ±6, 

and make the construction shown by the dotted lines. This gives us 

AB=55. 3, so that the yield of the 4-inch well, if pipe friction could 

be avoided, would be 55.3 cubic feet per minute. 

D 

FIG. 47.-Diagram illustrating graphical solution of an artesian-well problem. 

From Table VII, column 3, we observe that this value should be 

increased about 5 per cent if the diameter of the well be changed to 

f3 inches. ·This gives us 58.1 cubic feet per minute for Qo for a 6-inch 

well. The discharge of 1,000 feet of 6-inch pipe under a head of 50 

feet is found on page 102 of 'Veston's tables to be 730 gallons, or 97.3 

cubic feet, per minute. Then in fig. 47 lay off AB=BC=58.1 and 

0D=97.3. Following the construction explained, we arrive at the 

value of Q or AH, which is found to be 45.6. Therefore the yield of 

a 6-inch well will be 45.6 cubic feet per minute. The yield of the 

4-inch well was 2.!.6 cubic feet per minute, so that a 6-inch well under 

these conditions should be expected to have a capacity about 85 per 

cent greater than that of a .!-inch well. 
SLICHTER.] YIELD OF ARTESIAN WELLS. 89 

The foregoing problems may also be solved by means of the curves 

of fig. 48. These curves show the relation of Q, the discharge of a 

well, to Qo, the theoretical yield, but on a scale in which the unit of 

discharge is equal to q, the capacity of the well tube under the given 

static head. In order to illustrate the use of the diagram, we shall use 

the same examples .that we have just solved. The first problem calls 

for the yield of a 4-inch well 1,000 feet deep whose static head is 50 

feet, the transmission constant and thickness of water-bearing stratum 

being given as before. Table VIII gives the theoretical yield Qo= 

55.3 cubic feet per minute. From a hydraulic table the capacity of 

FIG. 48.-Graphical rept•esentation of the relations between Q and Qo in the equation on page 85, 

q being taken as equal to unity. The lower curve is a replat on larger seal£ of the portion of 

the upper curve between Q0 =0and Q0 =1.&3. From this diagram the value of Q0 can be obtained 

when Q and q are given. The unit of measure is q= 1, so that Q must always be less than unity 

on this scale. In other words, the ordinates in the diagram are equal to Qfq, the abscissas 

to Q0 /q. 

1,000 feet of 4-inch pipe under a head of 50 feet is found to be 34.3 

cubic feet per minute. Using this value of q as theunitof measure gives 

Qo/ q= 55.3-:-34.3 = 1. 6. Finding this value on the horizonal scale of the 

diagram (fig. 48), we determine Qlq to be 0.725. To reduce to cubic 

feet per minute, multiply 0.725 by 34.3, the value of q, which gives 

24:.9 cubic feet per minute as the yield of the well. The result is 

slightly different from that obtained by the graphical construction. 

The same diagram can also be used to solve the inverse problem 

previously discussed: If a 4-inch welll,OOO feet deep, having a static 

head of 50 feet, yields 24.6 cubic feet per minute, 'vhat will be the 
90 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

yield of a 6-inch well under the same conditions? From a hydraulic 

table we obtain, as before, the yield of 1,000 feet of ±-inch pipe, viz, 

34.3 cubic feet per minute. '"rhis is the value of q. Then Qjq is 

24.6-;-3-!.3, or 0. 7'2. Finding 0.72 in the vertical scale of the diagram 

(fig. -!8) gives Qo/q=l.55. According to Table VII this should be 

increased about 5 per cent in order to give the value of Qo/q for a 

6-inch well, making its value 1.6:3, so that Qo=l.63x 34.3, or 56 cubic 

feet per minute. A hydraulic table gives q for 1,000 feet of 6-inch 

pipe, head 50 feet, equal to 97.3 cubic feet per minute, so that for a 

6-inch well Qo/q=56-;-97.3=0.60. Using the lower curve of fig. 48, 

we find. corresponding to 0.60 that Q/q=0.-!7, and since q=97.3, 

Q=97.3x0.47=45.7, which is the yield of the 13-inch well in cubic feet 

per minute. 

SIMPLE METHODS OF MEASURING THE YIELD OF FLOWING 

WELLS. 

Prof. J. E. Todd, State geologist of South Dakota, has recently 

issued a bulletin describing very simple methods of determining the 

yield of an artesian well, which give fairly accurate results with little 

trouble and in a short time. The following tables and explanations 

are from his bulletin. All that is necessary for the purpose is that 

the water be discharged through a pipe of uniform diameter, a foot 

rule, still air, and care in taking measurements. Two methods are 

proposed, one for pipes discharging vertically, which is particularly 

applicable before the well is permanently finished, and one for horizontal discharge, which is the most usual way of finishing a well. 

The table below is adapted to wells of moderate size as well as to 

large wells. In case the well is of other diameter than that given in 

the table its discharge can without much difficulty be obtained from 

the table by remembering that, other things being equal, the discharge 

varies as the square of the diameter of the pipe. If, for example, the 

pipe is one-half inch in diameter its dis<-~harge 'vill be one-fourth of 

that of a pipe 1 inch in diameter for a stream of the same height. In 

a similar manner the discharge of a pipe 8 inches in diameter can be 

obtained by multiplying the discharge of the -!-inch pipe by 4. 

In the first met,lwd the inside diameter of the pipe should first be 

measured, then the distance from t,he end of the pipe to the highest 

point of the dome of the water above, in a strictly vert,ical directiona t,o b in the diagram, fig. -!H. Find these distances in the table 

(IX, A), and the corresponding figure will give the number of gallons discharged each minute. "\V ind would not interfere in this case, 

so long as the measurements are taken vertically. 

The method for determining the diseharge of horizontal pipes 

requires a little more care. First, measure the diameter of the pipe, 

as before, then the vertical distance from· the center of the opening 
( 

r 

! 

SLICHTER.] YIELD OF .ARTESIAN WELLS. 91 

of the pipe, or some convenient point corresponding to it on the side 

of the pipe, vertically downward 6 inches, a to b of the diagram, then 

from this point strictly horizontally to the center of the stream, b to e. 

With these data the flow in gallons per minute can be obtained from 

the table (IX, B). It will readily be seen that a slight error may 

make much difference in the discharge. Care must be taken to measure horizontally and also to the center of the stream. Because of 

FlG. 49.-Diagram illustrating flow from vertical an\1 horizontal pipes. 

this difficulty, it is desirable to check the first determination by a 

second. For this purpose columns are given in the tables for corresponding measurements 12 inches below the center of the pipe. Of 

course the discharge from the same pipe should be the same in the 

two measurements of the same stream. Wind blowing either with 

or against the water may vitiate results to an indefinite amount; 

therefore measurements should be taken while the air is still. 
92 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

TABLE IX. 

