Characterization of mobile aluminium in acid soils

Geoderma, 15(1976) 91--101 © Elsevier Scientific Publishing Company~ Amsterdam -- Printed in The Netherlands

91

C H A R A C T E R I Z A T I O N OF MOBILE ALUMINIUM IN ACID SOILS

B.W. BACHE and G.S. SHARP

The Macaulay Institute for Soil Research, Aberdeen (Great Britain) (Received November 13, 1974; revised version accepted September 23, 1975)

ABSTRACT Bache, B.W. and Sharp, G.S., 1976. Characterization of mobile aluminium in acid soils. Geoderma, 15:91--101 Two approaches to defining AI status were investigated for a group of twelve acid soils. The pattern of AI release from 1 g soil when leached slowly with 1.0M KCI solution showed the difficulty of distinguishing exchangeable from non-exchangeable AI. A1 displaced in the first 10 cm 3 of leachate was related to the exchangeable fraction, and comprised between 0.2 and 0.8 of the total mobile A1 released by 500 cm 3 KC1 solution, for different soils. Shaking 4 g soil with 100 ml KCI for 30 min provided an adequate rapid estimate of exchangeable A1, but under-estimated large amounts and over-estimated small amounts. The equilibrium-solution concentration of A1 was determined by a serial saturation procedure, but the activity ratio (aD)3/(aA1) 2, or its logarithm, is suggested as a more appropriate function to characterize the cation balance. It can be evaluated approximately in a saturation extract, or after equilibrating soil with dilute CaCl2 solution at 1 : 1 ratio.

INTRODUCTION The a l u m i n i u m ion is i m p o r t a n t b o t h in the c h e m i s t r y o f acid soils ( C o l e m a n a n d T h o m a s , 1 9 6 7 ) and for its effects on p l a n t g r o w t h (Jackson, 1967). There is, h o w e v e r , considerable u n c e r t a i n t y over h o w t h e A1 status o f soils s h o u l d be described. In c o m m o n w i t h all o t h e r soluble c o n s t i t u e n t s in soils, there are t w o a p p r o a c h e s t o this p r o b l e m . The first a p p r o a c h is t o use the a m o u n t (mi!li-equivalents per kg soil} o f A1 t h a t is in e q u i l i b r i u m with the soil solution. Most o f this is a d s o r b e d o n the soil surfaces a n d a p p r o x i m a t e s t o w h a t is generally u n d e r s t o o d b y " e x c h a n g e a b l e " A1. Its e s t i m a t i o n b y s t r o n g salt e x t r a c t i o n is c o m p l i c a t e d b y the conc o m i t a n t release o f n o n - e x c h a n g e a b l e A1 f r o m s o m e soils so t h a t it is difficult t o define an e x c h a n g e a b l e f r a c t i o n ( P r a t t a n d Bair, 1961), a l t h o u g h KC1e x t r a c t a b l e A1 has p r o v e d useful f o r e s t i m a t i n g the lime r e q u i r e m e n t o f acid soils ( K a m p r a t h , 1970). T h e s e c o n d a p p r o a c h is t o use a c o n c e n t r a t i o n (mole per litre o f solution) in the soil s o l u t i o n or in s o m e equilibrium suspension. A l t h o u g h a straight-

92

forward concentration measurement in an arbitrary extraction gives a useful practical measurement (Hoyt and Nyborg, 1972), the distribution of ions within the electrical double layer, resulting from the charged nature of soil surfaces, necessitates the use of an activity ratio (8chofield, 1947) to characterize the cation balance of a soil. The reference ion can be taken as the sum of divalent cations (Ca + Mg) 2÷, and the appropriate activity ratio becomes (aD)3/(aA1)2, where D represents the divalent cations. The logarithm of this ratio can be expressed 2pA1-3pD, or as log ARD_A1. The "corrected lime potential" of Turner and Clark, (1966) is a similar function, being equal to 1~3pAl- 1/2pD plus a constant. The purpose of the work described here was first to determine these two complementary parameters of A1 status for twelve acid soils by relatively rigorous methods. This throws further doubt on the concept of a definite exchangeable A1 fraction, at least for some soils. A second objective was to see to what extent rapid empirical extraction methods could give results that are sufficiently close to the more rigorous methods to be useful for practical purposes. SOILS USED

