American Anthropologist [Vol 1 Issue 3 - 1899] Franz Boas - The Cephalic Index

7/30/2019 American Anthropologist [Vol 1 Issue 3 - 1899] Franz Boas - The Cephalic Index

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T H E C E PH AL I C I N D E XBY F R A N Z BOAS

IThe top views of the skulls of the races of man show great

differences in form. For this reason the shape of the skull hascome to be one of the best-studied racial characters. Th e moreor less elongated form of the skull has been proved to be a goodmeans of characterizing varieties of man. The degree of elonga-tion is concisely expressed by the proportion between the antero-posterior diameter or length and the transversal diameter orbreadth of the skull. Generally the lat ter diameter is expressedin percents of the former, and this value is called the cephalicindex. The object of the following investigation is a study ofthe biological significance of this index.

The statement that in a certain race the breadth of the skullis, on the average, a certain percentage of it s length, would seem t oimply that there exists a certain characteristic relation betweenlength and breadth, so that individuals of a certain length ofhead would, on the average, have a breadth of head correspond-i n g to th e length multiplied by the cephalic index. I t is wellknown that this is not the case, but that the heads which haveabsolutely the greatest lengths have the lowest indices. I haveobtained the following results from a study of 239 Sioux Indianswhich were measured for me by M r G. H. Kaven in 1892:

Nunaber of IndividuaZs. Leq th o j Head. Correlated CepiaZic lmfex.I 1 180-184 m. 84.935 185-189 81.586 190-1114 79.925 200-204 77.612 205-210 75.9

448

7 0 * 95-199 78.3


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B O A S ] T H E C E P H A L l C 1 N D E X 449The cephalic index is also greatly influenced by causes other

than the length and breadth of head. A comparison of stature,height of face, and breadth of face with the cephalic index of t hesame series of Sioux Indians, is given i n the following table :

. V n m 6 e r S t a t u r e . Correlated ~fndz7,idu-als.

Cr;ohalirIndex.(rnni. ) ($)

16 160@1649 81.649 1650-1699 78.986 1700-Ij49 79.468 175O-Ij9c) 7 9 . 619 1800-1649 78.4

Although these values do not change quite regularly, theyclearly show correlations between the th ree measurements whichI selected and the cephalic index.

T he index-like all other indices-is a complex value depend-ing, as it does, o n two measurements. In order t o gain an insightinto its significance, it will be best to investigate the correlationsof its const ituen t elements. The correlation of length andbreadth of head, determined from a series of 9 2 3 male adultIndians of the S i o u x , Ojibwa, and Crow tribes, is as follows :

GI-ozLp. I I 1 111 IV V V ILength o f Head (mm.) 1S0-18+ 185-189 190-194 195-199 200-204 205-209Average Breadth of ilead. 153.8 1 5 3 . 5 154.8 156.2 157.8 159.4

This table shows tha t th e average breadth of head of individ-uals whose length of head is very great or very small, differs li ttlefrom the average breadth.

When we investigate the correlation of l ength and breadth ofhead with stature, it is found that th e length of head is moreinfluenced by sta ture than th e breadth of head. Correlationbetween breadth of face and horizontal diameters of t he headshows the t w o transversal diameters to be very closely correlated,while the length of head is more closely correlated with height offace. The following table illustrates these observations :

AM. A N T I ( . N. S., 1-29,


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450

153.1152.6154.31 5 5 . 3

A M E R Z C A N ANTHROPOLOGIST [N. S., I , 1899

27 115-119 191.37 1 120-124 192.160 125-129 193.355 130-134 196.0

243 Sioux Indians. (Adult males, 20-59 years.)Nuniber Stature.

I?Adzuidu-als.!f

(mm.)16 160-164949 1650-169986 1700-174968 1750-179919 1800-1849

Corrclnted 1LengthofHead.(mm.)187.5193.3194.I194.5196.5

rovrzlaiedBreadth Nuniber Height of CorrelatedFace. Lenfth ofHead.ofHcad. ! 1nd;iZu-Number Greadth of Correlated CorrelaiedFace. Lengfh of Breadth ofIndiuidu-als. Head. Head.(mm.) (mm.) (mm.)

