Regression Towards Mediocrity in Hereditary Stature.

Regression Towards Mediocrity in Hereditary Stature.
Author(s): Francis Galton
Reviewed work(s):
Source: The Journal of the Anthropological Institute of Great Britain and Ireland, Vol. 15
(1886), pp. 246-263
Published by: Royal Anthropological Institute of Great Britain and Ireland
Stable URL: http://www.jstor.org/stable/2841583 .
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246 AnthropologicMaliscellanea.

ANTHROPOLOGICMAILSCELLANEA.

REGRESSIONtowvarMdsEDIOCRITYin IIEREDITARYSTATURE.
By FRANCISGALTONF, .R.S., &c.

[WITH PLATES IX AND X.]

TuIismemoircontainsthedata uponwhichthe remarkosntheLaw
ofRegressionwerefoundedt,hatI madein myPresidentiaAl ddress
to SectionH, at Aberdeen. That address,whichwill appear in
due coursein the Journalofthe BritishAssociationh,as already
been publishedin "Nature," September24th. I reproducehere
theportionof it whichbears uponregressiont,ogetherwithsome
amplificatiownherebrevityhadrendereidtobscurea,ndI haveadded
copiesofthediagramsuspendedatthemeetingw, ithoutwhichthe
letterpresiss necessarilydifficutlto follow. Myobjectis to place
beyonddoubtthe existenceof a simpleand far-reachinlgaw that
governsthehereditartyransmissioonf,I believe,everyoneofthose
simplequalitieswhichall possess,thoughin unequaldegrees. I
once beforeventuredto drawattentionto thislaw on farmore
slenderevidencethanI nowpossess.

It is someyearssinceI madean extensiveseriesof experiments
onthe produceof seeds of differenstize butof the same species.
Theyyieldedresultsthatseemedverynoteworthyan,dI usedthem
as thebasisofa lecturebeforethe Roval Institutionon February
md9tidohrn,1eom8t7te7edn. idoItctoraretpehpseaemnartbheldeetfyhr-eotimorptbahreeessnemtesxaelpeldeerrstiinhmaseninzteth,sbheuapttattrhoeebnoetfasfli,swfptaryhiseng
parentswerelarge; to be largerthanthe parentsi,f the parents
wereverysmall. Thepointofconvergencweas considerablbyelow
theaveragesizeoftheseedscontainedinthelargebagfulI bought
at a nurserygarden,outofwhichI selectedthosethatweresown,
andI had somereasonto believethatthesize ofthe seedtowards
whichthe produceconvergedwas similarto thatof an average
seedtakenoutofbedsofself-plantesdpecimens.

The experimentsshowedfurthetrhatthe meanfilialregression
towardsmediocritwyas directlyproportiontaol theparentaldevia-
tionfromit. Thiscuriousresultwas basedon so manyplantings,
conductedformebyfriendlsivingin variouspartsofthecountry,
fromNairnin thenorthto Cornwallinthesouth,duringone,two,
dorouevbetonftthhreeterguetnheorfamtiyocnoosnfctluhseipolnans.Ttsh,teheaxtaIcctroautlidooefnrteegrtraeisnsnioon
remaineda littledoubtfulo,wingto variableinfluencest;herefore
I did not attemptto defineit. But as it seemsa pitythat no

AnthropologicMaliscellanea. 2474

recordshouldexistin printofthe generalaverages,I givethemn,
togetherwitha briefaccountof thedetailsof the experimentin,
AppendixI to thepresentmemoir.

Afterthelecturehadbeenpublishedi,t occurredto methatthe
groundsof mymisgivingsmightbe urged as objectionsto the
igneqnueirraylchoandclbueseinonssu.rI rdoiudnndoetdwthitinhkmthaenmyosfmmalolmdiefnftib,cuutlatsieatsnhde
mattersof detail,itwould be scarcelypossibleto givea briefand
tyheetna bfluinlldatnodwahdaetqIunaotweapnesrwceeirvteotosubcehthobejseicmtipolneesx. pAllasnoa,Itiwonoafs
the phenomenonso, I thoughtit betterto sayno moreuponthe
subjectuntil I should obtain independentevidence. It was
anthropologicaelvidencethatI desiredc,aringonlyforthe seeds
as meansof throwinglighton heredityin man. I triedin vain
fora longandwearytimetoobtainitin sufficienabtundancea,nd
myfailurewas a cogentmotivet,ogetherwithothersi,n inducing
me to make an offerof prizesfor FamilyRecords,whichwas
largelyrespondedto, and fuirnishemd e last yearwithwhat I
tgwoiavtnehtnietsdop.taIhreteisrcpeuetlcuairrainnllqsyg.uuIiranryiodnwemdcmaynypssreeoclsfuapgreeaclityncusosltne,msttaekamibnpilgaaasnttseyhhaoelulpulodssibsoien-
bilityoftherecordsofheighthavingbeenfrequentldyrawnup in
a carelessfashionb, ecauseno amountof unbiassedinaccuracycan
iancctohuenitrfsoigrtnhifeirceasnuclett,hs,caotnartreadsetreidivnedtfhreoirmvcaolumespbaruitsoconnbsectuwrreeennt
differengtroupsofthereturns.

An analysisof the Recordsfullyconfirmasnd goes farbeyond
theconclusionIsobtainedfromtheseeds. It givesthe numerical
valueofthe regressiontowardsmediocritiyn the case of human
stature,as from1 to 2 with unexpected coherence and precision
[seePlate IX, fig.(a)], and it supplies me with the class of facts
I wanted to investigate-the degreesof familylikernesisn different
degrees of kinship, and the steps through which special family
peculiaritiesbecome merged into the typical characteristicsof the
race at large.

My data consisted of the heights of 930 adult childrenand of
theirrespectiveparentages,205 in number. In everycase I trans-
muted the femalestaturesto their correspondingmale equivalents
and used them in their transmuted form,so that no objection
groundedon the sexual differencoef statureneed be raised when I
speak of averages. The factorI used was 1-08,whichis equivalent
to adding a little less than one-twelfthto each female height. It
differsa verylittlefrom the factors employed by other anthropo-
logists,who, moreover,differa triflebetween themselves; anyhow,
it suits my data better than 107 or 109. The final result is not
of a kind to be affectedby these minute details,for it happened
that,owing to a mistakendirection,the computerto whom I first
entrusted the figures used a somewhat differentfactor,yet the
resultcame out closely the same.

I shall now explain with fulness wliy I chose stature for the

NUMBER OF ADULT TABLE I.

