-T L I B R.AFIY OF THE UNIVERSITY Of ILLINOIS 57 2. OS FA M 2.0 FA LDIANA . ANTHROPOLOGY Published by CHICAGO NATURAL HISTORY MUSEUM Volume 36 February 4, 1947 No. 3 CRANIAL CAPACITIES, A STUDY IN METHODS Wilfrid D. Hambly Curator, African Ethnology LITERATURE AND TECHNIQUE 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 THE UBRARY OF THE FEB 2 0 1947 ONIYERSITY OF ILLINOIS 26 FIELDIANA: ANTHROPOLOGY, VOLUME 36 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 considered. 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 m,05 ■s HAMBLY: CRANIAL CAPACITIES 27 the general run of measured averages for other male Melanesian groups. 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 28 FIELDIANA: ANTHROPOLOGY, VOLUME 36 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 HAMBLY: CRANIAL CAPACITIES 29 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 formula. 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 30 FIELDIANA: ANTHROPOLOGY, VOLUME 36 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. Differences in CO. and percentage -29.0 -2.2 +37.0 +2.6 -15.0 -1.0 -26.1 -1.9 +51.0 +3.7 -20.0 -1.5 -10 -0.7 -58 -4.1 +19 +1.3 a/Pa 1.36* 1.28* 3.95 1.21* 3.30 0.84* 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. NEGROES AND EGYPTIANS 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 HAMBLY: CRANIAL CAPACITIES 31 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. 32 FIELDIANA: ANTHROPOLOGY, VOLUME 36 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. MELANESIANS 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 published. 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, HAMBLY: CRANIAL CAPACITIES 33 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. fDeformed. Differences in CO. and percentage a/Pa -3.0 -0.20 1.36* -69.1 -5.1 7.10 -26.8 -2.0 1.0* -5.0 -0.04 0.04* -2.6 -0.2 0.16* -7.9 -0.6 0.63* -52.0 -3.9 2.7* -7.0 -0.5 0.3* +93.0 +6.6 4.3 -14.0 -0.9 0.4* +66.0 +4.8 3.9 -29.0 -2.0 1.2* -24.0 -1.6 1.4* -17.0 -1.3 0.80* +61.0 +4.6 1.9* +35.3 +2.7 1.15* -56.1 -4.3 3.80 -18.0 -1.3 1.7* 84 FIELDIANA: ANTHROPOLOGY, VOLUME 36 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] FIELDIANA 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 institution. September 19, 1945 86 FIELDIANA: ANTHROPOLOGY, VOLUME 36 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 appearance, might serve to calculate the capacities for series of Australian skulls whose cranial content is unknown. The formula of von Bonin reads C = . 000263 X BLH' + 404.9±35.1/Vn7 The following table gives the capacities calculated by the two different formulae and shows the divergence of the results from the measured capacity. Australian Skulls Source Number of skulls Robertson (1910-11) 78 d^ Robertson (1910-11) 22 9 Hrdlifika (1928) 505 d^ Hrdlieka (1928) 395 9 Divergence from Capacity by measured von Benin's mean, in cc. and percentage formula 1232 1145 1283 1172 -62 -4.8 -2 -0.2 -11 -0.8 +25 +2.2 Capacity by Isserlis' formula 1306 1179 1381 1122 Divergence from measured mean, in cc. and percentage + 12 +0.9 +32 +2.8 +87 +6.7 -25 -2.2 The table indicates that the formula of von Bonin is to be pre- ferred to that of Isserlis for calculating the cranial capacities of Australian skulls. When the two formulae are applied to cranial measurements of male skulls, supplied by HrdliSka (1928) from five regions of Aus- tralia, the following results are obtained (p. 37, top). The samples are satisfactory in size. HAMBLY: CRANIAL CAPACITIES 37 Australian Males Divergence Divergence from from Capacity by measured Capacity by measured Number von Benin's mean, in cc. Isserlis' mean, in cc. Region of skulls formula and formula and percentage percentage South Australia 194 1278 -16 1374 +80 -1.2 +6.2 Northern territory 102 1256 -38 1341 +47 -2.9 +3.6 Victoria 73 1327 +33 1446 +152 +2.5 +11.7 New South Wales 57 1297 +3 1402 +108 +0.2 +8.3 Queensland 49 1283 -11 1381 +87 -0.8 +6.7 Crude average 475 1288 -6 1389 +95 -0.5 +7.3 The figures show that for male Australian skulls the for- mula of Isserlis gives capacities that are too high, that they are consistently so, and that they would give an approximate error of 7.3 per cent above the expected measured value. Australian Males Number Source of Measured skulls capacity Morant (1927) 146 1294.6 ±6.68 Wagner (1937) 98 1294.0 ±10.28 Australian Females Morant (1927) 67 1147.4 ±6.60 Wagner (1937) 11 1103.4 ±16.28 •Difference not statistically significant. Capacity by formula of Isserlis 1368.0 ±5.38 1253.0 ±6.57 1176.8 ±7.94 1173.3 ±19.60 