!
J. Jpn. Soc. Soil Phys.
No. +*3, p. 011. ,**2­²³*ῌ´µ¶**Error Correction Method for Hydrometer Analysis in Test Methodfor Particle Size Distribution of SoilsYasuaki KOMIYA* and Toshiya SHINJO*** Faculty of Agriculture, University of the Ryukyus, Nishihara, Okinawa, 3*-ῌ*,+-, Japan** Subtropical biomass research center, Nishihara, Okinawa, 3*-ῌ*,+-, JapanAbstractIn test method for particle size distribution of soils, sieve analysis result and hydrometeranalysis result may not be skillfully connected. It is said that in hydrometer analysis, much errorarises from many causes, and it brings about the error for the values of percent ﬁner by mass andparticle size calculated using Stokes’ law. This fact was estimated by the trial, and instrumentalerror of hydrometer, density error of the water, viscosity coe$cient error of the water wasclariﬁed. Hydrometer analysis result was corrected using these.

It was conﬁrmed that thecorrected hydrometer analysis result agrees almost with the sieve analysis result using ./ mmsieve, -, mm sieve and ,* mm sieve. Then, as convenient method, the method for moving particlesize curve by hydrometer analysis parallel in the vertical direction was proposed so that thepercent ﬁner by mass of -, mm particle size by the hydrometer analysis may agree with thepercent ﬁner by mass of -, mm particle size by the sieve analysis, and the result was good.
Key words : test method for particle size distribution, hydrometer analysis, error, -, mm sieve6;NF@KOPQCRS+,- TUBC+Y+ZWK2["#Q*\6^1Q*_ `BTaWbW6cQ!d123456789:*% ; <=>?

HVWXX>*T]D+*, ]@] ef!VWGCg=hN eSiKOPQ*@2ABCDEFG "#HIJKLMFCD+*,!"#KSjDkNFC*, JIS A +,*. .!"2 JIS lmn='(oT `BK# - =2 pX *.*1/ mm qrsKtQ*u+Dvw] pxyz{|} 6~])*+nTCqKtQ*lmn6=>*, ;E JIS !"#]Dpxyz{61Q*, lmn=2 Bg

C lmn=2!iX8BCD+*X l21 +,K}Bg;oKSjD'(X] pxyz{)*mnKtQ*5"# 2}T=+nTlmnXigVW];+TX>>? =2$%&*, ZW  /  ,***0 K2 .*.*1/lmn0 Ku+Dvw]D+*,mm O=z{X*, C2K;*TXT`e`¡FCHp8¢X£;*T5 lm,/$%i6+ n¤¥K¦§¨X©8];+T;eS? ª«')*+nK+FC*¬­)*+2 1/ mm =>(XD]gi25®6¯;+, ZWK2z{*, g lmn@F¯FC*¬¤p2°±*  3*-ῌ*,+ +** NPO *-ῌ*,+ : !"# $%&  '( -, mm )*+ +-68

+*3 . ,**2

/012 345  ms, V, t, Cm, L167"89:;<=>?2@
B F 1C A&34T =DE FG

HIJ K r 1L<&IJM;<3NO h & rw 1 JIS 41P =" GQ RST3UV;<1B2W  rs 1 JIS 41X
YZ=[E:" GQ 89:3B2\WV;<]B2W  A 8 W^_8  `!&NO ;<1ab4? Pῌ+ '#$% (!

rsVrrwrwrsrCmFms rsrw῎rsrwrs+**"#$%&d )Fig. + Combination of sieve test result andhydrometer result observed in particlesize distribution curverwr sd ῌh῎,῍ hrsrwrwrsrsrw῏῏AAP d r h rw rs 1 `!;41 .* mm cd45  A GQ  !

< ;< e"f #g;<  ;<"#$& '#$ hi1jῑ+ k@8 W .

 ;<n opqr3%?   b 1 ! "UOG1&s P d r h rw rs & <45 Z ;<45  lm/0&WQHhiE '#$%1&t&'(? A )]unH ;< ^_3v*?:" d 1 ! "U&! B"hi&W 3 +,wxy ,*** z{ ;<|_@ ;<PA 8 Whi1}3KaZ~-O4R&d n":X0E:I  X0 &E: VE:"W"i./ 30EGiW +,*** ml T,2* ms// g rs,.1 g/cm- &@ @2 X345   a & c 1 !

,+ "U&1~ hi&W  A 8 Wi1JIS! "#8M] '# BW;<3:"+.*/*&F  EHE 4H;<35 &'(?

