A l5U--1Ill-I)M-l.l S0

TEXAS AGRICULTURAL EXPERIMENT STATION

A. B. CONNER, DIRECTOR
COLLEGE STATION, BRAZOS courvrr. ‘PIEXAS

BULLETIN NO. 426 APRIL, 1931

DIVISION OF AGRICULTURAL ENGINEERING

Determination 0f Soil Moisture by
the Method 0f Multiple Electrodes

 

AGRICULTURAL AND MECHANICAL COLLEGE OF TEXAS
T. O. WALTON, President

STATION STAFFT

ADMINISTRATION:

A. B. CoNNER, M. S., Director

R. E. KARPER, M. S., Vice-Director
CLAmcE MixsoN, B. A. Secretary

M. v. IIOLLEMAN, m. Chief Clerk

J. K. FRANcRLow. Assistant Chief Clerk
CnEsTER Hmns. Executive Assistant

C. B. NEBLETFE, Technical Assistant

CHEMISTRY:

(l. S. FnArs. Ph. D., Chief; State Chemist
S. l-I. Asnunv, M. S.. Chemist

J. F. Funnn. Ph. l), Chemist

Ii. C. CARLYLE, B. S.. Assistant Chemist
WALDO ll. WALKER, Assistant Chemist
VHLMA GRAHAM, Assistant Chemist

T. L. Oman, B. S., Assistant Chemist
ATuAN J Srrtncrzs. B. S , Assistant Chemist
JEANNE M. Fur-icAs, Assistant Chemist

HAv TREmnLrux, M. S . Assistant Chemist
RALPH L SCHWARTZ, B. S., Assistant Chemis
C. M. PouNunns, B. S., Assistant Chemist

I-IORTICULTURE:
S. II. YAHNHLL, Sc. I). Chi?
L. R. IIAWTIIOHN, M. S.. I orticulturist

RANGE ANIMAL IIUSBANDRY:
J. M. JONES, A. M., Chief
B. L. WARWIcK. Ph. D., Breedin Investigations
STANLEY P. DAvls, IVool Gra er

ENTOMOLOGY:
F. L. 'I‘nuuAs, Ph. D., Chief; State
Entomologist
II. J. RmNuAno, B. S., Entomologist
R. K. FLETcuEn, Ph D., Entomologist
W. L. OWEN, Jn., M. S.. Entomologist
. N. RoNEv, M. S , Entomologist
C GAINEs, JR. M. S., Entomologist
Ii. JoNEs, M. S., Entomologist
F. F. Bmnv, B. S., Entomologist
CECIL l‘). llEAm), B. S., Chief Inspector
O'r'r0 MAcKENsEN, B. S. Foulbrood Inspector
W. B. WRrrNEY, Foulbrood Inspector

AGRONOMY:
E. B. REvNoLns, Ph. D., Chief

L .

R. E. KARPER. M. S . Agronomist
P. C. MANoELsnonw, Sc. D., Agronomist
D.  KlLLovnu, M. S., Agronomist

n-
an
p-

.. REA, B. S., Agronomist
—-——————~—, Agronomist
iB. C. LANGLEY, B. S.. Assistant in Soils

PUBLICATIONS:

A. D. JACKSON. Chief
VETERINARY SCIENCE:

‘M. FRANcIs, D. V. M., Chief

ll. Sclnum‘, D. V. M., Veterinarian

F. P. MATHEWS. D. V. M., M. S., Veterinarian

\V. T. HARDY, D. V. M., Veterinarian

F. E. CARROLL, D. V. M., Veterinarian
PLANT PATHOLOGY AND PHYSIOLOGY:

J. J. TAuEENHAus, Ph. D., Chig

W. N. EzEKlEL, Ph. D., Plant athologist

W. J. BACH, M. S., Plant Pathologist

Li. Plant Pathologist
FARM AND RANCH ECONOMICS:

L. P GABBARD, M. S.. Chief

W. E. PAuLsoN, Ph. D., Marketing

C. A. BoNNEN, S., Farm Manaegment
"W. R. NlsaEr, B. S., Ranch Management
"A. C. MAGEE. M. S.. Farm Management
RURAL HOME RESEARCH:

JESSIE WHITACRE. Ph. D., Chief

MARY ANNA GnmEs. M. S.. Textiles

F.uzAnE'rR D. TERRILL, M. A., Nutrition
SOIL SURVEY:
"W. T. CARTER, B. S , ChieI/

E. ll. TEMPLIN, B. S.. Soi Surveyor

A. l-l. BEAN, B. S.. Soil Surveyor

R. M. MARSHALL, B. S.. Soil Surveyor
BOTANY:

V. L. CoRv, M. S., Act Chief

SmoN E. WOLFF. M. S., Botanist
SWINE HUSBANDRY:

FRED HALE. M. S . Chief
DAIRY HUSBANDRY: _

O. C. CoPELAND. M S . Dairy Ilusbandman
POULTRY IIUSBANDRY:

R. M. SHPRWOOD, M S . Chief
AGRICULTURAL ENGINEERING:

H. P. SMITH, M. S.. hief
MAIN STATION FARM:

G. T. McNEss, Superintendent
APICULTURE (San Antonio):

H. B. PARKS, B. S.. Chief

A. H. ALEx. B. S., Queen Breeder
FEED CONTROL SERVICE:

F. D. FULLER. M. S.. Chief

S. D. PEARcE, Secretary

J. H. RoGERs. Feed Inspector

K. L. KIRKLAND, B. S., Feed Inspector

SIDNEY D. REYNoLns, JR.. Feed Inspector

P. A. MooRE, Feed Inspector

E. J. WILSON, B. S.. Feed Inspector

H. G. Wxcxes. B. S., Feed Inspector

SUBSTATIONS

‘No. I, Beeville, Bee County:

R. A. IIALL. B. S., Superintendent
No. 2. Troup, Smith County:

P. R. JOHNSON. M. S., Superintendent
‘No. 3, Angleton, Brazoria County:

R. ll. STANSEL, M. S.. Superintendent

‘No. 4, Beaumont, Jefierson County:
R. II. WYCHE, B. S., Superintendent
No. 5. Temple, Bell County:
HENRY l)uNLAvY, M. S., Superintendent
, Plant Pathologist
H. E. REA, B. S., Agronomist; Cotton Root R0!
Investi ations
SmoN E. \ OLFP, M. S.. Botanist; Cotton Root
Rot Investigations
No. 6, Denton, Denton County:
P. B. DuNKLE. B. S., Superintendent
No. 7, S ur, Dickens County:
R. E. IhcKsoN. B. S.. Superintendent
——-——————————, Agronomist
No. 8, Lubbock, Lubbock County:
l) L. JoNn-zs. Superintendent
FRANK CAlNEs. Irrigalionist and Forest
Nurseryman

No. 9, Balmorhea, Reeves County:
J. J. BAYLEs, B. S.. Superintendent

No. l0, College Station, Brazos County:
R. M. SRERwooo, M. S., In charge
L. J. McCALL, Farm Superintendent

No. ll, Nacogdoches, Nacogdqches County:
H. F. MoRms, M. S., Superintendent

**No. l2, Chillicothe, Hardeman County:
J. R. QUINBY, B. S., Superintendent

"J. C. STEPHENS, M. A.. Assistant Agronomist

No. l4, Sonora, Sutton-Edwards Counties:
W. H. DAMERON, B. S._, Superintendent
—-i———-—-—, Veterinarian
W. T. HARDY. D. V. M., Veterinarian

"O. G. BABcocK, B. S., Entomologist
O. L. CARPENTER, Shepherd

No. 15, Wealaco. Hidalgo County
W. ll FRIEND, B. S., Superintendent
SHERMAN W. CLARK. B. S.. Entomologist
W J. BAcR, M. S.. Plant Pathologist

No. l6, Iowa Park, Wichita County:

N C. ll. MCDOWELL, B. S.. Superintendent
o. 11. --———i—-

No. l8,

, Superintendent

—-——————————. Superintendent
No. I9. Winterhaven, Dimmit Countiy:
E. MoRTENsEN, B. S., Superinten ent
L. R. HAwTuoRN, M. S., Horticulturist
No. 2o, iZ—-~——
. Superintendent

Teachers in the School of Agriculture Carrying Cooperative Projects on the Station:

W. ADRIANcE. Ph. D., Horticulture

W. BILSING, Ph. D., Entomology

P. LEE, Ph. D., Marketing and Finance

SCOATES, A. E., Agricultural Engineering
. K. MAcREY, M. S., Animal Husbandry

‘Dean School of Vclcrmary Medicine.

J. S. MocPoRD, M. S., Agronomy

F. R. BRISON, B. S.. Horticulture

YV. R. IIORLACHER, Ph. D., Genetics

H. KNox, M. S.. Animal Husbandry

‘(AI oi April l. 193].

"In cooperation with U. S. Department of Agriculture.

This Bulletin reports the theoretical principles used in
adapting electrical measurements of soil resistivity to the
determination of soil moisture, and the results obtained during
the summer of 1930 at Substation No. 7, located near Spur,
Dickens County. Comparison of soil-moisture measurements
by the auger method with the moisture measurements given by
the calibration obtained during this investigation has not been
suflicient to determine the accuracy of the method. However,
readings made on the control plats of Substation No. 7, indi-
cate that the method should prove useful in obtaining relative
measurements of soil moisture and may possibly be used to
determine the percentage of moisture in soils at various loca-
tions. There is also included a brief statement of the steps to
follow in making moisture determinations by resistance meas-
urements of soil at other locations. The apparatus is such that
it can be readily obtained from companies dealing in scientific
and laboratory supplies, and is reasonably portable.

CONTENTS

Page
lntrurluvtiuln . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Pn-viuus nml rvlutvd \\"0rk.< . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5

Appurnllls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 6

'l‘hv<n'_\' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

I‘lx]>0|'i11u-11t:1l p1'0<~0d11I'0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1O

l*]x]><-1'i11|vl1t:1l results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

l)is<-u.<'.~'io|| uf rvsults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15

Nfoisfurv (lvtvnllination by soil resistance . . . . . . . . . . . . . . . . . . . . . .. 16

SlllIlll]ilI‘_\' and vonvlusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19

Al§il>li<>g|':1|»l1_\' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

."\('kllU\\'l("(lglll(’llf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

BULLETIN NO. 426 APRIL, 1931

DETERMINATION OF SOIL MOISTURE BY THE METHOD
OF MULTIPLE ELECTRODES

W. H. McCORK LE*

In connection with a study ('2) ot factors influencing runolT and soil
erosion in which the lield work was done at the Spur Experiment;
Station located in the rolling“ plains region, it seemed desirable to devise
some better method than soil sampling tor use in determining the relative.
moisture contents of ditferent plots being studied, since the many
samplings required b_v the auger method would enter as an erosion
factor. To this end the project leaders—i\"lr. .~\. B. Conner, Mr. h’. E.
Dickson, and Mr. l‘). Scoats—-initizited a plan to use the electrical con-
ductivity method tor measuring the relative soil moisture in the series
of plots.