Twelve acid soils of varied texture and origin were chosen, mostly from NE Scotland. They included pairs from different horizons of four profiles. Three of the soils were under cultivation, the remainder coming from woodland and permanent pasture. Further details of the soils are given in Table I. CONCENTRATED SALT EXTRACTION OF ALUMINIUM

Experimental methods Release of A1 from the soils by KC1 solution was investigated by a leaching technique at a sufficiently slow rate that equilibrium was considered to be established between the soil and the leachate (Sivasubramaniam and Talibudeen, 1972). Some Al-saturated clay minerals were also extracted by a shaking-centrifuging procedure. One-gram samples of air-dried soil, sieved <:1.0 mm, were held on porosity 3 sintered glass filters and leached with 1.0M KC1 solution at a rate of 8--10 cm 3 per hour. Aliquots of the leachate were collected on a fraction collector up to a maximum of 500 cm 3 and A1 was determined in each aliquot. This gave curves of A1 released against volume of leachate. Routine single extraction estimates were obtained by shaking amounts of soil ranging from 0.50 to 10.0 g with 80 cm 3 1.0M KC1 solution for periods ranging from 0.5 to 24 hours, filtering, and washing the soil on the filter with two 10-cm 3 portions of KC1 solution and making up to 100 cm 3. In all experiments A1 was determined chemically by the eriochrome cyanine colorimetric m e t h o d {Hill, 1956) modified for use with a Unicam AC 60 chemical processing unit, and (Ca + Mg) was determined by EDTA titration.

basic igneous till

glacial sand

sand over K e u p e r marl

drift over Corallian sand

granitic till

red lacustrine clay

Old Red Sandstone till

Brown forest soil, Insch

Brown forest soil, Cawdor

Ground water gley, Quorndon

Brown forest soil

Humus iron podzol, Countesswells

Surface water gley, Tipperty

Iron podzol, Aldbar

Ap B2

Ap Bg

(i) Ap (ii) Ap

Ap

Bg

A1 B2

Ap B2

Horizon

5.6 1.5

8.3 1.3

5.2 4.6

0.4

1.0

5.3

5.6 2.1

(%)

Organic carbon

11 7

24 26

9 9

10

19

8

10 3

%

Vm, Ka Vm, Ka, II

II, Ka, V m 1], Ka, V m

]], Ka Vm, Ka

1]/Sm, I1

1]/Vm, 1], Ka

1]/Sm, 1]

Vm Vm

Dominant minerals*

Clay fraction

5.1 5.0

4.5 4.8

4.7 5.2

4.5

4.1

4.O 3.9

4.O 4.7

pH

(mequiv. kg)

Exch. Ca+Mg

-1.50 -3.20

0.16 -1.50

1.80 3.9O

-0.51

1.20

-O.86 -2.20

0.39 0.16

11 4

46 15

62 92

21

38

8 2

58 19

ARCa_~A1 per

log

Equilibrium solution

* Vm = vermiculite; 11 = illite; S m = smectite; Ka = kaolinite; / indicates interstratification.

Parent material

Major group and series

Soils

TABLE I

57 22

101 107

17 2

6

25

12 25

73 23

Exch.

115 52

156 144

55 9

11

42

15 43

143 74

Total

Mobile a l u m i n i u m

0.50 0.42

0.65 0.74

0.31 0.22

0.55

0.59

0.80 0.58

0.51 0.31

Exch. Total

94

Results release o n leaching. Some contrasting patterns of Al release that were found on leaching are shown for four of the soils in Fig. 1. These curves show a gradually decreasing release of A1 with progressive leaching, illustrating dissolution of non-exchangeable A1, rather than the sharp drop in release expected for a well-defined exchangeable fraction (see below). Nevertheless, Sivasubramaniam and Talibudeen (1972) claimed that exchangeable and non-exchangeable A1 could be unequivocally distinguished because their results showed a linear rate of release after the first few fractions. While the later l~arts of the curves for the subsoils in Fig.1 may approximate to linearity, the earlier parts (up to 150 cm 3 leachate) do not, nor do the curves for the topsoils. The behaviour of these soils may be different from those used by Sivasubramaniam and Talibudeen (1972); or their results may have arisen because they leached soil with KC1 acidified to the pH of a KCI: soil suspension, thus ensuring a lower constant pH during the course of leaching. In our experiments the pH rose from about 4 to about 5 as H and A1 ions were progressively removed. Aluminium

150 t

I

i

x

..,...x

- *""" """ .x . . . . . . . . .

x ....

