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Volume 36 February 4, 1947 No. 3


Wilfrid D. Hambly
Curator, African Ethnology


Capacity by Experiments and Calculation. — The object of this
research is to make a survey of the cranial capacities of various
peoples. Consideration will be given to different techniques, and
to the compatibility of results obtained by direct measurement
and by calculation.

Research in measuring cranial capacities of 429 Melanesian
skulls in the Museum collection established several principles that
have been previously described (Hambly, 1940, 1946):

(1) Measuring the cranial capacities of a test sample of 50 skulls
from New Guinea by the mustard seed method gave an
average of 1258 cc. The second average measurement was
1257 cc, and therefore the results are practically identical.
I strongly favor the method of weighing the seed and multi-
plying by a factor to give volume. Pouring the seed into
a measuring glass introduces sources of error.

(2) Two students working independently but by the same
technique measured the cranial capacities of 47 skulls. The
greatest difference for a single skull was 10 cc. The averages
were 1267.4 and 1268.8 cc, respectively.

(3) For the 124 skulls of male Melanesians of New Guinea the
formula of Isserlis (1914) gives a calculated capacity of 1277,
a difference of only 3 cc. from the measured capacity. This
formula (Isserlis, 1914, p. 189) reads

C = . 0003849 X BLH + 96 ± 65/ VN

and it is based on study of 110 male and 81 female skulls
from the Gaboon area of west Africa. Since the formula
relates to Negro skulls it is not surprising that satisfactory
application may be made to the Melanesian skulls of New
Guinea, which are Negroid in appearance and have many

No. 687 25


FEB 2 1947



average measurements that do not differ significantly from
those of African Negroes.

Various Techniques. — We may be satisfied that the mustard
seed technique gives consistent results when used by the same worker
or by different students following the same procedure; but, unfortu-
nately, comparative study has to deal with different techniques used
by different workers and the nature of these variations should be

Martin (1928, vol. 2, pp. 643-648) describes many methods of
direct measurement by water, shot, and seed. Stewart (1937) also
summarizes such data. The cranial capacities given by Martin
(op. cit., pp. 745-746) show variation by sex and race, but he fails
to give the number of skulls on which the observations are based,
and some of his examples are out of date. It is possible, however, to
allow for differences in technique and so make results comparable.

Turner (1884, Zoology, vol. 10, No. 4, pt. 1, p. 9) came to the
experimental conclusion that Broca's (1875) method of measuring
cranial capacities with shot gave a result about 6.9 per cent higher
than that yielded by filling the skull with water or very fine seed;
water and fine mustard seed give about the same results in cubic
centimeters. My own experiments with a crdne etalon showed that
fine shot gave a result which is 5.4 per cent too high compared with
that given by fine dry mustard seed, and I have therefore used my
own figure as a correction. For example, MacCurdy (1914) measured
the capacity of eight female skulls of New Britain with shot, which
gave a high result of 1214, but if this is reduced by 5.4 per cent a
result of 1152 is obtained, and this is compatible with the general
trend of capacities for Melanesian females when made by careful
measurement. There is no certainty, however, that 5.4 per cent
deduction from capacities measured with shot is always necessary.
If a worker uses the finest bird shot and weighs the shot instead of
measuring it in a cylinder, there is a possibility that techniques
by shot and seed will give compatible results.

Davis (1867) used fine sand (S.G. 1.425) in his experimental
work, and tests made with sand of the same specific gravity in the
Museum laboratory indicate that the cranial capacities given with
this sand are 8.4 per cent higher than those arrived at by using
mustard seed. Davis gave 1432 as the average capacity of nine
male skulls from the New Hebrides, and this is obviously high, but
a reduction of 8.4 per cent gives 1312, which is reasonably close to
1280 for 124 Melanesian males of New Guinea, and harmonizes with



the general run of measured averages for other male Melanesian

One should emphasize the paucity of measurements that have
been made carefully with mustard seed. But fortunately we do
have some well-described techniques. Tildesley (1921, p. 177)
states that the capacity of Burmese skulls was "taken with mustard
seed tightly packed in the skull and then weighed, the worker having
previously performed this operation on one of the crdnes etalons."
Wunderly (1939) packed Tasmanian skulls with fine seed that was
poured from the skull and measured in a glass cylinder. This
method is not so accurate as that of Tildesley. Morant's publication
(1927) on Australian and Tasmanian skulls states that "all capacities
were accepted, although the different methods used to determine
them might well have led to substantially different results." This
statement gives us a critical acceptance of the measured capacities,
but if we reject them no research is possible. For the European
races Morant (1928) stetes that capacities were obtained by
various methods but these were compared and found to be accepta-
ble. Evidently there are different degrees of dependability in our
samples; yet we can accumulate enough reliable data to give an
accurate idea of the measured capacities by race and sex for a large
number of peoples.

