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of the cranium another element enters in: the form. The cranial circumference of an extremely brachycephalic cranium (almost circular) may contain a larger surface (and consequently include a larger volume), than a maximum circumference of the same identical measure, which belongs to an extremely dolichocephalic cranium (approaching the shape of an elongated ellipse). This may be easily understood if we imagine a loop of thread laid out in the form of a circle: if we pull it from two opposite sides, the enclosed area diminishes until it finally disappears as the two halves of the thread close together, while the length of the thread itself remains unaltered.

Nevertheless, the maximum circumference still remains the linear index best adapted to represent the volume; indeed, the authorities take its proportional relation to the stature as representing the reciprocal degree of development between head and body at the different successive ages.

Here are the figures which Daffner gives in this connection:

DEVELOPMENT OF THE STATURE AND OF THE CEPHALIC PERIMETER FROM BIRTH TO THE AGE OF ELEVEN YEARS

Males Females Number of subjects Age Stature in centimetres Cranial perimeter, centimetres Number of subjects Age Stature in centimetres Cranial perimeter, centimetres 65 At birth 51.17 34.58 65 At birth 50.27 34.23 11 1.55 74.18 46.74 10 1.39 77.20 46.45 30 2.43 85.32 48.03 30 2.45 83.48 47.23 53 3.34 91.88 49.20 49 3.43 89.97 47.73 112 4.43 96.64 49.55 81 4.50 96.07 48.37 244 5.42 103.21 50.21 208 5.40 100.61 48.76 234 6.41 106.49 50.73 179 6.37 104.92 49.87 30 7.30 114.47 51.66 25 7.36 117.36 50.38 28 8.38 112.10 51.97 24 8.41 121.58 50.72 27 9.40 128.41 52.38 30 9.40 126.76 51.10 21 10.34 129.12 52.24 28 10.40 130.00 51.08 20 11.42 135.84 52.50 31 11.46 137.04 51.42

DEVELOPMENT OF THE STATURE AND OF THE CEPHALIC PERIMETER BETWEEN THE YEARS OF 13 AND 22

Number of subjects Age Stature in centimetres Cranial perimeter, centimetres 13 13.39 147.92 52.83 24 14.50 149.21 53.53 20 15.38 163.55 54.34 41 16.43 162.53 53.34 35 17.36 167.93 55.89 26 18.35 171.65 54.91 15 19.40 172.97 55.48 6 20.05 173.97 56.50 342 21.02 168.08 55.37 171 22.22 168.08 55.62

One very important research made by Daffner is in reference to the maximums and minimums that are normal for each successive age. This is extremely useful for the purpose of diagnosing the morphological normality in relation to the age. He naturally bases his figures upon subjects studied by him personally, who altogether form an aggregate number of 2,230, and are not always sufficiently numerous when distributed according to their ages. Nevertheless, in the great majority of groups, especially those including the younger children, the number of subjects is sufficient and even superabundant.

At all events, Daffner's researches may serve as a valuable guide in the researches that lay the foundation for diagnosis; and every future investigator will find it an easier task, under such guidance, to make his own contribution to it and to correct those inaccuracies which (for certain epochs) are to be attributed to an insufficient number of subjects.

Daffner distinguishes, for each year, a maximum and a minimum both for the stature and for the cephalic perimeter; but since the person having the maximum stature does not always have the maximum cephalic perimeter, and vice versa, the author indicates, in connection with the maximum and minimum figures, the other of the two measurements which, as a matter of fact, corresponds to them in each given case.