Table for determining yield of artesian wells. 

A. Flow from vertical pipes. B. Flow from horizontal pipes. 

Discharge in gallons per minute. [i ; Flow in gallons per minute. 

~ ! .... 

:: Diameter of pipe in inches. I ~ ~ ~ . ii 

l-inch pipe. 2-inch pipe. 

12-inch 

level. 

6-inch 

level. :; 1 '.'. ll .I U I 2 f 3 : ·E 6-inch I ~ , • ! - ,

1

' ] 1 ~ level. 

In:.-~-~---~-~~~ ·~---- t 3,96 6,2 I 8,91 15,8 35,61 6 7,01 4,95 27,71 

1 5. 60 8. 7 12. 6 2"2. 4 51. 4 II 7 8.18 5. 77 32. 33 2 7.99 12.5 18.0 32.0 71.9 8 9.3.5 6.60 36.94 

3 9. 81 15.3 22. 1 39. 2 88. 31 9 10. 51 7. 42 41. 56 

4 11.33 17.7 25.5 45.3 10'2.0 10 11.68 8.25 46.18 5 12. 68 19.8 28.5 50. 7 113. 8 . 11 12. 85 9. 08 50. 80 6 13. 88 21. 7 31. 2 55. 5 124. 9 12 H. 02 9. 91 55. 42 ,. 7 14. 96 23. 6 33. 7 59. 8 134. 9 13 15.19 10. 73 60.03 

8 16.00 25. 1 36. 0 64.0 144.1 14 16. 36 11.56 64. 65 

9 17.01 26.6 38.3 68.0 153.1 15 17.53 12.38 69.27 

10 17.93 28.1 40.3 71.6 161.3 16 18.70 13.21 73.89 

11 18. 80 29. 5 42.3 75. 2 169. 3 17 19. 87 14. 04 78. 51 

12 19. 65 30. 7 44. 2 78. 6 176. 9 18 21.04 14.86 83.12 

13 20.46 31.8 45.9 81.8 184.1 19 22.21 15.69 87.74 

14 21. 22 33. 0 4 7. 6 84. 9 190. 9 20 23. 37 16. 51 92. 36 

15 21.95 34.2- 49.3 87.8 197.5 21 24.54 17.34 96.98 

16 2"2. 67 35. 2 50.9 90. 7 203.9 22 25. 71 18.17 101. 60 

17 23. 37 36. 3 52.5 93. 5 210.3 23 26. 88 18. 99 106.21 

18 24. 06 37. 5 54. 1 96. 2 216. 5 24 28. 04 19. 82 110. 83 

19 24. 72 38. 6 55. 6 98. 9 22"2. 5 25 29. 11 20. 64 115. 45 

20 25. 37 39. 6 57. 0 101.6 228.5 26 30. 38 21. 47 120. 07 

21 26. 02 40. 6 58. 4 104. 2 234. 3 27 31. 55 22. 29 124.69 

22 26. 66 41. 6 59. 9 106. 7 240. 0 28 32. 72 23. 12 129. 30 

23 27. 28 42. 6 61. 4 109. 2 24f). 6 29 33. 89 23. 95 133. 92 

24 27. 90 43. 5 62. 8 111. 6 251. 1 30 35: 06 24. 77 138. 54 

25 28.49 44.4 64.1 114.0 256.4 31 36.23 25.59 143.16 

12-inch 

level. 

19.63 

22.90 

26.18 

29.45 

32.72 

35.99 

39.26 

42.54 

45.81 

49.08 

52.35 

55.62 

58.00 

62.17 

65.44 

68.71 

71.98 

75.26 

78.53 

81.80 

85.07 

88.34 

91.62 

94.89 

98.16 

26 29. 05 45.3 65. 3 116.2 261. 4 3'2 37. 40 26. 42 147. 78 

27 29.59 46.1 66. 4 118. 2 266.1 33 38. 57 27. 25 152. 39 

.23 30.08 46.9 67.5 120.3 270.4 34 39.64 28.08 157.01 

101.43 

104.70 

~ft:~~ l 

114.52 

117.79 

29 30. 55 47. 5 68. 5 121. 9 27 4.1 35 40. 45 28. 64 161. 63 

30 30. 94 46. 2 69. 4 123. 4 277. 6 36 41.60 29. 46 166.25 

36 34. 1 53. 2 76. 7 136. 3 306. 6 48 39. 1 61. 0 88. 0 156. 5 352. 1 

60 43.8 68. 4 98. 6 175. 2 394. 3 

72 48. 2 75. 2 108. 0 192. 9 484. 0 84 51.9 81.0 116.8 207.6 467.0 

96 55. 6 86. 7 125. 0 2'22. 2 500. 0 

108 58. 9 92. 0 182. 6 23.5. 9 530. 8 

120 62. 2 98. 0 139. 9 248. 7 559. 5 

182 65.1 10'2. 6 146. 5 260. 4 585.9 144 68. 0 106. 4 15B. 1 272. 2 612. 5 

Continue by adding for each inch1.151 0.82 I 

! 3.21 

NoTE.-To convert results into cubic feet, divide the number of gallons by 7.5, or, more accu- rately, by 7 .48. 

The flow in pipes of diameters not given in the table can easily be 

obtained in the following manner: 

Fort-inch pipe, multiply discharge of 1-inch pipe by _____________ _ 

For !-inch pipe, multiply discharge of 1-inch pipe by _____________ _ 

For 1t-inch pipe, multiply discharge of l-inch pipe by ____________ _ 

For 1t-inch pipe, multiply discharge of 1-inch pipe by ____________ _ 

For 3-inch pipe, multiply discharge of 2-inch pipe by _____________ _ 

For 4-inch pipe, multiply discharge of 2-inch pipe by _____________ _ 

For 4t-inch pipe, multiply discharge of 2-inch pipe by _______ ~ ____ _ 

For 5-inch pipe, multiply discharge of 2-inch pipe by _____________ . 