""""

loo ~~ ~

f

i

÷ ........ ÷':

"

....--b

........

.4" . . . . . . .

',

o .

0

50

25

.

.

.

,

1 O0

200

"soo

Fig.1. Cumulative release of a l u m i n i u m during leaching w i t h 1.0 tool/1 KC1 at 8--10 cm 3 per hour. Legend: o, Countesswells topsoil; A, Inseh topsoil; X, T i p p e r t y subsoil; +, Q u o r n d o n subsoil.

95 The curve for the Tipperty subsoil (Fig.l) shows a relatively sharp charge in slope when 10 cm 3 of leachate had been collected and 0.74 of the total extractable A1 was released. This indicates the presence of fractions that differ sharply in mobility, and appears to be the nearest one can get to a well-defined exchangeable fraction. The topsoils show a more gradual release, with only 0.31 of the extractable A1 occurring in the first 10 cm 3 of leachate for the Countesswells (i) soil sample. In an a t t e m p t to obtain a different pattern of behaviour from that shown by the soils, some pure clays that were unlikely to hold interlayer A1 were examined. Samples of well-crystallized illite (from Dunnett Head sandstone, Caithness) and of kaolinite (from St. Austell, Cornwall) were saturated with A13÷ by shaking with AIC13 and then washed free of chloride to pH 4.6. Because the leaching technique was unsatisfactory for clays, these were extracted with successive lots of 1.0M KC1 at 1:50 ratio and centrifuged. Three extractions only were sufficient to remove all the mobile A1 from the clays (183 and 34.6 mequiv./kg, respectively), and gave a definite clearly defined maximum for the exchangeable A1 fraction. Lin and Coleman (1960) leached Al-saturated montmorillonite and subsoils with 1.0M KCI at 100 cm3/h, compared with 10 cm3/h used here. After a b o u t 50 cm3/g, a definite A1 fraction had been released, similar to our results for Al-saturated clays. Our soils, however, behaved differently.

Distinguishing exchangeable aluminium. The pattern of continuing b u t decreasing A1 release from the soils, and particularly from the A horizons, suggests that a transport-controlled mechanism is operating to govern K ÷ access to Al-desorbing sites and A1 removal from these sites along reaction paths that become longer with progressive extraction. It thus becomes impossible to differentiate clearly between exchangeable and non-exchangeable A1, because non-exchangeable fractions do n o t have a constant rate of release. The possible sources of this slowly released A1, such as disordered aluminosilicates (Mitchell and Farmer, 1962), A1 interlayers in vermiculitic clays (Wilson, 1973) and organic A1 complexes, are more abundant in A horizons than in subsoil layers. One is reduced to making empirical arbitrary distinctions between these t w o fractions of mobile A1, and from the evidence above it seems reasonable to suggest the A1 released in the first 10 cm 3 of leachate approximates to an exchangeable fraction. This corresponds to the initial rapid release from the Tipperty subsoil (Fig.l), b u t for surface soils it probably includes some of the more mobile non-exchangeable A1.

Rapid estimates of exchangeable aluminium Duplicates in the shaking experiments showed more variability than in the leaching experiments. The effect of time of shaking was examined in detail for t w o soil samples, and it had no significant effect between 0.5 and 24 h.

96

There was however a considerable rise in A1 extracted between 10 and 30 min, which indicates t h a t the suggestion of Pratt and Bair (1961) of shaking for 1 min may not be appropriate. The effect of soft: solution ratio was less than had been anticipated. For nine of the soils a 1:100 ratio extracted more A1 than a 1:10 ratio, but the difference was only great for two less-acid soil samples which contained proportionately more non-exchangeable A1 than the other soil samples. Three of the samples were anomalous in that the narrower soil:solution ratio extracted slightly more A1 than the wider ratio. The shaking methods tended to under-estimate exchangeable A1 when the latter was large (e.g. 93 mequiv./kg rather than 107) and to over-estimate it when it was small (e.g. 2.4 mequiv./kg rather than 1.8). For this reason leaching procedures may be preferable, and a more convenient routine leaching m e t h o d was devised by leaching 5.0 g soil over-night with 50 cm 3 1.0M KC1. The regression equations and correlation coefficients between A1 released in these routine methods, and that in the first 10 cm 3 in the main leaching experiment are given in Table II. As expected, the shorter leaching m e t h o d was preferable. A shaking m e t h o d is more convenient for routine work than a leaching method, and that using 4.0 g soil with a total of 100 cm 3 KC1 has been found to be suitable both for A1 and for other exchangeable cations. A m m o n i u m chloride can be substituted for KC1 if exchangeable K ÷ is required because these two salts were shown earlier (unpublished work) to be equally effective in displacing A1 from acid soils.

