estimating femur and tibia length from fragmentary bones: an evaluation of steele's (1970)...

AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 89:333-345 (1992)

Estimating Femur and Tibia Length From Fragmentary Bones: An Evaluation of Steele’s (19’70) Method Using a Prehistoric European Sample

KENNETH JACOBS Departement d’anthropologce, Uniuersite de Montreal, Montreal PQ, H3C 357 Canada

KEY WURDS Mesolithic, Neolithic

Estimation of !ong bone dimensions, Lower limb,

ABSTRACT Steele’s (1970) regression method for estimating femur and tibia length from fragmentary bones is tested on a sample of complete femora (female N = 26; male N = 33) and tibiae (female N = 16; male N = 22) from a number of European Mesolithic and Neolithic sites. Over half of the regression equations given by Steele for predicting maximum length of the bone from the length(s) of one or more of its constituent segments are shown to produce inaccurate predictions in this test sample. However, a closer evaluation of these results, including calculation of regression equations for the test sample itself, reveals that this inaccuracy does not derive from any inherent flaw in Steele’s method. Rather, it is shown that differential distribution of maximum bone length among the various bone segments as defined by Steele may occur due to variation in muscular activity pattern and intensity. This argues for the retention of Steele’s basic method, with care being taken to match closely the activity pattern typical of the sample from which regression equations are derived with that of the population to which the equations are to be applied. The equations calculated in this study thus are provided for use where deemed appropriate. o 1992 WiIey-Liss, Inc.

For obvious reasons, paleoanthropological concern for the hominid lower limb has been disproportionately directed toward our ear- liest evolutionary phases, when anatomical adaptations to habitual bipedality were first being established. After this period, a scanty fossil record, punctuated solely by the occa- sional “unexpected discovery (e.g., a tall Homo erectus; Brown et al., 1985), and a relatively restricted lower limb variability in later hominids combine to mitigate against the kind of research concentration that is focused on cranio-dental remains.

Still, the lower limb has not been entirely ignored. Several studies have speculated on the possible techno-behavioral inferences to be drawn from Neandertal femora and tibiae (e.g., Lovejoy and Trinkaus, 1980; Trinkaus, 1976, 1980, 1983). In addition, Neandertal lower limb proportions have

played a role in the discussion of possible climatic adaptations in late Pleistocene and early Holocene human populations (e.g., Holliday and Trinkaus, 1991; Jacobs, 1985a,b; Trinkaus, 1981). For more recent prehistoric periods, some researchers have investigated human postcranial changes during the forager/agriculturalist transition. Most of this work has emphasized the upper limb, but size and robusticity changes associated with subsistence shifts have been noted in the lower limb as well (e.g. Bridges, 1989; Jacobs, n.d., b; Larsen, 1981). Over- arching all such studies are of course the ubiquitous reconstructions of prehistoric human stature, typically based on lower limb dimensions (e.g., Constandse-Wester-

Received October 8,1991; accepted April 20, 1992.

0 1992 WILEY-LISS, INC.

334 K JAC

mann et al., 1985; Feldesman et al., 1990; Formicola, 1983; and others).

The common link in these and any other such studies is the need to have adequate estimates of mean femur and tibia lengths for whichever cultural and/or chronological groupings are to be compared. These estimates are needed whether they alone are the data of comparison, or some derivative variable (e.g., robusticity or stature) is to be compared. Yet obtaining meaningful estimates often can be seriously impeded by small sample sizes This constraint is evelz more pressing if the research interest lies in the analysis of intra-population variation of long bone length or related dimensions (e.g., Jacobs, n.d., a.). Although a site may pre- serve a large number of quite sizeable frac- tions of the femur or tibia, these long bones may be found intact only rarely. Personal observation of ten site samples from the Me- solithic and Neolithic of the European USSR, for example, found that femur and tibia samples could be increased nearly six- fold, were it possible to accurately estimate the length of the abundant fragmented bones.

A possible solution to this predicament was suggested by Steele and McKern (19691, who calculated regression equations for estimating long bone length from fragmentary bones. Their study used skeletal material from three geographically and archaeologi- cally related Amerindian sites. The equations computed from the intact long bones in the sample might then be used with high confidence to reconstruct the lengths offrag- mentary bones from the same or similar sites. Unfortunately, samples of adequate size for the calculation of site-specific regressions are, to say the least, rare. This requires the derivation and eventual use of generalized equations, a task accomplished subsequently by Steele (1970; Steele and Bramblett, 1988).