CHILDREN OF VARIOUS STATURES BORN OF 205 MID-P
(All Female heightshave been multipliedby

Heightsof Heightsof the Adult Children.
the Mid- 62 2 63-2 64 2 65-2 66 2 67 2 68-2 69-2 70-2 71'2 72-273-2 Ab
parentsin

inches. <Below

Above .. .. . . .1 3 ..
72-5 .1 2 1272
71-5 .1 3 4 3 5 10 4 9 2 ..
70-5 1 1 1 L 3 12 18 14 7 4 3 ..
69-5 1 1 16 4 17 27 20 33 25 20 11 4 ..
68-5 .. 7 11 16 25 31 34 48 21 18 4 3 ..
67-5 1 3 5 14 15 36 38 28 38 19 11 4 ..
66-5 1 3 3 5 2 17 17 14 13 4 ..
65-5 1 9 5 7 11 11 7 7 5 2 1
64-5 1 4 4 1 5 5 .. 2 .. .. .
2 4 1 2 21 1 . . ...
Below ..

Totals .. 5 7 32 59 48 117 138 120 167 99 64 41 17 1

Medians .. j .. 66-3 67-8 679 677 679 683 685 69,0 69 70..0 ..

NOTE.-In calculatingthe Medians,the entrieshave been takenas referringto t
Idsticasontnrdic.bluuTdtheedebdterhtewaatsetoehnn6ew2hhaenyaddtih6n3eg,hs6,ae3sadaanidndogp6st4re,ud&n,cb.6e,2stt-h2se,art6ei3bs-ef2iin,e&dgtcah.,seticrnoosnntdegbaitdiiaoosfnins6.2fT-ah5v,ios6u3irn8oafe,qi&nucat.le
Mid-parents.

Plate IX.

RATE OF REGRESSION IN HEREDITARY STATURE.
Fig(.a)

HEIGHT The Deviates of the Children are to those of DEVIATE
incinhes their Mid-Parents as 2 to 3. incinhes

72 34

_4

71 YviWhMenid-Parents are taller than mecliocrity, , D +3
their Childrentend to be shorterthanthey.a
j/9I0t
70 +619

68 ,75i 0~~~~

0

67~~~~~~~~~~~~~~~~~~~~-

65 l 4C 1 / WthheenirMCidh.Piladrreennttseanrde tsho boretteartllhearntmhaendtihoecyri.ty, -2
65
-aid65
A~ -3

~ ~~~~~~~- JY &i~~~R.Emslie1idi0.5

PlateX.

DIAGRAM BASED ON TABLE I,

(all femaleheightsare multiplieclb1y08)

MID-PARENTS ADULT CHILDREN
theirHeights, and Deviations from 68Linehes.

|ieiignhtsI Deivniaes| 65 66 67 68I 6I9 70 71 72 73
-1 0 +1 +2 (a)4
indces indies -4 ---3

72-

+3 8l
71-

+2 320 1 1 0 6 03
70-

69-69~~+~16l

68/ f . r ~~~~~~~~~~- -I:IXgS

67

J?p6 WJzCsmle lidi.

AnthropologicMal iscellanea. 249

subject of inquiry,because the peculiaritiesand points to be
attendedto in theinvestigatiownill manifesthemselvesbest by
doingso. Manyofitsadvantagesareobviousenough,suchas the
ease and frequencywith which its measuremenits made,its
practicaclonstancyduringthiry-fivyeearsofmiddlelife,its small
dependenceon differenceosfbringingup, and its incon.siderable
influenceon the rate ofmortality.Otheradvantageswhichare
not equaallyobviousare no less great. One of theseLiesin the
factthatstatureis nota simpleelementb, uta sumoftheaccumu-
lated lengthsorthicknesseosf morethana hundredbodilyparts,
eachso distinctfromtherestas to have earneda namebywhich
ibtocnaensb,sietsupaetceidfinietdh.eTshkeullils,tthofestphienme,itnhcelpuedlevsiasb,tohuettfwifotlyseegpsa,arnatde
thetwoanklesandfeet. The bonesin boththe lowerlimbsare
countedb, ecauseitis the averagelengthof thesetwo limbsthat
contributesto the general stature. The cartilagesinterposed
htbheetaawdntaehneendtbohofetnbheoesnsteohsle,etmswosofetalhtveeefsa.ecTehhtcjeoonfinlcetlsu,hadryepteahrreatltsihsotef.rtAmhceocrsoceuannluptmsohfeortuholudes
also be takenof the shape and set ofmanvofthe boneswhich
conduceto a moreor less archedinstep,straightback,or high
head, I noticedin theskeletonofO'Brien,theIrishgiant,at the
Cmoullseeguemoft, hSuatrhgeisonexsw,trhaiocrhdisi,nIabrseytlaietvuer,teohfetabaloluestt7skfeeleetto7niinncahneys
hwaodubldehenavmeobreeepnaartalrlieflalie-nncdrheiassbeadicfktchoenfsaecqeusoefnhtilssydtroarisgahlvteerrt.ebre
Thebeautifurlegularityin thestaturesofa populationw, henever
theyare statisticallmy arshalledin the orderof theirheights,is
duetothenumberofvariableelementsofwhichthestatureis the
sum. The bestillustrationIshaveseenofthisregularitwy erethe
ccuarrevfeuslomfemasaulreeamnednftmesmadaeleasttamtuyrAenstthhartoIpoombettariLniacebdofrraotmortyhine
theInternationaHl ealthExhibitionlastyear. Theywere almost
peTrfheecmt.ultiplicitoyfelementss,omederivedfromone progenitor,
somefromanotherm, ustbe the cause of a factthat has proved
veryconvenientin the course of my inquiry. It is that the
statureofthe childrendependscloselyon the averagestatureof
the two parents,and may be consideredin practiceas having
nothingto do withtheirindividuahl eights. The factwas proved
as follows:-Aftertransmutintghe femalemeasurementisn the
wwahyoaslerveeardaylelxydpilfafinerede1dI,,s2o,r3t,e4d,tahnedad5uolrtcmhiolrderienncohftehs,oinsetpoasreepnat-s
rate lines (see Table II). Each line was then divided into
sdiimffielarrceld1a,ss2e,s,3sh, o&wc.i,nignthcheensufmroibmetorhfceacseosminmwohnaicvhetrhaegcehoifldtrheen
alcavhreiglrdeargfeaeonmifnieltaiehcsheoifmrrsieigsxhptecbchetiilavderftearnmuasintlwidesou.rpItwhcpyaoornidnfsti,nothferdamteftyehrienencqoucmeir.Tmyhtooen
entriesin each of the differenlitnes werethenseen torunin the
VoL. XV. S

250 AnthropologicMal iscellanea.

fsaaminetwteanyd,eexncceypttothfaatlilnintthoetlwasot of themthechildrenshoweda
sets,one takingafterthe tall
tphareseunmtt,mheaortyThaebraleftIIertthhaestIhaonrntoenxe.; this,howeveri,s notvisiblein
Thereforew,hendealingwith
the transmissionof staturefromparentsto childrent,he average
heightof the two parents,or, as I preferto call it,the"mid-
parenta"l heighti,s all we needcareto knowaboutthem.

