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Cranial capacity studies.

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CRANIAL CAPACITY STUDIES
T. D. STEWART
Diviaion of Physicd Anthropology, U. S. National Museum
Two PLATES
INTRODUCTION
This series of studies is the outgrowth of a suggestion of
Doctor HrdliEka that it would be of interest to see how much
variation occurs in the capacities of skulls having approximately the same external dimensions. The writer felt that
first the direct methods of capacity determination required to
solve this problem should be tested for their accuracy. It so
happened that the capacity machine here to be described was
ready for testing at that time, so the two problems were combined. The other phases of the study developed in the course
of time from this original plan. Indeed, the answer to Doctor
HrdliEka 's suggested problem, though important, now occupies a minor place in the completed studies.
I. INVESTIGATION O F A NEW CAPACITY MACHINE
All methods for determining the capacity of dried skulls
which have attained wide usage depend on the principle that
the filling material must be packed into the skull. Only Bnsk
(Topinard, 1885, p. 600) and Wilder ('20) seem to have
advocated that packing be avoided, and it is significant that
neither of these have obtained a following. In the method
with packing as usually done by hand there is naturally a
chance for large personal error, increasing as the element of
fatigue enters. To minimize this error various detailed procedures have been recommended, but none standardized by
international agreement. Obviously, if a machine could be
' A preliminary report on this part was read before the fourth meeting of
the American Association of Physical Anthropologists, Atlantic City, 1932.
337
AMERICAN JOURNAL O F PHYSICAL ANTHROPOLWY, VOL. SVIII. NO.
JANUARY-MARCH, 1934
3
338
T. D. STEWlLBT
made to give the same degree of packing on each trial, and
every observer had such a machine, the problem of personal
error as affecting capacity would practically be solved. This
ideal seems to have had its first serious consideration in 1906
when Jarricot described a capacity machine without, however,
completely investigating its practicality. I n 1927 Bushkovitch
described a machine of somewhat different principle and indicated by his results that the ideal could be reached. Unaware of the work of Jarricot and Bushkovitch, Mr. M. S.
Goldstein, during his temporary employment in this division
from 1928 to 1931, also devised2 a machine for taking cranial
capacities. Circumstances have prevented Mr. Goldstein
from testing his machine, so this task has fallen to the lot
of the writer.
Goldstek machine
Plates 1 and 2 show the general arrangement of the machine.3 Essentially, it is a vibrating mechanism, the vibrations being produced by two eccentrics, one fixed, the other
adjustable in relation to the first, through a set screw, so as to
produce a variable eccentricity (maximum about %S inch).
The resulting motion is transmitted through two sliding
frames to a horizontal table. On this table is attached a
cradle in which the skull is fastened with base upward, and
which rocks from side to side while the machine is vibrating.
A jointed tube of 14 mm. internal diameter, and fitted with
a sliding valve, leads the seed down into the skull from a
suspended container (capacity about 5 liters; base a 120"
funnel). Power is supplied to the vibrator by a motor (%2
H.P.) through a pulley system producing a speed varied by a
six-step rheostat from about 1350 to 1550 rev./min. The
cradle receives power from the same motor through a different system of pulleys and has its speed further reduced by
gears to about 34200. I n the illustrations the cradle is shown
in its maximum swing.
'The mechanical details were worked out with the cooperation of the U. S.
Bureau of Staiidards and Mr. C. R. Denmark, engineer, U. S. Natioiial Museum.
' Made in the museum shops.
339
CRANIAL CAPACITY STUDIES
I n comparison with Goldstein’s machine, the one suggested
by Jarricot is very similar. I t is also a vibrating machine,
but consists of a single non-adjustable cam revolving about a
vertical shaft so as to strike two rectangular sliding frames
set at right angles to one another. The mechanism for attaching the skull and seed container (not pictured) is essentially like that used by Goldstein, except that the cradle
is lacking. Power is supplied by a motor through gears and
controlled by a rheostat.
The capacity machine more recently described by Bushkovitch is much simpler in construction than either of the
others and substitutes vertical for horizontal motion. I n this
case a cam in the form of a cogwheel, bearing four teeth,
is arranged so that each tooth in turn raises a stand bearing
the skull and then permits it to fall of its own weight. Packing is accomplished solely by the repeated impacts resulting
from the 11mm. vertical fall of the stand. As in Jarricot’s
arrangement, the skull is fastened in one position. Here
also, only speed is adjustable.
It will be appreciated that Goldstein’s machine has all of
the features of the other two while at the same time being
more easily adjustable as regards amplitude and period of
vibration. Moreover, the cradle would seem to insure more
complete filling of the skull. By testing this machine, therefore, it should be d e h i t e l y proved whether mechanical
methods are applicable in cranial capacity determinations.