In the course of a separate study (Jacobs, n.d., b.), Steele’s general equations were applied to a series of fragmentary femora and tibiae from Mesolithic (Olenii ostrov; Vasi- lyevka I and 111; Voloshskoye) and Neolithic (Igren; Surskoi; Vasilyevka 11; Volnenskoye; Vovnigi I and 11) cemeteries located in the Soviet Ukraine and Karelia. The results obtained differed markedly from those gener-

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ated by data from the intact bones at these sites. Before proceeding any further with this work, it seemed necessary to investi- gate more closely the applicability of such generalized equations to prehistoric skeletal remains. To that end, Steele’s (1970) equations are applied here to a different sample of European Mesolithic and Neolithic individuals, one for which maximum femur and/or tibia length was directly measure- able. This sample consists of 33 male and 26 female femora, plus 22 male and 16 female tibiae.

When maximum bone length is estimated from the length of the various bone segments defined by Steele (see below), several systematic and statistically significant devi- ations from actual length are observed. In order to eliminate the null hypothesis-that the bone segments had somehow been mis- identified in this study-regression equations were then calculated for the European (Mesolithic and Neolithic) sample itself.

The results of this analysis eliminated inconsistency or other error in bone-segment identification as a cause for the inaccurate estimates. They instead pointed to a different source of error. The equations provided by Steele (1970) that are relevant here are those for North American “white males” and “white females.” The skeletal collection on which these equations were based was the Terry Collection, a sample deriving from a modernhistorical cadaver “population.” It seemed reasonable to posit that the originally noted inaccuracies of the Steele-based estimates might derive, at least in part, from activity-hence, muscularization-differences between the prehistoric sample and the reference population.

Within the European sample itself, the pattern of correlations between the bone- segment lengths and the maximum length of the bones support the idea that variation in activity pattern or intensity may be expected to influence certain of the bone-segment proportions. This variation will thus have a negative impact on the predictability of maximum bone length, when the population under study is internally variable with regard to activity factors, or differs greatly from the reference population from which the equations were derived. In short, the re-

FRAGMENTARY FEMUR AND 335

distally toward the condules [alternatively, if following the lines proximally, the point a t which they become parallel];

4. the most proximal point on the perime- ter of the intercondylar fossa;

5. the most distal point of the medial condyle.

TIBIA LENGTH ESTIMATION

For the tibia, the breakpoints are on the anterior aspect. In descending order from proximal to distal, they are:

1. the most proximally prominent point on the lateral half of the lateral condyle;

2. the most proximal point on the tibial tuberosity;

3. the point of confluence of the lines ex- tending distally from the medial and lateral borders of the tibial tuberosity;

4. the point at which the anterior tibial crest begins its medio-distal descent toward the medial malleolus;

5. the most proximo-lateral point on the tibio-talar articular surface, opposite the tip of the medial malleolus;

6. the most distal point on the medial malleolus.

sults here underscore the need for extreme caution in the use of such equations.

MATERIALS AND METHODS All skeletal material reported here was

measured by the author. The primary Sam- ple derives from Mesolithic and early to mid- dle Neolithic archaeological horizons from a number of European countries. A further sample discussed briefly below consists of pre-contact Amerindian material from Texas. All measurements are in millimeters; data from Steele (1970; reported in cen- timeters) have been converted. All regressions referred to here are least-squares regressions.

Measurement error was estimated by cal- culating the mean difference (in millimeters) between once-repeated measurements of all segment and maximum lengths for roughly one-half of the European sample. The time between the original measurement and its repetition invariably exceeded two weeks (repetition usually occurred during a subsequent visit to the museum housing the skeletal material). Positive (over-measurement) and negative (under-measurement) error averages were calculated separately. Cases with identical original and remea- surement values were equally partitioned between the positive and negative error sets for the calculation of averages. The resulting error values are -0.8 mm and +0.9 mm.