Differences in cc. and percentage +73.4 +5.6 -41.0 -3.2 +29.4 +2.6 +69.9 +6.3 a/Pa 8.5 3.3 2.8* 2.7* On the contrary, the formula of von Bonin gives results that are all fairly compatible with the general measured mean of 1294. For a large group of female skulls (395) pooled by Hrdlicka for L, B, H measurements, the formula of von Bonin gave a capacity of 1172. This is by no means unacceptable by comparison with the measured standard of 1147, which is that of Morant (1927) based on measurements of 67 skulls. The formula of Isserlis, though generally unacceptable for male skulls, gives for female skulls results by no 38 FIELDIANA: ANTHROPOLOGY, VOLUME 36 means unlikely, namely, 1122 for Hrdlifika's sample and 1179 for Robertson's sample. On the whole, I think that either von Benin's or Isserlis' formula will give a reasonable approximation to the cranial capacity of female Australian skulls, and without making changes in the formulae; but for calculating the capacity of male Australian skulls the formula of von Bonin is preferable to that of Isserlis and may be used without amendment. Tasmanian Males Number Capacity by Differences Source of Measured formula of in cc. and A/P^ skulls capacity Isserlis percentage Tasmania 14 1247.1 1376.1 +129 4.8 (Wunderly, 1939) ±20.48 ±17.37 +10.3 Tasmania 33 1264.3 1344.5 +80.2 4.6 (Morant, 1927) ±13.34 ±11.32 +6.4 Tasmanian Females Tasmania 25 1153.8 1210.8 +57.0 3.4 (Morant, 1927) ±10.18 ±13.00 +4.9 Tasmania 14 1242.8 1297.4 +54.6 2.4* (Wunderly, 1939) ±13.61 ±17.37 +4.4 ♦Difference not statistically significant. These averages of cranial capacities of Tasmanians are based on small samples, and according to this slender evidence the capacity for males is about 1264 and fchat for females approximately 1153. Morant's data are based on numbers almost twice as large as those of Wunderly. These are measured capacities that are used as standards of comparison for the calculated capacities given in the following table. Tasmanian Skulls Divergence Divergence Capacity by from Capacity by from Number formula of measured formula of measured Source of skulls Isserlis capacity in von Bonin capacity in cc. and cc. and percentage percentage Robertson (1910-11) 54 6^ 1371 +107 1276* +12 +8.5 +0.9 Hrdligka (1928) 22 cf 1457 +193 1334 +70 + 15.3 +5.5 Robertson (1910-11) 30 9 1229 +76 1179* +26 +6.6 +2.2 Hrdlieka (1928) 15 9 1235 +82 1182* +29 +7.1 +2.5 •Acceptable result. HAMBLY: CRANIAL CAPACITIES 39 The data given in the three tables on page 38 clearly indicate that the Isserlis formula gives capacities that are too high, as it did for Australian skulls. The lower table shows the approxi- mation to measured capacities given by the formula of Isserlis, and also by that of von Bonin, both without amendment. The L, B, H measurements are provided by Hrdlicka and by Robertson, but these investigators did not measure cranial capacities. Only three results, namely, those marked with an as'terisk, and all of them from application of von Bonin's New Britain formula, are acceptable. The details of inquiry confirm the opinion empha- sized on page 35. POLYNESIANS The following tables make a comparison of the measured and calculated capacities of several groups of Polynesian male and female skulls. Polynesian Males Number Capacity by Differences Source of Measured formxila of in cc. and A/P^ skulls capacity Isserlis percentage Sandwich Islands (Hawaii) 56 1456.0 1515.0 +59.0 3.1 (Wagner, 1937) ±13.37 ±8.69 +3.4 Hawaii 16 1437.8 1462.7 +24.9 1.0* (Hambly, unpublished) ±17.23 ±16.25 +1.7 Marquesas Islands 19 1475.0 1473.0 -2.0 0.06* (Wagner, 1937) ±31.11 ±14.91 -0.1 Tonga and Samoa 9 1460.0 1519.0 +59.0 1.7* (Krause, 1881) ±27.88 ±18.76 +4.0 Easter Island 36 1462.0 1493.0 +31.0 1.85* (von Bonin, 1931b) ±12.76 ±10.83 +2.1 Moriori 57 1438.8 1479.3 +40.5 3.30 (Thomson, 1915-17) ±8.93 ±8.61 +2.8 Moriori.... 29 1454.9 1481.4 +26.5 1.40* (Scott, 1894) ±12.52 ±14.18 +1.8 Maori, North Island 13 1405.0 1440.8 +35.8 1.48* (Weisbach, 1890) ±5.99 ±18.03 +2.5 Maori 40 1450.5 1470.0 +19.5 1.32* (von Luschan, 1907) ±10.66 ±10.27 +1.3 Maori 45 1476.0 1467.5 -8.5 0.61* (Scott, 1894) ±10.06 ±9.68 -0.6 Maori 35 1435.0 1450.0 +15.0 0.95* (Wagner, 1937) ±11.40 ±11.00 +1.0 *DifTerence not statistically significant. 40 FIELDIANA: ANTHROPOLOGY, VOLUME 36 Polynesian Females Number Source of Measured skulls capacity Maori 21 1362.9 (Wagner, 1937) ±16.04 Maori 32 1307.5 (von Luschan, 1907) ±13.00 Moriori '. 