8 135-139 187.8 147.3

ig 150-154 194.5 156.517 155-159 197.1 160.0

o

44 140-144 190.9 150 . 1145-149 194.4 152.9

Correlo edBreadth ofHead.(mm.)150.9154.8154.6154.71 5 5 . 5

Wh en we wish to consider the joint influences of all thesecauses upon either length or breadth of head, we must sub-.divide each group according to t h e varying values of the newcause and calculate the correlated averages of t h e breadth ofhead. I t will be seen a t once that, i n ordet- to carry on theinvestigation in this manner, practically unlimited materialmust be available, otherwise the number of individuals in eachclass will be very small, owing to the great number of classes.Problems of this kind were first discussed by Francis Galton,' butthe method of treatment has been fully developed by Karlfearson.'

It may be well, on account of the importance of this method,to give an elementary deduction. The correlations of severalorgans are to be investigated, the first of which has the averagevalue Z,. The various observed values of this organ may beexpressed by I , + , , where x 1designates the difference betweena n observed value and the average value. The second, third , andfourth organs have th e average values, respectively, I , , 13, l a , . . .'N a t u ~ a Z~ z h e r i f a n c e .2 Mathematical Contributions t o th e Theory of EvoZution, I I I ; Philosophical

Transactions of the Royal Society of London, vol. 187,pp. 253 f f .


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BOAS] T H E C E P H A L Z C z i vnEx 451and the observed values may be expressed by is f x, , Z3+x g ,i4 x 4 , . . . The values x l , x , , . . . are determinedby a great many very small causes which we will call e . Thenwe maysay-

x , =a l l 1 + 1 2 2 +a13 3 + * * *x Z =21 1 f Y 2 2 2 + y 2 3 3 + . . .x,,=a,,, 1 +a, 2 + n 3 3 + . . .

where the ar are constants. When we wish to investigate the cor-relations of the series of organs with t he first organ, we may sub-stitute t he value of e l from the first equation and we find :

c s r r = q 2 1 X 1 + . . * 2 C : ! + ~ ~ 3 3 + . .I x,, =g,,, t /jZ3>2 +P3 3 + . * .

Here the q and /3 are new constants which result from theSince the causes 8 are subject to chance only, their

If, then, we assume x 1 to be constant,substitution.averages will disappear.we have(2) Average x, ,=q n l x,.

N ow we will form the products x1x,,.These may be arrangedin such order that all the x 1 that have equal values shall begrouped together. Then each of these values for x1 will be mul-tiplied by the s u m of all th e correlated values of x ,. Supposingthere are p individuals i n which the first organ has the deviationfrom its average x l , we may subst itute for the sum of all th e cor-related values x ,, p times the average of x,, r according to ( 2 ) ,p q,,Ix I . Therefore the s u m total

z x , x,,=X x , ,, r XI =2 y,,, , y e .N o w , th e sum of all the xla s equal to th e mean square

variation (or standard variation) of L,, which we will call p , .Thereforeor when n th e total number of individuals measured

2 x * XI, =2y, , r / ( I z ,

=ngnr /A, z .


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45 AMERICAN A N T H R O P O L O G l S T [N. S., I, 1899We can show, in t he same manner, tha t

2 x 1 x,,=n q r n / U * 1 2 .p"r P I * =p111

ThereforeW e will call

q , , =r E m ;A 1Then

( 3 )

and

We call Y the coefficient of correlation, g the coefficient ofregression, because it measures th e regression of the correla tedvalue toward the average.'

I t remains to determine the variability of the array ofvalues x , which are correlated t o a given value xl. Accordingt o ( I ) this variability does not depend upon x l , since the E are notfunct ions of x l , but are entirely independent. The variability ofeach array is equal to t he mean square of th e differences betweenth e members of t he array and their average. The latter isIn+qnr x l, while the value for each member of the array isI,, + ,. Their difference is

xu- 111 X Iand t he mean square variability of the array

Since the value o n the left-hand side of this equation remainsthe same for all values of x l, we may substitute for it p, thevariability of the array. If we form the sum of these equationsfor all th e values of xl, we have

2 X I2 = l Pn2,B x , 2 =72pA,9.Thereforen p e =?z v , , ~ q,,?P 1 - 7 2

See Galton, NafuraZT d e r i t u t t r e , pp. 95 f f .