‘Le Cubage’
It is only in the first part of the entire operation of capacity
determination-the filling of the skull (‘le jaugeage ’)-that
the machine is to be used. I n testing, it is necessary, therefore, that the second part-the measuring of the seed (‘le
cubage’)-be free from error. Indeed, the second part of the
operation may give as great an error as the first, unless the
observer fully understands the few principles involved. The
volume of the filling material may be determined in two ways :
1) I t may be poured from the skull into a graduated cylinder
ANERICAN JOURNAL O F PHYSICAL ANTRROPOLOGY. POL. X V I I I , NO.
3
340
T. D. STEWABT
and the reading made directly, provided the densities are the
same in skull and cylinder; or 2) the m i n g material may be
weighed and its volume calculated indirectly by a density
factor. Bushkovitch used the first method; Jarricot the
second.
I n using the cylinder with a given granular filling material,
there are three factors influencing the result: The diameter
and height of the cylinder and the size of the funnel opening;
a slender tall cylinder and a funnel with a small opening all
tend to increase the packing of the seed, thus giving a smaller
volume (Topinard). Even with these three factors constant,
there is still a small error due to the varying height of fall
of the seed as the cylinder fills (Bushkovitch). This instrumental error may be minimized as Bushkovitch found by
dividing the seed into two lots and combining the readings.
The main difficulty in using the cylinder method, however, is
to insure equal densities in both skull and cylinder. If the
packing is greater in the skull than in the cylinder, the result
will be larger than the true capacity (Schmidt, 1882). This
error, it is true, represents only a small percentage of the
whole, and yet in the case of large skulls can amount to more
than 40 cc. (using dried mustard seed). Moreover, the error
from this source usually remains constant for any one observer and method; that is, he always packs too much or
t,oo little and hence his mean result is high o r low, as the
case may be.
An example will make these facts more impressive: The
first part of the Catalogue of Human Crania in the United
States National Museum Collections ( '24) contains capacity
determinations made by Dr. Paul Van Natta under the supervision of Doctor HrdliEka and according to the latter's
method ( '20). Several years ago this catalogue was revised
(not yet published) and the capacities taken again by the
writer, using the same method and instruments. Again during the course of the present study some of these skulls
(selected only f o r size) were reexamined by a carefully controlled method to be described later (p. 348). Table 1shows
341
CRANIAL CAPACITY STUDIES
the results. Several errors are here illustrated: 1) The
variation of two observers using the same method and the
same instruments (A, B ) ; 2) the difference between the results of two methods, both of which are intended to give the
TABLE 1
Illustrating persond error and its increase with sise of skull
I
'
I
CAPACITY
DIFFEREBCJE
NO.
A-0
I
B-C
Large skulls
CC.
279485
279453
279581
279466
228281
Average
CC.
3610
1620
1640
1640
3620
1626
I
2274S4
1440
279505
1430
279661
1480
279490
1520
279488 -~1535
Average
1481
279528
279561
279463
228277
279390
Average
1193
1543
1390
1370
1420
1450
1470
1365
1385
1410
1440
1460
1420
1195
1210
1250
1190
1120
1
CC.
1550
1580
1580
1610
1550
1574
1160
1150
1210
1155
1080
1151
+ 90
+80
+ 85
1520
1540
1555
1565
1535
I
1412
1150
1160
1210
1145
1095
I
1152
cc.
cc.
+ 30
+ 40
+ 25
++ 4515
+
+83(5.4%)
75
+85
+ 31
+ 25
+ 10
++ 1010
+ 75
+ 45
+ 70
- 15
+ 80
+ 75
+
I -694.9%)
I
+ 10
+ 45
+ 50
+ 40
+45
25
l
+
(3.6%)
8
- 10
....
- 15
+ 10
+
I
-
1
true capacity (A, B-C); 3) the increase in error with size
of the skull, indicating that a greater density of seed existed
in the skull than in the cylinder; 4) the increasing percentage
of this error in relation to true capacity, due largely perhaps
to the error of the cylinder-seed of the upper part less dense,
hence greater in volume.
342
T. D. STEWART
These defects would seem to make continued use of the
measuring cylinder defenseless, and yet further consideration
will show that the main fault lies in another quarter, namely,
the filling of the skull. According to Hrdli6ka’s instructions,
one should have preliminary practice on standard skulls. The
only skulls of known volume which have been available heretofore in this laboratory have been of bronze, and so heavy
that any experience gained from their use could not be transferred to the natural skull. When one really learns to pack
seed into the skull to the same density as that determined by
the particular cylinder and funnel used, then the only remaining errors are personal and instrumental. The cylinder
has an advantage, moreover, in permitting rapid work.