The femur and tibia lengths are maximum lengths. The estimation of maximum length is done by using the lengths of various bone segments, each segment being defined by two particular “breakpoints.” In this study the segments are denoted as: Fe- mur-F1, F2, F3, F4; Tibia-T1, T2, T3, T4, T5. All breakpoints are defined with the bone in the position of maximum length (Fig. 1). The definitions here follow Steele (1970).

For the femur, the breakpoints are on the posterior aspect. In descending order from proximal to distal, they are:

1. the most proximal point on the head; 2. the mid-point of the lesser trochanter; 3. the point at which the proximal exten-

sions of the medial and lateral supracondylar lines cease being parallel and diverge

RESULTS Table 1 presents the maximum-bone and

bone-segment lengths for the European femora used in this study. Table 2 presents the same data for the tibiae. For comparative purposes, the corresponding values are re- produced from Steele (19‘70). It can be seen that the maximum bone lengths are quite similar, the largest difference being 14 mm (male tibia). Any discrepancy between actual bone length and that predicted for this sample by Steele’s equations thus cannot be attributed to a dramatic difference in gross bone size between the two samples, but must be due to a differential partitioning of length among the bone segments. These segment lengths in fact do differ, despite the overall length similarity of the bones. F1 and F2 are smaller in both sexes in the present sample, while F3 is longer in both sexes, and F4 is roughly the same in the two samples. The F1, F2, and F3 differences were statistically significant in both sexes.

For the tibia, both sexes in the present sample were smaller for T1 and T3, but

336 K. JACOBS

A B

POSTERIOR VIEW ANTERIOR VIEW

Fig. 1. Bony breakpoints and bone segments for the femur (A) and tibia (B) as used in the present study. See text for definitions.

larger for T2. Males and females differed in the remaining two segments, males being smaller here €or T4 and larger for T5 than in Steele’s sample. Females were larger here in T4, with T5 being equivalent. The male T1, T2, and T5 differences were statistically sig-

nificant; this was true as well of the female T1, T2, and T3 differences.

The predictive power of Steele’s regression equations €or the prehistoric European sample was evaluated by paired t-tests. These compared, for males and females sep-

FRAGMENTARY FEMUR AND TIBIA LENGTH ESTIMATION 337

TABLE I . Means (with standard deviationi for maximum length o f femur and length of femoral segments I

Females ~ ___- Males

___._._.___._______ ~

This studv Steele '70 This study Steele '70

(N = 33) (N = 61) (N = 26) (N - 52) 421 8 126 41 426 9 127 11

71 1 16 21 x. 254 5 121 31

68 0 17 61 192 2 121 11

ii 71 2 [ lo 51 125 6 116 61 65 117 91

462 4 130 61 80 6 17 91

271 3 I23 11

Femur 457 4 125 61 F1 75 1 17 01 F2 215 1 125 61 F3 128 5 117 31 F4 39 4 14 81 39 0 12 81 35 8 I4 11 35 5 12 81

' Data are from the present study and from Steele (1970) and are given for each sex. = two-way t-test P < .05 or better.

TABLE 2. Means (with standard deviation) of maximum, length of the tibia and of the tibia1 segments'

Females __ _ _ _ _ _ _ _ _ _ _ _ _ ~ Male . . _ _ _ ~

This study Steele '70 This study Steele '70

(N = 22) (N - 61) (N - 16) (N = 52) 343 0 121 91

28 5 13 31 59 9 I8 41

159 8 112 41 87 2 110 21 13 2 12 21

370 8 125 61 32 0 14 31 66 7 18 71

100 9 L12 71 14 3 12 31

341 6 121 01 23 0 13 51

Tibia 384 8 124 41

71 6 17 71 TI 27 5 15 41 T2 80 0 18 91 T3 157 4 122 01 163 5 115 91 141 2 114 31

90 2 ill 31 13 9 12 71

T4 98 6 116 21 T5 16 3 13 11

Data are from the present study and from Steele (19701 and are given for each sex. = two-way t-test P < 05 or better.