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BOAS] 7'HE CEPHALIC I N DE X 45

We will apply this result to a discussion of the correlationPearson' has calculatedetween length and breadth of head.th e following da ta :

Adult Male C~mtia: IAncient Egyptians (Flinders-Petrie). ...... 0.2705Bavarian peasants ( R a n k e ) ................ 0.2849Modern Parisians (Broca). ................ .0474

I have calculated the coefficients of correlation for thefollowing series :

1

Sioux, l iv ing, 2 4 3 adult males.. . . . . . . . . . . . . . . . .+0.24Skulls of 57 adult male Sioux Indians '. .........+0.24Skulls of 47 adult male Eskimo, S m i t h sound '. . . +0.47Indians of the northern coast of British Columbia ;adult males.. ............................ $-0.08Shuswap Indians ; adult males.. . . . . . . . . . . . . . . . +0.04Skulls of adult males, Baden *.. ............... +0 . 09Brigdi caste of Bengal ; adult males '. . . . . . . . . . . . +0.13It appears from these data that the degree of correlation

between length and breadth of the head is very slight, and th atits values differ considerably among various races. T h e lat terfact is rather surprising, since we might expect th at i n the humanspecies th e same organs are subject t o th e same laws. T h ecoefficient of correlation i n the Parisians, for instance, is exceed-ingly low, in fact so low that we may say that the breadth ofhead in the Parisians is entirely independent of the length ofhead.

The most plausible explanation of this phenomenon lies inthe effect of mixture of types upon the coefficient of correlation.

'LOG.it., pp. 2 7 9 , 280.9 George L. Otis, List of S p e c ~m ~ i z sn the Anntoniicul Section of theU. S. A . Medi-

cal Musezm, 1660, pp. 104 f f .Ibid., pp. 9 f f .

4 Die Schau'el in der Grossherzogliclzerz A~za tomi schenAnstalt ZZL Heidelberg;5 H. H. Risley, T h e Tribes and Castes of BensaZ, vol. I, pp. 16 f f .Archiv f u r Anthropologie, vol. 24, pp. 24 f f .


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454 AMERICAN A N 7 H R O P O L O G Z S T [N. s., I , 1899Supposing two types which have the measurements I , , C,, . . .I,,, and A ,, A ,, . . . A,, respectively, inhabit t he same area, sothat it is impossible to determine t o what type each individualbelongs. If the component types are not known, we should findfor the whole series the averages L,, L,, . . . L n with the varia-bilities M I , M , . . . M ,, and the coefficient of correlationcalculated according to the method given above would be

2 X1X,R = n M , M,If we divide this s u m into two groups, the one embracing all

the individuals of one type, the other those of the other type,we may substitute for the former

for the la tterL, + X I =I . , +6 ,l,, +X" =A" +En x, =A , - 1 f Elx, =A, - , +En

and b y substituting th e values of r , , r , and of

Supposing that i n the component elements of the series rl andrn,pl and pl', p, , and p,' are equal, we have

P I .& n , % v 1 - - A , ) V " - - ~ , , )=' -+1, Mn b1, M,I t will be noticed that whenever the second term of this s u m


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BOAS] THE CEPHALIC IN DE X 45is negative, R will be less than r .I , is larger than A 1 and I, , smaller than A,, or vice versa.

I think this effect of mixture is a sufficient explanation of t helow value of the coefficient of correlation for Paris, where we finda very heterogeneous population embracing narrow- and long-headed subjects from northern France and very broad- and short-headed ones from southern France. The same explanationseems plausible for the Shuswap and the tribes of northernBritish Columbia. The high value for Eskimo skulls may be du et o the fact that a number of female skulls were counted as maleskulls. Th is would have th e effect of raising the coefficient ofcorrelation between th e diameters of th e head.