Considering now the second method of ‘cubage,’ it may be
remarked that weighing is advocated at the present time
chiefly by the Karl Pearson school. It is interesting t o note
that MacDonell ( ’04) who revived this method did so because
he despaired of always attaining the same density of seed
in the cylinder as in the skull. Furthermore, since the Flower
method of packing the seed in the cylinder was then in use,
MacDonell found that weighing reduced the labor, though not
necessarily the time. As now used by the Pearson school, this
method depends upon a density factor representing the
weight of seed per unit of volume as packed into the standard
skull. Naturally, unless this factor is frequently checked, the
packing of the observer must be assumed to be constant; and
if the factor does not represent the density of the seed in the
skull, an error exists comparable to that of the cylinder. It
is true that the Pearson school makes a point of testing the
variability of the factor over a period of days, but some of
their reports (Morant, ’22-’23 ; Hooke, ’26) suggest two possible sources of error: 1) The use of a single standard skulllarge and small skulls may be packed differently, and 2) the
occasional use of maximum rather than average density. With
due regard to these two minor sources of error, it may be
said that the flexibility of this method makes its use desirable
whenever the seed must be packed into the skull by hand.
CRANIAL CAPACITY STUDIES
343
Naturally, it is equally useful when filling is done by any
other method.
Summarizing the main features of the two methods: 1) A
cylinder of given height and diameter, together with a funnel
opening of given diameter, will pack seed to a density which
slightly decreases indirectly with volume. There is no way
of telling whether the density of the seed in the skull is the
same as that given by the cylinder-funnel combination, except
by use of a skull of known volume or by using a machine
which constantly packs the seed to the same density. 2) The
weighing method, because of its flexibility, is the more reliable
of the two when the seed is packed into the skull by hand; that
is, when the density of the seed in the skull as packed by
different observers cannot be controlled. The accuracy of this
method depends on the density factor. In general, however,
it is more time consuming and little, if any more accurate.
In view of the complexity of the machine, and since there
is little difference' in the accuracy of the two methods of
'cubage' when the density of the seed in the skull can be
controlled, the choice of method to be used should be decided
by the factors of time and simplicity. This reasoning was
followed in selecting the cylinder for testing the machine. As
will be pointed out later (p. 349), the method of weighing has
been used in another phase of the testing.
The cylinder in use is rounded at the inferior end, measures
6 em. in internal diameter, 71 cm. in height, and is calibrated
every 10 cc. from 500 to 2000 cc. As the opening of the funnel
is 5 mm. above the top of the cylinder, the total height from
which the seeds fall is 71.5 cm. The funnel (Hrdlicka, '20) has
an opening 2 em. in diameter. This opening can be decreased
to 1.5 cm. by inserting a piece of rubber tubing with a 2 em. external diameter. By inserting a second piece of tubing within
the first, the opening may be decreased to a diameter of 1cm.,
but this is impractical as the seed then flow too slowly and
tend to jam. The instrumental error has been experimentally
determined for different heights and all readings are corrected.
344
T. D. STEWART
Since Bushkovitch used essentially the same method of
cubage, it is of interest to compare the relative densities of
seed in the two cylinder-funnel systems. He states that his
cylinder had an internal diameter of 6 cm., but was .only
57 cm. high.‘ On the other hand, his funnel (also of the
HrdliCka model) had an opening of only 11 mm. I t seems
likely, theref ore, that the increased density of seed resulting
from the smaller funnel opening was partly overccme at least
by the lesser height of fall and hence his system probably
gave about the same density as that obtained in the present
study with the 1.5 cm. funnel opening.
Cr6nes e‘talom’
Mention has already been made of the use of skulls of
known volume (‘crhes &talons’) for checking the ‘cubage.’
Naturally, the volume of a standard skull must be accurate.
There is general agreement that the true capacity of a skull
is represented by the volume of water which it will contain,
water being incompressible. For testing purposes, therefore, it is necessary to have a series of skulls of which the
exact water capacity is known.
To make a skull water-tight is a considerable task. In the
present study the skull was first sectioned, all of the larger
foramina, excepting the foramen magnum, filled with plasticine, the inner surface painted with melted paraffin, and finally
the two parts reunited with p a r a h . When a skull prepared
thus is filled with water there is a possibility that complete
filling may not be accomplished because of the formation of
air pockets. These may be largely prevented from forming,
as Bushkovitch has stated, by holding the skull with the base
vertical until the water level has reached the foramen
magnum, then gradually inclining the skull until the base is
horizontal, the latter position being reached just as the skull
becomes full. This method of filling was used, but even then
a few small air pockets were found to remain in the occipital
region. However, their locations were easily determined by
‘An extension added 14 em. t o the 43 an. glass cylinder.
345
CRANIAL CAPACITY STUDIES
inspection and small drilled holes allowed the air to escape.
The limit of error in such a standard skull probably does not
exceed 5 cc.
Table 2 gives the details of ten standard skulls made in
this manner. Attention is called to the fact that a wide
TABLE
2
Standard skulls w e d in testing machine
NO.
BACE
244080
American Negro
73.-
1070
1075
1075
341791
European
83.5
1205
1210
1210
244063
American Negro
75.8
1290
1290
1290
255051
African Negro
72.7
1330
1330
1330
225035
Eskimo
67.2
1360
1360
1365
244055
African Negro
76.1
1370
1365
1370
244076
American Negro
75.3
1390
1390
ce.