TABLE II.

EFFECT UPON ADULT CHILDREN OF DIFFERENCES IN HEIGHT OF
THEIR PARENTS.

Proportionper 50 ofcases in whichthe
Heights'ofthe Childrendeviatedto various
Difference amountsfromtheMid-filialStatureoftheir
Hbeeigtwheteson'tfhtehe respectivefamilies. Numberof
Childrenwhose
Parentsin Heightswere
inches. o ~ observed.

~_
0 C~l -I- ~--A~ - --

TTnder1 .. 21 35 43 46 48 50 105
1 andunder2.. 23 37 46 49 50 122
2 3.. 2146, 34 41 45 49 .. 112
3 ,, 5.. 35 41 47 49 108
5 and above .. 18 30 40 47 49 50 78
50
50

1 Everyfemaleheighthas been transmutedto its male equivalentbymulti-
plyingit by 1-08, and onlythosefamilieshave been included in which the
namberofadult childrenamountedto six,at least.

NOTE.-When these figuresare protractedinto curves,it will be seen-(1)
thattheyrunmuchalike; (2) thattheirpeculiaritiesare notin sequence; and
(3) thatthecurvecorrespondintgothefirstlineoccupiesa mediumpnosition.It is
thereforceertainthatdifferenceins theheightsof theparentshaveon thewhole
an inconsiderableffecton theheightsoftheiroffspring.

It mustbe notedthatI use thewordparentwithoutspecifying
the sex. The methodsof statisticspermitus to employthis
abstractterm,becausethecasesofa tallfatherbeingmarriedto a
shortmotherare balancedbythoseofa shortfatherbeingmarried
to a tall mother. I usethewordparentto save anycomplication
dhueiegthotoafftahcet acphpialdrrenentolyfbrbooutghhsteoxuetsb, byuttheesspe einciqaulliyrtihesat,thoafttthhee
daughterst,akesafterthe heightofthe fathermorethanit does
afterthat of the mother. My presentdata are insufficientot
enablemeto speakwithanyconfidencoenthispoint,muchlessto
hdeeArteenrdomitthyiinestreghtrheeraaatttmmioaserarrtiiitasofgfaesscettlaoetrcuitrliyeoa.nstaakseusblijtetcltefoorrninoqaucicroiuensintotfo

AnthropologicMaliscellanea. 251

shortnessor tallness. There are undoubtedlysexual preferences
formoderatecontrastin height,but the marriagechoice is guided
by so many and more importantconsiderationsthat questions of
statureappears to exertno perceptibleinfluenceupon it. This is
by no means my only inquiryinto this subject,but, as regardsthe
presentdata, mytest lay in dividingthe 205 male parentsand the
205 femaleparentseach into three groups-T, M, and S-that is,
tall, medium, and short (medium male measurementbeing taken
as 67 inches and upwards to 70 inches), and in counting the
numberof marriages in each possible combinationbetweelnthem
(see Table III). The result was that men and women of con-
trastedheights,shortand tall or tall and short,marriedjust about
as frequentlyas men and women of similar heights,both tall or
both short; therewere 32 cases of the one to 27 of the other.

TABLE III.

S.,t. 2~0~Mca.ts)e. s. 18Tc.,atse. s.
12 cases. M., m. T., m.
51 cases. 28 cases.
S., m. M., s. T., s.
25 cases. 28 cases. 14 cases.

S., s.
9 cases.

Shortand tall, 12 + 14 = 32 cases..
TShalolratnanddtaslhl,o1r8t 9 -_2277cs.cases
In applyingthe law of probabilitiesto investigationsinto here-
dity of stature, we may thereforeregard the married folk as
couples picked out of the general populationat haphazard.
The advantages of stature as a subject in which the simple laws
of hereditymay be studied will now be understood. It is a nearly
constant value that is frequentlymeasured and recorded,and its
discussionis little entangledwith considerationsof nurture,of the
survival of the fittesto, r of marriage selection. We have onlyto
considerthe mid-parentageand not to trouble ourselvesabout the
parents separately. The statistical variations of stature are
extremelyregular,so much so that their genieralconformitywith
the resultsof calculations based on the abstractlaw of frequencyof
erroris an accepted factby anthropologists. I have made much
use of the properties of that law in cross-testingmy various coln-
clusions,and always with success. For example,the measure of
variability (say the " probable error") of the system of mid-
parental heights, ought, on the suppositions justified in the
preceding paragraphs, to be equal to that of the systemof adult
male heights,multipliedinto the square root of 2; this inferenceis
shownto be correctby directobservation.

s2

252 AnthropologicaMl iscellanea.
The only drawback to the use of stature is its small variability.

One-halfof the population with whom I dealt, varied less than 17
inch fromthe average of all of them,and one-halfof the offspring
of similarmid-parentagesvaried less than 1'5 inchfromtheaverage
of theirown heights. On theotherhand,the precisionof my data
is so small,partlydue to the uncertaintyin manycases whetherthe
heightwas measured with the shoes on or off,that I findby means
of an independentinquirythat each observation,taking one with
another,is liable to an errorthat as often as not exceeds 2 of an
inch.

The law that I wish to establish refers primarily to the in-
heritance of differentdegrees of tallness and shortness,and only
secondarilyto that of absolute stature. That is to say, it refers
to measurementsmade fromthe crownof the head to the level of
mediocrityu, pwardsor downwardsas the case maybe, and notfrom
the crown of the bead totbe ground. In the populationwithwhich
I deal the level of mediocrityis 68? inches (withoutshoes). The
same law applying with sufficientcloseness both to tallness and
shortness,we may include both under the single head of devia-
tions,and I shall call any particular deviation a "deviate." By
the use of this word and that of " mid-parentage" we can define
the law of regressionvery briefly. It is that the height-deviate
of the offspringis, on the average, two-thirdsof the height-deviate
of its mid-parentage.

Plate IX, fig. a, gives a graphic expression of the data upon
which this law is founded. It will there be seen that the relations
betweenthe statures of the childrenand their mid-parents,which
are perfectlysimplewhen referredto the scale of deviates at the
right hand of the plate, do not admit of being brieflyphrased
when theyare referredto the scale of staturesat its left.