For 6-inch pipe, multiply dischat·ge cf 2-inch pipe by _____________ _ 

For 8-inch pipe, multiply discharge of 2-inch pipe by________ _ _ _ _ _ 

0.25 

0.56 

1. 56 

2.25 

2.25 

4.00 

5.06 

6.25 

9.00 

16.00 
_) 

SLICHTER.] FAILURE OF .ARTESIAN WELLS. 93 

Whenever fractions occur in the height or horizontal distance of 

the stream, the number of gallons can be obtained by apportioning 

the difference between the readings in the table for the nearest whole 

numbers, according to the si_ze of the fraction. For example, if the 

distance from the top of the pipe to the top of the stream in the first 

case is B! inches, one-third of the difference between the reading in 

the table for 9 and 10 inches must be added to the former to give the 

correct result. 

In case one measures the flow of a well by both methods he may 

think that the results should agree, but such is not the case. In the 

vertical discharge, there being less friction, the flow will be larger; 

so also in the second method differences will be found according to the 

length of the horizontal pipe .used. 

As pipes are occasionally at an angle, it is well to know that the 

second method can be applied to them if the first measurement is 

taken strictly vertically from the center of the opening, and the second measurement from that point parallel with the axis of the pipe 

to the cent,er of the stream, as before. The measurements can then 

be read from the table. 

FAILURE OF ARTESIAN WELLS. 

It is not uncommon to find that the flow of an artesian well is 

gradually growing less or failing altogether. The cause of the failure 

may be purely local and pertain to that particular well, or it may 

be general and associated with some depreciation of the artesian basin 

as a whole. If the failure is due to local causes it may not be duplicated in neighboring wells, while causes affecting the artesian basin 

as a whole must of course be evidenced by a diminution of flow in 

all of the wells. 

Perhaps the most common cause of failure of single wells is 

improper casing. Some wells are not properly cased from the beginning. Or the trouble may be due to poor jointing or packing where 

the casi~g meets the uncased rock, or to poor packing where a reduction in the size_ of the casing occurs. Casing is sometimes omitted 

where a porous stratum really requires it, or where a friable or fractured rock is subject to constant caving. The leaks around the casing or into porous strata may easily cause the total destruction of a 

well, or so injure it that it can be repaired only at, great expense. 

The filling of the lower portion of a well with sand and debris falling from an upper stratum, or brought into the well by the water, is 

a common cause of the falling off in the flow of an artesian well. 

This difficulty is easily remedied by cleaning out the debris by means 

of a sand pump. 

Sometimes the water-bearing rock is so friable and the pressure so 

great that the well must be cased to the bottom and the end of the 

tube be driven fast into the bottom rock, the water being admitted 

IRR 67-02--7 
04 MOTIONS OF UNDERGROUND WATERS. [NO. 67. 

int,o the well through numerous holes drilled in the lower sections of 

the casing, which act on the same principl13 as the cylindrical screens 

in a common driven well. 

A cause of the partial failure of wells, which is not yet thoroughly 

understood, is the apparent clogging of the water-bearing rock in the 

immediate neighborhood of the well. Whether this clogging is due to 

the deposit of fine silt in the pores of the rock or to a growth of microscopic plant life, or to a gelatinous deposit of iron, etc., has not, to the 

writer's knowledge, been ascertained in any of the cases in which the 

phenomenon has been observed. In the old artesian wells at Savanl1ah, Ga., it was found that the explosion of dynamite at the bottom 

of the wells did not remove the difficulty. Later, in the new wells at 

the same city, it was found that strong back flushing of the wellsthat is, the forcing of large quantities of water into them-caused a 

very marked restoration of the flow. This matter will be especially 

referred to on a later page (p. 100), where the wells at Savannah are 

more fully discussed. 

Failure due t,o causes pertaining to the entire artesian basin is 

also rather common. It is probably true that in nearly all artesian 

basins the original pressure gradient in the water-bearing rock is 

apprecia~ly lowered by the artificial drafts made upon the subterranean supply, with a consequent actual decrease in the capacities of 

the wells. A small decrease of this kind is to be expected, and it does 

not necessarily indicate approaching disaster to the wells. Even in 

the Dakota basin, which seems thus far to be quite adequate to the 

enormous demands made upon it, it is thought that there is evidence 

of a slight depreciation of the wells on higher ground, and even some 

wells of low pressure have ceased to flow, as at Scotland, rrripp, and 

elsewhere. Most, wells, however, have failed but little.a 

It must be kept well in mind that there is a limit to the amount of 

water that can be withdrawn from an artesian basin. There is no 

such thing as an inexhaustible supply in this connection. The amount 

of water available is limited on the one hand by the amount of rainfall upon the catchment area and the facility with which the rainfall can obtain entrance to the porous stratum, and on the other 

hand by the capacity of the water-bearing rock to transmit the water 

over long distances and diminution through leakage and seepage. 

These two limiting conditions are usually of sufficient magnitude to 

render the overdrawing of the supply a pt·actical and present danger 

which should be constantly kept in mind. 

One of the most striking examples of a general and gradual failure 

of the wells of an entire basin is presented by those at or near the 

city of Denver. b ~rhis basin was discovered in 1884, and in a few 

a Geology and water resources of a portion of southeastern South Dakota, by J. E. Todd: 

Water-Supply and Irrigation Paper U.S. Geol. Survey No. 34, 1900, p. 31. 

b See Artesian wells of Denver Basin, by G. H. Eldridge: Mon. U. S. Geol. Survey Vol. XXVII. 

Also see The artesian wells of Denver; a report by a special committee of the Colorado Scientific Society: Proc. Colo. Sci. Soc., Denver, Vol. I, 188.'3-84, pp. 76-108. 
SLICHTER.] MUTUAL INTERFERENCE OF ARTESIAN WELLS. 95 

years about 400 wells had been drilled within an area extending a 

distance of 40 miles along South Platte River in a strip about 5 miles 

wide on both sides of the stream. Most of the wells were within the 

limits of the city itself. Many of the wells had a good pressure and 

strong flow when first constructed. In 1886 it was not thought that 

any general decrease in the flow of the wells could be detected. 

Between 1888 and 1890, however, a continuous decrease in the flow of 

the city wells took place, and by the end of the latter year all but six 

of the city wells had to be pumped, while numerous wells in the basin 

were permanently abandoned. a 

It is thought that the cause of the remarkable failure of this basin 

is not lack of rainfall upon the catchment area or the size or absorption power of the latter, but the low porosity and transmission power 

of the water-bearing strata. It is believed that during the early 

years in the history of the wells the water withdrawn represented 

a supply stored in the rocks but not readily transported by the strata 

to meet the enormous draft. Van Diest estimated in 1890 that if all 

the wells in Denver "Were plugged it would be forty years before the 

water-bearing strata of the Tertiary of the Denver Basin would be 

again in the condition of saturation existing when the first well 

was sunk.b 

MUTUAL INTERFERENCE OF ARTESIAN WELLS. 