....
' Page
244074
American Negro
72.6
1405
1405
1410
244067
American Negro
73.7
1475
1470
1475
341794
European
83.9
1535
1540
1540
346.
I
346
T. D. STEWART
range of physical type is represented. It should be noted also
that on three trials of each skull a capacity variation of only
5 cc. resulted. Doubtless even this amount of variation is
too large in some cases, because readings were made only to
the nearest 5 cc. Since a special effort to remove all bubbles
was made on the third trial, this figure was usually largest
and was considered the true value. As a check on the method,
two bronze skulls were tested in the same way:
Stated capacity
Two trial.
ee.
Dipencm
1250.6
1245
1245
1300
1300
- 5.6
cc.
1306
cc.
-6
This result is especially satisfactory because the abnormal
depth of the foramen magnum in these bronze skulls makes it
diflicult to eliminate bubbles. A further check was given by
skull 244076: The presence of a trephine hole in the vault
made it possible to use this for the entrance of water instead
of the foramen magnum, thus making it certain that no
bubbles could be caught in surface irregularities. On each
of two trials this skull gave 1390 cc., which was the same as
when using the foramen magnum.
Testing
With a reliable method of ‘cubage,’ it is a simple matter
to test the ability of the machine to duplicate known volumes
in a series of ten skulls. Since the amplitude and period of
vibration are readily adjustable, it was thought advisable
first to try to reproduce with the machine a low density of
seed-that given by the cylinder and the 2 cm. funnel opening
(about 768 gm./lOOO cc.). At the beginning of each trial
either the amplitude or the period of vibration was readjusted
to give approximately the correct reading for one skull
(244080) and then both kept constant for the whole series of
skulls. The time that packing was continued after the seed
reached the level of the foramen magnum was arbitrarily set
as the interval required for two complete revolutions of the
wheel turning the cradle.
347
CRANIAL CAPACITY STUDIES
The results of five trials are shown in table 3. It will be
noted that for each skull the results are fairly consistent,
but in one case (24.4063, for example) they may be much too
high, while in another (244076) they may be much too low.
An attempt was made to correlate these differences with
physical type, but without success; note that 244063 and
244076 are of the same race and have approximately the same
cephalic index. On trial no. 4, however, skull 244076, which
had previously given low readings, gave a high reading. This
sudden change was accounted for by the fact that the skull
TABLE 3
Differences from true capacities given b y machine packing seed to different
amities
DENSITY ABOUT 768
SKULL NO.
a
244080
341791
244063
255051
225035
244055
244076
244074
244067
341794
c u . / l O O O cc.
Trial number
....
+ 35
+ 15
- 5
- 35
20
+ 5
+
+ 20
+5
+lo
I
3
....
+ 15
....
....
Trial number
4
+ 5
15
50
5
+
+
+ 10
- 5
- 5
+ 20
+ 10
....
+ 15
+ 25
+ 35
1
1
....
....
+ 45
....
....
+ 20
2
....
-15
+lO
- 5
....
....
+la
+lO
+15
+
+lO
5
+
5
....
+ 30
had been placed in the cradle so that :he occiput was more
elevated than before ; apparently the temporal fossae had not
been filling. Trial no. 5 confirmed this finding. The discovery that so small a change in the position of the skull
could lead to such a large error definitely finished the testing
at this density.
Since Bushkovitch claimed near perfect results with a
density greater than that mentioned above, it was next decided to increase the density by use of the 1.5 em. funnel
opening (about 798 gm./1000 cc.), with appropriate changes
in the machine. Table 3 also shows the results of two trials
348
T. D. STEWART
under these conditions. It will be noted that variability still
persists, though much more limited; indeed, only about 15 cc.
Apparently, even with this increased packing, the position of
the skull influences the filing. However, it seems likely that
variability can be still further decreased by increasing the
packing both in the skull and the cylinder. The reason for
discontinuing testing at this point will appear in the next
part.
11. EFFECT O F ALTERED INTERNAL SKULL SURFACE ON PACKING
O F SEED
It will be recalled that an objection to those methods which
attempt to pack seed into both the skull and cylinder is the
possibility that the smoother surface of the glass may increase
the packing in the cylinder over that in the skull. A similar
condition exists in the case of natural and standard skulls;
the internal surfaces of the latter have been made smooth
by the application of a paint, so the possibility exists that
when the Goldstein machine is adjusted to give approximately
correct volumes for standard skulls, it may give an error
for natural skulls.
To check this point it was necessary to compare the result
given by the machine with that given by another method in
which packing has a minor part. The method of Busk, with
modifications, seemed to answer the latter requirement. It
was found possible, by following a simple routine procedure,
to repeatedly a 1 a standard skull with minimal packing, and
by weighing the seed get remarkably uniform results; then
with this density factor determine the volumes (within 15 cc.)
of the other standard skulls from the weights of the seed
which they held.