INDIVIDUAL VARIATIONS

MAXIMUMS AND MINIMUMS OF STATURE AND OF CRANIAL CIRCUMFERENCE

Age Measurements
S.—Stature
Cc.—Cranial circumference Maximum (M.) and minimum (m.) in millimetres Measurements occurring in combination with the M. or m. measurements Males from birth to the age of eleven years At birth Cranial circumf. M. = 372 (S. = 625). m. = 326 (S. = 500). Stature M. = 550 (Cc. = 369, 365, 354). m. = 480 (Cc. = 343, 341, 337). 1 year Cranial circumf. M. = 491 m. = 456 Stature M. = 805 (Cc. = 491). m. = 680 (Cc. = 456). 2 years Cranial circumf. M. = 506 (S. = 855). m. = 462 (S. = 800). Stature M. = 920 (Cc. = 496). m. = 785 (Cc. = 467). 3 years Cranial circumf. M. = 521 m. = 462 (S. = 915). Stature M. = 995 (Cc. = 521, 501). m. = 795 (Cc. = 472). 4 years Cranial circumf. M. = 530 (S. = 1035). m. = 465 (S. = 900). Stature M. = 1090 (Cc. = 510). m. = 835 (Cc. = 499, 481). 5 years Cranial circumf. M. = 527 (S. = 1070). m. = 481 (S. = 930). Stature M. = 1173 (Cc. = 519). m. = 920 (Cc. = 495). 6 years Cranial circumf. M. = 532 (S. = 1090). m. = 481 (S. = 1045). Stature M. = 1163 (Cc. = 517). m. = 950 (Cc. = 495). 7 years Cranial circumf. M. = 541 (S. = 1232). m. = 502 (S. = 1156, 1223). Stature M. = 1276 (Cc. = 527). m. = 1092 (Cc. = 514). 8 years Cranial circumf. M. = 542 (S. = 1207, 1292). m. = 496 (S. = 1158). Stature M. = 1375 (Cc. = 537). m. = 1099 (Cc. = 497). 9 years Cranial circumf. M. = 548 (S. = 1333). m. = 507 (S. = 1250). Stature M. = 1383 (Cc. = 546). m. = 1185 (Cc. = 522). 10 years Cranial circumf. M. = 553 (S. = 1303). m. = 497 (S. = 1270). Stature M. = 1372 (Cc. = 538). m. = 1218 (Cc. = 534). 11 years Cranial circumf. M. = 543 (S. = 1350). m. = 505 (S. = 1307). Stature M. = 1466 (Cc. = 542). m. = 1300 (Cc. = 513). Note. ——- indicates that the number of subjects is abundant. _____ indicates that the number of subjects is sufficient. ..... indicates that the number of subjects is scarce.

FEMALES FROM BIRTH TO THE AGE OF ELEVEN YEARS[Pg 240]

Age Measurements
S.—Stature
Cc.—Cranial circumference Maximum (M.) and minimum (m.) in millimetres Measurements occurring in combination with the M. or m. measurements Observations At birth. Cranial circumf. M. = 372 (S. = 500). (The most frequent S. was 500 mm. combined with CC. = 357, 337.) m. = 324 (S. = 480). Stature M. = 565 (Cc. = 355). m. = 475 (Cc. = 333, 325). 1 year Cranial circumf. M. = 486 (S. = ) m. = 450 (S. = 750, 740). Stature M. = 810 (Cc. = 486). m. = 705 (Cc. = 455). 2 years Cranial circumf. M. = 495 (S. = 850). m. = 448 (S. = 810). Stature M. = 910 (Cc. = 491). m. = 720 (Cc. = 464). 3 years Cranial circumf. M. = 501 (S. = 865). m. = 457 (S. = 870). Stature M. = 1015 (Cc. = 473). m. = 810 (Cc. = 476). 4 years Cranial circumf. M. = 510 (S. = 1050). m. = 455 (S. = 920, 870). Stature M. = 1060 (Cc. = 507). m. = 860 (Cc. = 461). 5 years Cranial circumf. M. = 515 (S. = 1035). m. = 462 (S. = 905). Stature M. = 1140 (Cc. = 492). m. = 875 (Cc. = 481). 6 years Cranial circumf. M. = 522 (S. = 1020). (The maximum S. was found in a child of 6 years and 11 months; the next highest stature was 1177 mm., Cc. 512; another little girl of 6 years and 11 months had S. = 1099; Cc. = 507). m. = 460 (S. = 965). Stature M. = 1221 (Cc. = 516). m. = 920 (Cc. = 489). 7 years. Cranial circumf. M. = 524 (S. = 1215). m. = 479 (S. = 1185). Stature M. = 1270 (Cc. = 513). m. = 1058 (Cc. = 499). 8 years Cranial circumf. M. = 542 (S. = ). m. = 484 (S. = ). Stature M. = 1328 (Cc. = 542). m. = 1082 (Cc. = 484). 9 years Cranial circumf. M. = 526 (S. = 1272). m. = 493 (S. = 1306). Stature M. = 1325 (Cc. = 520). m. = 1173 (Cc. = 499). 10 years. Cranial circumf. M. = 533 (S. = 1291). m. = 476 (S. = 1204). Stature M. = 1403 (Cc. = 530). m. = 1153 (Cc. = 506). 11 years. Cranial circumf. M. = 537 (S. = 1420). (The next higher S. was 1495, with a Cc. of 529). m. = 478 (S. = 1284). Stature M. = 1464 (Cc. = 512). m. = 1255 (Cc. = 497).