It is a common experience to find that the yield of an artesian well 

is noticeably influenced by the construction of a new well in the same 

neighborhood. When this phenomenon is associated with a general 

lowering of the water pressure throughout the region, it is more properly considered a case of partial failure of the artesian basin than 

a case of interference. One well may interfere with another well 

without the basin being subject to general depreeiation. The interference of two wells, in the technical sense, is determined by a comparison of the flow of one of two wells ·when both are flowing freely 

with the flow of each well when the other is shut off. In a similar 

way we may determine the interference of several wells with one well. 

To illustrate the distinction between the general depreciation of an 

artesian area and the interference of wells wit,h one another we will 

consider the case presented by the Chicago wells. The large .drafts 

made upon t,he various zones of supply in that district have caused 

the head of wells constrqcted in 1864 to fall about 100 feet. This 

would be referred to as depreciation or partial failure of the basin. 

But if at the time mentioned two wells had been constructed 50 feet 

apart, the flow of each well during the entire period of gradual depreciation would fluctuate with the shutting down or starting up of the 

other well. This is what is meant by interference. 

a Artesian wells of Denver Basin, by G. H. Eldridge: Mon. U.S. Geol. Survey Vol. XXVII, 

p. 4:'*'. 

blbid., pp. 426-427. See also The artesian wells of Denver: Proc. Colo. Sci. Soc., Denver, Vol. 

I, 1883-84, pp. 76-108. 
~6 MOTIONS OF UNDERGROUND W .ATERS. [NO. 67. 

It is more surprising to find cases in which no interference between 

neighboring wells can be detected than to observe cases in which it 

is very pronounced. The enormous 12-inch Ponce de Leon well at St. 

Augustine, Fla., seems to suffer no interference from a neighboring 

6-inch well. The Ponce de Leon well is 1,400 feet deep and flows 

10,000,000 gallons per day under a closed head of 17 pounds per 

square inch.a While a dynamo was being operated by the 12-inch 

well, the 6-inch well (capacity 400,000 gallons daily) was suddenly 

turned on and off, but the closest observation did not detect the 

slightest trembling of the pressure gage on the 12-inch well. The 

latter well, however, is much deeper than the 6-inch well, and furnished 3,000,000 gallons daily at the depth reached by the 6-inch well. 

This fact and the disparity in their total yield may sufficiently account 

for the failure to detect any interference. 

At Savannah the flow from the first 7 of 12 wells arranged 30(') feet 

apart in a straight line was observed in 1892 to be 6,500,000 gallons per day, an average of 930,000 gallons for each well, at an 

elevation of 8 feet above the sea. The water stood in wells Nos. 10, 

11, and 12 at altitudes of 14.93, 15.96, and 16.20 feet, respectively. 

The total yield of the 12 wells under the same head was 9,500,009 

gallons per day, an average of 792,000 ga1lons for each well. In 1897 

a measurement of the mutual interference of these wells and the 

Springfield well, 2,000 feet east, was made, and it was ascertained 

that when the Springfield well was shut off the total flow of the 12 

wells was 6,910,000 gallons per day, and that when the Springfield well 

was in use the flow was 7,258,000 gallons per day. r:rhe net gain from 

that well was, therefore, 348,000 gallons per day, which would be 

increased to 468,000 gallons per day if the leakage between the well 

and the works be allowed for. The latter quantity (468,000 gallons) is 

therefore the net gain due to t.he use of the Springfield well. The 

latter well, however, was actually flowing at the rate of 1,000,000 gallons per day. Therefore the 12 wells suffered a decrease of 552,000 

gallons per day, which is an interference of 8 per cent due to the 

Springfield well. 'rhe Savannah wells are discussed more fully on 

the following pages. 

What is reported to be int.erference of wells sometimes proves to 

be a fault largely due to defective construction. Such was in part 

the case at Rockford, Ill. b The first well drilled was 8 inches in 

diameter and 1,530 feet deep. The water rose about 28 feet above the 

ground and flowed about 1,000,000 gallons per day. Three more wells 

were sunk, and when all were connected with the pump the total flow 

was 3,000,000 gallons per day. 'I:'his would indicate a mutual interference of 25 per cent. This flow was not permanent, however, and 

soon diminished to 2,500,000 gallons per day, while a paper mill1 

mile south of the works and at 17 feet lower elevation drilled a well 

a Engineering News, Vol. CCLXXI, pp. 183, 328. 

bEngineering Record, Vol. XXII, p. 7. 
SLICHTER.] ARTESIAN WELLS AT SAVANNAH, GA. 97 

which aft'ected the original yield still more. An additional well was 

then drilled~ but, the supply failing to increase as much as was 

expected, an investigation was made. 'V ell No. 1 was found to be 

flowing only 70,000 gallons per day at the surface and only 210,000 

gallons at the place of connection. The well was recased and 

repacked, the result being a flow of 177,000 gallons at the surface and 

400,000 gallons at the point of connection. Similar work on well No. 

4 increased the delivery at the surface from 142,000 gallons to 254,000 

gallons and at the point of connectfon to 700,000 gallons. The wells 

were faulty in construction, leaking considerably in the upper strata. 

ARTESIAN WELLS OF SAVANNAH, GA. 

One of the most carefully planned artesian water supplies of this 

country is that of the city of Savannah, Ga. A brief account of these 

wells is of much interest, not only as illustrative of an intelligently 

designed and well-constructed engineering work, but also because of 

the valuable lessons to be learned from the way in which difficulties 

were met and overcome as t.hey arose. The works were planned by 

}fi~. Thomas T. Johnston, consulting engineer, of Uhicago, Ill., and 

the following description is taken largely from his paper in the Engineering News. a 

Prior to 1887 the water supply of Savannah was taken from the 

river, but in that year 14 artesian wells were put in use (a fift,eentlt 

~ well being nearly ready) near the old pumping station (see fig. 50). 