The detailed procedure of filling was as follows: A skull
was held under the opening of the funnel-container attached
to the machine at such an angle that the seed fell into the
frontal region (much as when filling with water) ; the skull
was then brought to the horizontal position as filling neared
completion. Before filling was complete, however, the index
CRANIAL CAPACITY STUDIES
349
h g e r was introduced through the foramen magnum in the
directions of the petrous temporal bones, lightly pushing the
seed into the temporal fossae. A similar procedure induced
complete filling of the occipital regions surrounding the foramen magnum. One soon learns not to overcome the resistance
encountered. It was found absolutely necessary thus to make
certain with the finger of the filling of the fossae, this constituting the only packing. By this method a density of about
757 gm./lOOO cc. was obtained. Continued use of this method
requires frequent checking with standard skulls because the
observer will find that he unconsciously changes his technique
over a period of time.
The two methods thus far described, one depending on
maximal mechanical packing (‘cubage’ by cylinder), the other
on minimal packing by hand (‘cubage’ by weighing), and
both giving satisfactory results with standard skulls, were
next used on natural skulls of unknown capacity. The results
differed astonishingly in every case, sometimes by as much
as 50 cc., and always the higher figure was obtained by the
minimal packing method.
To further investigate the effect of surface on packing, five
sectioned skulls were tested (table 4). With the two sections
firmly fastened together, each skull was first tested in the
natural state by the two methods ; then, as shown in the table,
the internal surface was treated with talc, shellac, celluloid
or paraffin, and the effect on packing noted. The different
results given by the two methods before the surface was
altered is clearly shown in this series. It will also be noted
that when all the surfaces had been painted with paraffin the
results by the two methods again became alike; in other
words, the change in surface did not change the results by the
minimal packing method, but did increase the packing by the
machine. No effect could be definitely established when talc
was used in combination with shellac or celluloid, although
it may possibly increase packing slightly when used alone
(342420). Single applications of shellac or celluloid do not
form as thick a coating on the bone as in the case of p a r a h ,
350
T. D. STEWART
and to this fact is attributed the lesser effect upon packing.
Nevertheless, had sufficient shellac or celluloid been applied,
TABLE 4
Effect of altered internul skull surface on packing of seed
CONDITION
NO.
241947
or SUBFACE
Natural
Paraffin
242006
Natural
Paraffin
241969
Natural
Paraffin
242370
Natural
Celluloid
Celluloid
+ talc
Celluloid + paraffin
342420
Natural
Talc
Shellac
Shellac
Shellac
Shellac
+ talc
+ celluloid
+ celluloid + paraffin
ODACITY
Yhx. PACKLNG)
CAPACITP
YIN. PAOKINO)
cc.
cc.
1225
1230
1230
1245
1240
1235
1310
1300
1300
1340
1335
1340
1330
1320
1320
1370
1370
1375
1360
1365
1365
1395
1395
1390
1400
1405
1330
1330
1340
1350
1350
1365
1365
1355
1395
1395
1235
1335
1335
1375
1405
1395
1390
as when making a ‘crBne &talon,’it is believed that the effect
would have been equal to that of paraffin. It seems likely,
therefore, that all packing methods depending on standard
CRANIAL CAPACITY STUDIES
351
skulls, however made, must give a considerable error when
applied to natural skulls.
111. COMPARISON O F T H E MINIMAL PACKING METHOD WITH T H E
METHODS O F BROCA AND FLOWER
Since it has been shown in part I1 that different results
are obtained when the capacity of a dried skull is determined
by the minimal packing method and by the Goldstein machine,
i t is of interest to compare the results by minimal packing
with those of other maximal packing methods. For this purpose a unique opportunity is afforded by two small series of
skulls in the National Collections, received in exchange from
the British Museum in 1913. Each series contains six skulls,6
one being a part of the 1864 series of Gaboon Negroes reported on by Benington ( ’12), the other of the Papuans of
Torres Straits reported on by Thomas (1885). Benington determined the capacities by the Flower method of packing
seed into both skull and cylinder. Thomas used “. . . .
Broca’s method as revised by Topinard (‘Rev. d’Anthrop.’
1882, p. 394), using, however, the cylindrical rammer recommended by Dr. Garson instead of the conical pointed
rammer of Broca” (Thomas, p. 336). I n 1928 the writer,
without knowledge of these earlier reports, took the capacities
of these skulls by HrdliEka’s method and the results, together with other measurements, are reported in the Catalogue
of Crania (HrdliEka, ’28).
Table 5 shows how varied are the results by different
methods in the hands of three observers. It is interesting to
note that. the writer’s results by two methods show about the
same relationship as they did 4 years previously (compare
table 1). Both Benington and Thomas, on the other hand, average about 50 cc. higher than the new figures obtained by minimal packing. This agreement of the two methods is interesting
in view of the fact that, as originally described, Broca’s
method gave results that were much too high. It should be
noted, too, that all three packing methods give larger differences with increased capacity.