If this remarkable law had been based onlyon experimentson
the diameters ofthe seeds,it mightwell be distrusteduntil con-
firmedby other inquiries. If it were corroboratedmerelyby a
comparativelysmall number of observations on human stature,
some hesitation might be expected before its truth could be
recognisedin oppositionto the currentbeliefthat the child tends
to resemble its parents. But morecan be urged than this. It is
easily to be shown that we ought to expect filial regression,and
that it should amount to some constant fractional part of the
value ofthe mid-parentaldeviation. It is because thisexplanation
confirmsthe previousobservationsmade both on seeds and on men
that I feel justifiedon the presentoccasion in drawing attention
to this elementarylaw.

The explanation of it is as follows. The child inheritspartly
from his parents, partlyfromhis ancestry. Speaking generally,
the furtherhis genealogygoes back,the more numerousaTndvaried
will his ancestrvbecome,until theycease to differfromany equallv
numerous sample taken at haphazard from the race at large.
Their mean staturewill then be the same as that of the race; in
other words,it will be mediocre. Or, to put the same fact into

AnthropologicMal iscellanea. 253

anotherformt,hemostprobablevalueofthemid-ancestrdaleviates
in anyremotegenerationis zero.

For the momentlet us confineour attentionto the remote
a-ncestraynd to the mid-parentageasl,ndignorethe intermediate
generations.The conibinationof the zero of the ancestrywith
the deviateof the mid-parentagies the combinationof nothing
withsomethingan, d theresultresembletshatofpouringa uniform
proportioonfpurewaterintoa vesselofwine. It dilutesthewirne
to a constantfractionof its originalalcoholicstrengthw, hatever
thatstrengthmiayhave been.

The intermediatgeenerationws ill each in theirdegreedo the
same. The mid-deviatien any one of themwill have a value
intermediatbeetweenthatof the mid-parentagaend thezerovalue
of the ancestry. Its combinationwith the mid-parentadleviate
will be as if,not purewater,but a mixtureof wineand waterin
some definiteproportionh,ad been pouredinto the wine. The
processthroughouits oneof proportionatdeilutionsa,nd therefore
thejoint effecotf all of themis toweakenthe originalwiniein a
constantratio.

We havenowordtoexpresstheformofthatidealandcomposite
progenitorw, homthe offsprinogf similarmid-parentagems ost
nearlyresemble,and fromwhose staturetheirown respective
heightsdivergeevenlya,boveand below. If he,she,orit,is styled
the" generan"t of the group,thenthelaw of regressionmakesit
clearthatparentsare notidenticawl iththegenerantosftheirown
ofTfhsperaivnegr.ageregressionofthe offsprintgo a constantfractionof
theirrespectivemid-parentadleviationsw, hichwas firstobserved
in thediametersof seeds,and thenconfirmebdyobservationosn
humanstaturei,s niowshowntobea perfectlryeasonablelawwhich
mighthave been deductivelyforeseen. It is of so simple a
characterthatI havemadean arrangemenwtithpulleysand weights
pblaaywrwetnhetilsclcshahntehbaevepimlryoeabcghaabainlnesiactvatelhrlyreagefceukhlloehnigeehrd(tesoedfeitPtahlraetytrceahInXils,dmfrieigsnso.bifo).nokfnTaohnwiysn
pgaifrte,nastaognel. yTahefmewoorfeemxcaenpytciohniladtlhreenawmoouulndtroefstehmegbilfettht, ehiermmoidre-
exceptionawl ill be the good fortuneof a parentwho has a son
whoequals,and stillmoreif he has a sonwhooverpasseshimin
that respect. The law is even-handed;it leviesthe sameheavy
succession-taoxnthetransmissioonfbadnessas wellas ofgoodness.
If it discouragesthe extravagantexpectationosf giftedparents
that their childrenwill inheritall their powers, it no less
discountenanceesxtravagantfearsthat theywill inheritall their
weaknessesand diseases.

The converseof this law is veryfarfrombeingitsnumerical
opposite. Because the mostprobabledeviateof the son is only
tthwaot-tthheirmdtsohsattporfohbiasbmleidde-vpiaarteenotfatghiete,dmoeidsn-poatrinentthaeglieesas3,tfoorllo1w
thatoftheson. The numberof individualsin a populationwho

254 A4nthropologiMcailiscellanea.

differlittlefrommediocrityis so preponderantthat it is more
frequentlythe case that an exceptionalman is the somewhat
exceptionalsonof rathermediocreparentst,han the averageson
ofveryexceptionapl arents. It appearsfromtheverysametable
of observationsbywhichthe value of the filialregressionwas
determinedwhenit is read in a differenwtay,namelyi,n vertical
columnsinstead of in horizontalines,that the most probable
mid-parentagoefa manis onethatdeviatesonlyone-thirads much
as themandoes. Thereis a greatdifferencbeetweenthisvalueof
a3I2 hanaldftthimenesusmmearlliecras,clionncve4er-,soemre9n-, tbieoinnegmdabuolvteiopfliAedi;nittois31f,iosuerqaunadl
to 8

It willbe gatheredfromwhathas beensaid,thata mid-parental
fadnrevcoemiastttheroeafslueoannnietduionntihttihemredpnaletixae,stabgymemnideer-tgahtroiaodnnsotdfhpa-at,rIeanncdtdaaneslvnoiooatntse.otfoIp3,nraoemcwkitodon.
explain,butwilldo sointheAppendixt,hattheheritagederivedon
an averagefromthe mid-parentadleviate,independentloyfwhat
it mayimply,orof whatmaybe knowncioncerningthe previous
osainnnlcgye-ls-et. rpyari,senotnilsyo1.nlyC1onasneqdutehnattlyft,rhoamt saimsiinlagrlleydgerrainvdepdfarreonmtias
Letitnotbe supposedfora momenthatanyofthesestatements
invalidatethegeneraldoctrinethatthe childrenof a giftedpair
are muchmorelikelyto be tghifattetdhtehaabnletshtecchhiillddorfeononfeagimfteeddipoacirre
pair. Whattheyassertis
is notlikelyto be as giftedas theablestofall thechildrenofvery
manymediocrepairs. However,as,notwithstandinthgisexplana-
tion,somesuspicionrmaryemainofa paradoxlurkinginmystrongly
contrastedresults,I will call attentionto the formin whichthe
table of data (Table I) was drawn up, and give an anecdote
connectedwithit.
It is deduced froma large sheet on which I enteredevery
child'sheight,oppositetoitsmid-parentahleighta,nd ineverycase
eachwas enteredtothenearesttenthof an inch. ThenI counted
the numberof entriesin each square inch,and copiedthemout
uasndtheresytaopopdbeyaerxinamthpleetsa. bTlhe.usT,ohuetmofeaatnoitnaglooff9t2h8ecthabillderiesnwbehsot
werebornto the 205 mid-parentosn mylist,therewere18 ofthe
heightof 69-2inches (countingto the nearestinch), who were
bornto mid-parentosf theheightof 70 5 inches(also countingto
thenearestinch). So again therewere25 childrenof70-2inches
bornto mid-parentosf 69 5 inches. I foundit hard at firsto
catchthefull significancoef the entriesin the table,whichhad
ccaumrieoouusrtedliasttiionncsttlhywathwenerIe"vesmryoinotthereed"stthinetgeonitnrvieessbtyigwarteit.Tinhgaety
each intersectioonf a horizontacl olumnwitha verticalone,the
sumoftheentriesin thefouradjacentsquares,and usingtheseto
workupon. I thennoticed(see PlateX) thatlinesdrawnthrough
entriesofthesamevalue formeda seriesof conceiitriacnd similar

