Huygens Institute - Royal Netherlands Academy of Arts and Sciences (KNAW)
Citation:
Frets, G.P., On Mendelian Segregation with the Heredity of Headform in Man, in:
KNAW, Proceedings, 20 I, 1918, Amsterdam, 1918, pp. 435-448
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-1-
)
r
"On fr'/endelian 8egrepation with the Heredity oj'
Headforrn in Man". By G. P. FRETS. (Cornmunicated by
Prof. C. WINKLER.)
Anatomy. -
(Communicated
In
the meeting of June 30, 1917).
The significance of the shape of the head as an anthropologiral
charactel'Ïstic was bl'ought to IIgbt by the investigations of ANDERS
RETZHJS (18~2-1860) 1). RETZHJS introduced craniometry and based
tbe cJasslfication of races on the dirnensions of the cranium. He
dlscriminates the brachycephahc Ol' sbort and round, ocrasionally
square, and the dolirhocephalic or long and oval skull type.
With this methoq. of investigation began a new period in anthropology. The task was, to examine with varIOus peopJes and races
the index of the cranium i. e. the shape of the skull, expressed in
100 X width
h ' ft was furthel' inqmred into - fixed values
the proportion h I
t e engt
having been accepted for the dolichocephalic and the brachycephalic
skull - how dolichocephaly and brachycephaly are spread over
r
the various countries.
For the experimental doctrine of heredity tb'e significanee of tbe
shape of tbe bead is a different one, \·iz. its bebaviour in heredity.
This question is not entirely strange in anthl'OpoJogy, but \"as eliminated tbere. A. RETZIUS e. g. points out tb at - in order to be sure
of baving to do with the pure type, - one bas to choose material
from the country, and when he disposes of a considerable collection
of skulló, e. g. Swedish ones, he selects by a first comparative examination, a few of tbose that do not show acmdental or strange
properties.
The experimental doctrine of hel'edity examines the heredity with
regal'd to its signifieance in connection with the pl'oblem of tbe
origm of species. Besldes witb regard to its practical signifirance
fol' man, as to the breeding of animals and tbe cultivation of plants,
and also with regard to diseases of man and the lmprovernent of
race. This latter part of the scienee of heredity is distinguished I as
engemcs.
Only few investigations into the heredity of race-charactel'istics
1)
A.
RETZIUS.
Ethnologlsche Schriften. Stockholm 1864.
-2-
436
bave been made as yet. Tbe inheritance of tbe headfol'm has not
yet been in vestigated methodically, HURST 1) mentions in a list
of propertïes, wbich segregate according to Ml!lNDEL'S rules, th at roundheadedness is dominant over longheadedness and E. FISCHER 2) eoncludes, from bis bastard-material, that tbe headform is most probably
heredital'Y according to the mIes of MENDEL, FrSCHEH gives moreover
quotations from the literatul'e of non-mendelistie investigations, w:hich
are in favour of the theol'Y that brachycephaly is dominant over
doJichocephaly.
The above-mentioned twofold signification of analytic investigations
into heredity in man has induced me to investigate the heredity
of the headform. Tbe present fit'st communication regards tbe re8nlts
of a thousand measurements. My material consIsts of the visitol'S
ealling on the patients of tlle lunatie asylum Maasoord of Rotterdam.
By numerous joul'neys to Rotterdam and other places, consequently
somewbat in the manner of the field workers, I have measured as
completely as possible all tbe members of thosê families fol' whom
this was of impol'tance. Also a few other families have been inserted
into the tables. The extensive tables, on whieh the rommunication
rests, will be published later. All the measnrements ,aIld calculations
have been executed by myself.
The anthl'opologiral kriowledge of the headform may likewise
serve as a guide fo'r the choice of the shape of the head for
a Mendelean investigation. A. RETZIUS has not given any fixed values
for the dolichocephalic and the brachycephalic skull. In a letter to
DUVERNOY (1852) he says~) that with the dolichocephalic slmll the
length as a rule sUl'passes the width by t, w hereas with the brachycephalic skull this difference varies between tand -li-. These figllres
mean for the dolichocephalic skull an index \Talue
75 and for
the bl'achycephalic one an oscillation of the index between 83 and
88. G. RETZITJS adds to tbis infol'mation the interpretation th at bis
father left a space between the typical measures, fixed fol' the two
groups; he fixed centres, round which the various sizas of the skull
can be al'l'anged.