When the typ e is dis-homogeneous owing t o mixed descent,the coefficient of correlation will depend upon th e law of heredity.If the mixed race should range in a probability curve around atype intermediate between the parental types, we should expectt o find th e coefficient of correlation slightly influenced by mix-ture, if any. If th e mixture should result i n a tendency of rever-sion t o either parental type, the effect would be similar to tha tobserved i r i th e case of mechanical mixture which was discussedbefore. Evidently in such cases t he coefficient of correlation hasno direct biological significance.

This will be th e case when

111I t is quite evident tha t both breadth and length of head ar e

influenced by a great number of causes, some of which act uponboth measurements in th e same manner, while other s mayinfluence each i n a peculiar way. Such causes may be investi-gated by determining their correlations with length and breadthof head separately. Thus , we may determine the correlationbetween capacity of skull, sta ture, dimensions of face, and thetwo diameters of the head. 1 have calculated a number of suchcorrelations for adult males of a few Indian tribes with thefollowing results :


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456 AMERZCAN A N THRO OLOGZST [N. S., I , 1699Coeficient of CorreZation.

Ind ians of Northevn Coastof BrifishColumbia.Stature and Length of Head.. ............Stature and Breadth of Head.. . . . . . . . . . . .Breadth of Face and Length of Head.. +0.30Breadth of Face and Breadth of Head. +0.53Height of Face and Length of Head.. +0.24Height of Face and Breadth of Head.. - .10

ShziswapInd ia NS.........+ .28+ . 6 2+ .27+ .22

SioctxIm f i a n s .+ .2 6+ .09f . 2 7+ . 5 2+0 .30+ .22

If we desire to eliminate the influences of these causes fromthe apparent correlation between length and breadth of head, w emust consider each of these a function n ot only of the other, bu talso of all the measurements the effect of which we desire toexclude. I n doing so, we may pursue th e same method t ha t weused in the beginning (p. 450) nd b y a series of substitutions in( I ) we find(4 ) Averagex,=p, , , . . , . I ~ x z + ~ 1 3 2 .. p x , / - . . r P 2 . p - I ~ X p

The values q may be determined in the following manner.W e will call( 5 )By multiplying (4) successively with x , , x , . . x , , we have+Yr32. . . y g l +. . . + I I J Z . . y - r ) Y,,,I- T I ? * . . . +. . . + r p z . . p-1) r,,3T I , = r z 3 . . .r 1 g =Y I Z 3 . . . Y z 3

r , p = 1 ' 1 2 3 . . Y c p +TI)?. . . y 3 p + . . . + 1 p * . . p - qi I

By multiplying the last of these equat ions successively byr , ,, rp , . . and subtracting from the first, second . . . quation,we f ind

~ z * - r ~ p ~ r > ~ = ~ * ~ ~ ~. p ( 1 - ~ z p r y z ) + r r 3 2 . . p ( ~ 3 z - 7 * 3 p r p n )+ . . . . . . + r ' ( p - , ) 3 .. ( r ( l > - , ) * - ( p - I ) p T p JThis low value may be due to the cause that on the coast of British Columbia two

types come into contact, one with a very high face, the other with a low face. Thei rmixture would probably result in a decrease of the correlations for height of face inthe mixed race.


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BOAS]

We callT f f E C E P H A L f C ZLVDEX 457

r 1 2 p = z 2 ; . , . . . . 1 + r 3 ? . , . p 1 - ; ? I +. . + ,(p-,,* , , 1, l , p - r ) *p+. .+ l ( p - I ) ? . . p Y(p - r ) 3pr g p = r , , ; . . . . . p Y , 3 p + 7 - , ; 2 . . , . ,i .() L Y I W - 1 ) P = 7 r * ] , . p?2(p- , )1> + - 1 3 ? . . . , ~ 1 - ; l L l - L l x +. , + y ( I p - I ) z . . PI t will be seen that (7) is identical with (6) except insofar as

t o all the r representing correlations between two measurements,the element p has been added, and insofar as the number ofequations and of unknown quant ities has been decreased by one.We may, therefore, continue a series of successive substi tut ionswhich will always result i n equations of the same form. Th enext substitution would be

The last substitution will give u sY X 2 3 . .I

- 3 1 1 4 5 . . ! - 12(,51. p) l ) , ( a g . . P !- I - . 2 ; ( < 5 . . P ) + 3 - ( 4 5 . . p,Thus the coefficients of correlation between p variables may bereduced to those between ( p- ) variables.