Of these wells, 2 were 10-inch, 12 were 6-inch, and 1 was 4-inch, and not 

one was more than 400 feet deep. In 1888 the entire supply of the city 

was drawn from these wells, the total for the year being 2,135,842,000 

gallons, or about 5,1;50,000 gallons per day. At the close of 1889 5 new 

wells had been put in nse, the 20 wells being distributed very irregularly within a 10-acre lot.. About this time, however, it became necessary to open th~ river supply to some extent. Experience and observation showed conclusively that the water supply was materially 

affected by the tide, and it was supposed th~t the shallowness of the 

wells caused a filling by sand to a greater or less extent, thus affecting the supply. But little better results were had, however, from 

deepening some of the wells; one of them was deepened to 1,009 feet. 

Two additional 10-inch wells, 502 and 505 feet deep, were connect~d 

with the old works on December 29, 1890, but in November, 1891, it 

was necessary to again draw water from the river. Nothing resulted 

from dynamiting the wells. 

In June, 1891, it was found that water in well No. 1, close to the 

old pumping station, was 9 feet lower than in well No.2, distant from 

well No. 1 about 1,600 feet 1 and it was determined to abandon the old 

wells. 

a Vol. XXIX, p. 527. 
98 MO'l'IONS OF UNDERGROUND WATERS. (NO. 67. 

Twelve new wells in a new location were finally decided upon, and 

7 were put in use on December 9, 1892, and the others on March 

21, 1893. 'rhe relative locations are shown on the accompanying map, 

fig. 50. The wells are arranged along a highway which· runs nearly 

parallel to the ocean and some distance from the old pumping staFIG. 50.-Map showing location of artesian wells at Savannah, Ga. The old wells are near the 

old waterworks, shown in upper left-hand corner of map. The new wells are on Styles avenue 

and are numbered 1-12, inclusive. (From .Journal of Western Society of Engineers, Vol. II, 

No.6.) 

tion. They are 300 feet apart. and flow into a brick and concrete conduit on the opposite side of the highway. The strata through which 

they are bored belong to the Cretaceous. Sands and clays were met 

to a depth of about 250 feet, wl:}_ere a cherty lime rock was found. 

The rock v.aries in character at greater depths. The first water was 

found at 325 feet, and the supply continually increased until the depth 
SLICHTER.] ARTESIAN WELLS AT SAVANNAH, GA. 99 

exceeded 500 feet. The water-bearing rock is uniformly a porous 

limestone, or rather one full of cavities, very similar to the rock outcrop from which flow the mammoth Suwanee springs in northern 

Florida. Water is occasionally found below 500 feet, but not in ~nfficient quantity to justify deeper wells. The 12 wells of the new 

waterworks average 500 feet in depth. They are cased to the rock 

(about 250 feet) with casing of 12 inches internal diameter. Below 

this there is a 12-inch clear opening. The normal position of 

water in the wells, as determined by the position in the old wells 

when first dug, showed that it reached the static level at, an elevation of 41 feet above mean low tide. Subsequent wells, bored in 

a wide range of country, show about the same elevation. After a 

number of wells had been bored the elevation of this static level was 

lowered. At the time of an examination in 1890 about 6,000,000 gallons per day were being pumped at the old works. The static ·level 

was then 7 feet; at the site of the new works it was at an elevation of 28 feet, while 9 miles south of the old works it was at the 

original elevation, 41 feet. The influence of the heavy pumpage 

was noticed to be greater in wells in the same line perpendicular to 

the shore of the ocean than in wells in a line parallel to the ocean. 

To predetermine the probable flow from the new wells, the Springfield well, 2,000 feet east of t.he new station, was examined, with the 

following results: a · 

TABLE X. 

Flow of Springfield well, Savannah, Ga. 

I Elevation of static 

level 

above 

mean low 

tide. 

Feet. 

22.67 

25.67 

24.40 

22.77 

22.68 

21.80 

21.79 

20.57 

13.00 

I 

Equiva-1 lent head. 

! 

.b~eet. 

0 : 

2.00 

3.27 

I 4.90 

4.99 I 5.87 I 5.88 

I 

7.10 

14.67 

Year. I 

1890 

1890 

1891 

1890 

1891 

1891 

1891 

1890 

1890 

I 

Flow. 

Gallons per 24 hours . 

482,000 

623,000 

1,000,000 

977,000 

1,133,000 

1,172,000 

1,360,000 

2,500,000 

~~'------

It was estimated that about 3,000,000 gallons per day could be 

obtained with the static head reduced to an elevat,ion of 7 feet, which 

reduction is practicable at the pump house, as constructed. The old 

wells spread over an area about 1, 700 feet wide at its largest part, and 

their flow at an elevation of 7 feet was about 6,000,000,gallons per day. 

The first seven wells embraced a line 1,800 feet long. Reducing 

the level to 8 feet, the flow was 6,500,000 gallons per day. The level 

in wells Nos. 10, ·11, and 12 was at this time 14.93, 15. 96, and 16.20 

a Section of this well is shown in Engineering News, Vol. XXX, p. 4. 
100 MO'l'IONS OF UNDERGROUND WATERS. [NO. 67. 

feet,, respectively. On March .21, 189B, the 12 wells were put into 

service, with elevation of water at 8 feet, and the flow was 9,500,000 

gallons per day. At the beginning of 1897 the flow of the 12 wells . . 

had decreased to ti,900,000 gallons per day, and the fear was entertained that the history of the old plant was to be repeat,ecl. :Mr. 

Johnston was again called in consultation. The results of his measurements of the flow of each of the 12 wells were as follows: 

TABLE·XI. 

Yield of Savannah u1ells in 1897'. 

~~---~ w~~~ __ ~~--='low. _______ ~----~---;~w. I 

-~ -- Ga.llon~~:;;, I Gallonsperf!4 ! 

No.1 . I ho;;;;:· ... , No. • ...... -·--...... --····I ho,;;,;:·,"' 

i~I:::;~;;;~\n~~~;~;;f _l:i . ::~~eld:~e .. :::::: ::1 ~:~_;; I 

From this table it is seen that wells Nos. 4, 6, and 11 showed a very 

small flow, ent,irely out of proportion to that of the other wells .. 

It having been determined that the flow of water in some wells was 

more obstructed than in others, the work of attempting to remove the 

obstructions was undertaken. The method used was back-flushing, 

or t.he forcing of a strong reverse flow back into the well. The first 

effort was made on well No. 2 by means of fire hose attached to a 

neighboring hydrant. Only a slight improvement resulted. The next 

attempt was made on well No. 10, fire engine No. 2 being used. But 

little improvement resulted. A more powerful fire engine (No. 3} was 

next employed, and the process was tried on well No. 6. A radical 

improvement was -the resuU, t,he net gain in the yield of the well being 

100,000 gallons per clay. Encouraged by this result, the next effort 

was made on well No. 4, fire engines Nos. 1 and 3 being used. The 

result was even more radical, the net gain in yield for this well being 

200,000 gallons per day. a The actual results on well No. 6 were as 

follows: 

TABLE XII. 