28 1304.5 (Thomson, 1915-17) ±13.89 Sandwich Islands (Hawaii) 45 1324.6 (Wagner, 1937) ±8.73 Polynesians, pooled 136 1320.0 (Hambly, unpublished) ±5.32 *Difference not statistically significant. Capacity by formula of Isserlis Differences in cc. and percentage 1350.2 ±14.18 -12.7 -0.9 1290.5 ±11.49 -17.0 -1.3 1327.2 ±12.28 +22.7 + 1.7 1345.2 ±9.68 +20.6 +1.5 1328.5 ±5.57 +8.5 +0.6 a/Pa 0.59* 0.98* 1.2* 1.57* 1.10* The formula of Isserlis gives for Polynesian male crania a result 1.8 per cent too high, and for female crania 0.4 per cent too high. The crude average capacity for males by measurement is 1451 cc. and the calculated capacity is 1477 cc. For female crania the measured and calculated capacities are closer. The crude average for females is 1324 measured and 1328 by formula. The results for female Polynesian skulls support the previous suggestion (p. 36) made for Australian skulls. The formula of Isserlis was worked out for Negro skulls with flat foreheads (a female trait) ; therefore the formula gives more acceptable results for females of other racial groups. Polynesian Males Source Marquesas Islands (von Luschan, 1907) Maori (Morant, unpublished) Maori, North Island (Morant, unpublished) Maori, pooled 115 (von Bonin, unpublished) Polynesians, pooled 157 (von Bonin, unpublished) Loyalty Islands, Lifou (Bertillon, 1872) Number of skulls Calculated capacity by Isserlis' formula Divergence from Polynesian general measured mean (1451 cc.) in cc. 16 /1462 \1436 + 11 -15 74 /1451 \1425 ±0 -26 42 /1491 \1464 +40 +13 115 /1469 \1443 +18 -8 157 /1467 \1441 +16 -10 10 /1454 +3 \ 11428 -23 HAMBLY: CRANIAL CAPACITIES 41 The foregoing table (p. 40) gives a comparison of cranial capaci- ties. The upper of the bracketed figures are the results obtained by- using the unchanged formula of Isserlis, and the lower figures are those obtained by reducing the result by 1.8 per cent (vide supra). Unfortunately there are no capacities by direct measurement for these groups of skulls. The table (p. 40) indicates that 1451 cc. is the crude average capacity for Polynesian male skulls, and if this is accepted then the calculated results by Isserlis' formula either amended or unchanged give plausible results. For Morant's 74 Maori skulls the unchanged formula gives a capacity of 1451 cc, and 1425 if 1.8 per cent is deducted. Acceptance of either of these capacities would be preferable to measuring the capacity of 74 skulls by the slow mustard seed technique. Other calculated results come close to the general mean (1451 cc), and perhaps most craniometrists would be willing to accept them instead of actually measuring the capacities. EUROPEANS Old English. — The following tables (pp. 41-43) indicate that if the formula of Isserlis is used to work out the capacity of Old English skulls the result is likely to be 2.1 per cent too low. Therefore, when making estimates of the capacity of Old English skulls we must add 2.1 per cent to any result given by the original formula of Isserlis. Morant (1926) calculated some capacities by Hooke's (1926) formula C = .000366 X LBH + 198.9 and found the results given in the table below, upper series of figures: English and English and Formula Scottish English Scottish Scottish Anglo-Saxon Neolithic Bronze Age Bronze Age Iron Age Hooke 1533 1564 1561 1488 1543 Isserlis + 2.1%.... 1530 1564 1561 1481 1542 Since Hooke's formula is based on measurements of English skulls we may assume that the capacities which Morant gives (upper series) are correct, for his samples are all English and Scottish skulls, and the application of Hooke's formula for finding their capacities was therefore appropriate. The lower line of figures, which make a very close fit with the upper, indicates that, had there been no formula specially applicable to Morant's data, the formula of Isserlis +2.1 per cent would have given dependable results. 42 FIELDIANA: ANTHROPOLOGY, VOLUME 36 Old English Males Number Source of Measured skulls capacity Farringdon Street 86 1481.5 (Hooke, 1926) ±9.46 Whitechapel 72 1476.9 (Hooke, 1926) ±9.73 Moorfields 22 1473.8 (Hooke, 1926) ±19.01 Hythe 110 1456.3 (Stoessiger and Morant, 1932) ±7.00 •Difference not statistically significant. Old English Females Farringdon Street 132 1296.5 1257.9 -38.6 4.6 (Hooke, 1926) ±6.12 Whitechapel 80 1299.9 1261.4 -38.5 3.4 (Hooke, 1926) ±8.51 Capacity by formula of Isserlis Diflferences in cc. and percentage a/Pa 1438.1 ±7.01 -43.4 -2.9 3.68 1438.1 ±7.66 -38.8 -2.6 3.14 1447.7 ±13.85 -26.1 -1.8 1.11' 1443.0 ±6.19 -13.3 -0.9 1.4* 1257.9 ±5.6 -38.6 -2.9 1261.4 ±7.27 -38.5 -2.9 1296.6 ±11.67 -68.7 -5.0 1279.0 ±7.13 -39.0 -2.9 Moorfields 31 1365.3 1296.6 -68.7 3.8 (Hooke, 1926) ±13.68 Hythe 83 1318.0 1279.0 -39.0 3.8 (Stoessiger and Morant, 1932) ±7.30 Irish Skulls. — Howells (1941) does not give the cranial capacities of 120 male skulls from Gallen Priory, but he supplies the average L, B, and H' measurements. These dimensions, when used in the formula of Isserlis, give a cranial capacity of 1530, and the addition of 2.1 per cent brings the capacity up to 1562. This is somewhat high compared with the crude general mean of 1472 for Old English male skulls and 1488 for European male skulls. But the Irish skulls are long and broad, and the dimensions suggest that the capacity will be a high one. Perhaps one ought not to apply anything English to the solution of an Irish problem, but, according to Hooke's formula, which was prepared from measurement? on English skulls, the capacity of the Irish skulls should be 1563. This is only one cubic centimeter greater than the cranial capacity (1562) obtained by the revised formula of Isserlis. Scottish Skulls. — Data relating to cranial capacities of Scottish skulls are based on a study of a modern collection of 700 specimens (Young, 1916, 1931). But no cranial capacities of these Scottish HAMBLY: CRANIAL CAPACITIES 43 European Males Ancient and Modern Number Capacity by Differences Source of Measured formula of in cc. and A/P^ skulls capacity Isserlis percentage (Morant, 1928) Serbo-Croats 79 1524.6 1454.3 -70.3 6.2 ±8.61 ±7.31 -4.6 Greeks 86 1489.0 1418.3 -70.7 6.5 ±8.25 ±7.01 -4.7 Turks 39 1457.1 1435.2 -21.9 1.4* ±12.26 ±10.41 -1.5 Slovenes 48 1406.2 1414.5 +8.3 0.6* ±11.05 ±9.38 +0.6 Rumanians 38 1478.9 1413.6 - 65.3 4.0 ±12.42 ±10.54 -4.0 Czechs 108 1438.4 1391.2 -47.2 4.9 ±7.36 ±6.25 -3.3 Swiss, Valais 159 1542.7 1468.6 - 74.1 9.3 ±6.06 ±5.15 -4.8 Swiss, Sierre 28 1547.1 1502.6 -44.5 2.3* ±14.47 ±12.28 -2.9 Wurttemberger 91 1493.8 1423.4 - 70.4 6.7 ±8.03 ±6.81 -4.7 Badensians 78 1524.9 1473.1 -51.8 4.6 ±8.67 ±7.36 -3.4 French 56 1473.1 1396.0 -77.1 5.7 ±10.23 ±8.69 -5.2 Guanche 76 1503.9 1444.2 -59.7 5.6 ±8.78 ±7.45 -4.0 Etruscans 78 1456.0 1446.2 -9.8 0.9* ±8.67 ±7.36 -0.7 Pompeians 51 1503.6 1404.7 -98.9 7.0 ±10.72 ±9.10 -6.6 *Difiference not statistically significant. skulls have been measured by mustard seed. Nevertheless, the following table gives a fair indication of the approximate capacity judged by (1) measurements with shot (No. 8B), (2) calculations of capacity by the formula of Hooke for English skulls, and (3) by the formula of Isserlis for the Negro skull +2,1 per cent. This is the addition we agreed to allow after testing that formula against the carefully measured capacity of several groups of English skulls (p. 41). 44 FIELDIANA: ANTHROPOLOGY, VOLUME 36 ' Method Males Females f 1526 f 1322 By shot (No. 8B) 1511 1314 i 1478 i 1300 By Hooke formula 1473 1315 By Isserlis formula + 2.1 % 1465 1315 There is fairly good agreement in the three methods of determin- ing the capacity. The three quotations for measurement by shot relate to results obtained by division of the collection. Two of the measurements by shot seem somewhat high, but according to our experiment (p. 26) a reduction of 5.4 per cent is permissible in order to make shot measurements comparable with those arrived at by using mustard seed. For female measurements there is identity of result (1315 cc.) arrived at by the formulae of Hooke and of Isserlis (amended), and these calculated results are in harmony with the three capacities (1300-1322) measured with shot. The figure of 1322 (shot) for female Scottish skulls is high com- pared with capacities measured with mustard seed for four groups of female English skulls (p. 42). A crude average for the English females is 1274, and reduction of 1322 (shot) by 5.4 per cent gives 1251 for Scottish skulls, which is close to the English capacity. According to the collated data of Martin the crude average for European females is 1296, which is quite close to the Scottish value of 1300-1322 by shot. We have also pointed out that a value of 1315 for female Scottish skulls is given by two independent formulae, and one feels dubious about reducing the shot measurement in this particular instance. Turner (see p. 26, this work) himself, who is responsible for the measurements of these Scottish skulls by shot, thought that 6.9 per cent should be deducted, which is rather more than my own experi- ments would allow. But my suggestion is that he used such fine shot (No. 8B), and furthermore that he packed the skulls and then the measuring