If this should
so, one might expect that, in case a population
contained besides dolichocepalic also brachycephalic race-elements,
the indices caiculated from many observations, being nnited in a
<
ue
1) C. C. HURST. Mendelian Characters in Plants, Animals and Man. S. 192.
Mendel Festschrift in Verh. d. nat. forseh. Ver. in Brünn. 49. Hd, 1910.
2) E. FrscHER, Die Rehobother Bastarde und das Bastardierungsproblem beim
Menschen. Jena H113.
S) l. c. p. S. 18.
-3-
437
curve, this difference would appeal' in the shape of the curve, viz.
a twotoppedness. One top wOllld be found at about 75 and another
at 85. As fal' as in literature such curves have been communicated,
no distinct twotoppedness is to be seen (RETzruS and FÜRST 1), BOLK ~),
E. FISCHER 3); comp. also WEI.CKER 4) S. 42.) Also in the curves of
my material they are failing (Fig. 1-5). This is possible, wh en the
dolichocephalic type, whilst crossing with the brachycephalic, originates equally all possihle intermediate shapes, b~t still the mor:e so, if
there are not two types, but sevel'al. The solution of these problems
is being searched for by the experirnental science of hel·edity.
Generally biological the question is: are the dolichocephalic and
the brachycephalic headforms characteristic marks of distinction
between two ra('es, consequently of elementary species, and expressed
mendelianly: is the headform determined by units of heredity
and by how many? ThllS the investigation of the headform is a
hel'editary-analytical problem,~ to be studied by family investigations.
The material, of which the composition is represented by the
Curves (Fig'. 1-5), consists of families from one generalion (brothers
and sisters), from two generations (parerits and ehildren), and fr'om
three generations (one to foUt' grandparents, parents and children),
At a tÎrst glance at the material the impression is made that of
a farnily of brothers and sisters the brothers of ten have lower indices
than the sisters. In the curves 6a and 6b 169 brothers ano169 sistel's
have been brought togerhel', w ho are chosen in such a way that
constantly frorn each fnmily as many brothers as sisters have been taken.
If consequently two brothers and two sisters of one family have been
measured, then two brothers and two sisters (i.e. lhe two elder)
have been insel'ted into the cur\'es. From these curves it appears
still more di,stinctly than fl'om the curves of the total nurnber of
men and women (Fig. 2 and 3) th at as a ru Ie the men have a
somewhat lower index than the women, Of the men (Fig. 2 and 3)
one top lies at 77,5, and another at 82, of the women the top lies
at 80; of the brothers (Fig. 6a ) the top lies at 79, of the sisters at
81,5. 33 brothers and 12 sistel's have indices nnder 77. The
mriability of width of the sisters (74-89) is likewise sornewhat
smaller than that of the brothers (72- 90).
1) RETZIUS und l<'URST. Anthropologia Suedica. 1902.
2) L. BOLK De bevolking van Nederland in haar anthropologische samenstelling.
(Uit Gallee. Het Boerenhuis. Utrecht 1908).
3) E l<'!SOHER 1. C,
4.) H. WELOKER. Untersuchungen über Wachslhum und Bau des menschlichen
Schädels. 1. Theil. Leipzig. 1862.
-4-
o
o
...
....
=
ca
IC
o
Fig. 3.
IQ
o
~
?'
p.
,/-1
1/0
Ss
BI
&0
118
J
:
I
Fig. 1-5. Curves glVlng a general survey of the material. Fig. 1. The material containing 1C
measurements. ~'Ig. 2 The measurements of women 661. ~'ig 3. The measurements of men 353. ~'ig
120 natives of the islands of Sou th Holland; of the parents and hkewise usually of the grand·parE
lt is known that they were born fhere. Fig. 5 100 persons, natives of Rotterdam, as Iikewise parE
and grand-parents.
-5-
439
If now we pass to' the examination of the behaviour of heredity
of the headform of the material at our disposal, then we follow,
when doing so, the way taken by other investigators (RUDIN.