In this preliminary paper it is the purpose of the author to set forth
an adaptation of the electrical method tor determining .\‘()ll—]ll()l>'i.lll'0
content by electrical resistance measurements in which a sutlicient num-
ber of electrodes are used to make it possible to eliminate. the changes ot
contact between the soil and the electrodes by solving simultaneous equa-
tions which involve the changing c-ontzlcts as unknowns. It is also
desired to give the results obtained so far in determining the possibilities
of the method in making relative measurements of soil moisture, and its
usefulness in determining the percentage of moisture in the soil.

PREVIOUS AND RELATED WORKS

In one of the earliest attempts to connect the QIOCtTICtII eoi1di1ctivit_v of
soils with their moisture contents, Whitney, (lzlrdner, and Briggs (7)
obtained some promising results but the zippar-attis used required too
frequent calibration for practical purposes. Results of investigations
(mostly unpublished) have usually not been very encouraging and have
caused a somewhat general feeling of doubt concerning the reliability
of the electrical method (lfitlQtGflllllillllg moisture (rontent when &l])|)llC(l
to soils.

A theoretical “co11si<lerzitio1i ot’ a tour terminal conductor method ot
measuring earth resistivity has been given by Wenntei" (tit). This
method, using an zilternziting current 1ioteiitionietei‘ to lltlltllHT‘. potentials,
when applied to earth resistance mcasilreiiieiits by lvlt-(‘olliiiii and
Logan (5), gave results which seemed sutliciently accurate. tor the study
of the electrolysis of underground structures. The investigators found
the instruments and method too tmwieldy for most measurements, and
no entirely satisfactory method of correcting for (rhanging contact be-
tween the soil and the electrodes was developed. The method of \\'cn-

*Assistant Professor of Physics, A. and M. College of Texas.

6 BULLETIN NO. 426, ’I‘EXAS AGRICULTURAL EXPERIMENT STATION

ner ((3,) has been developed further by numerous investigators and used i11
(jeophysical researches and prospecting.

APPARATUS

'.l‘hc apparatus used in this investigation consisted of an Alternating
(Jurrt-iit ltridge (which will be referred to as an A. C. Bridge through
the remainijlei‘ oi’ this paper) with sensitive telephone receivers and
microphone hummer, with a battery of five tlrv cells connected in series,
soil angers, drying oven, balances weighing to 1/100 gram, and ther-
inonieters "for determining the temperature of the soil. The above in-
struments were all olf standard make and can be procured from companies
dealing‘ in scientilic and laboratory apparatus. y

ln addition to the apparatus mentioned, soil electrodes were con-
structed oil.’ if-iiicli carbon rods about 6 inches long secured to No. 14 rub-
ber-insnlatetil copper wire as follows: at one end of the wire for a distance
of zipproxi11iatel_v' .2 inches the insulation was removed, after which the
bare wire was lniavily tinned by application of solder and non-corrosive
ilnx, and a loop liiirriicd on the end ol’ the wire, which was inserted in a

[a f l
‘VIIJJIJJIIJIJJJIIIHII/

L<_____E Zectrodc’ Depth

 

Fig. 1. Broken-away sectional view of an electrode.

hole drilled in one end of the carbon rod. The hole, enlarged at the
bottom, was tilled with molten type-metal, which adhered closely to the
tinned wire and expanded on cooling to form a firm connection between
the carbon rod. and the copper wire. The copper wire was cut sufficiently
long to leavt: 72 to 3 inches exposed to connect with the A. C. Bridge
wires by a Fahnestock connector when the electrode was inserted in the
soil to the desired depth. The insulation was removed from about three
inches of the top end of the wire and this part of the wire also was well
tinned. The carbon rod and attached wire were then secured in a
glass tube olf suitable bore and length and the joints sealed against
moisture by sealing wax, leaving the carbon rod extending 4 inches out
ol’ the glass tube. (This length was chosen as a convenient length for
use in the experiment.) The electrodes thus had the appearance of two
coaxial cyflinilers of different radii joined end to end with a slight en-
largement at the juncture as shown in Fig. 1. A rod of nearly similar
shape was obtained from a local blacksmith shop a11d used to form the
holes in the soil to the desired depths, after which the electrodes were
put in place by filling the holes with a thick mud slush and carefully
working‘ the electrodes up and down to remove air bubbles and allow

DETERMINATION OF SOIL MOISTURE BY MULTIPLE ELECTRODES 7

the slush to settle around the carbon rods. Suflitiient; slush was used to
fill the holes to overflowing, thus preventing the formation of depwssioiis
in the soil immediately‘ surrounding the electrodes, which otherwistw
would permit ivater to collect around the electrodes and give a much
lower value for the resistance of the soil between the electrodes than
should be found. The electrodes, once installed, were left undisturbed
and after sufficient time had elapsed for the moisture of the slush to
distribute itself evenly through the surrounding soil, measurements of
soil resistivity were begun.

The general arrangement of the apparatus for determining soil re-
sistivity is shown in Fig. 2 (a). _

For measurement of resistivity at any one location and depth, four
similar electrodes were used, arranged as indicated in Fig. 2 (b).

   

To 502'] EI€CtFOdP$ ‘I'll

(d)

1 2 o’
75p Pia/v View of Soil E Zectrodcs in Posiliofl

(°:: Z fl‘. ( Distance be! warn centers of adjacent ciecimdes)

(b)

Fig. 2. Resistance-measuring apparatus, (a) schematic diagram of The A. C. Bridge
and other essential apparatus, (b) top plan view of electrodes placed in the soil.