1  a8  '#$3! "#$8Mz5 i45M  c  di1`?345 ":ab89:0? rs+**VPrwrCmF+ms rsrwd

  ῌ῍

3 *.**+"'#X F¯G° rs :Z rw :>$ I Cm : ² F :  h :   L :³$>´ Hµ7? gn : gDI t : ¶Jd ·`C45 <1 *.**+ &Q:678 +303 OG JIS 8 4 GQ ,*.**+/

#g;<30@ A&WM A8  `!;<ῑ + Xqq - H
#g:EGi/ 0 ;¡¢=k@ jῑ, £¤ (=<=@ 8 2:"+303 >+.*/* 2¥¦?$1b

678

1+/*PH§G&B @EGU"$ A?¨©B  r : 1 *.33/ ++.*** =k@8 2:"  /541 >2ῐ#g2 3 3 U +/* 41b ῎ 8M,..-ῐ &W AA P :  `! d :  V : e"f ms : *.**+ &IJM1 *.***/  `!&1q 9=X"=b ῐ C:E ª«D8¬­=E®E:±QG] 45 MpDTcosqVv, d rwv+ rῌM : #g° gῐ :   ! "#$%&ῌ+ 69'(Table + Dimension of hydrometerNo
)M g*+D cm/0-A1+-A+22-B223-B.,+-C.2/-C-14/2.
-04...-4+*2-04//-/4.-.
-/4-/+*4.1/*4.1/*4/+**4.1/*4.//*4.//*433/῍+4*/* ,-*L cml, cm++4-+*43/++4**+*42/++41+++42,./V cm-+/ 0,1 d-/43,-.42,,.+4+01-.43,+--42,,--41//+4**,++4**+1+4***,+4**+++4**+*+4**+3342,34/3343340/+*4-2+*4,22 3,45*66789:;<= >F ?4&@2A*BC >* 6A28 $ *.**+2>D3 +.*** ?EFGH I

 JDK3 +  6AH NO. /0 C NO.

.2/ L3I$ , M*= >* N2O BP8*NQR SF 0ῌ T/U#$2VDBCAW῍. 3῍+  ' ( X Y +.*/   6 8+.*. +.*- +.*, +.*+ +.** *.33/ ZL[ῌ   C\=$ ]$C^

>NKL_]$3<= >[9 ]$C`a3:;b`a >* BP3cd  @3A
H  L *.33/ 68 +.*/ [ #$Cefgh_*3ihef #$2_E jk3ῌ, blG mk3bn!FGAop X;Fig. , hydrometer*BC2?Oq"[PN blG2r[*K3]$ #$C1AKop3r[*2V : d, si./ cm FG*K3]$ W>D?  tu#Dv+ : vw-_*./ cm-$%2_ B? A]$xP 3yz?Ov, : {.-_*./ cm-|AONl}2~8PN *Vd : {.*BC2 [P B? -Cr : vw& gῌcm ]$3|AET/U'op3FG*K66rw : +/ ,& *.333+ gῌcm-789 JIS L3T : {.)* 1- dyneῌcm

A* +q :  ,* 2 8P*K2_2 D : *+ cm$3[P*A* ῌ : *T 32* cmῌsec,gh - ih M -  &AB>D? P -. +303 6 3/2 B-3< <EN'(3|AO* BP8 ,40,-6¡NCGC,4`a2W῍ L_ 3 &a¤ F1yz& C

TN=L_ BBL3 13±L *.***+ ZLO* ²8³G3_B>N]$3([P*3yz&C,[ LLK]]$3& 3?O730L_E1CK¢£ ! "%&23¡GL_,, JIS L3 ¥¦C§¨©yªE«¬­®¯°´ ®µ®E«¬­®¯°¶·E«¬­®

!"#$ % +*3 & ,**270ῌῌFig. -

Relationship between value of hydrometer and water temperature in distilled waterῌῌ.
Fig. .