AnthropologicaMl iscellanea. 255

ellipses. Their commoncentrelay at the intersectionof the
verticaland horizontalines, that correspondedto 68' inches.
Their axes were similarlyinclined. The pointswhere each
ellipsein successionwastouchedbya horizontatl angentl,ayin a
straightlineinclinedto theverticalin theratioofA; thosewhere
theyweretouchedby a verticaltangentlay in a straightline
inclinedto thehorizontailn therationof1. Theseratiosconfirm
the values 2offravomermagide-rpeagrreensttsoioonfalfrsepardiynoagbn,tdaoinfeIdfbryoamodfifffsperrienngt
methodo, f
to mid-parentb,ecauseit willbe obviouson studyingPlate X that
thepointwhereeach horizontaline in successionis touchedby
an ellipse,the greatestvaluein thatlinemustoccurat thepoint
of contact. The same is true in respectto the verticallines.
These and otherrelationswere evidentlya subjectfor mathe-
monatthicraelaeenlaelmyseinsatnadrdyvaetrai,fsiucpaptioosninT. ghtehyewlaewreoafllfcrleeqaurelyndceyopfenerdreonrt
to be applicablethroughoutt;hesedata being(1) themeasureof
racialvariabilityw,hencethatofthemid-parentagmesaybeinferred
a(csouhnastianlrgtehadeoyfbfesepnreixnopgflaliikneedm,(i2d)-ptharaetnotfacgoea-ssfammeimlyvbaerriosafbitlhitey
sameco-familya),nd (3) theaverageratioof regression.I noted
thesevalues,and phrasedthe problemin abstracttermsuchas a
competentmathematiciancould deal with,disentangledfromall
referencteo hereditya,nd in that shape submittedit to Mr. J.
HamiltonDickson,of St. Peter's College,Cambridge. I asked
himkindlyto investigatfeormethe surfaceoffrequencyoferror
thatwouldresultfromthesethreedata,and thevariousparticulars
of its sections,one ofwhichwouldformthe ellipsesto whichI
havealluded.
I maybe permittedto say that I neverfelt such a glow of
loyaltyand respecttowardsthesovereigntayndmagnificonswt ay
ofmathematicaalnalysisas whenhisanswerreachedme,confirm-
ing,bypurelymathematicarleasoningm, y variousand laborious
statisticaclonclusionswithfarmoreminutenestshanI had dared
tohope,forthe originaldataran somewhatroughlya,nd I had to
smooththemwithtendercaution. His calculationcorrectedmy
observedvalue of mid-parentarlegressionfrom13 to 176 6 the
relationbetweenthe major and minoraxis of the ellipseswas
changed3 per cent.(it shouldbe as 47: /2), theirinclination
was changed less than 20 (it should be to an angle whose
tangentis 1). It is obvious,then,that the law of errorholds
throughoutthe investigationwithsufficienptrecisionto be of real
asnerdvdiciseca,onndntehcattetdheetvearrmioiunsarteisounlbstu,sotfstmriycsttlyaitnitsetricdsaerpeennodtecnats.ual
In thelectureat theRoyalInstitutionto whichI havereferred,
I pointedout the remarkableway in whichone generationwas
sI utchceereedheaddbytoandoistchuesrstthhaetpvraorvioeudstaogbeenictisessotfattihsteiscuacrl ovuivnatloefrtpharet.
fittesto,f relativefertilitya,nd so forth; but the selectionof

256 AnthropologicMaliscellanea.
hgeutmriadnosftaatlul rtheaessethcoemsupbljieccattoiofniansnvdetsotidgiastciuonssotwhiesnvaebrlyecsmureiotuos
questionunderits simplestform. How is it,I ask,thatin each
successivegenerationthereprovesto be the samenumberofmen
perthousandw, ho rangebetweenanylimitsof staturewe please
ttaolslppeacriefnyat,lst,ohrotuhgehtshheotratlml menenfraroemreaqruealyldlyesshceonrdt?edfHroowmeqisuatlhlye
balancefromothersourcesso nicelymade up ? The answeris
thatthe processcomprisestwo oppositesets of actions,one con-
centrativeand the otherdispersivea,nd ofsucha characterthat
theynecessarilyneutraliseone anothera,nd fall intoa state of
stable equilibrium(see Table IV). By the firstset,a systemof
scatteredelementsis replaced by anothersystemwhichis less
scattered;bythe secondset,eachof thesenewelementsbecomes
a centrewhencea thirdsystemofelementsare dispersed.

The detailsare as follows-:In thefirstof thesetwostageswe
tsthaerutnfirtosomftthheeppooppuullaattiioonnggrenoueprtahlleymi,nstehlveefsai,srsittgweneerreabtyiocnh;tahnecne,
intomarriedcouples,whencethe morecompactsystemof mid-
parentagesis derived,and thenbya regressionof the values of
tishdeemriidv-epda. rInentthageteshesceosntidllsmtaogreeecaocmhpgaecntseyrsatnetimsoafctehnetgreewnehreannctes
the offsprindgivergeupwardsand downwardsto formthesecond
generation. The stabilityof the balance betweenthe opposed
tendenciesis due to the regressionbeingproportionatteo the
fdstoerrvecitaectsohiofenuss.pnIrttiinliagtcastnrsedlsiwiklieeeingatfhostprarcreeibnianglaasngtcaaiebnsltsehteeqawuwieliiebgigrhhitut,tmh;tef;hnoetrhsifpetrtwihnoeg
weightbe liftedby the hand,it will obviouslyiall downagain
whenthe hand is withdrawna,nd,if it be depressedbythe hand,
the resilienceofthe springwillbe therebyincreaseds,o that the
weightwillrisewhenthehandis withdrawn.

A simpleequationconnectsthethreedata ofracevariabilityo,f
theratioofregressionain,d of co-familyvariabilityw, hence,ifany
two are given,the thirdmaybe found. My observationgsive
separatemeasuresof all three,and theirvalues fitwell intothe
equation,whichis ofthesimpleform-

v2p2 + f 2=P2,

wherev=2, p=147, f=1-5.
It will thereforbee understoodthatthe completetableofmid-

parentaland filialheightsmay be calculatedfromtwo simple
numbersa,nd thatthe mostelementardyatauponwhichit admits
of being constructeadre-(l) theratio betweenthemid-parental
and therestof theancestrailnfluenceas,nd (2) themeasureofthe
co-familvyariability.