TABLE 3. Estimated femur lengths (mean and standard deviation) for the prehistoric European sample using

Steele's regression equations (Steele 1970: Tables xxxvl [white males] and X2XVIII luihite femaleslil

TABLE 4. Estimated tibia lengths (mean and standard deviation) for the prehistoric European sample using Steele's regression equations (Steele 1970: Tables X L

(white males] and X I I [white femalesiJ1

Male Female Male Female (N = 16) (N = 22)

..-____. (N = 26) _ _ _ ~ (N = 33)

~ ~

[Actual Mean Length] 1457.41 1421.81 [Actual Tibia Length1 Fern1 457.9 14.61 424.3 14.71 Tibl Fern2 414.1 122.01* 369.3 119.61" Tib2 Fern3 671.5 L63.21" 617.1 152.31* Tib3 Fern4 463.7 126.41 427.6 117.41 Tib4 Fern1 + Fern2 401.8 [29.51* 358.6 126.01" Tib5 Fem2 + Fern3 465.0 123.41" 414.4 i21.91* Tihl -t Tih2 Fern3 + Fern4 510.1 125.11" 481.2 122.21" Tib2 + Tib3 Fern1 i Fem2 i Fern3 458.7 i25.2i 420.6 Y24.1: Tib3 T Tib4 Fern2 t Fern3 t Fern4 466.0 125.01" 415.0 123.51" Tib4 + Tib5

Tibl + Tib2 t Tib3 Tib2 + Tib3 + Tib4 Tib3 + Tib4 + Tib5

Measurements in millimeters. = paired t-test significant difference at P < .05 or better.

1384.81 1341.61 363.0 125.01" 332.6 110.51 442.6 143.71" 356.3 L4.91* 373.5 115.21" 337.0 19.41 375.4 110.21 357.9 17.91* 381.9 17.01 401.7 [l1.01* 387 6 k18.21 362 3 L12.91;- 390.2 i19.81' 346.5 !18.0!" 368.6 [29.3i" 334.1 119.9j' 383.2 121.41 355.1 115.91" 385.6 119.81 340.0 118.91 382.6 125.31 345.8 119.61" 372.1 127.51" 335.2 119.11"

Tibl + Tib2 + Tib3 + Tih4 Tib2 + Tib3 + Tib4 + Tih5

378 3 124 61 385 6 124 0Ir

340 2 [20 41 345 1 119 11"

arately and for all of Steele's (1970) single- segment and combined-segment equations, the predicted versus the actual bone lengths. Not surprisingly, the lengths estimated for the European sample reflect this sample's diEerent division of maximum bone length among the various segments (Table 3,4).

The single-segment equations over- or un- derestimated maximum length, depending on whether the given segment was relatively longer or shorter than its homolog in Steele's sample. The results of the com-

Measurements in millimeters. % = paired t-test significantly different a t P cc .05 or better.

bined-segment equations were more complex. For the femur, the greater length of F3 tended, in males, to skew to the high side the results of those equations in which it was present. In females, by contrast, the shorter F2 tended to dominate, even when combined with F3. For the tibia, the relatively longer length of T2 tended, in both sexes, to have the largest impact in those equations in which it was present.

338 K. JACOBS

TABLE 5. Femoral maximum and segment lengths (with standard deviation and range) for the sanzple used in the calculation of regressions in the present study

Male (N = 331 Female TN 7 261

457 4 125 61 75 1 17 01 215 1 [25 61 128 5 [17 31 39 4 14 81

421 8 126 41 68 0 I7 61 192 2 121 11 125 6 116 61 35 8 [4 11 1402-5021 [60-871 1165-2551 ~98-1651 132-551

13654821 150-851 1150-2381 195-1701 125-42 I Combined 443 9 131 01 72 1 17 91 206 0 126 31 127 6 116 81 3771471 Sex IN - 631 1365-5021 150-871 [150-2551 195-1701 125-551

In terms of accuracy, Steele’s equations for the femur were the less predictive (Table 3,. Presented here are the mean estimated lengths for this sample using his single- and combined-segment equations. Judging solely by the mean lengths of the test sample, Steele’s equations would seem to more or less accurately predict the actual length of