Results of flushing well No. 6, Savannah waterworks, in 1897'. 

Flow before flushing: 

May 12 . ____________________________________________ . May 18 _______________ . _____________________________ . 

Flow after flushing: 

Gallons per 

24 hours. 

29.),000 

304.000 

May 18 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 433, 000 

May 19 ___________________________________________________ 395,000 

May 20 ____________________________________________________ 400.000 

May 24 ____________ .. ________________ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 389, 620 

aReport of Thos. T. Johnston to chairman of water commiEsion, Savannah, Ga., dated May 

24. 1897. 
SLICHTER.] ARTESIAN WELLS AT SAVANNAH, GA. 101 

After t,hese experiment,s 1\Ir .• Johnston recommended that a special 

8-inch water main of the city sy~tem be laid along the row of 12 wells, 

and that it be connected to eaeh well by means of a (:)-inch pipe and 

gate. By opening a gate any well can now be flushed at any time, 

and Superintendent Kins~y of the waterworks states that all of the 

wells have been flushed and tested regularly every year sinee Mr. 

Johnston's tests in 18£17. The following is the record of the test for 

the year 1900: 

Resnlts of flushing Savannah wells h1 1900. 

Yield before flushin~ ______ _ 

Gallons per 

24 hours. 

-- 5,104,275 

Yield after flushing ________ _ ------- 5,850,878 

Gain _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ______________ _ 746,603 

The yield before flushing given above is 385,825 gallons less than 

the total yield before flushing in 1897. 

The resultis at Savannah are especially valuable on account of their 

reliability and the fulness of the information. In the first place, the 

yield of the wells can be closely relied -upon, for they were determined 

by a special current meter designed by Mr. Johnston, which can at 

any time readily be lowered into one of the wells. In the second 

place, it was found by actual measurements at the old waterworks 

that there had been no lowering of the water table during the years 

1892 to 1897, as the measurements made in the two years were in sub-

. stantial accord. ~rhus the depreciation of the wells must be referred 

to the clogging of the pores in the rock in some unknown way, and 

not to a general depreciation of the basin. 

Reliable data upon which to base discussion of artesian phenomena 

are not common. _Most of the round-number estimates of yield, such 

as 500,000 or 1,000,000 gallons per uay, are not even approximations 

of the actual facts. 

INDEX. 

Page. 

Ableman, Wis., sandstone from, porosity 

of .... --------------------------- 16 

Alford, N.C., reference to________________ 42 

Argyle, Wis., sandstone from, sections of_ 20 

Arizona, underground flow in, rate of___ 26 

Artesian well, view of_.___________________ 62 

Artesian wells at Savannah, Ga., yield 

of_ __________________ -------- 96,97-101 

conditions necessary to ____ ------ _____ 82 

failure of_ ____________ -------------- ____ 93-95 

general discussion of ________ ---------- 79-83 

mutual interference of_ _______________ 95-97 

yield of __________ ------------- __________ 83-90 

methods of measuring ___________ . 90-93 

Ashland, Wis., sandstone from, porosity of _________________________ ------ 16 

Berlin, Germany, fluctuations of water 

table at, diagram showing____ 72 

Berlin, Wis., granite from, porosity of___ 16 

Bradfield, S. A., reference to------------- 42 

Bridgeport, Wis., limestone from, porosity of _________ ----------________ 16 

Buckley, E. R., porosities determined by_ 16 

reference to___________________________ 21 

Building stone, porosities of _ _ _ _ _ _ _ _ _ _ _ _ _ _ 16 

Cache la Poudre River, growth of ________ 45-46 

diagram showing----------------- 44 

Canals. See Subcanals. 

Carpenter, L. G., cited on underflow_____ 42 work of ___________________________ ----- 44 

Cesspools, contamination of wells by_____ 68-69 

Chalon, --, cited on position of thalweg.------ ______ ---------------- 33 

Chamberlin, T. C., quoted on requisite 

conditions for artesian v.·31ls. _ 82 

Channel, underground, view of, plate 

showing________________________ s-z 

Chlorine method of determining rate of 

underflow, curve obtained in._ 47 

description of. _____ ------ ______________ 46-48 

Clay loams, porosity of____________________ 17 

Coffin, F. C., reference to-----------______ 84 

Contamination of wells from cesspool, 

diagram illustrating. ____ ------ 69 

discussion of _________________ ------ 68-69 

from rivers, diagram showing________ 73 

Dakota artesian basin, map of.___________ 57 

Dakota formation, catchment area of, 

map showing------------------ 57 flow in, rate of _______ _.________________ 26 

water in, discussion of---------------- 57-59 

Page. 

Dam, subsurface, on Pacoima Wash, 

views of _____________________ 74, 76,78 

Dams, subsurface, discussion of_ __________ 76-77 

Darcy, H., laws of flow formulated by___ 18 

Darton, N.H., cited on flow in Dakota 

formation ...... ---------------- 26 

map by _______ -------------------------- 57 

Deep zones of flow, discussion of _________ 52-60 

distinguishing features of_------ ______ 53-54 

percolation into _______________________ 54-57 

Delesse, A., estimate of underground 

water by----------------------- 15 

Deltas of disappearing streams, map 

showing ________ ------ ____ ------ 38 

Denver, artesian wells near, failure of.__ 94 

Disappearing streams, deltas or fans of, 

map showing------------------ 38 

Ditch, water table near, shape of_________ 29 

Dodge, Kans., flow, underground, at, rate of_______________________________ 26 

Drinker, H. S., cited on water in St. 

Gothard tunneL............... 16 

Dug well, figure showing_--··· _______ ----- 63 

Dug and tubular well, figure showing____ 67 

Dunnville, Wis., sandstone from, porosity oL ______ ______ ______ ________ ____ 16 

Echo River, Mammoth Cave, size of _ ____ 31 

Effective size of soil grains, determination 

of, methods of---------------·- 22-23 

variations in velocity of flow based on 

differences in------------------ 27 

Eldridge, G. H., cited on wells of Denver 

Basin ____________ ----- ____ . _____ 94,95 

Electrical method of determining rate 

of underflow, curve obtained 

by ______________ :_______________ 49 

description of_ _________________________ , 48-51 

diagram illustrating ____ -------------- 48 

Failure of artesian wells, discussion of___ 93-95 

Fans. See Deltas. 