Relationship between scale and instrumental error of hydrometer'()*+,-./0 12345678/.9:;<=>?@AB'( 3.+ g ABCB>?@ABDEFGHIJEK LDM$NE'( +.2 g, OP>?@AB'( *.0 g QIR-./0STAUVWMDXE*/.YZ- [23E\] JIS ^_`:;<=>?@AB'(abIJ456cde^f-H+Qgῌ/ gῌ0 ^h0_ ,*  +** ml 7i ,* g EIj- kl123gj3LDM$N_[2m2cdenoQpq7rs./0tu+\s./vd+7wxyz{7vd- 1_4560 -j-\Q3 |j34j0}7 ~Q. Ew>\/1Q4j0,* g `:;<=>?@AB'(_ +** ml JIS ^_456)*e_ 4567jj37.IR0 1}7K-HIJ7klQabIJ +* ml Z-./0 123456Ers./\/^+ 456cde_7,* 77I\\0^dGHZH)*e3/7\  !"#$YZLD IJ +* ml 456eE | ῌ , 7fH |ῌ, 7f}7 ,* abIJ +* ml 7 `¡ +310¢0}7456cde_£E¤G0H`:;<=>?@AB'(E¥d-.abI#$%&' : ()*+,-./0123456ῌ/Fig. /ῌ0Fig. 0Relationship between density of waterand dissolution quantity of dispersingagentῌ, 71

Relationship between viscosity coe$cientof water and dissolution quantity of dispersing agent789: ,* ;Table , Properties of saturated aqueous solution of dispersing agent at ,*?

<=ml

;g

9;
g

9>
gg/cm-pH@ABCDEFGH'IJK NaPO-0Na/P-O+*'ILIEFGH'IJKNa.P,O1MNEFGH'IJK+*+*+*+.43/2++4,21+*4./*34++3+411,*4/.1/42-334/+/343*-+4.30+4+,3+4*./.4224/+*4.

:*O-PQRSTJIS UR789: +* ml V[\4R]^_ `abEWXYZRVc WXd*e12*fWg\4O-`*ShgT-JIS *iX@ABCDEFG789:j'ILIE

FG789: +* ml VklO-YZRmn , gopa-`*SE q*rWX?VlT-Rsata *.**+. gῌcm-  *.**1.+*Paῌs u,c O-`*S- `av12*b-=wxy12V? ῍  ῎ *z{O- 12*b- =wxy12R ..*῍ SE|}~dT 5 1212v-12!d R  sd R*bhgSm 'U- / mm UR /.**,mm S- WXmhg ῌ1Fig. 1Measuring example of soil particle densityof respective grain diameter*b-12R12*b-md12*b-R T 12V34O-URO-bE 789:VV Wg*9O-5m£¤U-,-   (&  (V*rWXU- R "¡¢v¥ agT-UR*bhgSq῏1 R ©ª«¬5*­O-U-®¯&E ` UR *., gῌcm- ¦§¨WgT- `[°±S-²³|´µ¶eV? ῌ  ῍72ῌ2Fig. 2

  +*3, ,**2Comparison of soil particle size distribution curve modiﬁed by , error correction methods!"#$%&!'()*+,-. +/2*ῌ / *./-.+ῌ 01 .: ;<=>?@<:AB CA    +310*%23 '3 456789D.9!" + EFG HI+,/**  !

J.DKB' L' *., gῌcm-  ;+,%M +* ml NOP%"=" +2 cm QRSKTῌ U 0  +,d   V"W1#X +* ml %YZ[\!]$^%23' _B 

/ mm ..1 mm 01  __0SK 

4# >=a%*bcU ;+,)0! &%'dU '3ef!'gh<=. i+,ghj 0kR=0no G l =m l = ()0G()(pqr%)sU '3 JIS t RB"=- l =u*l =+ ./ mm -, mm ,* mm vl =%, !"l =m%wV'-+ +,.`D:=(-  xyz-, {.W13 a % | -} ῍ 2  A  - a%~=" - .zO .  /O +  O P 01 !'.   , mm l =*4!"4#!'> 

G %ef!'0 +/ F9:V"R'
G  JIS "w7. +,*  0 .2* 4567D%, ! +,<=>%?o'3i%e!'G "!'5]a%^6 /, g a%

,2 >0 ,  A 0 B  m"wV' A ¤¥¦§¨©ª«¬­® , g %"! 4567 NO. .2/ ¯CD°, *.**+3 %()02"3 JIS !'> G 70l = 7B.8KB  ;!' 567,bi+,0r+,%"="!
'>mm ;0@A ;,.kR=¡B!"= ;  +,U+, ,*}῍/ ¢£ _ 71.    V"G 7l= 7°±< *"=' B ¬²¬©ª«¬­® + g %">E°!"=  __0. JIS ! 4567 NO. 23/ ¯CD°, *.**++ %"³ _0%!"= =' }῍- ¢£ =B´="> 567,M¶!"F!' }῍. ¢£aµ"l = JIS Z 22*+ t RB l =+&.sGRB"=HI·¸JK¹ ,*** L'./01 : 234 56 789:-ῌ3, 
Fig. 3Comparison of clay fraction contentmodiﬁed by , error correction methods73ῌ+*Fig. +*Comparison of content of particle of+.. mm particle size or less by pipettemethod and hydrometer method +.. mm 