An immediate consideration in the wake of such results must concern methodological consistency. Were the bony breakpoints identified inconsistently within this study? Or, were the bone segments defined here in a manner inconsistent with that specified by Steele? The former concern, inconsistency in the identification of the segment break-

the femur based on the various segment points, seems unlikely given the high corre- lengths. The paired t-tests for all single- lations obtained in this study between sin- and combined-segment equations, however, gle- and combined-segment lengths and demonstrated that on an individual basis, the equations are of limited accuracy. Fully 6 of the 9 equations produced statistically inaccurate estimates (at P < .05 or better) in both males and females. Interestingly, among the single-segment equations F1 and F4 produced, in both sexes, remarkably accurate estimates, despite these equations having among the highest Standard Error figures attached (Steele, 1970). It would seem that of the four femur segments, the two most intimately involved in joint me- chanics (and thus most canalized develop- mentally?! retain their high predictive value.

For the tibia (Table 4), the results were only somewhat more accurate. Again, the mean predicted lengths give an initial im- pression of high accuracy. The paired t-tests, however, clearly show that individual estimated tibia lengths are generally less than accurate. For the males, 8 of the 14 equations produced statistically inaccurate results (at P < .05 or better), while for the females 10 of the 14 equations were significantly imprecise. For both the femur and the

maximum bone length within the European sample. The latter concern is partly ad- dressed by the very nature of Steele’s breakpoints, these having been chosen by him for their ease of recognition and security of rep- licability.

Four of the eleven breakpoints are simply the most proximal or distal points on the bone. A further four out of eleven are found on clearly demarcated bony structures. Only the remaining three breakpoints require a purely subjective decision on the position or orientation of a bony line or crest. By using such obvious bony features, gross error should be minimized. Inter-observer error cannot be ruled out entirely, however. Its estimation warrants further investigation (a joint venture to this end is in fact antici- pated by the author and Steele).

Summary data of the sample used here for femur and tibia regressions are given in Ta- bles 5 and 6, respectively. The male and female subsamples are given, as is the total sample. This latter contains several addi- tional individuals for which sex could not be determined reliably. . -

tibia, then, it would seem tht Steele’s equations predict, to a certain extent, the central tendencies of the test sample, but fall short of requisite accuracy as regards the individual estimates.

Correlations between single- and combined-segment lengths and maximum femur length are significant, with rare exception, at P < .01 or better in all three data sets (Table 7). Among the exceptions, only F3

FWGMENTARY FEMUR AND TIBIA LENGTH ESTIMATION 339

TABLE 6 Tibial mmrntum and segment lengths (with standard deviation and range) for fhe sample used in the

T1 T2 ~3 T4 T5

calculation of regressions in the present study

_____-_-___________ - _ _ _ _ _ _ _ - _ _ _ _ _____ ~ - _ ~ _ _ Tibia

Male 384 8 124 41 27 5 L5 41 80 0 18 91 157 4 122 01 98 6 116 21 16 3 13 11

Female 341 6 [2101 23 0 13 51 71 6 17 71 141 2 114 31 90211131 13 9 12 71

15 3 [3 11 Combined 370 6 [31 71 26 0 [5 41 76 8 [9 51 153 0 L22 01 95 7 [14 71

IN = 221 13344241 [20-381 165-951 1125-195 1 168-1301 110-201

[N - 161 1309-3751 117-281 160-901 1120-167 I [65-1101 il0-191

Sex LN = 411 I3094241 [17-381 [GO-951 [120-2051 165-1301 11 0-20 1

TABLE 7. Correlation coefficients of single-segment and combined-segment lengths with maxirnum femur length for

the Euroaean samale '

Segrnent(s1 Male Female Sex ~ __________ ~

F1 F2 F3

,725 ,655 .758 .754 .674 .783 002'"* 238"" ,134"'

F4 .412* ,770 ,599 F1+ F2 372 ,799 ,880 F1 + F3 ,726 ,702 ,770 F1 + F4 ,753 ,842 ,812 F2 + F3 ,948 .946 ,962 F2 + F4 .766 334 324 F3 + F4 .439* ,787 ,633 F1 + F2 + F3 ,986 ,992 ,991 F1+ F3 + F4 ,761 ,863 ,831 F1 + F2 + F4 ,874 ,882 ,894 F2 + F3 + F4 ,973 ,967 ,979

'All correlations are significant a t P < .01 or better unless otherwise indicated. * = P < .05; ** P >. .05.

was not significant (in all three data sets). The remaining two exceptions were male F4, and F3 and F4, where significance was only at P < .05. For the tibia (Table 8) , the first appearance is of a high frequency of less significant or non-significant correlations. For males, 16 of 28 possible single- or combined-segment correlations were in fact significant at P < .01 or better, with 5 of 28 significant solely at P < .05. Seven of the correlations were non-significant. A similar pattern prevails for the female tibia: 13 of 28 significant at P < . O 1 or better; 9 of 28 significant at P < .05; six non-significant correlations.