One of the most recent contributions to the study of cranial
capacities has been made by Simmons (1942). Most of the data
were assembled under the direction of the late Professor Wingate
Todd. The details of a plastic method are described, whereby the
halves of a skull which has been bisected sagittally are filled with
removable plastic whose volume can be measured. Professor Todd
concluded that the plastic method need produce a measuring error
no greater than 10 cc. for a single skull and is therefore more accurate
than the water or seed method.

Todd also found that capacities obtained by the seed method
tend to surpass capacities obtained by the water method by 80 cc.
Capacities obtained by the water method are shown to exceed
capacities measured by the plastic method by 15 cc. The article
indicates that the technique of the plastic method requires great
care. The greatest objection to the method is that it involves
bisection of the skull.

Simmons (op. cit., p. 482) gives the average cranial capacities of
groups of American White and American Negro skulls obtained by
water measurement of large samples. Capacities were 1517 and


1338 for Whites, male and female respectively. These estimates
are acceptable and are compatible with a great variety of estimates
quoted in this article (pp. 41-45). Todd's experimental determina-
tion of capacities of Negro skulls is probably too high. He gives
1467 for Negro males and 1311 for Negro females. Judged by the
data assembled in this work (pp. 30-32) the estimates of Todd were
about 100 cc. too high. Hrdlidka's figure (1928) for full-blooded
American Negroes is 1357, which is very close to several measure-
ments of cranial capacities made on African Negro skulls. For
American full-blooded Negro females Hrdlidka gives a capacity of
1205, which again agrees well with capacities of African Negro
skulls, whether measured directly or calculated by formula.

My conclusion is that, although the cranial capacities given by
Simmons for American Whites are acceptable, those for American
Negroes arejiot, unless the Negro population of Todd's experiment
included a considerable Negro-White mixture. Assumption of a
Negro- White mixture in Todd's population would make his estimate
of cranial capacities plausible, because his figures of 1467 (male) and
1311 (female) are somewhere between the usual estimates for crania
of pure White and pure Negro stock.

Calculated Capacities. — The word "calculated" refers to the
application of a formula for determining the average cranial capacity
of a group of skulls. The word "measurement" is used throughout
the text for the process of filling the skull with seed or other medium,
then measuring the cubic contents of the medium so used.

The experiment mentioned (p. 25) shows that a simple arith-
metical calculation may give a satisfactory result, that is, one which
is almost identical with the figure obtained by the tedious process of
direct measurement. But the question is, which formula shall we
use? The formula of Isserlis gave an accurate cranial capacity for
124 male skulls of New Guinea, but the general formula of Lee
(Lewenz and Pearson, 1904, p. 395) gave a capacity 160 cc. too high
in comparison with the measured capacity.

Dr. Hrdli5ka's suggestion (1925, p. 250) that the cranial module

o niay give a close approximation to the measured

capacity of skulls is an attractive proposition, for its use would
be a time-saving device. The table given by Hrdli6ka compares
seven samples of cranial capacities with a view to showing the
similarities and disparities resulting from measuring cranial capaci-
ties and using the module (mean skull diameter). Some items of


Hrdlicka's table indicate that one could have obtained exactly
the same result in a fraction of the time by using the cranial module
calculation. But selection of other examples from the same table
indicates that use of the module instead of experimental measure-
ment of cranial capacity might give a discrepancy of more than
100 cc.

The module method of Hrdlicka bears a close resemblance to
use of the Manouvrier (1884, see Martin, 1928) formula, C=LBH/2.4,
for males. Hambly (1940, p. 94) found that this formula gave
a capacity of 1279 for 124 male New Guinea skulls. The formula
of Isserlis gave for the same sample 1277, and actual measurement
with mustard seed gave the capacity as 1280. This possibility of a
complete agreement between measured and calculated capacities
shows that it is a thankless task to spend many hours in direct
measurement if we can get such reliable results by calculation.
The data contained in the following tables help a student to judge
the chances of calculating average cranial capacities by use of a

The method adopted in the following pages is to apply the
unrevised formula of Isserlis to the L, B, H measurements of 114
groups of skulls, 83 male groups and 31 female, of various sizes.
Sometimes we have to use the measurement H' instead of H;
usually the difference is a very small one (von Bonin, 1934, p. 11).
The table (pp. 30-31) gives measured and calculated capacities,
their differences, and the A/P^ value, which has been explained
on page 31. If this value is below 3, one must assume that the
difference between the two averages, measured directly and cal-
culated by Isserlis' formula, is possibly due to the nature of our
random sampling and is not necessarily significant.