cylinder so carefully, that he has obtained in this particular instance a result very close to that which would have been obtained by using water or very fine seed. In the textbook of Rudolf Martin (1928, p. 745) average capaci- ties are given for fifteen geographical groups of European skulls. All these capacities were measured by shot, and they yield a crude average of 1543 for males and 1370 for females. If this result is HAMBLY: CRANIAL CAPACITIES 45 reduced by 5.4 per cent (p. 26, this work) the average capacities for European males become 1460 and for females 1296. Martin then gives (op. cit., p. 746) a list of European cranial capacities for 13 male and 12 female geographical groups, all of which were found by measurement with water or mustard seed. The crude average capacities are 1447 for males and 1296 for females. Comparison of the capacities collated by Martin suggests that my deduction of 5.4 per cent from capacities calculated by use of shot is experimentally sound, for we have from Martin's collated data: Capacity by shot Capacity by Differences (reduced 5.4%) seed or water in cc 1460 (cf) 1447 (€?•) -13 1296 (9) 1296 (9) ±0 SOUTH AMERICAN INDIANS The following table (p. 46) has been compiled from data kindly supplied by Dr. T. D. Stewart and Dr. Marshall T. Newman. From these figures I have calculated a general weighted average cranial capacity for 513 South American Indian males and for 226 females. The average capacity of the male skulls is 1442. 96± 3 cc. and for the females, 1315.70 ± 4.43 cc. The cranial content of the average male skull is about 8.8 per cent in excess of that of the average female skull, a result compatible with the data tabulated. The table of sex differences in cranial capacities (p. 62) shows a percentage difference of 13.1 for Australian skulls. This is a max- imum excess of male over female cranial capacity. The smallest excess of male over female cranial content is 4.6 per cent for Tas- manian skulls. The average cranial capacity for South American Indian male skulls (1442.96) is close to the capacities for skulls of North American Indians and Eskimo (p. 47). The capacity for female crania of South America (1315.70) fits very well with the capacities of some groups of females of North American Indian tribes (p. 48). The variability of cranial capacities in the groups of South American Indians may be judged to some extent by the standard deviations given by Dr. T. D. Stewart. For males, the ranges of the standard deviations are 142,85 (72 Calchaqui) to 99.68 (45 Parana Delta Indians). The standard deviation for cranial capac- ity of 753 Egyptian males is 113.51 i 1.97 (Pearson and Davin, 1924) and the interracial standard deviation for male cranial ca- pacity is 100.2 ± 2.53 (Hambly, 1946, p. 115). The high standard 46 FIELDIANA: ANTHROPOLOGY, VOLUME 36 deviation of 142.85 for 72 Calchaqui Indians may represent a wide scatter of values in the array of measurements. But it is also true that any careless filling of the skull or failure to tamp the seed in the measuring glass will lead to a very wide range of measurements in the results. The standard deviations for measurements of cranial capacities in female skulls for South American Indians range from 128.25 to 92.26. The latter is normal ; the former is high. For 472 Egyptian female skulls the standard deviation of the cranial capacities is 98.68 ± 14.19. This figure is close to the standard deviations of that trait for South American Indian skulls, which for the several groups are 111.90 ± 7.47, 112.45, 112.22, 117.85. On the whole, the cranial capacities of the South American Indian skulls show a normal variability. South American Skulls By courtesy of Dr. T. Dale Stewart and Dr. M. T. Newman Number of skulls Mean cranial capacities Tribe ■ ■ • Males Females Males Females Rio Negro Patagonians 76 51 1452.10± 9.48 1356.56±10.57 (Marelli, A. 1913) Rio Chobut Patagonians.... 41 29 1531.58±13.28 1359.68±16.04 (Marelli, A. 1913) Calchaqui 72 44 1417.06±11.35 1247.86±11.44 (Kunike, H. 1911) Calchaqui 70 30 1466.14±10.40 1339.00±11.36 (Constanzo, M. 1942) Ona 22 8 1426.25±16.14 1355.62 (Gusinde, M. 1939) Yahgan 33 19 1435.74=tl3.37 1289.63 (Gusinde, M. 1939) Paucarcancha 108 1371.92± 6.95 (MacCurdy, G. G. 1923) Botocudo* 32 . . 