When the combined-sex sample is considered, however, it becomes clear that small sample size plays a major role in the pattern of correlations, especially as regards the tibia. With this larger sample, nearly all single- and combined-segment tibia1 correlations are significant at P < . O 1 or better. The sole exceptions are 7'2 (which is signifi-

TABLE 8. Correlation coefficients of single-segment and combined-segment lengths with maximum tibia length for

the European (Mesolithic and Neolithic1 sample

Segrnent(s)

T1 T2 T3 T4 T5 T I 4 T2 T1 t T3 T1 + T4

T2 + T3 T2 + T4 T2 + T5 T3 + T4 T3 + TR

T1 + T5

T4 + T5

T1 + T2 + T4

T1 + T3 i T4

T1 + T2 T3

T1 + T2 + T5

T1 t T3 + T5 T2 i- T3 + T4 T2 + T3 + T5 T3 + T4 + TR Ti + T2 + T3 + T4

T1 t T3 + T4 + T5 T2 + T3 T4 T5

T1 t T2 + T3 + T5

Cornbind Male Female Sex

--.___ _____ ,205"" ,0174" 599 ,602 154"" 207" ,648 ,650 ,263"" ,757 .608 .159"* 394 .602" ,603" .772 .666*

,941 ,651" ,968 ,762 ,909 ,992 ,778 ,955 ,976

.263**

523" ,411"*

.413 033*1 ,624" .714 .706' 55'p" ,837 ,665" .419":*: ,918 ,585" 668"" ,887 .729*

.926

.717* ,986 ,837 ,923 ,991 390 .935 ,990

,582"

658""

540 ,370" ,695 347 .201** .587 .793 ,759 ,561 .881 ,671

,905 ,765 ,597 ,948 ,800 .983 ,881 ,938 .995 .905 ,967 ,988

cant at P < .05), plus T5, and T2 and T5 (which are not significant). The small sample sizes of the single-sex data sets would appear to confute what are in fact significant relationships between segment-lengths and maximum tibia length.

Despite this generally high frequency of significant correlations, it is nontheless instructive to consider those cases where segment length and bone length do not correlate. In the tibia, for example, T5 is non- significant in all three data sets. This should perhaps not be surprising, since in Steele's original study, T5 was significantly corre-

340 K. JAC

lated only in the females. Of perhaps greater interest is the predictive behavior of segments T1 and T2. Neither is significantly correlated with bone length in males, while in females only T1 is correlated (at P < .05). The two segments share a common breakpoint, that being the most proximal point on the tibial tuberosity. Thus, any factor which might cause variation in the proximal development of the tibial tuberosity, independent of actual maximum tibia length, would tend to disrupt the correlation of both T1 and T2 with that length.

One such factor might be varying stress on the tibial tuberosity due to M. quadriceps fernoris loading via the patellar ligament (Frankel, 1971; Kaufer, 1971). Higher levels of quadriceps activity should be associated with a larger cross-sectional area of the patellar ligament and, in turn, an expanded tibial tuberosity. Conversely, lesser quadriceps activity might translate into a more distally placed proximal border on a (smaller) tibial tuberosity. This functional “model” thus predicts that a relatively longer T1 will be typical of relatively less active populations. In order to evaluate this prediction, the al- ready small European sample was broken into its Mesolithic and Neolithic components. While this renders meaningful statistics im- possible, the resulting pattern is interesting.