THEORY

In measurements of soil resistivity, or specific» resistance, the soil, with
its salts, organic matter, water, etc., is considered as an electrolyte. The
conductivity (conductivity being the reciprocal of resistivity) of elec-
trolytes is shown by Kraus (4) to be a function of the temperature, the
viscosity of the solution, the dissociation of the salts, the kind of salts,
etc. Usually the conductivity of the soil electrolyte is considered chiefly
a function of the dissociation and temperature, but the effect of the fluid

t! BULLETIN NO. 426, TEXAS AGRICULTURAL EXPERIMENT STATION

state, or viscosity, should rwiileritlyf be considered. As shown by Ander-
son and .\lattson (l), eolloitlal material in the soil must influence
viscosity); theretore, we should expect soil conductivity to increase gen-
erally with dissociation ol‘ the salts, with increase of temperature, and
with deereast» of viscosity. '\t'ist-osityi' should depend on the soil colloids
and moisture content. 'l‘hus the conductivity‘ function must have a com-
plicated form which could. l1artlly' be stated from theoretical considera-
tions alone. lly the flppllctltlOll of divided difference theorems (9) to
observed soil resistance measurements and corresponding moisture con-
tents (olitallletl during this investigation) the" equation relating soil
resistivity’ and moisture content was found to be a cubic equation. The
[Hie oi (equation I

YIA/IU-l-B/Xg-l- C 1

satisfied the relation between soil resistivity and moisture content, Where
IY is soil resistivity,  is soil moisture content, and A, B, and C are
constants which may be (letermiicied.

lt is well known that soils uruflerlyriiig‘ any considerable area are not
uniform in moisture content, as auger borings have shown. Thus it is
understood when we speak of moisture content we mean the average
moisture content of a number of samples, and resistivity is also the
average resistivity of the soil in the volume considered. Treating the
soil as uniform in moisture content a11d resistivity at any specific per-
centagt‘ of moisture, we may then state our problem of resistivity deter-
minatioii in terms of resistance measurements between electrodes placed
in a iuiiform medium.

It has been shown by Jeans (3,) that the resistance between parallel
cylindrical electrodes placed a great tlistance apart in a uniform infinite
metlium may be representetjl b_v the equation

i» I (iv/iv) 10s‘ (pi/ab) 53

where it is the resistance of the medium between unit length of electrodes,
‘r is resistivity of the medium, p is distance between parallel cylindrical
electrodes, and u and b are the radii of the electrodes employed.

It can be readily appreciated that change in area of contact between
electrodes and soil would zliftlCt the resistance measurements unless cor-
rectioit could be made for such changing‘ contact. Attempts have been
made to overcome this error by frequent recalibration of electrodes. The
method, out’ course, is inconvenient and not satisfactory. From Equa-
tion L’, when applied to electrodes of length l, may be obtained

‘u.’ II (T/2 1r  lOg (pg/ab) 3

where n’ is the resistance between parallel cyflintlrical electrodes of
length l and radii a and b, placed a. great distance p apart in a uniform
infinite medium.

Jeans (3) states that if two electrodes of any shape are placed in an
infinite metlium at a distance p apart which is great compared with their

DETERMINATION OF SOIL MOISTURE BY MULTIPLE ELECTRQDES 9

linear distance, we may express to a first zipproximatien the resistanrée,
between the electrodes by the equation

R I 7/477 (p11 + p22) ‘l

where 1' is the resistivity of the medium, and p], and p22 are the co-
efficients of potential.

“It accordingly appears that the resistance of the infinite medium may
be regarded as the sum of two resistances—a resistance 1' pn/4-1r at the
crossing of the current from the first electrode to the medium, and a
resistance r p22/4 1r at the return of the current from the medium to the
second electrode. Thus we may legitimately speal; of the resistance of
a single junction between an electrode and the conducting medium sur-
rounding it.”

From Equation 3, it is clear that a decrease in Z (the length) causes an
increase in resistance between the electrodes. Change in contact area
must, consequently, change the elfective length of the el<>ct;if<><les and
could be considered as causing an ‘added resistance at the electrodes be-
cause of poor contact. Letting If represent the resistance measurements
between two electrodes, as determined. by an .-:\. (l. Bridge or some other
suitable device, we may write,

RIPJ+T1+T2 5

where a’ is the resistance of the soil when electrodes make contact with

_2 the soil over their entire surfaces, 1', the increase of resistance caused by
poor contact between the first electrode and the soil, and r2 the increase

of resistance caused by poor contact between the second electrode and
the soil. The Values r, and 1'2 may change from day to day, or following
rains; thus it is essential that corrections be made that may eliminate
r, and r2.

Equation 5, however, contains three unknowns; therefore it is necessary
to obtain further equations relating the unknows to make possible the
elimination of the contact resistance between the several equations.

By placing four similar electrodes at known distances apart, as shown
in Fig. 2 (b), and taking resistance measurements between two electrodes
at a time, we may obtain equations as follows:

B1IFI1+T1+T2 
R2IILI2+T1+T3 (b)
R3IFI3+T1+T4 (C)
R4IILI4+T2+T2 
R5:Iu’,5+r2+r4 (C)
Rezltie+ra+r4 

where R1 is resistance reading between electrodes 1 and 2, R2 between
1 and 3, R2 between 1 and 4, R4 between 2 and 3, R5 between 2 and 4,
and R6 between 3 and 4; a’, is actual soil resistance between electrodes
1 and 2, M2 between 1 and 3, a’, between 1 and 4, p’, between 2 and 3, n’,
between 2 and 4, and a’, between 3 and 4 5 r1, r2, r2, and r4 are the added

10 BULLETIN NO. 426, TEXAS AGRICULTURAL EXPERIMENT STATION

resistances caused by poor contact with the soil at the respective electrodes-
From Equations (b) and (c) we may obtain

It, I ab, + h’: —— a2 — r3 + r4 6-
By zidiling Equations 6 and (f) we have
E6 + R3 —— R2 I '11.,“ + ,a'3 — [u/Q + '31; 7'
Also, from Equations (a) and (c) we obtain
I{,,:;r'3+,R,-—;i'1—r2+r‘ 8
By adding Equations 8 and (e) we have
1i,’ + 1{;,—— R1 z a’; + ‘M's ——',LL/1 + 2r‘ 9

Subtracting '7 from 9 gives

(Rs+R2)_“(Ro+R1):(F,s+/*,:)'_(P~'u+/*,1) 10

which is free of added resistances caused by poor contact at the electrodes.