ESTIMATES OF SOLUTION COMPOSITION

Experimental methods The concentration of the solution in equilibrium with soil was estimated by a serial saturation procedure suggested by Dr. B.G. Davey (personal communication, 1973), based on the principle that if the composition of a solu-

T A B L E II R e g r e s s i o n e q u a t i o n s a n d c o r r e l a t i o n c o e f f i c i e n t s (r) b e t w e e n m e q u i v . / k g o f e x c h a n g e a b l e a l u m i n i u m (Y) a n d e s t i m a t e s (X) given b y a n u m b e r o f r o u t i n e m e t h o d s

S h a k i n g soil w i t h 80 c m 3 1 . 0 M KC1 a n d w a s h i n g to 100 c m 3 L e a c h i n g 5 g w i t h 50 c m 3 KCI

1 g soil 4 g soil 10 g soil

Regression equation

r

Y = - 3 . 6 + 1.22 X Y = - 0 . 7 + 0.98 X Y = - 0 . 2 + 1.23 X

0.971"** 0.973*** 0.968***

Y = - 1 . 7 + 0.99 X

0.988***

97

tion remains unchanged when shaken with a soil, then that solution must be in equilibrium with the soil (Schofield, 1947). The electrical conductivity of the solution was used as a sensitive indicator of total ionic concentration. A 200-g sub-sample of slightly moist soil (sieved <2 mm) was gently shaken with 500 cm3 water for 0.5 h at 2O”C, and filtered under reduced pressure. The electrical conductivity of the filtrate was measured, the filtrate was shaken with a further 200-g sub-sample of the soil, and this procedure was repeated until there was no further increase in conductivity. The solution was then analysed for Al, Ca, Mg and pH. For five of the soil samples the conductivity was constant after 10 equilibrations, but for the other seven it was still rising and there was insufficient solution left to continue. These solutions were then analysed also for K, Na, N03, Cl, SO4 and SiOZ and synthetic solutions of similar concentration to the 10th equilibration were prepared. The saturation procedure was continued using the synthetic solution with fresh subsamples of soil until the conductivity remained unchanged. This occurred after 16 equilibrations and the solutions were finally analysed for pH, Al, Ca and Mg. Soil saturation pastes were prepared according to Jackson (1958, p.45). The pH was determined and the paste was then filtered under reduced pressure. The electrical conductivity of the filtrate was measured and the solutions analysed for Al and for (Ca + Mg). Further approximations to the solution composition, appropriate for routine work, were obtained by shaking the soil sample for 1 h at 20°C with calcium chloride solutions of differing concentration and at soil:solvent ratios of 1: 1 and 1:2.5. The pH was measured in the suspensions and the filtered solutions were analysed for Al and for (Ca + Mg). Activity coefficient corrections, calculated from data given by Robinson and Stokes (1965), were applied to the analytically determined concentration ratios (m~)~/(mAl)’ to obtain ion-activity ratios. This involved a multiplying factor varying from 1.3 to 2.0 depending on electrolyte concentration, or an addition of from 0.11 to 0.30 to log ARD_M. In view of the wide range of values for these ratios (see Results) this correction may be unnecessary for routine work. The Al concentrations in solution were not corrected for hydrolysis of the A13+ion to A10H2+ because these corrections become important only at pH values above 4.7 where soluble Al is very low, and for routine purposes it is sufficient to use the Al figures as determined. Results The complete data are too extensive to reproduce in detail, but Table III summarizes the range of values for the 12 soil samples given by the different methods of equilibration, for five variables. The serial saturation procedure gave the composition of the solution in equilibrium with the soil. This was used as a reference against which the approximate methods were compared, and the results for aluminium concentration and log ARD-A~ are given in Table IV.

3.9--5.2 3.7--5.5 3.8--5.3 3.9--5.4 4.1--5.5 4.0--5.3 3.9--5.1

71--2,600 55--2,200 150--1,280 520--1,460 n.d. n.d. n.d.