The variability p of the array of x 1 which is correlated to aseries of values for x 2 ,x 3 . . .

p 2 =Average of ( x, - , 2 s . , x 2 - l S 2 . x 3 - . . . )2=Averageof(x , fg , i , . . x 2 + y 1 : 3 e . . x 3 2 + . . .

+ z p 1 & 3 . . p i 3 2 . . x 2 x s f * . . )- 4 1 2 3 . . x , x.r - 4 1 3 2 . . x i x3 - . .By substituting the values of the types Y and pa for theaverages of the types x x and x ? and for p its related Y,accordingto ( 5 ) , we find

/J* =p 1 ( I +1z3 . , +1 . 1z32 , , + . . .- r x e 3 . r 1 3 - 2 1 , 3 p , . r13- . . .+2 r 1 2 : s . , I , 5 . r23 + . . . 1


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458 AMERZCAN A NTHROPOLOGIS T [N. S., I, 1899By in t rodu cing in t h e negat ive e lem ents of th is sum h e va lues fo rr I 9 , I 3 . . . rom (G), w e obta in( ~ ) P * = / U ~ ~ ( I - - ~ ! ~. - r l i z . . - f - 1 3 8 . . 7 1 3 % . , y 3 2 - . .I,

P 2 = P I a [ I - r ( r r n . . P ' 711, . . 1 * raJ 1 ,o r i n a sho rter formin which sum a and 6 must be m ade to a s sume a ll th e va lues f rom2 t o p . I V

I have t rea ted , accord ing to t h i s m e t h o d , t h e m e a s u re m e n tsof the 57 skul ls of a du l t m a l e Sioux Ind i a ns t o wh ic h I referreda b o v e ( p a g e 453). I ha ve c om pa re d l e ng th (I) a n d b r e a d th (6) ofskul l wi th i t s he ig ht (h), he b izygom at ic d iam ete r of th e face (z),a nd w i th t he c a pa c i t y of t h e skull. F o r t h e l a st p u r p os e I h a v em ad e a reduc tion which seemed necessa ry , because th e ca pac i tyof t h e skull i s a cubic measure , whi le a l l th e oth ers are l ine armeasures. F o r th i s reason I ha ve c om pa re d t h e l a t t e r w i th t h ecubic roo t of th e capa ci ty of th e skul l s (c). T h e a v e r a g e s a n dvariabi l it ies of these m easure me nts a re a s fol lows :

C L b It ZAverage (mm. ) . . ...... 112.9 181.7 143.5 1330 141.6Standa rd variability.. .. F 2.6 F 6 . 3 & 5.6 &4.7 F . 3T h e following coefficients of corre la t ion w ere found :

I. Coeficients of SizgZe CorreZation.Deteriiiiiied by :

c I 6 Ir 2Average c . . .. . . . . . . $0.54 +0.67 +0 4 4 +0.49Average b.. .... +0.67 +0.24 .... 0.00 +0.61Averageh. . .... fo .4 4 +0 .3 6 0.00 .... +0.19Average2 ...... +0.49 +0.39 +0.61 -+c.19 ....

I t a ppe a r s f rom th is t a b l e t ha t t h e c o r r e la t ions of t h e d i am -e te rs wi th th e capac i ty a re s t ronges t , while tha t b e tween leng tha nd b re a d th is one of the lowest values in th e t a bl e. T h i s c on -di t ion is s t il l more s t rong ly b rou ght ou t when double , tr ip le , an dquadrup le cor re la t ions a re cons idered .