With the electrodes placed at known distances apart in a uniform

medium, we may obtain from Equation 3 the relations of Mo, #5, and [/2
to p’, and may then express Equation 10 as follows:

I _ (R5+R2) _ (Re+R1)

1”" 1
K
where a1 is the soil resistance between two electrodes at a known distance
apart; R5, R2, R6, and R1 are resistance measurements obtained by
A. (‘. Bridge or other suitable instrument; and K is a constant depend-

ing on distances separating the four electrodes used and their depth in
the soil.

11

EXPERIMENTAL PROCEDURE

In determining the moisture content of the soil, cores of the soil were
taken with soil augers having diametersof about L} inches. The parts
of the cores obtained from the soil at the same depth as the electrodes,
and also approximately equal in length to the contact portions of the
electrodes, were placed in aluminum sample boxes and Weighed. Later
the samples were dried for 12 hours in an oven at a temperature of
110° (‘. to 120° C. The moisture was then expressed in per cent of
dry soil.

To observe the effect of change of contact area between the electrodes
and the soil, on the soil resistance between the electrodes, two pairs of
electrodes of different contact lengths were placed in a small plat of
ground (called The Office Plat) near the Experiment Station Office.
One pair of the electrodes had a contact length of 10 inches and the
other pair of electrodes had a contact length of 3 inches. Both pairs
of electrodes were placed the same depth in the soil and the members
of each pair were separated the same distance.

An electrode set-up for the purpose of calibration was made outside of
the control plats in an area covered with Buffalo grass. Electrodes were

l

DETERMINATION OF SOIL MOISTURE BY MULTIPLE ELECTRODES ll

placed also in each of the eight control plats ol the Experiment. Stat ion at
depths of 12 inches, 1b’ inches, and 30 lllCllCS. The electrodes in the
calibration plat were placed at the same (lcpths and (listanees zipart as
those in the control plats. A space 1L} feet by 15;} feet on the grass
area containing the calibration electrodes was dammed up and flooded
with cistern water. At a depth ol? 1T2 inches the moisture content was
in excess o1": 24 per cent, as determined by the soil auger. After drying
out for a period of several days the plat was again flooded and a moisture
content of nearly 29 per cent was found at the 12-inch depth. During
the first few days following flooding of the plat, auger samples were
taken daily at various depths and records made of nloisture content,
temperature of the soil, and resistance measurements. This was con-
tinued until the change of resistance with changing moisture content
became considerably more than at first. The readings were then taken
at two-day intervals. Measurements of moisture content by auger, soil
temperature by mercury in glass thermometers, and resistance between
electrodes by the A. t‘. Bridge were also niadc on the control plats.

Since it was desirable to measure the moisture content of the control
plats under various conditions of weather, an instrument house was
erected at one end of the control plats and wires run from each control
plat to the instrument house, where readings were made in the same
manner employed on the calibration electrodes. The use of long con-
necting wires and their necessarily crowded arrangement required the
use of a small variable condenser of about .001 mqt. maximum capacitance
in parallel with the resistance coils OflEthQ bridge; to produce a sharp
minimum in the telephone receivers. The inductance of the connecting
wires seemed to cause no serious (liflicultyx l

The electrical resistance of the soil between electrodes was obtained

from the equation:
(R5 + R2) —— (R6 + R1)
K
Where a’, is the soil resistance between specified electrodes; R5, R2, R6,

and R1 are resistance readings obtained from the A. C. Bridge; and K
is a constant depending on the distance between electrodes and depth in

Fri 11

_ the soil.

Temperature of the soil was determined at the depths of the electrodes
by placing a thermometer, registering up to 50° (i. by tenths, in a hole
as deep as the middle of the contact portion ot’ the electrodes.

Temperature correction of soil resistance was made by employing the
average temperature coefficient for soils as determined by Whitney,
Gardner, and Briggs ('7).

A calibration curve tor the electrodes placed at specified distances
and depths was then obtained by plotting soil resistance between elec-
trodes against soil moisture, thus enabling soil moisture to be obtained
from the curve reading; (YOPTGSPODdlIIQ to a. soil resistance measured
between specified electrodes.

l2 BULLETIN NO. 426, TEXAS AGRICULTURAL EXPERIMENT STATION

EXPERIMENTAL RESULTS

'l‘ablc No. 1.  Resistance between l0-inch electrodes in oflicc plat and corresponding
moisture content.

Temperature Moisture
Resistance in ohms in degrees C. in per cent
60.15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20.7 20.92

63.4?» . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20.0 20.52

64.20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20.2 20.33

66.60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20.2 19.16

70.15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20.2 17.79

72.8(). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21.7 17.97

78.85 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22.8 17.49

81.75 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23.6 16.68

88.50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24.6 16.56

'l‘ahle. No. 2.——Resistane.o. between 11-inch electrodes in ofiice plat and corresponding
moisture content.

Temperature Moisture
Resistance in ohms in degrees C. in per cent
151.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 20.2 17.79

1.39.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21.7 17.97

172.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22.8 17.49

181.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23.6 16.68

183.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24.6 16.56

Moisture in Per-Cam‘ 0/ Dry

Fig. 3. Influence of electrode length on resistance measured between electrodes, (a)
10-inch electrodes 1 ft. deep, (b) 3-inch electrodes 1 ft. deep.