DAVENPORT, .[.UNDBORG): we examine if the data admit of a Mendelian
explanation. We assume in this resvect that the index of length-
o
op. ~ t~ r 111 "1 18 9 90 , U J e~ ! B~ 1 8! j 9Q
Fig. 6.
169 brothers and 169 sisters. Of each family as
many brothers as sisters have been inserted.
width types the headform. A. RETZIUS has answered to the objection 1)
that the index represents only two dimensions, that experience
teaches the index may in reality be taken ,as the expressiol1 of the
headform. Another questIOn is, wh ether the Mendelian analysis of
rhe fartors of hel'edity of the shd.pe of the head can restl'ict itself to
trace the heredity of the index. In this case we should have to do
here with one pair of units of heredity (for the large and smaH
mdex, or for several different large indices). If the length and the
. width mendel separately, we have to do either with two pairs of
units of heredity Ol' with two progressions of it (respectively for the
large and the smaH length and idem width or for several diffel'ent
large Ilengths and different lal'ge widths). Both possibilities will be
examined. If the length and the width of the head mendel separately phenomena of segregation wlll come to expresslOn in the index.
We begin by tl'acing these. 'rhis gives us the advantage, that the
complete material, likewise that of not fullgrown persons, can be
considered. In the ~l'St place we examine if there is segl'egation.
-In favour of segregation plead these cases where, with littJe differences
in the indices of thc parents, the children show a gl'eat divel'gence
of values, or if a single child has a strongly de\'iating index. In
the tables land lIsome of these cases are collected.
1)
A.
RETZIUS,
I.e. S 57.
-6-
440
TABLE I.
Little difference of the indices of the parents, great difference of those of the children.
...
Famdy.
C1I
.t::
~
number
~
I
~
I
I
I~
.....0
Children
---
Sons
Daughters
I1
-
j:E
... '""'
-
\ Q,)
C1I
,Q-
E~
::s-
1 2 1 3 1 4 1 5 1 6 111 1 2 1 3 ~ 4 1 5 Z
I
I
86 83.1 79.1 80.6 82.4 I
XLVIII 79.7 78.7 79.9 83.6
I
I
LVI 80.1 79.9 76.3
I
LXIVb 77.6 76.2 73.2
CXXIVa 80.1 79.8 78 9 82.1 86 5 85.1
I
82 1 76 9/
CLXXIII 180. 1 81 3 87 81.8
CXXXVII 80
I
1
I
CLXXVII 81.4 81.4 8l,. 4 84.5
I
81.8 83.6 80.5
XL
82.5 81.8 76.7
CXIV
/
I
84.8
I
80.9
I
85.9 79 (8 83.1 79.7
I
82.9 81.4 82.51
83.8 83.2 82.8
I
I
81.3 79.4 83.6 79.7
I
77.8 83.6 81.7 82.1
11
78 I
Ir
-
I
80.1 81.7
XXXIVa 79.7 79.1 78.7 81 9 8::\.6 80.3 84.8
1
84.7 79.1 80 3/
LXXXVIIc 82.2 81.8 81 8
111
III
I
III
77.8
L XXXVIId 82.7 82.2/ 75.9 80.9 84.3
I
/80.4 8\.3 79.71 73 . 7 80.8 81.779.2 80.1 88.8/
I
XCIIIa 81.8 82.6 83.7 78 4 81.7 86.1
I
I
I
88.9 86.7/86.61 82
CLXXIXa 180 8 80.9 80.9 84 7
83.5 79.6
XXIId 81 4 81.7 80.4 82.9
/
,
LXL 80
83.8 78.61
XXIIc 80.2 80
85.4 80.8
LXXXIV 84.7 85
CLXXVIId 81
77.9
I
I
8\.6 III
111
III
V
V
I
'rhe examples of table land II may be l'egal'ded af> the expl'ession
of the fOl'mula DR X DIl
DD 2 DR
RR, those of table II
of a ffiOl'e complicated segregation (v~ge page. 441). When pel'using
the lists made fl'om the material, we are stl'uck both by the great
val'iability and also b.Y the Ït'l'egularity of the indices. The gl'eat
variability rendel's it unhkely that hel'edity should simp!y be detel'mined by à pair of units of hel'edlty bl'aehycephalJ;-dolichocephaly.