The value of this statistical method should not be overestimated,
and our experience of cranial measurements, together with knowledge
of the small visual bulk of a cubic centimeter, must aid in judging
whether a difference is significant from the practical point of view.

For example, 753 Dynastic Egyptian male skulls (Pearson and
Davin, 1924) had a measured capacity of 1439±2.97, and the
capacity given by the unrevised formula of Isserlis is 1424.4zb2.37.
The difference is —15 cc, or one per cent, and most workers would
be willing to accept the cranial capacity as 1424 rather than measure
753 skulls by the mustard seed method. But statistically the dis-
crepancy of 15 cc. may be significant, owing to the fact that the series
of skulls is a large one and the probable errors of the averages by



Negro and Egyptian Males

Number Capacity by

Source of Measured formula of

skulls capacity Isserlis

Tanganyika, East Africa 37 1299.0 1270.0

(Kitson, 1931) ±11.48 ±10.70

Kaffirs, South Africa 21 1422.0 1459.0

(Kitson, 1931) ±24.80 ±14.20

Dynastic Egyptians 753 1439.0 1424.4

(Pearson and Davin, 1924) ±2.79 ±2.37

Negroes, Congo and Senegal

pooled 50 1336.0 1309.9

(Aziz, 1929) ±19.54 ±9.19

Negroes, American full-bloods.. 36 1357.0 1408.0

(Hrdligka, 1928) ±11.24 ±10.83

Wateita, East Africa 30 1316.0 1296.0

(Kitson, 1931) ±20.72 ±11.90

West Africa 7 1360 1350

(Hrdligka, 1928)

East Africa, near Nairobi 14 1401 1343

(Hrdlicka, 1928)

South Africa 6 1402 1421

(Hrdheka, 1928)

*DifTerence not statistically significant.

in CO. and

















measurement and calculation are both very small. On the contrary,
if the series of skulls is small, the probable error of the average
capacity is likely to be a large one, and therefore even a large dis-
crepancy of 50 cc. may be within the range which is not statistically
significant for such a small sample.

After completing the table of mathematical comparisons of
measured and calculated capacities we can proceed to amend the
formula of Isserlis. We must then make application of the formula
(revised if necessary) to some further cranial capacities. This must
be done to test the validity of the revised formula.


The tables (pp. 30, 31) make a comparison of average measured
capacities with the average capacities derived from the formula of
Isserlis. Differences in these capacities are expressed in the upper
figures as discrepancies in cubic centimeters, while the lower figures
give a percentage difference. Thus for the male skulls of Tanganyika
the measured capacity is 1299.0=^1 1.48 cc, and the capacity by
formula of Isserlis is 1270.0± 10.70 cc. The formula gives a result

Negro and Egyptian Females

Number Capacity by Differences

, Source of Measured formula of in cc. and A/P^

skulls capacity Isserlis percentage

Egypt, Dynasties 26-30 472 1301 1289 -12

(Pearson and Davin, 1924) -0.9

Egypt, Dynasties 18-21 74 1250 1275 +25

(Pearson and Davin, 1924) +2.0

Egypt, Prehistoric Naqada 123 1288 1259 -29

(Pearson and Davin, 1924) -2.2

South Africa 26 1245 1253 +8

(Hrdligka, 1928) +0.6

Nairobi region 28 1242 1201 -41

(Hrdligka, 1928) -3.3

West Africa 6 1182 1172 -10

(Hrdli5ka, 1928) -0.8

American full-bloods 19 1205 1205 ±0

(HrdliCka, 1928) ±0

East Africa 18 1211 1188 -23

(Kitson, 1931, from Widemann) - 1.9

Negroes of Egypt 20 1220 1209 . -11

(Kitson, 1931) -0.9

Wateita, East Africa 33 1192.4 1174.7 -17.7 1.23*

(Kitson, 1931) ±8.87 ±11.32 -1.5

Tanganyika 17 1152.1 1140.7 -11.4 0.57*

(Kitson, 1931) ±12.36 ±15.76 -1.0

*Difference not statistically significant.

29.0 CC. (2.2 per cent) lower than that determined by direct measure-
ment. In many instances throughout these tables, A/P^ values
between the measured and calculated capacities have been worked
out by application of the well-known formula

Mi-M2>3V(PE,)2+ (PEj)*.

If the difference between the means (Mi and M2) is greater than three
times the square root of the sum of the square of the probable errors
of the two averages, the result may be statistically significant.