DETERMINATION OF SOIL MOISTURE BY MULTIPLE ELECTRODES 13

'l‘able No. 3.——Resistance (corrected to 60° F.) between electrodes and corresponding soil-
moisture content for (?11l1l)1‘2111011 plat.

Electrodes 1 Ft. Deep Electrodes 1% Fl. l)eep lileetrodtxs 2% Fl. Deep
Resistance Soil moisture Rcsistamze Soil moisture Plesistanet‘ Soil moisture
1n in in hi in hi

(Nuns/Const perrmnt (Nuns/ConsL perrmnt (Nuns/ConsL percent
2.30 21.51 3.17 21.15 . . . . . . . . . . . . . . . . . . . . . . . . ..

2.59 20.18 2.99 19.81 . . . . . . . . . . . . . . . . . . . . . . . . ..

2.52 19.40 3.20 19.56 . . . . . . . . . . . . . . . . . . . . . . . . ..

1.29 28.80 2.00 25.40 . . . . . . . . . . . . . . . . . . . . . . . . ..

1.67 27.06 2.28 23.10 2.48 . . . . . . . . . . . . ..
1.86 26.23 2.24 23.20 2.88 20 0
1.86 24.00 2.24 22.30 2.98 . . . . . . . . . . . . ..
1.86 24.30 2.31 23.30 2.57 19 2
1.72 23 60 1.85 21.40 $.41 . . . . . . . . . . . . ..
2.80 23 20 1.96 21.80 1.16 17.0
2.38 20 35 2.49 19.50 2.66 . . . . . . . . . . . . ..
2.52 20 88 3.05 21.12 3.47 18.15
2.56 20.58 2.78 20.30 1.61 17.97
2.65 19.63 3.02 19.25 1.99 17.56
2.70 19.23 13.02 19.02 1.92 16.45
3.22 17.88 3.44 18.25 1.57 16.80 '
3.51 17.24 3.99 17.06 5.20 15.48
4.26 16.04 4.12 15.75 5.79 14.45
4.49 16.32 5.05 16.40 6.55 15.02
5.55 14.73 6.20 14.43 8.32 12.21
6.58 15.16 6.67 14 51 9 73 13.15

Table N0. 4.——Resistance (corrected to 60° F.)_ between edjacent electrodes in control plats and
corresponding soil-moisture content.

‘u/c in Ohms/ Moisture
Plat No. Const (in per cent) Depth.
(feet)
1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 8.73 13.5 1%
9.74 12.84 1
8.68 12.45 2%
2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13.5 1%
. . . . . . . . . . . . .. 11.48 1
48 10.48 2%
3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13.20 13.76 1%
13.90 11.58 1
9.25 11.68 2%
4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15.09 1%
. . . . . . . . . . . . .. 16.32 1
4.70 12.56 2%
5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4.35 16.72 1%’
5.48 17.12 1
5.57 14.4 2%
6 . . . . . . .., . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25.40 10.22 1%
29.90 8.96 1
19.90 7.35 2%
7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 14.82 12.26 11/21
13 72 11.82 1
8.55 10.68 2%
8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13.9 1%
. . . . . . . . . . . . .. 13.7 1
7.64 9.06 2%

14 BULLETIN NO. 426, TEXAS AGRICULTURAL EXPERIMENT STATION

   
  

A C9011 Belmrtn Eleclrodn in  Constant)

Fig. 4. Calibration Curve for the Apparatus Used to Determine the Moisture Content
by Soil Resistance.

DETERMINATION OF SOIL MOISTURE BY MULTIPLE ELECTRODES 15

Table No. 5—-——Readings on control plat electrodes (l-foot deep) following rainfall of 1.67 inches.

Resistance in Ohms Soil Resistance
iii ()l1iiis.’(§()|ist.
——~—— I l)at1 l’hit P40
I
R1 R2 R5 R6 1”" 1 I“ c
1 00 1% R4. 8 7/30

313.3 348.3 342.3 364.4 7.72 12.19 8/7/30 1
305.3 227.6 289.4 198.7 7.78 12.28 8 7/30 2
162.5 176.8 183.7 165.0 8.97 14.14 8/7/30 3

82.6 89 0 80.9 80.5 4.07 6.41 8/7/30 4

88.8 97.0 90.5 93.1 3.35 5.28 8/7/30 5
387.4 471.6 539.0 597 5 15.4 21.3 8/7/30 6
227.1 263.7 273.8 296.0 8.62 13.6 8/7/30 7
165.3 181 0 231.6 237 8 5.68 8.95 8/7/30 8

9 50 Au hi 8 8/30

304.0 348.2 314.8 347.7 6.76 10.22 8/8/30 1
306.7 226.6 289.2 197.7 6.82 10.45 8/8/30 2
163.3 177.5 163.8 166.1 7.12 10.75 8/8/30 3

84.3 90.5 82.4 82.5 3.65 5.52 8/8/30 4

90.8 98.6 92.2 94.6 3.23 4.88 8/8/30 5
397.5 473.8 546.5 601.0 13.05 17.7 8/8flH) 6
228.5 265.0 271.0 295.3 7.3 11.03 R/8/30 7
163.9 183.0 232.7 242.7 5.14 7.77 8/8/)0 8

Table No. 6.—Chan§e of moisture as determined from change of soil resistance for electrodes

1-foot eep in control plat and corresponding rainfall (penetrating).
Moisture (in per cent) Change of Rainfall
moisture (penetrating) Plat No.
4:00 P. M. 9:50 A. M. {in per cent) (in inches)
8/7/30 8/8 /30