Average l... .... +0.54 . . . . +0.24 +0.36 +0.39


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BOAS]

A vernge cDrterminrd by:1 b h z

fo .40 +0.57 . . . . . . . .+0.44 .... f 0 . 2 ' ) ....

T H E C E P H A L Z C ZNDEX

A oernge 1Determhr*n'by :c b I i

A v e r < z @ -bDrternrined by :

z c 1 11 zi+0.69-0.zz . . . . . . . . 0.76-0.17 .+0..$7 .... + O . I j .... $0.83 .... -

1 . Coeficients of Double CorreZntion.

A vera,p hDetermined by:

C 1 b z$ 0 . 3 5 + 0 . 1 7 . . . . . . . .+ .80 .+0.46 . . . . . . . .+0.38-0.10

459

A veragp zDetermiaed by:

C 1 b 11+0.39$0.18 . . . . . . . .+ o . r 5 . . . . +o.gr . . . .

. . . . . . . . + 0 . 2 6 + 0 . 5 5 ..... 0 4 + 0 . j I . . . . . . . . -0.04

Avrrnce cDetermined by:1 I > I1 7

+0 . 28 + . + + 0 . 3 5+o.41+ 0.59 .... -0.03. . . .A v n r q e 1 A verrigr hDefevwtinud b7 : Detrrmiaed hy:

C b h z C I h zfO.63 - .17 + 09+0.65 - .38 . . . $0.29 S o . 6 0 -0 .25 . . . . $0 41+0.69-0 I I -0.36 ....

Determined by c 1 b h z VnrinbaZ+ of A w q ) .Average c . . .... +0.32 +0.67 f 0.36 - .08 of c =0.47 ,Average 1 . . +0.63 .... - 0.36 +0.03 +0.29 of 1 =0.79 p,Averageb.. +0.69 - 0.16 .... -0 5 2 +0 4 1 o f b =0.54 bAverageh . +0.77 + o m 3 - 0 . 6 5 ... f o . 1 8 ofI i=o.78pi ,Average 2.. - .17 +o 2 7 fo.70 +o.r9 . . . . of z = o 6 ~ ),

These da ta show that t he diameters of the skull are primarilydetermined by its capacity. The height of th e skull appears t obe most closely associated with its capacity, the length seems tobe least closely related to it. I presume this is due to the fact

S0.32 .... + 0 . 2 7 + 0 3 2 + 0 . 3 9 ... $0 .16+ 0 .17.... + 0 . 6 7 + 0 . 4 5 0.001 .... + 0 . 0 6 + 0 . 3 r + o . 2 9 $0.66 .... -0 . j7$-0 .36.... +o.o~--o.Iq+O.63A oarnge It

Detannined by:c 1 b z

f 0 . 7 5 + . 0 7- .53+0.37 + .19 .... - .0 7.... $ - O . 3 4 - 0 . 1 c ) + 0 . 1 8

....t - 0 . 7 8 .... - 0 . 6 5 f o . 2 5

A vernpe zDetermined Cy:

C 1 b h-0.04 + .2 8 - t .58f , 4 3+ .19 . . . . - .0 6.... + 0 . ~ 2 + 0 . $ 6 + 0 12

....0.00 .... +o.61+0.16


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460 A MERZCAN A N THROPOL G lS I' [N. S., I, 1899th a t th e deve lopm ent of th e f ron ta l s inuses a nd of th e occ ip it a lp ro tube ra nc e s doe s no t de pe nd upon t h e fo rm of t h e i nne r c a v i tyof th e sku l l, bu t upon th e genera l dev e lopm ent of th e ske le ton .S inc e t h i s i s pa r tl y e xp re s se d b y s t a tu re , we m igh t e xp e c t t h a tth is inf luence would par t ly be e l iminated by the in t roduct ion ofs t a tu re i n t h e s e ri es of cor rela tions . Un for tun a te ly th i s e lem entc a nno t be i n t roduc e d on a c c oun t of lack of da t a . Fu rthe rm ore ,th e e r ro rs of th e va lues of mul t ip le cor re la t ions a re so gre a t t ha ti t is n o t adv isab le to ca r ry on t h e inves tiga t ion of a series ofn o m o r e t h a n 57 sku l ls beyond qua drup le cor rela tions whichma y b e cons idered appro xim ate ly correc t in th e i r f irst dec imal .