789 56 :-;<"$ JIS 789*+=>? :- @:-+ABCD, $"EFG HCI*J  KL M NOL PD* Q C9 56 :-=>+? :-UV789 56 :-W * XN'(C  DY  M ] ^NW3XL K% 789,`a*J D," O(_$YL -, mm b  , cd1eW C( f\hO( -, mm =>? WEi' Q C9 -, mm =>? -Wjk  D-Wo:-XN' 789p=>?

C9, -, mm Du*v RST'CINOO(Z=>[\gῌ +* +O(_$YL +..

mm W'LZ*J -+*./-.0῍tKO(C+.1῍ JIS ,@ 2.+  +..+῍ lmCWn'(C, d1e"$-'qCL rN#s =>[\789Q  KL M

*Z +.+ -,tKO(C  *+ wxyze{r^789W| }~B  W CL + WABk rrW -, mm 'L+  ./ mm *+78,J Lk 9ῌo +320 9 KZNCLk DYK*;<'L:-C%Y*Z=>? :-W!-῍ K*:-,KYrCD  ,***  KLAB*m $Y ,* mm *+ ,* mm Q C,*J Q C6Z hW"6(}^,J Lk*J  D ^N  M Wgῌ2-- JIS 234*+ gῌ+n'L ^ =>[O('L=>[\\Q C9789,N#NCL\*n'L  789+Q C

k 789FG W¡or +¢'C £}*9¤Nk$" ¥' O('L=>[\ Hª'(C gῌ3 + JIS  UVMm 1/ mm QC*¨©Cr m «*¬WR­'(®¨ N m 3  Wb+¦£§,X$Y¯,°*JOL¡o*m ­$C*J  '"'N,$ -, mm Q CQ C6W±=r'LZ*J  3² ³C

D""#$% &'( A )*+ +*.,῍ B )*+ /.3῍ µ¶:-, $" N  'L,O( -, mmQ

Q,?l BY(C  DY+:-3O(9FG,NC ¯´CC6W·}' ¯|´,N  +*3  ,**274 -, mm  -῍  !

* 456/789:;<=>?"<5"#$%&'()!*+,-./0123@&AB)5C/D5'(- 78"L3!5@&>?"M NO"'?NO6P!?"#$%78QR&'(MS()5 /M% TU -, mm 456&VM%45W 9:;&<=>?"FG)5 '("X6%K6&Y6 "#5&78Z[\E]^_ 2@/`ab@&c=5d@/e<M 78?>Mf#E"FG)5H -῍ IJ 5/DKg <6NOO  5 ShM NOK4K  556i"#5j -, mm '(kῒ ῑ ῔ ῐ&ldmi5S= 78_n6o"p456?>qM<6#E"r9"YEg  5sdtuv +310 : sd wx pp. 0/ῌ1+.

.ῌ ῎ ῍ ῏yz{|v }~JIS 2~"Xi578@/'( "6%MS >!SQRK#E 5+,*** : }~ / tuv/ yz{|v pp.

03ῌ21.

JIS A +,*. 78KZ[\E] "#5_ 2@/`ab@ 2@<?>sd@)5 Z[\E]
/_ 2@")5@KD `ab@")5@KAB6 3S j@#¡¢@ D6 +303 :2X#2  pp. ++2ῌ+,-.
ῌsdtuv +320 : ῌsd p. ,+.

{£¤¥v ,*** : ~456 + ; : ¦§¨456 ©ª«v pp. +ῌ++.

, Z[\E]¬_ 2@/`ab@῕ΐ2~ JIS A +,*. K 456QR/78QRE3­®M<6C/ 5 C!
KZ[\E&6578KB3¯3<°?>@M ^j±²"@L3!5S=/³´!%65 CC/&~²"#$%>?"MS 3S Z[\E] _
2@ _`ab@&>?"M C!>"#$%(MS78QRKVMS ./ mm 456 -, mm 456 ,* mm 456"#5456QR/XX#Hµ¶)5C/&·¸MS NO<'(/M% -, mm 456"#5456&VM j -, mm "Xi5456/78&78"L3!5d@/e<M C@&78?>MfK  5 : ,**0  3  ,3  : ,**2  /  +2 