=
r
I
77.5 84.7 85.3 80.8
CLXXXIIb 83.1/81.382.681.7/79.4/
r
III
V
,
181.5 75.2
~III
+
+
J) Number of the large tables which will be published later.
-7-
J
441
If this were the case we should mOl'e frequently meet with homozygotic pairs of parents, to whom would conseql1ently belong a
group of l~hildren with very slight differences of the indices, These
however do not occur in the lists. The Table WhlCh contains the
families with four g'l'andparents of which consequently th ree complete generations are known fUl'nishes mo['eover the inoubitable proof
that the headform is not inheritable on account of a single pair
of allolllOl'phic factors.
Oonsequently we reject the indication of the motion of heredity
according to the monohy bridic scheme.
lL is very wel! possible that inheritance of the headform is de termined by a progression of units. Hel'edity goes then accOl'ding to a
type that NU,SSON-EüLE 1) (1909-1911) has systematically worked
out for cereals and that according to dIfferent investigators (LANG,
T. TAMMES a.o.) may be applied to their results. If the head form
in the concf'ption of NILSSON-EHLE is determined by a few pairs of
units, consequently Al A,As . .. and al a,a s . " then of a paIr of
pal'ents, the fat her can possess a fartor of beredity that the mother
misses, ano the reverse, or in hetel'ozygotic form. Among the children
may then, by combination of factors, occur headforms with indices
lal'ger, resp. 'smaller, than those of the paren tb. Generally a great
variabihty is to be observed with mutually slight differences, which
in a restricted l1umber of individuals may give the impression of
intermediary heredity. By special rombinations which, as can easily
be calculated, are very rare, greater deviations may occur. By a
separate breeding of the third bastard-generation (Fz) lt can be
proved that a cl'osb-breeding follows this srheme. Thei! diffe)'ent
proportions of l1Ilmber must occur, according to the number of
Mendelian factors which has been adopted for the explanation of
the second bastal·d-generation. This took in deed place in Nn,ssoNEHI,E'S experiments,
The data of different families plead for the fact, that, if the
heredity of the headfüt'm follows the ru les of segl'egation of 1Vl ENm~L,
factors wOl'king in the same direction in fhe sense of NILSSONEüJ,E must be admitted. 80 e. g. those, that have been gathered in
table VI, where one index deviates considerably from fhe othe1'8.
Likewise those of table VII, where the indices of the children
sUl'pass thóse of the parents on both sides or on one side.
We find cOllsequently in the collected material indications for the
1) H. NILSSON·EHLE. Kreuzungsuntersuchungen aD Hafer uÏld Weizen. I und 1I,
1909 u. 1911. Acta Universitatis Lundensis Lund.
29
Proceedings Royal Acad. Amsterdam. Vol. XX.
-8-
442
TAB L E 11.
,Series of indices a single one of which strongly deviates
Number'
of the
Family
I
....
<11
..c::
~
u...
-
76.3
I
......
0<11
.... :0
Chlldren
....
<11
..c::
Sons
ë
<11«1
Daughters
,Q ....
5<11
~
I
80.3
J
80.3
I
2
80.2
3
1
81.1
80.6
I
I
2
3
I
4
I
I
5
I,
84.3
Z::s..c::
....
I
~
III
76.5
81.5
77.3
79.2
84.1
82.7
®.9
78.6
XVII
77.8
81 7
78.7
79.2
79.5
77.7
88.4
84.8
CLXIV
79.2
77.8
76.3
79.7
76.8
75.8
CXCVI
74.7
79.5
74.1
82
81 3
1
I
77.8
83.5
78.3
77.8
CLIV
82.3 -
I
I
75.1
79.6
82.5
79.2
11
XXXVII
77.3
76.8
77:9
CCXV
78.1
81
77.5
XVI
80.5
83.8
73.5
84
85.6
82 3
82
11
CXVb
76.3
76.8
77.7
83
75.4
79.6
79
IV
79.6
\
85.6
III
III
view, that segregation occurs with the heredity of the shape of the
head, and that some pairs of factors of heredity are concerned in it.