1431.81±13.58 (Ehrenreich, P. 1887) Parana Delta 45 19 1529.72±10.03 1343.16 (Torres, L. M. 1911) Cucurital 14 26 1488.71 1328.85± 8.65 (Marcano, G. 1893) ♦For further measurements see bibliography of T. D. Stewart, 1943, pp. 268, 269. HAMBLY: CRANIAL CAPACITIES 47 NORTH AMERICAN INDIAN AND ESKIMO The method of comparing the measured and calculated capacities of North American crania is the same as that used in previous chapters. The following table shows a close fit between measured and calculated capacities of North American crania. For five groups of data out of six, the differences between the capacities so ob- tained are not significant. On the average the formula of Is§erlis gives a result which is 1.4 per cent too low. North American Indian and Eskimo Males Number Capacity by Diflferences Source of Measured formula of in cc. and A/P^ skulls capacity Isserlis percentage North American Indians, Ken- tucky 24 1432.5 1386.6 -45.9 2.2* (von Bonin and Morant, 1938) ±15.63 ±13.26 -3.2 North American Indians, Chey- enne, Chippewa, Piegan, pooled 41 1514.0 1456.7 -57.3 3.6 (von Bonin and Morant, 1938) ±11.96 ±10.15 -3.8 North American Indians, East- Central, pooled 33 1500.0 1495.0 -5.0 0.3* (von Bonin and Morant, 1938) ±13.33 ±11.32 -0.3 North American Indians, Ohio, Indiana, Michigan, Illinois, pooled 25 1490.6 1480.6 -10.0 0.5* (von Bonin and Morant, 1938) ±15.31 ±13.00 -0.7 North American Indians, Cali- fornia 128 1349.1 1350.1 +1.00 0.11* (von Bonin and Morant, 1938) ±6.58 ±5.74 +0.07 Eskimo 200 1473.1 1470.0 -3.1 0.44* (Morant, 1937) ±5.41 ±4.59 -0.2 ♦Difference not statistically significant. A further test of the applicability of the Isserlis formula for calculating the capacity of male Eskimo skulls is made in the table on page 48. The measured capacities are given by Morant (1937) from various sources which he quotes in detail. Out of six applications of the formula three give results which, judging by the measured capacities, have errors of less than one per cent. Agreement of actual measurement and of calculation are not satisfactory in the two instances marked with a double dagger. It is difficult to understand why the Isserlis formula should give a discrepancy of only 0.2 per cent for 200 Western Eskimo skulls, and 48 FIELDIANA: ANTHROPOLOGY, VOLUME 36 Eskimo Males Capacity by Source Number Measured unrevised Isserlis Differences in cc. of skulls capacity formula and percentage tGreenland 217 1526 1451 -75t -4.9 Northwestern 45 1435 1466 +31 +2.2 Central 17 1558 1516 -42t -2.7 Nunivak Island 46 1504 1492 - 12 -0.8 Point Hope 126 1474 1460 -14 -0.9 Western 200 1473 1470 -3 -0.2 Crude averages 651 1495 1476 -19 -1.3 fPooled value from data of Fiirst and Hansen (1915) and HrdliCka (1924). The other data are from Hrdlifika (1924). JAgreement of actual measurement and of calculation are not satisfactory. a discrepancy of 4.9 per cent for a group of 217 Greenland skulls. One can readily understand that the measured and calculated capacities for small groups of skulls might be at variance, for example in the case of only 17 Central Eskimo skulls, but usually compati- bility of the calculated with the measured capacity increases with the size of the group. This is likely to be so because a small group, of skulls may be dominated by a few examples of exceptional shape or size. The general conclusion is that if we take a crude average for 651 male Eskimo skulls the measured capacity is 1495 and the cal- culated capacity is roughly 1476, so giving a discrepancy of —1.3 per cent. Some measured cranial capacities recorded by Hrdlicka for female American Indian skulls enable us to test the usefulness of a revised Isserlis formula. Hrdlifika gives the following measured capacities (upper figures) and below these are the capacities obtained by using the formula of Isserlis and adding 1.4 per cent to the result. Algonkin New York Crude & Iroquois State Kentucky Illinois Siouan Pueblos average (6) (9) (21) (21) (13) (43) (113) Measured . . 1349 1331 1280 1305 1334 1166 1294 Calculated . . . . . . 1343 1319 1240 1322 1302 1169 1282 HAMBLY: CRANIAL CAPACITIES 49 If Hrdlicka had not measured these skulls of female Indians, and we had used the formula of Isserlis (+1-4 per cent), we should have had results comparing very closely with capacities which were actually measured. The crude average capacity by measurement is 1294, and since the calculated capacity found by revised formula of Isserlis is 1282, there is a discrepancy of only 0.9 per cent. The revised formula of Isserlis gives satisfactory results when applied to groups of female Indian skulls, with the possible excep- tion of the Kentucky group, for which there is a discrepancy of 3.1 per cent between the rrffeasured and the calculated capacities. How- ever, the formula is not necessarily