In some instances a difference that is not statistically significant
is marked with an asterisk. In other instances the reader is left to
judge whether he would consider the differences important. The
working out of probable errors for all samples is a formidable task;
but enough have been calculated to show the general nature of errors
calculated from samples of various sizes.


The conclusions derived from these tables are:

(1) That the formula of Isserlis somewhat unexpectedly gives
for Egyptian skulls a result close to the measured capacity
of a large sample. For male skulls the difference is 15 cc.
(one per cent), for females —29 to +25 cc. For both sexes
the formula gives a little less than the actual measurement.

(2) The crude average measured capacity of Negro male skulls
is about 1346 cc. The largest sample of female Negro skulls
has an average capacity of 1192 cc.

(3) Ranges of average cranial capacities of Negroes are as follows:

By measurement By calculation

*Malo« / Max. 1422.0±24.80 South Africa Max. 1459.0± 14.20 South Africa

ividieb ^ jy^j^^ 1299.0±11.48 East Africa Min. 1270.0±10.70 East Africa

+Tr^rr,Qi^o / Max. 1245 South Africa Max. 1253 South Africa

jr emaies | ^^^^ ^ ^gg ^^^^ ^^^.j^.^ j^^^_ ^^^2 West Africa

*Results close by measurement and formula.

fVery small discrepancy between measured and calculated capacities.


The suitability of the formula of Isserlis for calculating the
capacity of Melanesian skulls is demonstrated in the attached
tables (pp. 33-35). A large series of measurements indicates that
the crude average capacity for males is about 1323 and for females
1192, and application of the unamended Isserlis formula gave 1317
and 1190 for the same data. There is a negligible divergence
between the measured and the calculated capacities.

We can therefore use the measured capacities of 1323 and 1192
as standards by which to judge the applicability of the Isserlis
formula to a series of male and female skulls from New Ireland. The
measurements on these skulls were made by Dr. 0. Schlaginhaufen,
who kindly permitted their use. His full data have not yet been

For a series of 238 male skulls the average L, B, and H' dimen-
sions are 181.2, 130.2, and 134.6, respectively, and these measure-
ments when used in the Isserlis formula give a cranial capacity of
1318, which is very close to our general Melanesian measured
standard of 1323. Martin (1928, p. 746) gives Schlaginhaufen's
measurement by seed as 1347 for males.

The data of Schlaginhaufen include also three groups of female
skulls from Ambitl^ (38), Babase (95), and Tatau (47), all of which,


Melanesian Males

Number Capacity by

Source of Measured formula of

skulls capacity Isserlis

New Guinea 120 1280.0 1277.0

(Hambly, 1940) ±6.06 ±5.84

New Guinea 98 1345.0 1275.9

(Wirz, 1926) ±7.20 ±6.56

New Guinea 15 1308.0 1281.2

(Graf, 1931) ±19.80 ±16.80

New Guinea 43 1250.0 1245.0

(Broek, 1923a) ±11.70 ±6.50

New Guinea 34 1317.0 1314.0

(Bondy-Horowitz, 1930) ±11.57 ±11.14

New Guinea, D'Entrecasteaux

Islands 65 1294.0 1286.1

(Sergi, 1892-93) ±9.50 ±8.06

New Guinea, Kaniet Island 18 1342.0 1290.0

(Hambruch, 1906) ±11.47 ±15.32

New Guinea, Woodlark Island . . 18 1394.0 1387.0

(Sergi, 1892-93) ±18.08 ±15.32

Fiji 21 1406.0 1499.0

(Krause, 1881) ±15.98 ±14.18

Fiji 8 1496.0 1482.0

(Flower, 1880) ±21.65 ±22.98

Fiji 35 1372.0 1438.0

(Krause, 1881) ±12.95 ±10.98

Loyalty Islands 18 1460.0 1431.0

(Quatrefages and Hamy, 1882) ±18.06 ±15.30

Loyalty Islands 34 1463.0 1439.0

(Sarasin, 1916-22) ±13.12 ±11.15

Ambrym 20 1318.7 1301.7

(Hambly, 1946) ±15.46 ±14.53

New Hebrides 10 1310.0 1371.0

(Krause, 1881) ±24.31 ±20.50

New Hebrides 9 1311.7 1347.0

(Davis, 1867) ±21.73 ±21.66

Malekula 33t 1298.5 1242.4

(Hambly, unpublished) ±9.35 ±11.31

New Caledonia 89 1420.0 1402.0

;- (Sarasin, 1916-22) ±8.10 ±6.60

♦Difference not statistically significant.