Faults, association of springs with------- 79 

Flow, deep zones of, di;;cussion of ________ 52-60 

distinguishing features of ________ 58---54-

percolation into------------------- 54-57 

diagrams illustrating _____ . _____ . _. 34, .35, 36 

filter for determining, figure showing----------------------------- 19 

formulas for determining_._... 18-21,24--30 

in open wells-------------------------- 62-68 

lines of, into well, plate showing_____ 82 

rate of ..... ------ ________________ ------ 26 

103 
104 INDEX. 

Page. 

Flow, variations in,duetochangein pressure, diagram illustrating____ 28 

due to temperature---·___________ 24 

velocity of, in sands of various effective sizes, table showing_______ 27 

See also Motion; Underflow; Surface 

flows. 

Fresno canal, California, seepage on _ _ _ _ _ 42 

Galleries and subcanals, use of, in obtaining water ______________________ 73-76 

See also Infiltration galleries. 

Garden, Kans., underflow at, velocity of_ 43 

well at, diagrams showing rise of water in ______ _ _____ _ _____ _____ 68 

Gas, diagram illustrating retention of___ 56 

Gerhardt, I. P., diagrams taken from ar- ticle by _________________________ 71,72 

Gilbert, G. K., cited on underflow in 

Arkansas River Valley_______ 43 

Grains of soil, effective size of, methods 

of determining ________________ 22-23 

variation in velocity of flow based 

on difference in________________ 27 

Granite, porosity of_______________________ 16 

Great Falls, Mont., section near__________ 58 

Ground water, depth of___________________ 14 

flow of, diagrams illustrating _ _ _ _ _ 34, 35, 36 

motion of, direction of ________________ 34--38 

map showing position of water 

table, thalwegsand ----------- 33 

position of, section showing__________ 13 

surface zone of,flow of_ _______________ 31-51 

See also Water table, 

Grunsky, C. E., cited on seepage in California ____________ ----------____ 42 

Hazen, Allen, law of flow formulated by_ 19 

method of determining effective size 

of soil grains devised by _ _ _ _ _ _ 22-23 

Hicks, L. E., cited on underflow near 

Loup River-------------------- 42 

Hoadley, J. C., apparatus devised by, 

figure showing _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 66 

experiments of________________________ 62 

Hobbs, W. H., cited on association of 

springs and faults_____________ 79 

Hurley, J. T., ref~rence to________________ 42 

Impervious floor, spring at outcrop of, 

plate showing __ : _____ "-------- 62 

springs along, formation of ___________ 61-62 

Infiltration galleries, longitudinal section 

of _______ ------------------------ 76 

plan of_________________________________ 75 

principle involved in construction of, 

diagram showing______________ 74 

Johnson, W. D., infiltration galleries designed by, diagrams showing_ 74,76 

work of __________________ -------------- 67 

Johnston, T., reference to________________ 100 

King, F. H., method of determining effective size of soil grains devised by________________________ 23 

work of________________________________ 20 

Land surface, area of_____________________ 14 

Latham, B., observations of______________ 71 

Laville, Wis., sandstone from, section oL 20 

Page. 

Limestone, porosity of __________ ------____ 16 

Lower Magnesian limestone, porosity oL 16 

Lueger, 0., cited ______ ---------------- ____ · 37,72 

Magnesian limestone. See Lower Magnesian limestone. 

Marblehead, Wis., limestone from, porosity of _____________ ------________ 16 

Missouri River, section along_____________ 58 

Mohave River, underflow on------------- 50 

Montello, Wis., granite from, porosity of_ 16 

Motion, cause and rate of------------, ____ 17-18 

direction of____________________________ 34 

See also Flow. 

Munich, fluctuations of water table at, 

diagram showing______________ 71 

Neighboring wells, nonuniformity of ____ 69-70 

Nettleton, E. S., cited on underflow of 

Rio Grande ___ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 40 

Newell, F. H., letter of transmittal by___ 11 

Niagara limestone, porosity of----------- 16 

Nonuniformity in neighboring wells, discussion of---------------------- 69-70 

Ocean water, amount of------------------ 15 

Oil, diagram illustrating retention of____ 56 

Open wells, flow of water in-------------- 62-68 

Orton, E., cited on Trenton limestone____ 53 

Quartz sand, porosity of__________________ 17 

Pacoima Creek, Cal., subsurface dam on, description of __________________ 76-77 

Pacoima Wash, views on, plate showing __________________________ 74, 76,78 

Peale, A. C., cited on association of springs 

and faults______________________ 79 

Percolation into deep zones, discussion of_ 54-57 

Permeability of rocks and soils, discussion of. _________________________ 15-16 

Pervious bed, seepage in, figures illustrating _____________________________ 37,38 

Porosities of soil, constants for___________ 25 

Porosity of rocks and soils, discussion 

- of------------------------------ 16-17 

Potsdam formation, map showing outcrop 

in Wisconsin___________________ 59 

waterin ____________ ---------------- ____ 59-60 

Pressure, decrease in, diagram showing . 83 

diagram showing variations in maximum flow due to differences 

in _______________ ---------------- 28 

River valley, section, ideal, across_______ 13 

Rivers, contamination of wells from, diagram illustrating ___ _ ___ __ ____ 73 

Rockford, Ill., artesian wells at, flow of__ 96-97 

Rocks, permeability of ________ ------------ 15-16 

porosity of soils and _____ -------------- 16-17 

Rogers, E. L., cited on flowinsands______ 26 

St. Augustine, Fla., artesian wells at, flow 

of_ ______________ ---------------- 96 

St. Peter sandstone, map showing outcrop in Wisconsin------------- 59 

water in _____________ ------------______ 60 

Sal bach, B., cited on unjerflow waters__ 40 

Sand quartz, porosity of------------------ 17 

Sands, veloeity of water in--------------- 27 

Sandstone, porosity of-------------------- 16 

sectionsof __________ ----------------.--- 20 
INDF.X. 105 

Pug e. 