6 0 n e skull (Papuan) is immature, hence not used.
352
T. D. STEWART
Todd ( '23) has suspected that Benington's figures were too
high, since he was unable to use Isserlis' formulae (derived
from Benington's data, '14) to reconstruct the capacities of
American Negro skulls. He says :
I have pointed out repeatedly that the cranial capacities in
the University College series are larger than our capacities
and there is a tendency therefore for these formulae to give
TABLE 5
Comparison of results b y muzilnol and minim1 packing methods
NO.
OAPAOITY
-
!
U.S.N.M. Br. Mus.
80WOE
Benington l'homas
(Flower's Broca's
method)
method)
cc.
276092'
276093
276089
276088
276090
276091
4
39
9
80
74
69'
Gaboon
Gaboon
Gaboon
Gaboon
Gaboon
Gaboon
1039
1060
1198
1210
1220
1230'
276078
276079
276076
276080
276077
34
37
25
30
23
Torres Stra
Torres Stra
Torres Stra
Torres Stra
Torres Stra
....
....
....
....
....
Stewart
HrdliEka's
method)
Stewart
Min.pack.
method)
cc.
cc.
cc.
....
7
....
....
....
....
1020
1170
1160
1180
1330
1000
1010
1145
1160
1160
1300
39
50
53
50
60
1107
1185
1217
1273
1439
1055
1140
1165
1220
1395
1055
1130
1160
1210
1370
52
55
57
63
69
....
'I
* Not measured for catalogue.
'Tildesley ('27) states erroneously that 69A was sent to Washington.
Probably a mistake.
a
a higher result than ours. Now it so happens that Benington's Gaboon skulls have a high mean capacity, high at least
for the Negro whose true mean capacity is, as Pearson suggests, not far from 1350 cc. (p. 178).
The significant point here is that formulae are being derived
from capacities greatly in error. These formulae in turn are
being accepted and applied by some anthropologists as a short
cut to the mean capacity, instead of taking the individual
capacities. Errors are thus being perpetuated. If formulae
must be made, a good example has been set by Todd who
CRANIAL CAPACITY STUDIES
353
critically analyzes the technique both of his linear measurements and his capacity method.
IV. VARIABILITY O F CAPACITY IN’ SKULLS O F SAME RACE, SEX
AND EXTERNAL DIMENSIONS
In the foregoing studies some of the methods for direct
determination of cranial capacity have been investigated and
it has been shown that the minimal packing method is free
from certain errors which are inherent in the others. Having
the necessary confidence in the method, it is now possible,
finally, to take up the problem which initiated these studies.
Apparently, no one has attempted to discover the range of
capacity variation in skulls of the same external dimensions,
although its existence is recognized. In her study on the correlation of cranial capacity with external dimensions, Lee
(’01) concludes that-
. . . . we cannot expect to reconstruct the capacity of the
individual skull without a fairly large average error. F o r it
is of the very essence of the principle of variation, on which
evolution itself depends, that in any population we should
have an array of skulls with the same length, breadth and
height, and yet having within certain limits a variety of
capacities. All we can hope to say is, that with such a length,
breadth and height such a capacity is most frequent (p. 260).
Miner ( ’24) has explained that “the greater variability of
skull capacity as compared with length, breadth or height may
be accounted for by its three dimensional nature.” Hoadley
( ’29) has shown further that the accuracy of prediction
formulae increases 23 per cent when internal skull dimensions
are used, but that even in one sex and a homogeneous race
(twenty-sixth to thirtieth dynasties Egyptian males) “the
thicknesses of the bone are so slightly correlated with the
external measurements that it is not possible to obtain from
the latter good approximations to their values.”
Anderson ( ’10)has given a practical demonstration of the
first sentence quoted from Lee’s conclusion, namely, that a
large error results from attempts to recoiistruct the capacity
354
T. D. STEWBRT
of the individual skull-or the living head. Using forty cadaVera, Anderson first measured the head, computed the capacity
with Lee’s formula no. 14, and then measured the capacity of
the skull directly with water. Even assuming that the water
method of capacity determination here used (the two halves of
the skull filled separately) can be as much as 50 cc. in error,“
and that formulae for the head are not as accurate as for
the dried skull, Anderson’s results are still impressive; he
found one of his calculated capacities (no. 11) to exceed the
actual by 293 cc. and two (nos. 18 and 38) to fall below the
actual by 244 cc. As the material used by Anderson was the
so-called ‘hospital population,’ his results could well reflect
the heterogeneity of that group.
The present study proposes to demonstrate in another way
that the capacity of the individual skull cannot be computed
with any accuracy from the external measurements. This
demonstration follows the suggestion originally given the
writer by Doctor HrdliEka but also contained in Lee’s second
quoted sentence, namely, that skulls with the same length,
breadth and height will vary in capacity. To be more convincing, the material used will be restricted to one sex and a
homogeneous race.