A, second qllestlOn is, if, with this alternative hel'edity, the fir5t
bastard-generation (F1 ) is intermedIal'Y or that there exists dominance.
If, as HURST indicates f!'Om literature, brachycephaly is dominan t
over dolichocephaly, only dolichocephalic clllidren wiU be born from
the marriage of two dolichocephalig, pel'sons. For the brachycephalie
headfol'm is then defined by the factor D (dominant) the dolich~­
cephalic one by the facto!' R (recessive), the former can be repl'esented
by the formula DD or DR, the latter only by RR an~ the pairing
of two RR's gives onty RR descendants. 'rhe gl'eat variability, the
non-oceurl ence of families in w hom a definite headform Ïi5 nearly
con5tantly inhel'ited, the complication in the cases, in whieh three
generations are com pletely known bl'onght us to the conclusion,
th at not one sillgle pair of facto'rs determines tbe inhel'ilance of the
headfol'm, but we think it possible that some more factors working
in the same dÎl'ection are active in this respect. MOI'eo\'er dominanee
may occur, and the occurrence of families (tabie lIl) among wholll
only compal'atively low head-l':'umbers are found, seems to speak
in favour of it. Families (tablé IV) of whom one of the parents is
brachycephalic, and all or most of the children are br'achycephalic,
-9-
443
occur likewise. There are however also families (tabie V) for whom
this is not the case, Iikewise families are met with (tabIe VI), for
whom the indices' differ very little, but are somewhat higher thjtn
t110se that hold for dolichocephály. ConsequentI)' we cannot admit
beside Regregation simple dominanee of brarhycephaly.
The cases mentioned ah'eady (tabie VII), where the indices of
children snrpass those of the parenls, either on one Ol' on both sides
are especially in favonr of the possibility, that the inheritancy is
determined by a series of factors working in the same sen se, which
each indhridually give an intel'mediary first bastal'd·generation (F!).
This method of explanation can moreOVE'r very weU be apphed
to other phenomena of our material. The great variability of the
indices of the children and the slight differences of those of tbe
parents (tabie I) can e.g. be occasioned by the f~ct that the parents
contain the factors in a heterozygotic form, 80 that exteriorly they
are in termediary . Conseq uen tly di fferen t homozygotic, th \1S greatly
divergent values of indices, will occur among the childl'en. The
separate occurrence of a strongly deviating index-value is caused,
according to this view, by the rare combination of two or more
factors working in the same dil'ection in a homozygotic form (one
of the 16 cases in the dihy bridic scheme, one of the 64 cases in
the trihybridic one). The slight mutual differences of tne tables UI
and VI can be eXplained by admitting, that the forms of issue contain
nearly the same factors, so that consequently no new divergent
cornbinahons oecur in the children. The cases of table VIII containing examples of extreme vallles of indices of one of the parents
may be explained in the same way. A vel'y low index-value is
caused by the deficiency of, a very high one by the existenee in
homozygotic fOl'm of some factors wOl'king in the same direetion.
It is consequently clear th at among the children, as a 1'ule, the
extl'eme vaIlle will not occur.
What gives Iikewise significanee to this mannel' of explanation,
is tbe possibility of explaining the limitedness of the selection : by
selection no more ran be reached than the form th at contains all
the factors of hel'edity working in the same direction in a homozygotic forn). Examples in our matel'ial of "selertion-working" (accordmg to NUSSON-EHLE'S explanation, consequently öf combination
of factors) are the fam. lIJ and XXXIV (vide the genealogical trees,
p. 448). The pal'ents and el even children of fam. XXXIV have
rather Iow indices viz. the parents 79 and the children 72-79.
If now we admit that the pal'ents possess each a different fador
\
for brachycephaIy, with which consequently absence of a similar
J
29*
- 10 -
444
TAB L E 111.
Low indices of the parents and the children.
....
Number
of the
family
....
CIJ
CIJ
..c
~
ti..
..c
I
.0ECIJ
;:s..c
:!;
,
I
1
1
XXI
XXVII
XXXIV
LXXXVI
CXXXVI
CCV
IX
XXXIIa
XXXVIIa
LXI
LXXXIII
CLI
CXV
CLII
CLXL
CLXXXII
....