11.9 12.5 .6 1.60 1
11.86 12.42 .56 1.43 2
11.4 12.35 .95 1.31 i
14.4 15.05 .6) 1.17 4
15.3 15.7 .4 .96 5

9.7 10.7 1.0 1.42 6
11.5 123 .8 1.53 7
13.0 13.6 6 1..' 3 8

DISCUSSION OF RESULTS

From Tables 1 and 2, which show, respectively, resistance readings
between pairs of electrodes 10 inches long and pairs of electrodes 3
inches long, with their centers 12 inches below the surface of the soil,
and the corresponding soil-moisture content, as determined by soil
auger, there can be seen a correspondence of tlecreasing moisture (zontent
to increasing resistance between electrodes. This correspondence between
resistance and moisture content is shown graphically. ltigure 3 (a),
which is a graphical representation of Table 1, shows, on comparison
with figure 3 (b), which is a graphical representation of Table 2, a much
smaller value for the resistance between the 10-inch electrodes for the
same moisture content than is found between the 3-inch electrodes. This
is to be expected and is in accord with Equation 3. Since irregularities
caused by changing contact between soil and electrodes were evident, the

H; BULLETIN NO. 426, TEXAS AGRICULTURAL EXPERIMENT STATION

relation ol rcsistaiici- between electrode pairs to soil-moisture content
ivas not found for niaii_v percentages of moisture content. ltoivevei", the
results tilitainetl t“llt'tllll'il§_"t‘tl further testing of electrodes ai'i'ziiig'ed to
eliminzttt- contact error.

Table It shows soil resistance (corrected to liu° F.) between zidjzlcent
(‘lt'(‘ll‘ty(l(‘>' ol the calibration plat and c0i'i'espoii<ling' soil-moisture con-
tent. as ilcteriiiiiied b_v the multiple electrode method and soil auger
samples, respectively. The values from 'l‘ztble I} and those from Table
-l (which shows similar deteriiiiiizitioiis made in the same maiinei‘ o11
the eight control plat areas) are representeil on Fig. 4 along with a
graph ol lfiqiizititin l,

v — .’\//X“ + ia/lv + e

'l'he soil-iiioisturt- content of the control plats was, iii general. very
unuiiil'<>riii, even with samples taken a short ilistantre apart. The agree-
ment lietiveen the observed values TTOIH the control plats and those front
lllquzltion l 2lll()\'(' (which satisfies the relation of SOlI resistance between
electrodes to moisture content as ileteriiiiiied lor ‘alibration (electrodes),

is close.

'l‘aliles 3 and ti, which are rezuliiigs made on the control plats follow-
ing a rainlall ol' 1.157 inches, indicate agreement between changes in
moisture content li_v percolation ol' rain water and the amount of water
penetrating the soil. 'l‘ablt2 5 also shows variations in R1, I._.. R;
and It" between the two successive readings, which are evidently caused
by clizlilgllig‘ contact between electrodes and soil as a result of
rainfall, since the value ot the soil resistance between electrodes,
if, I | (IL, —l— l{._,p) —— (R6 —l-,le{1)]/I\', (lecreasetl for all 0t the control
plats consistent with the amount olf rainfall penetrating the plats.

MOISTURE DETERMINATION BY SOIL RESISTANCE

'l‘o liiid the soil moisture with the resistaiice-measuring apparatus-
uscd in this ll1\'('h'tlg‘zltl0ll. the operator should place the tour electrodes
iii a line. the individual electrodes 2 lieet apart. Then measure the
resistances It“ H2. li’_._. and It“. which are indicated by Plig. 5;

1 ' z a’ +
PR6?)-

i<_-_ R,- r

Fig._ 5. Top plan view of electrodes in position, showing the resistance measurements.
used in determining soil moisture.

DETERMINATION OF SOIL MOISTURE BY MULTIPLE ELECTRODES 17

where R, is the resistance between electrodes 1 and '3, ll._. is the resistance
between electrodes 1 and 3, H, is the resistance between electrodes '3
and l, and ll“ is the resistance between electrodes I; and l.

Determine the temperature. ol' the soil h_\' placing a thernlolnetel" in a
hole of such depth that the thermolneter bulb will he the same distance
below the surface as the middle o|' the contact portion of the electrodes.

From the following equation
(R5  iliul _ (Ho + R1)
H 1\'

Vi] in
is (ibtainetl a], the average resistance ot the soil between: elcct.l'odes
2 feet apart. When the electrodes are 1 ft. deep .l\'. I 1.67’, when the
electrodes are 1.‘; ft. deep K I 1.45, and when the electrodes are 2i; ft.
deep k I 1.01. '

The resistance u’, is corrected to the value pfl. which it". would have at
60° F. or 155° (l, by the use out’ the equation,

IL/i
Iu/c I g l2
[1 + H (t— 1:15)]
where HI—.02'73, and t is the te111per'at111'e of the soil in zlcgrees

Centigrade. Then by the use of Fig. 4 the soil moisture. is read from
the curve for the value of a} obtained above.

As an illustration of the use of soil-resistance and telnptirature meas-
urements in determining soil moisture consider the following‘ example.
The values measured for electrodes 1 ft. deep are It, I ($0.0 ohms,
R, I 63.0 ohms, RSI "2.0 ohms, HUI 50.2 ohms, and the soil tem-
perature t I 25.5° C.