inaccurate. Errors in actual measurement are always possible, and the formula may be giving the more accurate result. ESKIMO SKULLS From the data supplied by Stewart (1939) we can calculate the cranial capacities of groups of male and female Eskimo skulls for which he gives average L, B, and H' measurements. Since Stewart did not actually measure the cranial capacities, we must use Morant's (1937) measured average of 1473 for 200 pooled male Eskimo skulls. This is a standard by which we can judge the accuracy of results given by the formula of Isserlis when used on^ Stewart's data. Formula of Isserlis Applied to Stewart's Data Males . . Females . Labrador Thule Greenland Old Igk (38) 1418 (21) 1485 (49) 1482 (30) 1480 (37) 1247 (10) 1379 (52) 1249 (31) 1283 The result given by the Isserlis formula when applied to male Labrador skulls is somewhat low according to Morant's general figure of a measured 1473 for pooled Eskimo. But the capacities for males of Thule, Greenland, and Old Igloo, arrived at by the unrevised formula of Isserlis, are very close to Morant's standard. We have no data for judging how accurate the formula of Isserlis has been in our calculation of the capacities of female Eskimo skulls, but probably the capacities are approximately correct, since they are on the average 12.1 per cent lower than the capacities of the male skulls (see table, p. 62). ASIATICS For the study of cranial capacities of Asiatic peoples we have three principal summaries: Morant (1924), von Bonin (1931a), and 60 FIELDIANA: ANTHROPOLOGY, VOLUME 36 Woo and Morant (1932). The bibliographies given by these writers are extensive and their items are critically examined. The most important bibliographical items are quoted in my own bibliography at the end of this work. Morant has placed in square brackets the cranial capacities obtained by what he calls "doubtful methods," and in the three compilations just quoted the respective authors acknowledge the hazards attending paucity of data and the pooling of results obtained by different workers. Yet, despite objections, the data give some acceptable cranial capacities for a large number of Asiatic peoples whose geographical location is given in a series of maps (von Bonin, 1931a) and in a general map by Woo and Morant (1932, p. 110). As a preliminary study I have collated in the following table a series of measurements of cranial capacities which appear to have been carefully made by the use of mustard seed, though the tech- nique is variable. Asiatic Males Number , Source of Measured skulls capacity Mongols 112 1573.0 (Woo and Morant, 1932) ±7.23 Japanese 129 1474.8 (von Bonin, 1931a) ±6.74 Chinese 46 1467.6 (Morant, 1924) ±11.29 Tibetan B 14 1537.7 (Morant, 1924) ±20.46 Tibetan A 36 1452.4 (Morant, 1924) ±12.76 Nepalese 47 1436.2 (Morant, 1924) ±11.17 Malayan 76 1424.4 (Morant, 1924) ±8.78 Burmese A 27 1406.9 (Tildesley, 1921) ±14.73 Philippines, Aetas 34 1415.6 (von Bonin, 1931a) ±13.13 Philippines, Tagals 27 1458.7 (von Bonin, 1931a) ±14.73 •Difference not statistically significant. Capacity by formula of Isserlis Differences in cc. and percentage a/Pa 1488.6 ±6.14 -84.4 -5.4 8.9 1460.6 ±5.72 -14.2 -1.0 1.6* 1397.8 ±9.58 -69.8 -4.7 4.7 1430.7 ±17.37 -107.0 -6.9 4.0 1323.8 ±10.83 -128.6 -8.8 7.7 1295.1 ±9.48 -141.1 -9.8 9.6 1409.8 ±7.45 -14.6 -1.0 1.3* 1401.1 ±12.51 -5.8 -0.4 0.3* 1406.1 ±11.15 -9.5 -0.7 0.5* 1425.2 ±12.51 -33.5 -2.3 1.7* HAMBLY: CRANIAL CAPACITIES 51 Dr. Tildesley (1921) followed the satisfactory method of weigh- ing the seed-contents of the skull and then multiplying that weight by a factor in order to give the capacity. Morant used a measuring glass into which he poured the seed-contents of the skull. Hrdlicka had a special technique in which fine dry mustard seed was used. He neither weighed the seed nor poured it into a measuring glass, but employed a specially constructed funnel and calibrated tube that registered the volume of seed used in filling the skull (Hrdlicka, , 1939, pp. 135-138). I have not seen the apparatus in use, but judging from the description and from the capacities obtained there is a tendency for Hrdlicka' s method to give results somewhat high. The table (p. 50) indicates that five out of ten comparisons of average cranial capacities show no significant difference (asterisks) between the measured mean and that calculated by the unamended formula of Isserlis. When compared with the carefully measured capacity of Burmese skulls the calculated capacity shows a dis- crepancy of only 5.8 cc. or 0.3 per