:ë
<IJ <'3
Daughters
Sons
"0
<IJ
Children
.
11
2
1
3
4
1
1
2
1
3
1
1
4
1
5
6
1
1
7
z.....
c
75.8 77.9 79.7 77.1
I
76.8 78 9 76.3
79.1 79.7 73 6 75.3 73.1 72
79 2 78.7 78.7 79.5 75.5
78.5 80 78 3
78.1 78 9 78.2
I
76 9 74.2 81.2
I
I
79.8 79.4 78 8
/
79.1 75.6 75.8 77 9 77.8 77.4 78.6 I
I
75 77.8 78.5
I
77.6
I
17.5
77.4 78.2 78.2
11
I
76.5 74.6 73.7
75.9
II
79.2 76.5 75.7
11
17.2 78 2 76.8 77 .1 76 8 79.8
76.7
79.5
11
74.2 76.9 77.6
11
79.2
76.5 74.9 ?6.61
II
78.3
78.8 78.5
11
73 77.8 74.3
74.9 76.3
I
III
78.8
79.9 77 .1
11
77.2 78.1 78.1 79.2/
79.3 77.3 78 8
V
77.6 79.8 78.3 78.3 78 74.5 80.7 77.4 79.5
1
[
-
/
TAB L E IV.
Families of which one of the parents and most of the children have a high index.
Number
of the
famlly
....
<IJ
..c
....
....
CIJ
..c
~
-
Sons
0
OCIJ
....<IJ :ë
<'3
Daughters
.0 ....
:!;
I
IlIb
LXXXIII
LXXXV
LXXXVIII
CLXVII
CCXXXIV
CLXXVIII
CLXXIX
XVIc
LXXXVIIe
CLXXIXb
CCXlI
IIIa
CXCVII
-I~
Children
I 82.4)78 3
77.3 85.3
75
84.7
78.3 83.2
76.4 89.2
82.2 87.3
75.5
74.3
77.8 85.6
75.4 87.8
77.2 85.2
2
1
1
3
1
1
83
84 7
83.6 78.9 79.4 81.3
83.3
76.4
83
85.8 86.1
86.3
84.5
80.4
84.2
82.5
85.9 84.3
81.6
78.7 86.2 81.9 84.6
80.6
85.8
82.5
84.5 82.4
83.6
85.7
86.5 85.3
- 11 -
2
1
3
1
4
1
I
5
'87.2 83.9 84 7 83
84.1 87.3
79.2 79
80
84
79.3
86.7 87.9
81.6/83.5
80.7
/
84.2 82.2 80.2 87
83.1
83 2 80.8 83
83.7 83.41 84 . 9
82.9 81.5
I
I
6
86.1
E
;:s
Z
I
1
1
III
I
1
11
11
111
111
111
11
II
11
445
TABLE V.
Famlly of which one of the parents has a higher index, whilst only one of the children has
a high index.
-
Number
of the
family
1ii
~
I t1.
,
<IJ
:ei
I
~
Daughters:S
Children
1ii
:g
~
Sons
'-6-
l' 2 , 3 , 4 , 5
11
-1---:--'··-2--'-'·-3---:-'4---:-,5-'''--6-'''--7-
lIIe 83 86 79.1 81 86.118585.218.2 80*)
81 8 80.8 84.5 86.584.2
CXLVII 85 79 79 380.284.4 80.8 85.2 78.5 78*) 86.8*) 81.2*) 80.2 81.8 '
CLXXIXc79.782.280.880.7
80.7 81.877.5
1
1 81.5
76.7
77.7
80
81.8
79.8
75.5
81 7
77
81 3*·)
82.6
77.1 **)
76.8
79.7
81.4
76.3
80.2
79.2
I
I
81.8
II
11
79.7 ï9.5 79.781.881.683.2 111
80
80.6 79.4
I
80.5 775 78.5
I
78.8
I
80.8 85
I
I
I
III
V
I
78.1 78.4
*) Sons, consequently 7 sons and 5 daughters and 9 sons and 2 daughters.
**) 2 daughters of the first marriage of the mother.
TAB L E VI.
Somewhat higher values of the indices of the
--
Number
of the
Family
...<IJ
'""
or:
a.>
and of the children.
t1.