Savannah, Ga., artesian wells at, flow 

of_----·--- __________________ 96,97-101 

map showing location of______________ 9R 

Seepage in pervious bed, figures illustrating _____________________________ 37,:38 

Sink-hole, connection with undergrounddrainage system, plate showing _ _____ ______ _______ ____ ______ 32 

Stichter, C. S., formulas for determining 

flow of water devised by_ 24-28,48-51 

work of------ ____ ---------------------- 20 

Soil grains, effective size of~ determination of, methods of------------ 22-23 

variations in velocity of flow based on 

differences in ____________ ------ 27 

Soils, mechanical analysis of______________ 21-23 

porosities of, constants for_ _ _ _ _ _ _ _ _ _ _ _ 25 

porosity of rocks and _________________ 16-17 

South Britain, Conn., springs near, map 

showing location of----------- 80 

South Dakota artesian basin, cross section through___________________ 55 

Spheres, pore space in mass of, unit ele- ment of________________________ 21 

pores in mass composed of, shapA of__ 20 

Spring at outcrop of impervious floor, 

plate showing__________________ 62 

Springfield well, Savannah, Ga., flow of. 99 

Springs, association of, with faults.______ 79 

formation of, diagrams showing______ 61 

water available for, conditions affectingamountoL___________ ______ 73 

Streams, disappearing, deltas or fans of, 

map showing------------------ 38 

Subcanals and gallerieg, use of, in obtaining water----·------------- ____ 73--76 

Subsurface dam on Pacoima Wash, views 

of. _______________ ------ ______ 74, 76,78 

Subsurface dams, discussion of _ _ _ _ _ _ _ _ _ _ 76-77 

Surface flows, recovery of underground 

water from-------------------- 61-78 

Surface wells, contamination of, from 

cesspools _______________________ 68-00 

diagram illustrating-------------- 69 

See also Wells. 

Temperature, effect on velocity and flow 

of water------__________________ 24 

Thalweg, definition of_____________________ 32 

Thalwegs, map showing position of water 

table, motion of ground water, 

and. ______ ---------- ______ -----· 33 

Thiem, A., method of determining rate of 

underflow devised by_________ 47 

Tile drainage, effect of.___________________ 46 

Todd, J. E., method of measuring yield 

of wells devised by____________ 90 

Tubular and dug well, figure showing__ 67 

Underflow, chlorine method of determining rate of, curve obtained 

by------------------------------ 47 

description of._------ ______________ 46-48 

electrical method of determining rate 

of, curve obtained by__________ 49 

description of. ..... ---·-- __________ 48-1)1 

diagram illustrating·------------- 4R 

Page. 

Underflow, general considerations con- cerning ________________________ 38-41 

movement of, rate of. ___ -------------- 41-43 

Underground channeL view of.__________ 32 

Underground drainage basins, discussion 

of.-----------------·-----------· 32--33 

Underground drainage system, sink-hole 

connection with, plate showing _______________ ---------·____ 32 

Underground water, amount of. _________ 14--15 

flow of, filter for determining________ 19 

formulas for determining ___ 18-21, 24-00 

motion of, cause and rate of. _________ 17-18 

origin and extent of _______ ------------ 13--30 

recovery of, from surface flows ______ 61-78 

See also Underground drainage; Underground channels; Water 

table; Ground watP.r; Wells; 

Springs; Underflow. 

Underground water supply, advantage 

of. ____________ --···-_---·· ______ 77-78 

Valley, ideal section across_______________ 13 

Van Rise, C. R., cited on limit of depth of 

ground water ____________ --···- 14 

cited on work of underground water_ 17 

reference to ______ --·-·- ___________ ···-- 15 

Velocity of flow. See Flow. 

Victorville, Cal., underflow near--------- 50 

Viscosity of water, variation in, with 

temperature _____________ ·----- 24 

Water, velocity of, in sands.-------------- 27 

viscosity of, variation in, with temperature _______ ----··__________ 24 

Water, ground, depth of _______ ---··______ 14 

flow of, diagrams illustrating ______ 34,35,36 

motion of, direction of. _______________ 34-38 

map showing position of water 

table, thalwegsand___________ 33 

position of, section showing_ .. _ _ _ _ _ _ _ _ 13 

surface zone of flow of ________________ 31-51 

See also Water table; Water, underground. 

Water, underground, amount of _________ 14--15 

flow of, filter for determining __ .. _ _ _ _ 19 

formulas for determining ___ 18--21,24--30 

motion of, cause and rate of---------- 17-18 

origin and extent of. ______ ------ ______ 13--00 

recovery of, from surface flows---·-· 61-78 

See also Underground drainage; Underground channels; Ground 

water; Water table; Wells; 

Springs; Underflow. 

Water surface, area of-------------------- 14 

Water plane. See Water table. 

Water table, definition and depth of_____ 13 

effect of pumping on, diagrams showing----------------------------- 64,65 

irregularities in, diagram showing___ 70 

position of, fluctuation in_. ______ . ____ 70--73 

map showing thalweg, motion of 

ground water, and--····--···· 33 

shape of. _____ -----· ____________________ 33--38 

near drainage ditch--------------- 29 

undulations of, section showing------ 13 

See also Ground water. 
106 INDEX. 

Page. 

Wauwatosa, Wis., limestone from, porosity of________________________ 16 

Well at Garden, Kans., diagrams showing rise of water in____________ 68 

Well, artesian, view of____________________ 62 

lines of flow into, plate showing______ 82 

Well, combination dug and tubular, figures showing------------______ 67 

Well, common dug, figures showing_____ 63 

Wells, contamination of, from cesspools, 

diagram showing______ _ _ _ _ _ _ _ _ 69 

from cesspools, discussion of _ _ _ _ _ 68-69 

from rivers, diagram illustrating _____ ------------____________ 73 

nonuniformityin neighboring ________ 69-70 

water available for, conditions affecting amount of----------------- 73 

Page. 

Wells, artesian, at Savannah, Ga., yield 

of_-------- _____ ----- ________ 96,97-101 

Wells, artesian, conditions necessary to__ 82 

failure of ------ ---~---- _____ ----- ______ 93-95 

general discussion of____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 79-83 

mutual interference of_ _______________ 9!>-97 

yield of __________________ ------. _______ 83-90 

method of measuring _ _ _ _ _ _ _ _ _ _ _ _ _ 90-93 

Wells, common open, flow of water in ___ 62-68 

Wells, surface, contamination of _________ 68-69 

diagram illustrating-----------·__ 69 

Weston, E. B., reference to_______________ 84 

Wisconsin, building stones from, poro- sities of _ _____ _ _ ____ ___ _ _ ___ ____ 16 

Potsdam and St. Peter sandstones in, 

map of------------------------- 59 

&'tndstone from, sections of_______ _ _ _ _ 20 

0 

. I