(~s)

Electrical Conductivity

0 . 1 5 - - 9.0 0 . 1 9 - - 7.6 0 . 8 0 - - 4.8 3 . 0 0 - - 7.0 0 . 5 0 - - 2.4 1 . 8 0 - - 3.8 8.40--10.6

(Ca + Mg) (mM)

0.015--0.27 0.004--0.40 0.005--0.22 0.009--0.43 0.007-0.10 0.01 - 0 . 2 6 0.01 - 0 . 6 0

A1 (raM)

0

--4.4

-3.2--3.9 -1.9--4.4 -1.4--3.9 -0.4--3.9 -1.0--2.6 -0.8--3.0

Log A R D _ A 1 .

Saturation Soil:CaCl 2 = 1:1 Soil:CaC12 = 1:2.5

extract 0.001 M 0.004 M 0.0005M 0.002 M 0.010 M

= = = =

0.03 0.03 0.04 0.06 Y= 0.06 Y = 0.06

Y Y Y Y

+ + + + + +

0.57 1.09 1.42 0.78 0.31 0.09

X X X X X X

0.906*** 0.804** 0.634* 0.347 0.341 0.326

Y Y Y Y Y Y

= -0.70 = -1.19 =-1.88 = -0.91 =-1.32 =-1.99

+ + + + + +

0.97 1.18 1.24 1.33 1.27 1.11

Regression

Regression

r

L o g ARD_A1

Aluminium concentration

X X X X X X

0.919"** 0.843*** 0.810"* 0.759** 0.795** 0.735**

r

C o m p a r i s o n o f six e s t i m a t e s (X) o f A1 c o n c e n t r a t i o n a n d o f log ARD_A1 w i t h v a l u e s (Y) given b y t h e serial s a t u r a t i o n p r o c e d u r e

T A B L E IV

* Italicized values are negatives; n.d. = n o t d e t e r m i n e d .

Equilibrium solution Saturation extract Soil:CaC12 0 . 0 0 1 M = 1:1 0.004 M Soil:CaC12 0 . 0 0 0 5 M = 1:2.5 0.002 M 0.010 M

pH

R a n g e o f s o l u t i o n c o m p o s i t i o n s for twelve acid soils

T A B L E III

99 The data in Tables III and IV show that the saturation extract gave a close estimate of the equilibrium-solution composition and it can therefore serve as a valid replacement for the longer procedure. In the dilute CaC12 equilibrations, the disturbance of the cation balance of the soil was less at higher soil:solvent ratios and although n o t shown so clearly by the statistical analysis it was less at lower electrolyte concentrations. This disturbance was negligible for soils containing > 50 mequiv./kg exchangeable Ca or having an equilibrium-solution conductivity > 1000 ~S, but it was considerable for soils with exchangeable Ca < 10 mequiv./kg and conductivity < 400 p S. The latter were the leached subsoils on uncultivated land, and these accounted for most of the p o o r correlations in Table IV. Equilibration with either 1 mM or 4 mM CaC12 solution at 1:1 ratio should therefore give a reasonable estimate of b o t h solution A1 concentration and log A R . Statistical tests described by Williams (1959) showed that the r values for A1 concentration by those two methods do n o t differ significantly from each other. The natural Ca concentration of most soils is nearer to 4 mM than 1 mM. There was no significant difference between the r values for any of the methods of estimating log AR. Subsequent experience has shown that clayey and peaty soils do not shake well using a 1:1 soil:solution ratio, b u t 100 cm 3 solution to 75 g soil appears to be satisfactory. GENERAL DISCUSSION The fraction of soil A1 investigated here, extractable with unbuffered salts containing non-coordinating anions, constitutes only a small part of the total A1 in a soil. It can be described as "mobile AI" and the equilibria between its components is established fairly rapidly: non-exchangeable Al ~ exchangeable A1 ~ solution Al The fraction described as "active AI" by Arai (1975) includes also undissociated surface A1 complexes that are coordinated by salicylate at pH 7, and is larger than the "mobile AI" considered here. For some soils it proved impossible to differentiate clearly between nonexchangeable and exchangeable A1, b u t an approximate value for exchangeable A1 can be readily obtained. Its usefulness in describing A1 status is however questionable. As far as liming is concerned, it is probably the total saltextractable AI that needs to be neutralized, rather than the exchangeable A1 as defined here. Furthermore, although exchangeable A1 governs the solution A1 concentration, it does this only indirectly, via the complementary cations and the selectivity coefficient for exchange ( K ~ 1) as expressed in the cationexchange equilibrium equation: KA1