I
79.6
8\.2
81.8
81.8
82.1
:s
I
1
82.1 I 80.8
84.4 83
80.4/ 78.7
77.8
80.2 80
81.6
80.3 80.7
79
82.3 78.8
I
2
I
3
82.2
78.8 81
80.4
81.3
~
QJ
1
81.4
81.3
79.1
77
81.5
81.6
79.9
80.5
82.6
- 12 -
I
2
I
3
I
4
I
5
I
6
79.2 78.1 78.4
78 78.5 83 5 82.2 82.4
77.5 77.6 79
8\.1
80 79.8 82.1
79.8 81.6
8\.3 82
I
....
....
0
.c
Daughters
Sons
0
~
:ë
Children
[
.c
1
XII
XV
CXXXla
CLX
LI
LX
LXXXVlIb
CLXXla
CLXXVlIb
parent~
QJ
I
~
III
1
CXCV 79.2 83.3 78.8
"
VII
84.2 74.5 79.7
XCVI
84.6 79
1
XVIb 78.7 84 77.9 80.7 79.783.4 80.7
XI 83.4 75 76
XIX 78.584.277.679.4
1
XVlIa 76.784.7 76.6176 76.2,
XXXII! 79.2 84.1 78.7
LXVIII 79.8183.6 78.7 77.8 79.8
LXXVI 78.7 85.9 77.4
CXXX 84.9 78.4 75.5
XXXIVc 75.3 83 75.585.2
XXIIe 75.6 83.881.181.1
XII 79.6 82.1 SO.8
11
78.1 78.7
..;
Z
I
I
I
I
11
II
IV
II
1 III
446
TAB L E VII.
Transgression of the variation-width to both sides towards the dolichocephalic and the
brachycephalic side.
Number
of the
Family
...
...cu
-
Children
cu
:Ei
,
Cl)
.c
.c
~
u..
Ö
:::e
Daughters
Sons
2 I 3 14 15
1
6
1 I 2 I 3 I 4 I 5 I 6
I
11
, I
-
81.7 79.4 82
XXII 77.91 81
76 3 75.6 79.7 76.5
XXXVIa 79.881.5 85.8
82.2
84~
I
CXCIII 81.8
85.9 85.2
76.7
I
V
74.1 70
76.7 76
IlIe 84.5 80.2 83.3 80
83.7
IIII 82.2 83.5
XXIIb 82.4 78
XXXVlb 78.8 84
81.5 84
84.6
86.7 88.2 79.7
LXXXIVa 80.4 75.5 84.7 79
81.3 81.5 83.3 82.2
LXXXIX 81.3 78.9 83.7 85.1
CIX 75.8 80
80.3
83.2
CXIII 183.1 83.7
CXXIV 82.2 86.9 80.8 84.9 86.3
CXLVIII 73.8 77.4 81.5
I
XXII 76.3 76.2 78.2 76.7
,
CXVa 74.3 78.2 79.8 76.8
79.7
I
83.1 83.5 81. 2 187 .4 80.2 86.7
81.11
I
1
81.4
1
83.8 80.3
I
89.5 84.'1
I
87.4 88.1 86 6
I
I
I
-
III
82.2
III
79.6 81.5 80
III
I
CLXV 85.1 83.8' 88.2 89.
CXXII
I
1
80
83.7180.5
1
87.5 91
83
CXVI! 77.8 76.3 80.7 81
I
178.6*) 79.1 75.6 75.8 77.9 77.8 77.4
86 83.5 86.7
XXXIV 79.1 79.7 73.6 75.3 73.1 72
LXXXVII
Il
III
XXXIVe 81.3 78.3 73.2
CXVIIJ
I
80.2 77.7 87.71 88
XXXIVa 73.1 76
~
IZ
I
1 76.4 78.1
77.3 82.8,82.6 79.8 80.3
XVa 83
cu
....0
)
CLXXI 178.3 79.8 77.4 81.7 82.7 81.5 81.2 81 8
-
~
.c
......