I t is of grea t in te res t to no te tha t w hen capac i ty is in t roducedin our cons ide ra tion a compensa tory g row th is found t o ex i s tbe twe e n b re a d th of he a d on t h e one ha nd , a nd he igh t a nd l e n g thof he ad on t h e o the r . W e f ind, the re fore , a s a re su lt of ourinves t iga t ion, tha t the law of compensat ion which Virchowformula ted a f te r an ana lys i s of th e form s of skulls with pre-m atu re synos tos is of sutures , hold s go od a lso in norma l skul ls ,Among shuZZs belonging t o the same type a bre ad th above t he nvercigeis compensated by a height and a length below the nvemoge. Thecor re la t ion be tween le ng th and bread th is no t an express ion of ab io log ical re la tion be tween th e two measurem ents , bu t an e f fectof t h e c ha nge s wh ic h bo th unde rgo whe n t h e c a pa c i t y of t h esku l l inc reases o r dec reases. T h e cepha l ic index , the re fore , isno t t h e e xp res sion of a law of d i rec t re la t ion betw een len gth a n db re a d th of t h e s ku ll. T h e p ropo r t ion be twe e n t h e d i a m e te rs ofth e sku l l an d i t s capac i ty , on t h e o the r ha nd , e xp re s se s a n i n -t im a te b iolog ical re la t ion be tween these measurem ents . I ta p p e a r s t h a t t h e d i am e t e rs of t h e h e a d m u s t b e c o ns id e re d a s d u et o t h e t e nde nc y of t h e i nne r c a v i ty of t h e s ku ll , o r m ore p rob -ab ly of th e bra in , t o assume a cer ta in s ize an d form in a g iventy p e of man , th i s fo rm be ing expressed b y t he p ropor t ion of th edia m eter s of th e bra in an d i t s s ize. If one of th e dia m eter s d i f-fers f rom th e norm in b e ing excess ive ly la rge , th e oth ers will


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BOAS] THE CEPHALIC I N D E X 46 Itend to be t oo small.when the t ransversal diameter differs from the norm.

This is definitely shown t o be the caseT h e variabilities of the arrays show th at t he reduction of vari-

ability of capacity is greatest. Th is proves that the four linearmeasurements which we have treated largely determine thecapacity. Th e variability of the length and height of skull isvery slightly reduced. This shows that these measurements arelargely influenced by causes which we have not included i n ourconsiderations. T he same is true of the bizygomatic diameter ofth e face. When we compare th e reduction in variability of thelinear measurements as determined by c, and as determined byth e quadruple correlation, we find the following :

Variabili ty of A i - i q .Detrl-v ii t i td by c. L)rtemri,red hy Qund-uple Cordrrtion.

1 0.84 0.79b 0.74 0 . 5 411 0.90 O 78L 0.87 0 . 69

This comparison proves tha t breadth, height, and bizygomaticdiameter have an insignificant effect upon length as comparedwith the effect of capacity. The great reduction of variabilityfor breadth of head and bizygomatic diameter is d ue to theintimate correlation between these two values.

It follows from these considerations that while the cephalicindex is a convenient practical expression of the form of thehead, it does not express any important anatomic relation. Onthe o ther hand, the relation between capacity and head diametersis found to be of fundamental importance, and among these therelation between transversal diameter and capacity is most sig-nificant. Since i n measurements on the living we are unable tomeasure capacity of th e head, it is necessary to find a substi tute.I t would seem th at circumferences are th e most available meansfor judging cranial size. Therefore such circumferences shouldbe included in all anthropometrical schedules designed t oinvestigate racial characters.

American Anthropologist [Vol 1 Issue 3 - 1899] Franz Boas - The Cephalic Index

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Transcript of American Anthropologist [Vol 1 Issue 3 - 1899] Franz Boas - The Cephalic Index