b-

~_qA1)2 q0 = (qD)3

×

(aD) 3 (aA1)2

100

where q represents equivalents of exchangeable cations, and q0 = qA1 + qD. Because both exchangeable and solution A1 are dependent on the complementary cations, there seems to be a case for describing the cation balance of an acid soil in terms of the solution-activity ratio, rather than using a function of A1 alone. For the group of acid ~oils described here, ARD_A1 covered a range from 5 • 10 .4 to 8 • 103, and it is convenient to express it as a logarithm as in Table III. Its significance in terms of exchangeable (Ca + Mg) and A1 can be calculated from the equation above for a given value of the selectivity coefficient, KD_A1. For instance, if KD_A1 = 50 (typical values for topsoils are 20--100, Bache, 1974), a strongly acid soil having 0.5 of its CEC saturated by A1 has log ARD_A1 = 1.4, a moderately acid soil with 0.1 A1 saturation has log ARD_A1 = 3.6, and a slightly acid soil with 0.02 Al saturation has log ARD_A1 = 5.0. The contribution of the activity-coefficient correction to these values is small (-~ 0.25). Adequate approximate methods for estimating ARD-A1 were described above. ACKNOWLEDGEMENT

The authors are indebted to R.H.E. Inkson for statistical advice.

REFERENCES Arai, S., 1975. Extraction of active aluminium from acid soils in Japan with different reagents. Geoderma, 14: 63--74. Bache, B.W., 1974. Soluble aluminium and calcium aluminium exchange in relation to the pH of dilute calcium chloride suspensions of acid soils. J. Soil Sci., 25: 320--332. Coleman, N.T. and Thomas, G.W., 1967. The basic chemistry of soil acidity. In: R.W. Pearson and F. Adams (Editors), Soil Acidity and Liming. Am. Soc. Agron., Madison, Wis., pp. 1--41. Hill, U.T., 1956. Direct photometric determination of aluminium in iron ores. Anal. Chem., 28: 1419--1424. Hoyt, P.B. and Nyborg, M., 1972. Use of calcium chloride for the extraction of plant available aluminium and manganese from acid soil. Can. J. Soil Sci., 52: 163--167. Jackson, M.L., 1958. Soil Chemical Analysis. Constable, London, 498 pp. Jackson, W.A., 1967. Physiological effects of soil acidity. In: R.W. Pearson and F. Adams (Editors), Soil Acidity and Liming. Am. Soc. Agron., Madison, Wis., pp. 43--124. Kamprath, E.J., 1970. Exchangeable aluminium as a criterion for liming leached mineral soils. Soil Sci. Soc. Am., Proc., 34: 252--254. Lin, C. and Coleman, N.T., 1960. The measurement of exchangeable aluminium in soils and clays. Soil Sci. Soc. Am. Proc., 24: 444--446. Mitchell, B.D. and Farmer, V.C., 1962. Amorphous clay minerals in some Scottish soil profiles. Clay Min. Bull., 5: 128--144. Pratt, P.F. and Bair, F.L., 1961. A comparison of three reagents for the extraction of aluminium from soils. Soil Sci., 91 : 357--359. Robinson, R.A. and Stokes, R.S., 1965. Electrolyte Solutions. Butterworths, London, 2nd ed., 571 pp. Schofield, R.K., 1947. A ratio law governing the equilibrium of cations in the soil solution. Proc. l l t h Int. Congr. Pure Appl. Chem., 3: 257--261.

101

Sivasubramaniam, S. and Talibudeen, O., 1972. Potassium--aluminium exchange in acid soils. J. Soil Sci., 23: 163--176. Turner, R.C. and Clark, J.S., 1966. Lime potential in acid clay and soil suspensions. Trans. Comm. II and IV, Int. Soc. Soil Sci., Aberdeen, pp. 207--215. Williams, E.J., 1959. The comparison of regression variables. J. R. Star. Soc., Ser. B, 21 : 396--399. Wilson, M.J., 1973. Clay minerals in soils derived from Lower Old Red Sandstone till. J. Soil Sci., 24: 26--41.