81.1 87.1
83.7 85.7
11
81.2 85.6 82.2
82.2 87.8
11
80.9 89
86.8 84.1 80.5 82.6
11
84.7 87.5
V
,
83.2
XXXIIe 76.7 81.7 85
I
*) Seventh daughter,
- 13 -
447
factol' (by which dolichoeephaly comes into existence) cOl'l'esponds,
and that they possess e. g. still a third factor in hetel'ozygotic form,
so tb at the formulas of the parents are AIAla~a2A3a3 <tud alalA2A~A3a3
then the low values 72 and 73 of the children are explained e. g. by
the absence of the two factors fol' bl'achycephaly (alala2a2A!as)'
The daughter and the two sons who marl'y into families where
several higher indices occur, will consequently among their seven,
five and foU/' ehildl'en see higher values show themselves, the son
73.1 however who, marries _a danghter 76 of a family whose members
have also rather Iow indicês, has a great chance, that there are
among his children some who represent a combination of factor5,
that answers to the absencè of e. g. threé factors of heredity
(alalblbl.CICI); suchlike childl'en Slll'paSS then the low in'iHces of the
parents towards th.e dolichocephalic side. This is indeed the case in
this family: Tbe two sons have an index of 74 and of 70. The
same reasoning,_ but now for the combination of the factors whose
TAB LEVlIl.
Extreme value of one of the parents.
Cl)
...
Number
of the
Family
Cl)
..c
~
I
I
...
Sons
ö
I ::s
1
LVII 72.6·) 78.9
LVIIa 72.6·)
LXXXVIIe
75.4
I
2
87.8
78.7
86.2
87.6
CXII
85.9
81.8
82
CXV
73
77.8
74.3
80.4
82.2
75 5
.
91.4
75.6
79.2
89.5
/75.3
80.5
80
79.8
82.3
XXXIVb
73.6
80.2
LXVI
CLXXIIIa
88.5
81.1
87
78.5
LVIIa 72.6
CLXXVIIa
-
81.9
I
1
1
85.7
1
79.8
75
73.5
3
75.3 ' 80.5
79
XVla
I
81.3
72
Cl)
Daughters
81.6
CVIII
~
.s
Cl)
.c
/
XLIII
:ë
Children
I
2
3
I
I
:S
.....0
4
I
I
I'
5
...:
Z
1
II
81
79,
84.6
83.1
III
82.2
83.1
II
78
81.3
II
II
74.9
76.3
75.5
82.5
79.7
79.7
82 ,
80.6
90
86.9
1I
80
86
") The same person i first and second marriage.
- 14 -
92
85.8 III
III
IV
79.8
81.3
III
III
)
I
80.5
I
IV
'I·
'I
I:)
~
g
.s
dl s:::
:0 fi)
CD
.=:
~
cO s::: 0>
s::: 0> '"0
cOons:::s:::
'0..
~o
~ "0 s::: .-
..d Q) c.;
0> ~ ..0 .,....
..0
...... s:::
+0>0>
,:::I
•
;... 0
~
s:::
• ....
<:..J
<:..J
0
~
lQ IZ
I "EO.s:::on
.....
~=58
~ s:::""" El
S
IZ
~
............
00
cS~a~
0>
Cl)
00
..0
i- .-<;::;
.-
= s:::
oS
00
~ ~
00
(l)
:.a
on .....
s:::
<:..J
.~
.!:!'
p:;..o . .
.g,..og~
~
......
0> ;;...
<:..J ....
-g~
;>,.0> ._
0>
~
Cl)
0
rIJ
....,
Cl)
.D
s:::
....
:;.-
._
B
'.:j
s:::p.
o 0>
~
ê
A~
iE .S
.:::
.....
Cl)
cD
~
..0 :...0"0
~'.D
<:..J
o
~
<:..J
:::I
0> s:::
0>
;...
IZ ....
00
:::
0>
<:..J
<:..J
ê
0>
....,..0
0
'+-0
0>
'f:<
AXXJj[ a
7I[d
:Jftv/7vIlI
J1I. Cl-Ct.
Fig. 7a.
fTtx4n. TXXI\7
lIIe
Fig. 7b. ,
:mN:~
IlII
:xxxJYc
6
Jl[
Nt(
::xxm-~
::x:xx::ri[d~
I
I
111
II
Jl1
- 15 -