130 A methd f cnstructng rck-analyss dagrams a statstcal basks. 0T~ By W. ALF~.D ll~ch).ra)so.~, ~.Se., B.Se. (Eng.), F.G.S. Lecturer n Petrlgy, Unversty Cllege, Nttngham. [Read January 18, 1921.] D R. HARKER ' has famlarzed us wth the use f varatn dagrams, n whch the Pereent~lge amunts f a cnsttuent are pltted aganst the amunt f slca present. He appled these dagrams chefly t study selected rck grups, but als gave certan generalzed eurves f llustrate the chemcal prpertes f hs ' Atlantc' and ' Pacfc' faces. Such varatn dagrams based n an adequate bdy f analytcal data frm a useful means f cnstructng dagrams fr the cmparsn f rck analyses. Sme means f generalzng analyses becmes a necessty as ther number accumulates and the labur f cmparng ndvdual analyses ncreases. Cnstructn f the varatn dagrams.--after 'sme delberatn the analyses selected by ddngs ~ t" llustrate rck clazsfeatn were adpted as data fr the cnstructn f varatn dagrams. The tables nclude rather mre than a thusand analyses. The dstrbutn f these analyses was checked by plttng ther frequency curve t the same scale as that drawn by Harker" wth Washngt's euectn as a bass. The tw curves clsely agreed, except that the selectn by ddngs shws a slght excess f analyses n the neghburhd f 75 per cent. slca. Varatn dagrams t a large scale were cnstructed n the usual way by plttng all percentages f the cnstuent aganst the crrespndng slca value. As an example, the alumna plttngs are reprduced n fg. 1 t a very much reduced scale. Out f the several types f curve that mght be cnstructed, the maxmum was fund t be the mst useful fr purpses f cmparsn. The upper curve n fg. 1 enclses all A. Harker, Natural Hstry f the gneus Rcks, Lndn, 1909, chaps, v and v. J. P. ddngs, gneus Recks, New Yrk, 1913, vl. 2, pp. 31-341. s A. Harker, ce. ct., p. 148, fg. 42.
_ W. A. RC~AltDSON ON ROCK-ANALYSS DAGRAMS. 3t values f alumna except sme three r fur slated ca~s. Alumna als shws a well-defned mnmum curve, but n ths respect s an exceptn. All ther xdes gve sme values nearly zer fr any slca percentage. n the regn frm 0 t 80 per cent. slca there s sme uncertanty, partly because f the small number f the analyses, and partly because f the lablty fr ther cnsttuents t ncrease rapdly as the slca fals. Hwever, all cnsttuents ther than rn and ttanum shw decded tendences t decrease sympathetcally wth slca. The varatn curves cnstructed n ths way are cllected n fg. 2. Ferrus and ferrc xdes are added tgether, largely because, pltted 3~ ~ pe rceqla~ e.~.~176 -~M~ Mu~ V~m~dr~( u Rv :--f,,,~ ~,lum l. tt9 e~ ~ 1:22 ~., _ ~ ;0...... Fz. 1.--Varatn curves fr alumna n gneus rcks. separately, they gve rather rregular results. Phsphrc acd, and ther cnsttuents present nly n small amunts, were nt pltted. Rck dafframs.--a vertcal lne drawn thrugh a thckly clustered regn f fg. 1 shws that a number f rcks f gven slca percentage may have dfferent values f alumna. A hrzntal lne ndcates that a wde range f rcks wth varyng slca may pssess the same value f alumna. t s suggested that these curves may be used t cnstruct analyss dagrams t ndcate 1. The percentage f slca. 2. The percentage f anther gven cnsttuent. 3. The varatn fthls cnsttuent n rcks wth the same slca value. 4. The range f rcks wth the same percentage f the gven cnsttuent.