(B. + R5) I (n, +1{,,) 125.0 -11s>.z

Then u’, I I
K 1.67
p’, I 3.47. I
F" 1
But flu: g
[1 + II (t—— 1545),]
#1

Therefore a’, I
[1 — .0273 25.? — 15.5)]

33.47
Iu/C i ‘l?
.727
pUc I 1.77.

From the curve of Fig. 4. the soil moisture corresponding to the value of
a’. I 4.77 is found to be 15.8%.

l8 BULLETIN NO. 426, TEXAS AGRICULTURAL EXPERIMENT STATION

'l.‘he calibration of the electrodtas given buv Fig. 4. will probably not
be the right one to use with soils that differ much from that of the con-
trol plats of the Spur Experiment Station. In such cases a new calibra-
tion can be obtained by making three determinations of the temperature-
eorlw-(zteul resistance a’, for three soil-moisture values which differ by
two per cent or more. Each of the moisture values should be obtained
from the average of live or more auger samples taken at the same time
that the value of p/c is (fleterminetl. From these three determinations
ot’ soil resistance between electrodes placed 2 ft. apart, and the soil-
moisture (sontent. a new calibration curve can be constructed using the
equation,

A B

+
X3 X2

Y: +0 1

where Y is the (letermined soil resistance corrected to 15.5° C. and
(lesignzited by a’, in Equation 12, X is the corresponding soil moisture as
<letei~niiiie<l from the 2Lllg(‘l' samples, and A, B, and C are constants

Fig. 6. Representation of electrodes in uniform soil, showing region where most of
the current is conducted between electrodes.
which can be found by methods of algebra When the three values of
resistantie and soil moisture are placed in the equation.

It’ the calibration provided by the curve of Fig. 4. gives soil-moisture
values that do not differ much from those obtained by auger samples, a
complete recalibration should not be necessary’. In this case» the only
(vhangtw necessary would be in the value of the constant K from the
equation

DETERMINATION OF SOIL MOISTURE BY MULTIPLE ELECTRODES 19
(R5 +  '_' (R6 +121)

K

The new value of K may be found by multiplyiing the present value of K

#1 11

. by the ratio of the observed value of iflc to the vialue of u’, which corre-

sponds t0 the moisture-content on the curve of Fig. 4-. as determined by
the average of a number of auger samples.

When resistance measurements are used t0 determine the soil nioistlirié,
the results obtained are modified if there is a very wet or very d ry lay/er
of soil close above or close below the contact portion of the eleet.i'o<les.
As shown in Elig. (3, above, most of the conduction of the current occurs
as represented by the dotted lines between the electrodes when the soil
is uniform in moisture content. If there is a wetter la_ver of soil close
above or below the layer which is to be investigated more of the current
will pass through the wet layer than is normally the case, and a lowered
resistance value will be (ibtziined. The amount; of this effect and its
influence on the airc~iiracy' of the results obtained has not yet been
determined.

SUMMARY AND CONCLUSIONS

The multiple electrode method of eliminating‘ r-ontziict errors from
the measurement of soil resistivity removes also the necessity ol’ con-
sidering the resistance of lead wires and increases the irccuracy of the
resistance measurements.

Use of the equation relating‘ soil moisture and resistivity' OIHIDlOS easy
calibration of the apparatus for different locations.

The change of salt content of soils throughout a period of time has
not been determined and it is not known if the change would require
frequent calibration of the apparatus. Data from the apparatus used
on the control plats show that the change of salt content of the soil at
the Spur Substation is not rapid enough to require more than one or- two
calibrations during a year. This would probably not be the case with
irrigated or fertilized soils.

The small amount of data obtained after completing the installation
of the apparatus does not permit definite conclusions to be reached, but
indicates that the method can be used successfully to measure relative
moisture contents and with further development may be used to measure
the percentage of moisture in soils at various locations.

BIBLIOGRAPHY
'(1) Anderson, M. S., and Matson, S. E. 1926. Properties of the

colloidal soil material. U. S. Dept. Agrie, Bureau of Soils,

Bul. 1452, 18-20.

(2) Conner, A. B, Dickson, B. E., and Scoats, D. 1934). Factors
Influencing Runoff and Soil Erosion, Texas Agricultural Ex-
periment Station, Bul. 411, 211-25, 33, 31, Illus.

21)

1111

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T111-

BULLETIN NO.

426, TEXAS AGRICULTURAL EXPERIMENT STATION

.11»1111.~". .1. 11. 111271, The 111111111-11111111-111 111e1_11'__\' 111' electricitbv 11nd
11111;_"111-1is111. 1'I11.-'1_,I1.'11)-I1T1'2. 111111111111.

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s,\'.<11~111.<, .1!1-171, 111-175. .11111s. .\'e\1' York,

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h‘. ,1 111111. 111T .»\;_»f1'ic111t111'e, Division o1’ Soils‘, B111. 6,
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1111-111 11111111111 111' 1111111111111111111‘ the 11-111111-111111111 o1’ soils.

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ACKNOWLEDGMENT

1111111111‘ \\'1.~11es to 11111111- 11c1<11o\\'1edgment to Mr. _:\. B. Conner,

i1)i1'1~1-1111'. '1‘1-.\'11.< .1\;_»'1'i1-111ts111'111 Experiment Station, and Mr. 1'1. E. Dick-
son, S11|11-1-i11te1111e11t. S1111st11tion X11, "T, 18111113 ’I‘1s~.\'11s, who were primarily
res|11111si111e 1111' initiathig" this study and securing" the tinnds necessary
1111' 1111» 111\'1-s1i;1'11ti1111Z to .\11'. I). .11o11i111;~tt o1’ t11e 1811111‘ Substation for
zlssishlnce in 11111111111111: s1111 s111np1es 111111 resistance measttrenients; and

111 111'.

1). \\'. Silvey. ]’1'o1'esso1' 111' i1.’11_\'sics, .<\g'1'ic111t11r111 and Mechanical

(‘ollege 111' '1_‘1-.\'11s, 1111' suggestions 111111 comments in connection with the
11re1111r11tio11 o1 this 111111111script.