in CO. and









































Melanesian Males — Continued

Number Capacity by Diflferences

Source of Measured formula of in cc. and A/P^

skulls capacity Isserlis percentage

New Caledonia 13 1385.5 1365.3 -20.2 0.91*

(Hambly, unpublished) zt 12.61 ±18.03 -1.4

New Caledonia 50 1344.0 1338.1 -5.9 0.44*

(Aziz, 1929) ±9.54 ±9.19 -0.4

New Britain, Baining tribe 43 1242.9 1305.6 +62.7 4.40

(Bauer, 1915) ±10.28 ±9.91 +5.0

New Britain 13 1312.0 1363.4 +51.4 3.90

(Hrdligka, 1928) ±23.51 ±18.03 +3.9

Solomon Islands 26 1274.0 1284.4 +10.4 0.52*

(Frizzi, 1913) ±14.97 ±12.74 +0.8

Solomon Islands, Santa Cruz... 26 1338.0 1312.9 -25.1 0.88*

(Speiser, 1923a) ±13.23 ±12.74 -1.9

Solomon Islands 5 1403.0 1368.0 -35.0 1.1*

(Hrdligka, 1928) ±11.53 ±29.09 -2.5

New Ireland 13 1302.0 1293.9 -8.1 0.28*

(Hambly, unpublished) ±22.26 ±18.03 -0.6

Melanesian Females ,

Number Capacity by Diflferences

Source of Measured formula of in cc. and A/P^

skulls capacity Isserlis percentage

New Guinea 70 1153.0 1161.0 +8.0 1.0*

(Hambly, 1940) ±6.08 ±5.24 +0.7

New Guinea 49 1233.0 1212.0 -21.0 1.9*

(Wirz, 1926) ±7.28 ±8.53 -1.7

New Guinea 12 1127.9 1126.8 - 1.1 0.04*

(Bondy-Horowitz, 1930) ±19.24 ±18.76 -0.1

New Guinea, Woodlark Island.. 30 1143.0 1127.0 -16.0 1.06*

(Sergi, 1892-93) ±9.30 ±11.86 -1.4

New Britain 8 1152.1 1170.0 +17.9 0.5*

(MacCurdy, 1914) ±23.53 ±22.98 +1.5

New Britain, Duke of York

Island 28 1189.0 1283,3 +94.3 6.05

(Krause, 1881) ±9.62 ±12.28 +7.9

Solomon Islands 13 1147.0 1217.4 +70.4 2.73*

(Frizzi, 1912-13) ±18.46 ±18.0 +6.1

Solomon Islands, Santa Cruz... 24 1233.0 1168.0 -65.0 3.9

(Speiser, 1923a) ±10.34 ±13.27 -5.3

*Difference not statistically significant.

[Note to Librarians]


In December 19^3, the name of Field Museum of Natural History
was changed to Chicago Natural History Museum. Since that time it
has not been practical to make the called-for change in the name of the
Museum's technical publications. Beginning in 194-5, these publica-
tions of the Museum will appear under the general title of Fieldiana,
with division as formerly into five series — Anthropology, Botany,
Geology, Zoology, and Technique. These series will be continuous
with the volumes already published and will carry their successive
numerical designations as if no change of name had been made. The
name "Fieldiana" will appear only in connection with these series and
all other publications of the Museum will carry other titles.

The correct citation for the publications in the Fieldiana octavo series
will be Fieldiana, followed by the name of the series to which the publica-
tion belongs, and its volume number, etc.; for example, Fieldiana, Zool-
ogy, vol. 00, no. 0, pp. 00-00. For the Memoirs (quarto size) the
citation should be Fieldiana, Anthropology Memoirs, vol. 00, no. 00,
pp. 00-00.

The new name will not be used for the concluding parts of volumes
now partly published nor for additions to sets devoted to a single sub-
ject, as, for example, the Flora of Peru. These volumes and sets will
be completed as soon as possible but will continue to bear the serial
designation with which they started and the former name of the

September 19, 1945



that the Isserlis formula was calculated from measurements on
Negro skulls, which have a flat frontal region, whereas the Aus-
tralian skulls have a heavy supraciliary ridge. This ridge is part
of the maximum skull length, but its thickness of perhaps 8 mm.
adds nothing to the internal capacity. This suggestion is to some
extent supported by the fact that the Isserlis formula gives more
acceptable results for Australian females than for males. The brow-
ridge is less developed in females than in males, and there is therefore
not so much bony prominence to add to the length of the skull
without increasing the internal capacity.

The formula of Dr. von Bonin (1934, p. 14), which was worked
out for male skulls of New Britain, and these are Australoid in

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