It is of course impossible to find many skulls of one sex and
race which have identically the same external dimensions. If,
however, a small range is allowed each diameter, say 4 111111.
(the possible error in reconstructing a skull), a large collection
will furnish a respectable series. Thus, among the recorded
measurements of Eskimo skulls in the United States National
Museum forty males were found with lengths varying between
18.4 and 18.7,’ breadths between 13.8 and 14.2, and heights
(bas.-breg.) between 13.4 and 13.8 cm. If a fourth measurement were considered, the series would have to be reduced
about half to still meet the requirements. For example, the
aur.-breg. height (not routinely taken in this institution) when
measured for this series ranged from 10.8 to 12.- cm.; yet
ePersonal error (Todd). It is not stated whether the dura was removed.
These figures were selected because of their frequency.
355
CRANIdL CAPACITY STUDIES
twenty-one specimens fell within the limits 11.2 and 11.6 cm.
The frequency distributions follow:
Length
18.4--15
18.5-10
18.612
18.7- 3
18.8- 0
Breadth
13.8-10
13.914.-14.114.2-
7
8
6
9
Aut.-brcg. ht.
Bas.-brcg. ht.
13.4-15
13.5- 2
13.6 5
13.7- 8
13.8-10
10.8-3
10.9-3
11.--1
11.1-3
11.24
11.3-1
11.44 21
11.5-8
11.6-4
11.74
11.8-2
11.9-1
12.- -2
I
-
-
-
Total 40
40
40
40
By the minimal packing method the above series was found
to have capacities ranging from 1350 to 1580 cc., a total variation of 230 cc. Of the twenty-one skulls having in addition
a restricted am.-breg. height, the range of capacity was from
1370 to 1580 cc., a variation of 210 cc., or very little less than
f or the whole group. The frequency distribution follows :
ac.
1350-1395
1400-1445
1450-1495
1500-1545
1550-1580
Total
11
12
10
4
3
40
5
7
5
3
1
21
Not all of the possible combinations of three measurements
occur in such a small series, especially since some of those
combinations represented occur more than once. In one case
where a combination (Lt. 18.4, br. 14.-, ht. 13.4) occurs three
times, a capacity of 1350 cc. is found twice in combination
with aur.-breg. heights of 10.8 and 11.1em.; the third time
the capacity is 1505 cc. and the aur.-breg. height 11.5 em.,
thus indicating the closer correlation of am.-breg. height with
capacity. With a larger number of specimens it may be pre-
356
T. D. STEWART
sumed that the unusual distribution favoring the smaller
capacities will give way to a normal curve, possibly even
extending the range.
Unfortunately, the capacities of the other skulls of the
Eskimo collection have not been taken by the minimal packing method, so it is impossible to reverse the above demonstration and show how much variation in external measurements
occurs in skulls of the same capacity.
Cameron ( ’28) has reported on the correlation between
capacity and external measurements in Eskimos, based on
some of the same material (Catalogue of Crania, ’24), and
has pointed out the homogeneity of the group as compared to
whites. The revised catalague to be published later will
necessitate reconsideration of this matter, yet it is not unlikely that the homogeneity of the Eskimo will then appear
even greater.
CONCLUSIONS
Personal error in cranial capacity determinations can be
greatly reduced by mechanical means, provided the principles
of ‘jaugeage’ and ‘cubage’ are clearly understood and applied. On the other hand, the reliability of a capacity machine
depends upon the intelligence and care of the operator ; it is
a tool in his hands and cannot be expected to perform the
whole operation without careful supervision. Indeed, the
human skull is most variable in shape and size, thereby requiring a very flexible device for its attachment to the machine
and consequently the expenditure often of considerable time.
Added to all this is the unavoidable noise of the machine during operation. In view of these disadvantages, which, moreover, do not include the matter of expense, it is doubtful
whether the use of a machine is justified by the degree of accuracy gained.
Aside from the above objectionable points, it has been
shown that the character of the internal skull surface affects
the packing of seed and results in a considerable error. This
must be the chief objection to the use of the machine, as well
CRANIAL CAPACITY STUDIES
357
as all other methods that pack seed into the skull. Although
the effect of surface on packing has been tested only with seed,
it probably affects the packing of shot as well, since Topinard (p. 606) has indicated that his results varied according
to whether the shot was new or used.
The minimal packing method as here used is not affected by
alterations of internal skull surface, is less tiring, less time
consuming, and applicable to the most fragile skulls. Machines are of no assistance in filling the skull by this method,
and yet with sufficient practice and constant checking of the
density factor, personal error may be reduced to a minimum.
It has been pointed out incidentally that the capacity determinations on Gaboon Negroes by a maximal packing method
are too high, thus confirming Todd’s suspicion. Because these
figures form the basis of capacity prediction formulae, use of
the latter is highly unscientific.