The meanregressionin statureof a populationis easilyascer-
tained; I do notseemuchusein knowingit,butwillgive thework
merelyas a simpleexample. It has alreadybeen statedthatiiaii

PROCESS THROUGH WHICH THE DISTRIBUTION TABLE IV. GENERA

OF STATURES, IN SUCCESSIVE
UNCHANGED.

Statistical DistributionofStaturesin the several System

ic Ou .u GENERATION MID-PARENTS. GENERANTS.
a'n I.

III.@Sfi

73 - 2

72 - 2 1
6 7
+ 3~~~~6~

10

NOTE.-Te15 a saner 13

69 -+1- 17 26 29
26
6- 0 - _ _ _ _ _ _ _ _ _ _ _ __ 16 ___ _ _ _ _ _ _ _- __
17
6 29
2
67- - 1- 15
100
6t6he 2- 1-2 13
65- 3~~~~~~1~0~~~~~~ Lower Quartile.
6 .57

1

64 -0- 2

Total .. .. 100 100
0's
Probable derivation... 117

bpeaeeclrohcwNecnotaTshte,Ee.adL-bTiovowhvideeeerttcQhhaeuseaeUnrsputapimrleeebr. esQyrTuomhafremctadielsitee-r,sfi(fc2aeab)rlol2eyvn5decicbestaephstoeewssMeebdeeendatbiewaointevheeonerartnmhQdeueabUarneptlpovilweaerlautQneh,dueaactrnohtdmeiltMemhaeoondnsdieambtnheeliaeosnMwtveeciadthliu,anreniec,osafp(l3le6y)c8tc21ia5vilnlecelcadyhseitenshst.eboe"TetPhqwrue

258 AnthropologicMaliscelltanea.
thepopulationvaryless than1P7inch frommediocrityt,hisbeing
whatis technicallyknownas the"probable"deviation. The mean
deviationis,bya well-knowtnheory1,18 timesthatoftheprobable
deviation,thereforien this case it is 1-9 inch. The meanloss
throughregressionis l of thatamount,ora littlemorethan0,6
inch. That is to say,takingone childwith another,the mean
amountbywhichtheyfall shortof theirmid-parentapleculiarity
ofstatureis rathermorethansix-tenthosfan inch.

The stabilityofa Type,whichI shoulddefineas "an ideal form
towardswhichthe childrenof those who deviatefromit tendto
regress,"would,I presume,be measuredby the strengthof its
tendencyto regress;thusa meanregressionfrom1 in the mid-
parentsto 2 in the ofspringwouldindicateonlyhalfas much
stabilityas ifit hadbeento 1.

The limitsof deviationbeyondwhichthereis no regressionb,ut
a new conditionof equilibriumis enteredinto,and a new type
comesintoexistenceh, avestilltobe explored.

With respectto my numericalestimatesI, wish emphatically
to say that I offerthemonlyas being serviceablyapproximate,
thoughtheyare mutuallyconsistenta,nd withthedesirethatthey
maybe reinvestigatedby the help of moreabundantand much
moreaccuratemeasurementtshanthoseI have had at command.
There are manysimpleand interestingrelationsto whichI am
stillunabletoassignnumericavlaluesforlackofadequatematerial,
suchas thatto wbichI referredsometimeback,ofthe relative
influencoef thefatherand themotheron thestatureoftheirsons
ancldaughters.

I do not nowpursuethe numeroubs ranchesthat springfrom
the data I have given,as froma root. I do not speakof the
continueddominationofonetypeoverothersn, orofthepersistency
ofunimportanctharacteristicns,or of the inheritanceof disease,
whichis complicatedin manycasesbytherequisiteconcurrencoef
twoseparateheritagest,he one ofa susceptibleconstitutiont,he
otherof thegermsofthe disease. Still less do I enteruponthe
subjectoffraternadleviationand collateradl escentw, hichI have
also workedout.

APPENDIX.

I.-ExperimentsonSeedsbearingontheLaw ofRegression.

I senta setofcarefullyselectedsweetpea seedstoeachofseveral
countryfriendsw, hokindlyundertookto helpme. The advantage
sotoehfflaesmtcwttuheecedehttyhpaterhemeaesassspoavmhtheeerressoicuitzabhelaje,.enrcdstToethefhdee-sxyaiptaaselrlrtehitmhaaltesetsonheateefhdytadserirodncoyntnoahnsteucdsrlatopmisnrsegofeplmeiorfditinicale.riIuseet,
botanists. Each sEeatcchonptaacikneetdsceovnetnaipnaecdkteetnss,neuemdsboefreexdKac,tLl,ytMh,e
N, 0, P, and Q.

AnthropologicaMl iscellanea. 259

sameweight; thosein K beingtheheaviest,L the nextheaviest,
and so on downto Q, whichwas thelightest. The preciseweights
are given in Table V, togetherwith the correspondingdiameter,
whichI ascertainedbylaying100 peas ofthe samesortin a row.
The weightsrunin an arithmetisceries,havinga commonaverage
differencoef 0-172grain. I do notof courseprofessto workto
thousandthosfa grain,thoughI didto less thantenthsofa grain;
thereforethe thirddecimal place representsno more than an
arithmeticawl orkingvalue,whichhas to be regardedin multiplica-
tions,lestan errorofsensibleimportancsehouldbe introducedby
its neglect. Curiouslyenough,the diameterswere foundto run
approximateliyn an arithmetisceriesalso,owing,I suppose,to the
lmarisgsehradpieaamndetceorrtrhuangaiftitohneosyfhthadesbmeeanlleprlsuemedpse,wdohuitchingtavoespthheemreas.
The resultsare givenin Table V, whichshowthat I was justified
in sortingthe seeds bytheconvenienmt ethodofthebalanceand
weights,and of acceptingthe weightsas directlyproportionatlo
the meandiametersw, hichcan hardlybe measuredsatisfactorily
exceptin sphericasleeds.