cent. But on the average the formula gives for Mongoloids a result which is 4.1 per cent too low. The Asiatic data are not jail satisfactory either in numbers or in the technique of measurement on which they are based. But con- sidered collectively they give a general impression of the true capacities. Details of the provenance of the skulls and discussion of the bibliographical sources are given by Morant (1924), and by Woo and Morant (1932). The objection to adding 4.1 per cent to the capacity by Isserlis' formula is that we are using 4.1 per cent as the average amount by which the capacity by formula falls short of the measured capacity. But instances occur for which the formula needs no addition, or perhaps an addition of less than 4.1 per cent. Despite the weakness of the data the results tabulated (table, p. 52) give definite and consistent information. The capacities by measurement have a small range for males, 1462-1498 for male skulls, a range of only 36 cc. This is small in view of possible variations in technique in the hands of different workers. Four out of five measured capacities are particularly close. Buriats have 1496, 1484; Torgods, 1489; and Kalmuks of Astrakhan, 1498. The maximum discrepancy of 14 cc. is negligible in an experiment of this kind. For female skulls there are few data, but perhaps a crude average of 1313 would be near the mark. For male skulls the measured capacities give a crude average of 1486, the capacity by unamended formula of Isserlis about 1454, and by amended formula ^, OF «i- ^^- 8 00 1- c» •3 »— I CO »— I 2 tH T-l tH ui j~t S ^hIh ooc- 00 WW 3 CQ O I— I Eh h- 1 OJ >»h >» b -M 3 +J 3 CO 1— ( 00 1-1 1^ U-^^ u*^ o o a c ■bo lb Of U3 O U3 t- U3 o •N •eo • T-l '? • a> Q> • -»J aa • P3 • o S" :§ i-o ^ . c ^ • « <1> J3 o pq pq pq T3(M O Oi bOi-l H S w y M o 7? t ,£3 o a> J3 c.2-i-> Has l2 ^ 2 C3 CO no 05 iJ =« •^ >-i v-i o 0>rH wT o OS o 02 52 HAMBLY: CRANIAL CAPACITIES 53 1513. The formula without alteration gives 32 cc. too low, and the amended formula gives 27 cc. too high. Apparently we have in this particular instance data to which the formula applies fairly- well without adjustment. JAPANESE Probably the estimated average capacity of 1475 given by von Bonin (1931a) is the best approximation available; the capacity is given for 129 male skulls. Martin (1928, p. 745) bases his figure of 1485 on shot measurements made by Adachi (1904) on male skulls. Morant (1924) gives 1503. I do not think there is any really satis- factory measurement available. If we use the average L, B, H' measurements quoted by Morant, the formula of Isserlis yields 1468. The capacity of 1475 given by von Bonin is based on the largest number of measurements yet pooled, and the figure is compatible with mean capacities of Mongoloid skulls (pp. 50, 52). For 30 female Japanese skulls Morant gives a capacity of 1308. By Isserlis' formula amended the capacity is 1347, and by Adachi (shot) 1319 (see Martin, 1928, p. 745). Ainu. — For Ainu cranial capacities Koganei (1894) is the original observer, quoted by Martin (p. 745), who gives 1462 for males and 1308 for females. These figures are quoted by Morant (1924), who says that the measurements were made by doubtful means. Martin states that the measurements were made by shot, and therefore they would have to be reduced 5.4 per cent to make them comparable with those known to have been made by fine seed or water. So reduced, the capacities are 1383 and 1237, for males and females. The Ainu have many features distinguishing them from Mongo- loid types and we have no sound criterion for judging the validity of these figures. This ancient reference (Koganei, 1894), which has been quoted and requoted, goes back fifty-tv^o years. The data deserve some experimental verification because the large collection studied by Koganei contains 76 male and 51 female Ainu skulls. Reference to Koganei's original article shows that for measuring capacities he used a mixture of shot varying in size from 1 to 2 mm. CHINESE The data for capacities of Chinese skulls give a general impression of the size of the Chinese skull. I do not think there is any direct measurement so satisfactory as to provide a crucial test of the validity of a revised formula. For measuring 39 skulls of the Hylam Chinese (from Hainan) Harrower (1928) used fine shot, as he did for the 36 0) 3 +s 8 »S S Tit -^U3 WW OS W3 WW 1452( 1470( 1524 1472 1483 1489 >> Xi g > 1 .a •8° * ft §•■3 WW WW WW 73 t- ooo o H CO J3 3 'b 'b "b ■bo "b ■b o CIS H o S "S A cii w So w > o ^1 o a)