Finally, if a male Eskimo skull is reconstructed with an
error of only 4 mm. for each of four external diameters
(length, breadth, bas.-breg. and am.-breg. heights), the error
in the predicted capacity may exceed 200 cc.
SUMMARY
1. The new Goldstein capacity machine is described and
compared with those of Jarricot and Bushkovitch.
2. The methods of ‘cubage’ are discussed and their sources
of error shown. The cylinder was selected for testing the
machine.
3. The methods of preparing and testing the ten standard
skulls (crgnes Qtalons) used in testing the machine are
described.
4. Detailed tests of the Goldstein machine are given, showing that satisfactory results may be obtained on standard
skulls.
5. A method of minimal packing (‘cubage’ by weighing) is
described and its results with natural and standard skulls
compared with those by the machine. It is shown that change
of internal skull surface affects packing.
358
T. D. STEWART
6. A small series of skulls formerly measured by Broca’s
method (Thomas) and another series formerly measured by
Flower’s method (Benington) are reexamined by the minimal
packing method and found t o average about 50 cc. too high.
7. Forty male Eskimo skulls, varying only 4 mm. in each
of three external diameters are shown to vary more than
200 cc. in capacity.
LITERATURE CITED
ANDERSON, J. H. 1910 An investigation aa to the most accurate method of
estimating the cubic capacity of the living head, together with some
remarks on the relative thickness of the cranial integuments. J.
Anthrop. Inst. Gr. Brit. and Ire., XL, 264-278.
BENINQTON,R. C. 1912 A study of the Negro skull with special reference
to the Congo and Gaboon crania. Biometrika, VIII, 292-337.
BUSHXOVITCH, V. J. 1927 An automatic apparatus for the measurement of
cranial capacity. Am. J. Phys. Anthrop., X, 355-363.
CAMERON,J. 1928 Craniometric studies no. 10: Correlations between cranial
capacity and cranial length, breadth, and height, as studied in the
St. Lawrence Island Eskimo crania, United States National Museum.
Am. J. Phys. Anthrop., XI, 269-278.
HOADLEY,
M. F. 1929 On measurement of the internal diameters of the skull
in relation: (1) to the prediction of its capacity, (2) t o the ‘preeminence’ of the left hemisphere. Biometrika, XXI, 85-123.
HOOKE,
BEATRLXG. E. 1926 A third study of the English skull with special
reference to the Farringdon Street crania. Biometrika, XVIII, 1-55.
H B D L I ~ AA., 1920 Anthropometry. Wistar Institute, Philadelphia.
1924 Catalogue of human crania in the United States National
Museum collections. The Eskimo, etc. Proc. U. S. Nat. MUS., LXIII,
Art. 12, 1-51.
1928 Same. Australians, etc. Proc. U. S. Nat. Mus., LXXI,
Art. 24, 1-140.
ISSERLIS,
L. 1914 Formulae for the determination of the capacity of the Negro
skull from external measurements. Biometrika, X, 188-193.
JAWCOT,
J. 1906 Sur un projet d’emploi de la succussion mhhanique d a m
le jaugeage dn crane. Bull. Soc. d’Anthrop. Lyon, XXV, 94-106.
LEE, AUCE 1901 A first study of the correlation of the human skull. Phil.
Trans., 196 (A), 225-264.
MACDONELL, W. R. 1904 A study of the variation and correlation of the human
skull, with special reference to English crania. Biometrika, 111,
191-244.
MINEB, J. R. 1924 The variability of skull capacity. Am. J. Phys. Anthrop.,
VII, 425-426.
MOUNT, G. M. 1922-1923 A first study of the Tibetan skull. Biometrika,
XIV, 193-260.
CRANIAL CAPACITY STUDIES
359
SCHNIDT,E. 1882 Ueber die Bestininlung der Schiideleapacitat. Archiv. f.
Anthrop., X I I I , Supplement, 53-79.
THOMAS,
0. 1885 Account of a collection of human skulls from Torres Straits.
J. Anthrop. Inst. Gr. Brit. and Ire., XIV, 328-343.
TILDESLEY,MIRIAM L. 1927 Determination of the cranial capacity of the
Negro from measurements on the skull or the living head. Biometrika,
X I X , 200-206.
TODD, T. W. 1923 Cranial capacity and linear dimensions, in White and
Negro. Am. J. Phys. Anthrop., VI, 97-194.
TOPINARD,P. 1885 lh8ments d ’anthropologie gbnerale. Paris.
WILDER,H. H. 1920 A laboratory niauual of anthroponietr~. Philadelphia.
PLATE 1
CRANIAL OAPACITY STUDIES
T. n. STEWART
F r o n t view of t h e maehine. eradle shown in its maximum swing to one side.
360
PLATE 2
CRANIAL CAPACITY S T U D I E S
T. D. STEWART
Side view of the machine showing the method of attaching the skull.
361
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