In each experimenstevenbedswerepreparedin parallelrows;
each was 11 feetwideand 5 feetlong. Ten holesof 1 inchdeep
weredibbledat equal distancesapartalong eachbed,and oneseed
was putintoeachhole. Theywerethen bushedoverto keepoff
thebirds. Minuteinstructionwseregivenand followedto ensure
uniiformitwyh, ichI neednotrepeathere. The end ofallwas that
tbhagessetehdastIassetnhte,ylebtetcearmedefrriopmewK etroeQc,otllheecstaemdferloemttteirmsbeetiontgimsteuicnk
at theendsof the beds,and whenthecropwas comingto an end
thewholefoliageof eachbed was tornup,tied togetherl,abelled,
and sent to me. I measuredthe foliageand the pods, both of
whichgave resultsconfirmatoroyf those of the peas,whichwill
be foundin TableVI, thefirstand lastcolumnsofwhicharethose
tehnaotuegshpheocwialtlhyiensettewreoswtuesr;etohbetraienmeadi.nIitnwgciolllubme snessehnotwhaintfgocrleeaarclhy
increaseofoneuniton thepartoftheparentseed,thereis a mean
increaseof onlyone-thirdof a unit in thefilialseed; and again
that the mean filialseedresemblestheparentalwhenthelatteris
about15-5 hundredthosf an inch in diameter. Taking then155
as thepointtowardswhichfilialregressionpoints,whatevermay
be the parentaldeviation(withinthe tabularlimits) fromthat
point,themeanfilialdeviationwill be in the samedirectionb,ut
onlyone-thirdas much.

This pointof regressionis so low thatI possessedless evidence
thanI desiredto provethe betteringofthe produceofverysmall
seeds. The seeds smallerthanQ weresucha miserablesetthatI

Ictoudlidd,hhaorwdelyvdeerah,lawpiptehntthheamt .inMaofreewovoefrtt,hheeyswetesrseovmereyoifnftehretQile.

seedsturnedoutverywell.
If I desiredto lay muchstresson theseexperimentsI, could

make mycase considerablystrongerby going minutelyinto the

260 AnzthropologiMcailscellanea.
detailsof the severalexperimentsf,oliageand lengthof pod in-
cluded, but I do iiot care to do so.

TABLE V.

WEIGHTSANDDIAMETERSOF SEEDS (SWEET PEA).

.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Letterof Weighotfoneseed 1L0e0nsegetdhsoifnrionwehoefs. Diamofeitnecrohfo. ne
seed. in grains.

K 111745507068 210 21
ML 11-026324 210922 2109
0NPQ *890 11117756'-0291 18
*718 111576

TABLE VI.

PARENT$SEEDSANDTHEIR PRODUCE.
Tabldeisfhfoewreinnsgtitzhese,pprroopdourcteidbonyaptaneruemntbseeerodfsasleseodosf(sdwifefeetpreeanssit)zeosf.

The measurementasrethoseof meandiameteri,n hundredths
ofan inch.

Diameters ofFilial Seeds. Mean Diameter of Filial
Seeds.
Diameter of Total.
Parent Seed. Observed. Smoothed.
Under Above
15 15- 16- 17- 18- 19- 20- 21-

21 22 8 10 18 21 13 6 2 100 17-5 17 3
20 23 10 12 17 20 13 3 2 100 1713 17-0
19 35 16 12 13 11 10 2 1 100 16 0 16 6
18 34 12 13 17 16 6 2 0 100 16-3 16-3
17 37 16 13 16 13 4 1 0 100 15-6 16 0
16 34 15 18 16 13 3 1 0 100 16-0 1517
15 46 14 9 11 14 4 2 0 100 15-3 15-4

II.-Separate ContributiofneachAncestotrotheHeritageofthe
Offspring.

Whenwe saythatthemid-parenctontributetswo-thirdosf his
tnabipsnheeocdetkeunhlsniliitmoimnhawrgiiepnsniltiaakemyotbm,nfeopodaihulfwyiteweatnidmghe,sdheodoetmpuetvsrnoieieatrttvtoehheti.ioeoonuLfkoigsefstnathfniomtsecwphemwpresldtihiinodeeairgvd-tt.g,it,aaiWhnrstaedeoenspfutdanhtprpohaepawtenorsmstseeoeanweimdlbdtttie-hlehqlptaaubhatterneitsneohtlngtm,apboth,uueuioagrnsf,ehtg

AnthropologicMal,iscellanea. 261

rohdtwptseuhhnereedDrvreeleuyynmmpoiicatoaaceta-fuirtdodeg3tshens,-weithbodeatattyfesyhnrfrdtyoicocyaehbseoletveulestnhsoisowttuautewofetciirmrefqeentstifsushsbohatspfasfumihaoluerattlenclifoye,onlntefauin;tostegscinafhxtchxaethitel(qpesmigltetmu+nideooneiatandcaila4tt3ee-sta+ir-gonote,afeaoryf1gtnn+smipyiit+ueeorsi&lsrpane-odo,ccoalpaps.rdrct,)oeaiauiosagnro=mdintiatnttni3heydhisuraa.foe,aellssfnratocacietwstmtrooci.oiwenFntosnpiiu.teoevrlrn?rfhyesHitetIeb,t,a,,emrhunbsnaiuteecmtuctcerpeaseoaesgptutnttfbeoshohrooesefeaterele

3 X 4=-2

bheeAirnintgoattghaewxeerosduulapdfpbroees-sihtiioninsetahcahtotfrsauncscmesissisvieodnism,o inthuattiotnthh,eepefrfopecetritvye

a (I+ + 3 + =) = (3r)

and thismust,as beforeb, e equal to a 2,3whencerI = 161.-
mgmodnreoiTveedsehit-ar-ueatwenntemhhcm,iseieorsinats"tdteotlrgiitan.mmekoantlraiahiebtgorielnu,(yasnstg.saliiuyytionpu)ntccpdwooboernu,serittntertitciohibtenoo.utTfshtgehaieinunmngmsettirdohha-reetaedifnoteicnhrssehcsasetnotgnwreaddnanaleoemnvsrtiiiagasdottnf-ieopoi"nfandprtoehaednnseioiyt-ral
iooi6iio(nnst1-nffs1d,)fTtf.caailhlhstmvnuopTeheiedsmrdohranesiutuealcniotytnsatdephguoglo2t,-ou,enlr.g4ftrma.rTsseootnoaTiffhadndnhwoie-pdtudepesaipsrnvarasaetrmademirwmlenieunavoi4nto6eyp,uit.vtsdlanoddfaeoulflti,oaefaif;itfvdla(rfph2tinlleaah)eybitrrimeumtnaeehc,pmtndiisctauditleiitwvridn-pigiegto-gtdhsparuiutuntnealahldprfadyilfatptelnutr-shnogtioemsetrmhnrmireteaacepsiny,enufolisabedolnetnt,iepxrasn.tdbeatrtofrHetgealtehke8uet4hn,nne,eehetainnecoern-remcrfa?dae6setttltesfhhsohia2ooo.nfeeerne