132 W. A. RCHARDSON ON r B n. cq
lqock-a~alyss DAGRAM. ~. 133 n ther wrds, the dagrams are desgned t shw bth the vertcal and lateral relatn f the analyss wth respect t a gven cnsttuent. Let the curve, fg. 3, represent the maxmum varatn f an xde wth respect t slca. Let a chsen analyss reprt a slca percentage B and an xde percentage b. f a vertcal lne be drawn thrugh B t cut the crate at B', the lne BB p shws the ttal varatn f that xde fr all rcks wth B per cent. f slca. Smlarly, f a hrzntal lne at heght b be drawn cuttng the curve at H and K, then HK shws the whle range f rcks that may pssess b per cent. f the xde. The pnt f tltersectn f the tw lnes gves the actual state f the analyss. m p( ~., / ~-~B, ', / ~,, E/ ~ ~\~F, "~....... - -1~,~. ~'. \ ".. ~.~,~ :... : ~T. ~'., ~ A ]5 C ~ Fr. 3.--Shwng mde f cnstructn f ndvdual and grup dagrams f rck analyses. Snce the gven percentage f the xde may be fund n all rcks wth slca values between ~" and X ~, these lmts may cnvenently be referred t as the Mlea razuje f that amunt f the xde. f, nstead f a sngle rck, t be desred t represent a rck famly, the fllwng cnstructn may be adpted t shw ts chemcal affntes. n fg. 8 let tbe extreme values f slca n the famly be A and C, and let vertcal lnes be drawn thrugh these pnts t meet the curve at A' and C p. Further let the extreme xde values n the famly be a and c, and at these heghts let hrzntal lnes ntersectng the curve at DG and EtV' respectvely be drawn. The area enclsed (shaded n the fgure) gves the affntes f the famly wth respect t the cnsttuent xde n a manner smlar t tle lnes f the ndvdual analyss.
134 W. A. RCHARDSON ON ~ wm
ROCK-ANALYSS DAGRAMS. 135 [uetr~{ns. 1. Rck GruTs.--T llustrate the applcatn f ths methd t rck classfcatns, dagrams f the platnc grups as defned by Hatch * are gven n fg. 4. The dagrams are cnstructed n the fllwng plan :- The vertcal clumns represent the great grups--theacd, ntermedate, basc, and ultrabase. The wdth f the clumn represents 100 per cent. slca. Hrzntal lnes dvde the clumns nt cmpartments, ne f whch s alltted t each cnsttuent xde. The famles wthn a grup are dfferentated by dfferent types R,.--.- m......, ; =!, ;... =..631 L... ;... J 10-SSJ........ J 9"29 11"87' ~0 L... l r%0 ',2s, ' CaO t-.---- ~... 150, -- 33.091 ~t9 0, :................ 130_ L ~O 14"~ +............., _%.~.. ' l.b8 12.8,! ~0 ' ' ' R,,! ' '.~ % O SOa 78.83 lo0 : 0 SC t 49"22 00 ; 0 35"05 S0=, 1O0... Fe. 5.--ndvdual rck analyses., Grante : Pne Lake, Ontar (H. S. Washngtn, U.S. Gel. Surv., 1917, Prf Paper 99, p. 56)., Gabbr : Red Mrs., Mntana (bd., p. 608)., Perdtte: Lake Abtb, Ontar (bd., p. 92~). f lne, althugh fr practcal use the famles wuld be separated n dfferent dagrams. The slca lmts f the grups are defned by vertcal lnes n each emnn, and the upper lmt t the varatn f the xdes s shwn by the thck lnes that span the slca clumns. These crrespnd t A'C' n fg. 3. Only thse prtns f the curves are drawn that frm the bundares f the grup dagrams. Smlar dagrams may be cnstructed fr any ther system f chemcal grupng. 2. ~vdua[ AnaZyses.--Fg. 5 gves the dagrams f three ndvdual analyses drawn n tle same plan as the grups n fg. 4---the areas n F. H. Hatch, Petrlgy f the gneus Rcks, Lndn, 1914, p. 159 et ~q.
136 W. A. RC:ARDSON ON ROCK-AN.ALYSS DAGRAMS. the case f sngle analyses becme lnes. The wdth f each dagram represents 100 per cent. slca. The cmpartments altt~d t the xdes are dvded n ths fgure by the hrzntal dtted lnes. Tle full hrzn~l lnes ndcate the amunt and slca range f each cnsttuent present. The vertcal lne s drawn at the slca value, and the lmt t the varatn f the xdes at ths slca percentage s ndcated by the pstn f the lalge dt n each cmp~,rtment. Fr cmparsn wth grup dsg,'ams, ndvdual dsgrams may be taken drectly frm the varatn curves by means f tracng-paper.