EXTREMES BETWEEN THE AGES OF 13 AND 22 YEARS
(The figures here given are less exact, because of the great scarcity of subjects)

Age Measurements
S.—Stature
Cc.—Cranial circumference Maximum (M.) and minimum (m.) in millimetres Measurements occurring in combination with the M. or m. measurements 13 years Cranial circumf. M. = 554 (S. = ). m. = 492 (S. = ). Stature M. = 1715 (Cc. = 554). m. = 1345 (Cc. = 492). 14 years Cranial circumf. M. = 564 (S. = 1560). m. = 515 (S. = 1555). Stature M. = 1630 (Cc. = 537). M. = 1405 (Cc. = 526). 15 years Cranial circumf. M. = 567 (S. = 1575). m. = 526 (S. = 1570). Stature M. = 1795 (Cc. = 566). m. = 1450 (Cc. = 534). 16 years Cranial circumf. M. = 566 (S. = 1675). m. = 519 (S. = 1460). Stature M. = 1807 (Cc. = 561). m. = 1330 (Cc. = 532). 17 years Cranial circumf. M. = 582 (S. = 1757). m. = 507 (S. = 1610). Stature M. = 1759 (Cc. = 560). m. = 1561 (Cc. = 555). 18 years Cranial circumf. M. = 565 (S. = 1785). m. = 522 (S. = 1702). Stature M. = 1930 (Cc. = 557). m. = 1604 (Cc. = 536). 19 years Cranial circumf. M. = 578 (S. = 1707). m. = 541 (S. = 1693). Stature M. = 1823 (Cc. = 545). m. = 1637 (Cc. = 549). 20 years Cranial circumf. M. = 594 (S. = 1671). m. = 551 (S. = 1780). Stature M. = 1832 (Cc. = 560). m. = 1629 (Cc. = 552). 21 years Cranial circumf. M. = 590 (S. = 1700). m. = 512 (S. = 1590). Stature M. = 1790 (Cc. = 581). m. = 1570 (Cc. = 571). 22 years Cranial circumf. M. = 595 (S. = 1730). m. = 510 (S. = 1650). Stature M. = 1790 (Cc. = 576). m. = 1570 (Cc. = 548).

Nomenclature Relating to Cranial Volume. Anomalies.—(In regard to the method of directly measuring or calculating the cranial capacity, and of taking and estimating the measurements of the skull, see the section on Technique.)

Limits.—The cranial capacity, according to Deniker, has normally such a wide range of oscillation that the minimum is fully doubled by the maximum, the limits being respectively 1,100 and 2,200 cubic centimetres—these figures, however, including men of genius. Furthermore, the mean average capacity oscillates between limits that change according to race—not only because the cerebral volume may of itself constitute an ethnic characteristic (superior and inferior races) with which the form of the forehead is usually associated, but also because the cranial volume bears a certain relation to the stature, which is another factor that varies with the race.

Deniker gives the following mean averages of oscillations:

Europeans from 1,500 to 1,600 cu. cm. Negroes from 1,400 to 1,500 cu. cm. Australians, Bushmen from 1,250 to 1,350 cu. cm.

The average difference of cranial capacity is 150 cubic centimetres less in woman than in man.

The following nomenclature for oscillations in cranial capacity was established by Topinard, based upon the figures and methods of Broca:

Macrocephalic crania from 1,950 cu. cm. upward Large crania from 1,950 to 1,650 cu. cm. Medium or ordinary crania from 1,650 to 1,450 cu. cm. Small crania from 1,450 to 1,150 cu. cm. Microcephalic crania from 1,150 cu. cm. downward

To-day, however, the terms macrocephalic and microcephalic have come to be reserved for pathological cases. Virchow has introduced the term nanocephalic to designate normal crania of very small dimensions; while Sergi has adopted a binomial nomenclature, calling them eumetopic microcephalics, which signifies possessed of a fine forehead: since, as we have seen, it is precisely the shape of the forehead which determines normality. And in place of macrocephalic, we have for very large normal crania the new term megalocephalic.

Pathological terminology includes the following nomenclature: macrocephaly, sub-macrocephaly, submicrocephaly, microcephaly.

Microcephaly may fall as low as 800 cubic centimetres; macrocephaly may rise as high as 3,000 cubic centimetres, and at these extremes the volume alone is sufficient to denote the anomaly. But in many cases the volume may fall within the limits of normality; in such cases it is the pathological form and an examination of the patient which lead to the use of the term submicrocephalic in preference to that of nanocephalic, etc.

The volume, taken by itself, if it is not at one of the extreme limits, is not sufficient to justify a verdict of abnormality.

The terms macro- and microcephalic are, in any case, quite generic, and simply indicate a morphological anomaly, which may include many widely different cases, such, for example, as rickets, hydrocephaly, pachycephaly, etc., all of which have in common the morphological characteristic of macrocephaly.

In rickets, for instance, macrocephaly may occur in conjunction with a normal or even supernormal intelligence (Leopardi). Microcephaly, on the contrary, could never occur combined with normal intelligence, since it is a sign indicative of atrophy of the cerebro-spinal axis and diminution or, as Brugia phrases it, dehumanization of the individuality.

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