ExplanationofPlatesIX and X.
icftsta[nTohtshaanlTTtPheolgthvlshhvseuiaheeeaveeMtirpnloneesseuerronimhIteedetfXoohosnsiaitfrn,avneelthintlnlfahttteecliit.ihhofusigcnrrteeeht.haIsctirhts.itzaloilceaeiongdRasfsnvndhrl,ipaoacetncettnlrehantouedl.aeloioal]ie,ocnunfnbttftmeetdehihRsclhacaroneaceoetoewlhgwlhllffeuyrteaeaoTfhmaelyrfttacfseo.bohnsttsofihlhatToeofwmheonhfITiseco.neetaesarashbtHsmskeeealteieatsianhrdrueIb,eoeex-raodhmptdcevoiheaeoteferaeepa,atddesrtnshhne,yeaa,Sbdeotndmtm"ustwda.hteTMtititvrdhushheao-readelepuseumiomega.aetrnhaseoheraasorensne.ue"rtts

262 Anthropologica7liiscellanea.

The slopingline AB passes throughall possiblemid-parental
heights.
The slopingline CD passesthroughall the correspondinmg ean
heightsoftheirchildren. It givesthe" smoothed' resultsofthe
actualobservations.
TheratioofCM toAM is as 2 to 3, andthissameratioconnects
thedeviateofeverymid-parentvalalue withthemeandeviateofits
offspring.
The pointofconvergencies at the level ofmediocrityw,hichis
681 inches.
The abovedata are derivedfromthe 928 adultchildrenof205
miid-parentfse,malestatureshavingin everycase been converted
to theirmaleequivalentsbymultiplyinegachofthemby1-08.
Fig. b. Forecastsofstature. Thisis a diagramofthemechanism
bywhichthemostprobableheightsofthesonsand daughterscan
be foretoldf,romthedata oftheheightsofeachoftheirparents.
thTemheowtheeigrahntdsfXatahnedroFnthhaevierrteosbpeecsteitvosepcpaloessi;ttethoetnhthe heweiegihgthstsodf
willshowthemostprobableheightsofa sonand daughteronthe
correspondinsgcales. In everyoneofthesecasesit is thefiducial
markin the middleofeachweightbywhichthe readingis to be
made. But,in additionto this,the lengthofthe weightsdis so
arrangedthatit is an equal chance(an evenbet)thattheheightof
eachsonoreachdaughterwill lie withinthe rangedefinedbythe
uTphpeelrenangdtholofwsrelrise3dginecohfets=he2wfe;igthhta,toins,t2hexirlre5s0pienccthiv. escales.
A,B, andC arethreethinwheelswithgroovesroundtheiredges.
eTahseilyyasorneistcsraexwise.dtTogheetwheeirsgohatssMtoanfodrFmaaresainttgalcehpeiedtcoetehitahtetruernnds
iotfsealfthhraneagdstfhraotmpaastshesroeavdewr thhicehmisowvarbalpeppueldltewyoDo. r The pulley
threetimes
roundthe grooveof B and is then securedto the wheel. The
weightsdhangsfroma threadthatiswrappedinthesamedirection
two orthreetimesroundthe grooveofA,and is thensecuredto
thewheel. The diameterofA is to that of B as 2 to 3. Lastly,
a threadwrappedin the oppositedirectionrounidthe wheel a,
whichmayhave anyconvenientdiameteri,s attachedto a coun-
tweirIttphoiosiusoetab.fvfieocutsitnhtghaterwaihseinelgsAMBw, ainlldctahuesreeFfotrowefiatlhl,oauntadfvfieccetvinesrgds;a,
that is to say,the parentaldifferencems aybe variedindefinitely
withoutaffectintghe statureofthe childrens,o long as the mid-
pchaTraenhngetesadclh,talheeieognfhtfhteiasmtouafnlsechdhewaignihlgltbesded.ciBfhfuaentrgifsfertdothomet2mhoaifdtto-hpfetaarhmeenmotuaahnlleetis.g,ehatcihs
femaleheightbeing laid downin the positionwhichwould be
occupied by its male equivalent. Thus 56 is writtenin the
positionof60-48inichesw, hichis equal to 56x 1-08. Similarly6,0
is Iwnrtithteeanicntuthalempoascihtiionneotfh6e4w-8e0ig,whhtisrchuins ienqugarlotoov6e0sx. 1 08.
It is also

Anthropologicaltiscellanect 263

tallerand has a longerscalethanis shownin thefigurew, hichis
somewhatshortenefdorwantofspace.
Plate X. smThoiostihs ead"daisagdreasmcbraibseeddinonthTaebmleemI. oiTrth,heefnilginuersewisnerite
werefirst"
drawnthroughpointscorrespondintgo the samevalues,just as
isobarsor isothermasre drawn. These lines,as alreadystated,
ftohfortahtmteherdeeeyllawltipeiorsneeotsfr. tuIheeehlilarimvpesaeajosls,raotnodetxvhpeelriairifmnieeidndthhooreawvxaeclsua,loecsfuItlhahteaiidonnocsblhitnoaaiwtnieeoddn
anonfudmthseeorsaefltosaorrttehhn.eoTcthodoeirredeliclnitpaltysdeeepsirnaisvtseihdnefgrftoihgmrutorhueegisshtmhooneoiertcohofemtdrhmeessouencl.tesnjTuthsrete,
mpoisspfoaostmxikrtiueamionexnouoimffsm.,eabaInatiucndthwattvrihhleeleerrnbstoeesiuycnfgamoolhlltiliminoncweete.detttrrhhIpitecaotalwlelialdantiycileimlhosanhilsOnssoooNirasbishzaeteonosnasd,netsdeauOlniitMtnthteh,hagtawerttihrohtpwihecresshetalsaomoercaneeit
rlotihefks2eepdbteoircate3gid,volanienklaydielnO,otcLfhl,ieIinnntefodOtiMo3g.t.aah,nIeafdsirtasOhdhNejoarwcweehnonbautydlcdtobhboeroeedtdnhoinnthtaoatevredaleesitcgnotrehiesnse.csgiirdoanebdd,wuietintifths
I a-nnexa comparisonbetweencalculatedand observedresults.
The latterareinclosedinbrackets.
Given-
" Probableerror" ofeachsystemofmid-parentage=s 1-22.
Ratio ofmean filialregression=3.
"Probable error" of each systemof regressedvalues = 150.

Sections of surface of frequency parallel to XY are true
ellipses.
[Obs.-Apparently true ellipses.]

MX: YO = 6 17-5,or nearly 1: 3.
Major[Oabxse.s-1t:o m3i.n]oraxes = 47: V 2 = 10: 5-35.
[Obs.-10 : 5-1.]
Inclination of major axes to OX = 260 36'.

[Obs.-250.]
Section of surfaceparallel to XYis a true curve offrequency.

[Obs.-Apparently so.]
"Probable error" of that curve = 1-07.

[Obs.-10 or a little more.]