There being no Neolithic females in the European sample, only males can be compared. Maximum tibia length in the Neo- lithic males (N = 7) is 378 mm; for the Me- solithic males (N = 151, maximum tibia length is 388mm. Yet, despite their abso- lutely shorter tibiae, T1 in the Neolithic males measures 25mm, as compared to 22 mm in the Mesolithic males. The Neo- lithic tibia is thus 3% shorter than its Meso- lithic counterpart, while Neolithic T1 is 12% longer than in the Mesolithic. This pattern, if it is in fact a function of tibial tuberosity development, would not be inconsistent with generally noted trends toward skeletal reduction as a consequence of “neolithisation” (e.g., Larsen, 1981; although cf. Bridges, 1989). It would also explain perhaps why female T1 is significantly correlated in the total European sample, since this group contains no Neolithic individuals; any possible

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impact of activity-related diversity as regards this variable is thereby avoided.

To further evaluate the potentially “dis- ruptive” role of tibial tuberosity development, 17 male and 12 female tibiae from precontact Amerindian sites in Texas were selected at random from the collections at the University of TexasIAustin. The archaeological context of this sample was Texas “Archaic” and “Late Prehistoric,” thereby corresponding roughly to the European (mixed Mesolithic and Neolithic) sample in terms cf probable activity lrvels and patterns. When T1 length is assessed as a percentage of maximum bone length, the Texas and European values cluster tightly to- gether and are, as predicted, smaller than the modern values as calculated from data given in Steele (1970). For males, European T1 is 7.3% of maximum tibia length, while T1 is 7.2% in the Texas sample. For the Terry Collection sample, the male value for T1 is 8.6% of maximum tibia length. For females, the same pattern pertains, with European (6.7%) and Texas (6.6%) values roughly equivalent, as compared to 7.1% for Steele’s sample.

As might be expected, the relative length of segment T2 varied in a way similar to that of T1 among the three samples. With increased tibial tuberosity development (clearly in a proximal direction, but most likely distally as well), T2 should consume a correspondingly larger percentage of maximum tibia length. European males (21%) and Texas males (23%) were similar in this regard and distinct from the modern males (18%). In females, the European (21%) and Texas (23%) values were again closest, with the modern female value being considerably lower (15%).

For these tibial segments, then, a pattern wholly consistent with intuitively obvious functional constraints seems evident, despite the lack of rigorous statistical support. The other tibial segments, being less clearly linked to a single, overriding functional constraint, are in fact highly correlated (with the exception of T5) with maximum tibial length. This suggests that possible functional factors might also play a role in the pattern of femoral segment correlations.

FRAGMENTAFtY FEMUR AND TIBIA LENGTH ESTIMATION 341

In the femur, only F3 is not significantly correlated with maximum femur length in males, females, or the combined-sex sample. It should also be recalled that F3 and F2 were two segments that differed significantly in length in the European sample from the values in Steele’s sample (Table 1). Furthermore, these two segments share a breakpoint, that being the point dividing the paralleydivergent portions of the proximal extensions of the supracondylar lines. In contrast to the similar case in the tibia, however, the utter lack of correlation for the F3 segment has no effect a t all on the proximally adjacent segment. F2 is very highly correlated with femur length in males, females, and the combined-sex sample (Table 7).

Of the two breakpoints for F3, the distal point (the proximal margin of the intercondylar fossa) is closely reflective of knee- joint architecture and might be reasonably assumed to be the less freely variable. It therefore seems not improbable that variation in F3 length should be due mostly to variation in the position of its proximal breakpoint. Complex interactions between the insertion of M. adductor magnus and portions of the origins ofM. vastus medialis, M. vastus lateralis, and M . biceps femoris are likely to play a role in the positioning of this point. Whatever the exact mecha- nism(s) in operation here, it is useful to com- pare the relative length of F3 in a series of presumably activity-different samples.

Twenty-two male and 16 female femora from the previously sampled precontact Texas Amerindian sites were compared to the Mesolithic (male N = 27, female N = 20) and Neolithic (male N = 6, female N = 6) subsets of the European sample. These three data sets were then compared to the modern sample values as calculated from data in Steele (1970). Expressed as a percentage of maximum femur length, F3 de- creased in both sexes (male value given first) from the Mesolithic (29%/31%) to the Neolithic (25%/26%) to the Texas pre-contact (23%/25%) to the modern (15%/15%) samples. This series represents a reasonable sequence of declining activity and muscularization. That the relative length of F3

declines in like fashion along the series would seem to suggest strongly that this bone segment also is highly sensitive to influence from activity pattern and level.

DISCUSSION The present investigation began with the

failure of Steele’s (1970) regression equations to accurately predict femur and tibia lengths in a prehistoric European human skeletal sample. Yet one consequence of this work must be seen as the verification of the methodological soundness of Steele’s ap- proach to length estimation. The bone segments as defined by Steele, with only a few instructive exceptions, are in fact highly correlated with maximum bone length within the European sample itself. Equations calculated in the manner of Steele can be used to reconstruct maximum length accurately from fragmentary bones. The results here thus contrast starkly with those described by Simmons et al. (1990) for the femur. In their evaluation of Steele’s method, they conclude that Steele’s choice of bony breakpoints is flawed and strongly argue for adop- tion of a different set ofpoints.

On the basis of the results here (see also, Brooks et al., 19901, it would seem that the rejection of Steele’s method might be, a t best, premature and that reasons other than a flawed methodology need to be considered when “aberrant” results are obtained. The possible nature of some of these “other reasons” can be clarified by consideration of those cases where Steele’s original equations failed when applied to the prehistoric European sample and of the few cases within that sample itself where strong segment- and maximum length correlations were not obtained.

It appears reasonably certain that some of the bony breakpoints used in segment defi- nition may be sensitive to activity pattern and intensity, as expressed in degree of muscularization. As noted above, even within the small and (it was thought at the onset of this work) presumably homogeneous European sample studied here, varying muscularization may underlie the failure of three bone segments (F3, T1, and T2) to correlate significantly with maximum

342 K. JA(

bone length. The pattern of variation in the relative lengths of these segments within this sample, as well as between it and the modern and the presumably analogous Texas samples, suggests that varying size and orientation of the attachments of parts of the femoral quadriceps and biceps may induce variability in F3 length. Similarly, activity-related size variation of the femoral quadriceps tendon and the patellar ligament may explain the otherwise anomalous pattern of variation in T1 and T2 lengths.

The remaining bone segments here show only moderate variation that is unrelated to maximum bone length. Still, some of them must be considered as at least theoretically susceptible to activity-level influence. For example, F1 length may vary along with the femoral neck angle (partially determined by habitual hip-joint reaction forces; Lovejoy et al., 1973), or with the development and orientation of the lesser trochanter (influenced by M. psoas major activity). For the tibia, the proximal breakpoint for T4 (the start of the medial descent of the anterior tibial crest) might be expected to vary in position depending on the overall cross-sectional ge- ometry of the tibial diaphysis. This feature itself is known to vary between technologi- cally and ecologically different populations (Lovejoy, 1970).

However, the need for caution in the interpretation of inter-populational differences in bone-segment proportions is underscored by the very lack of variation in these two segments, as opposed to that seen in the other segments analysed here. Bony dimensions not represented by the bone-segment lengths (e.g., diaphyseal diameters or cross- sectional areas; epiphyseal anteroposterior or mediolateral widths) might also vary between populations of different (or even, perhaps, similar) activity and muscularization patterns. Variation in these dimensions could increase or decrease the surface areas of muscular attachments independently of any change in the relative positions of the bony landmarks described here. By hiding a mechanical relationship that in fact exists, or by causing a spurious relationship to appear evident, such variation could easily serve to confound any attempt at a purely

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behavioral or mechanical interpretation of bone segment proportions.

In like fashion, any populational differences in intermembral proportions due to non-mechanical factors (e.g., climatic adap- tation) would have the potential to blur the presence (or absence) of activity-related variation in those populations’ bone-segment length proportions. This would be especially true to the extent that proportional differences in limb (and limb-segment) lengths are achieved through differences in the growth schedules of the various bones. In this context, the observation that bone- segments F3 and T2 are both problematic in the sample here and analogous in the timing of their growth and epiphyseal closure may be more than coincidental.

Such considerations partially demon- strate the extent of future research potential suggested by some of the results reported here. This is particularly true as regards our development of a broader appreciation of the role of behavioral and ecological factors in the production of skeletal variation in human populations. However, this and other similar research are beyond the scope of the present study, its less ambitious goal being to document the possibly confounding impact of some extraneous variables on regression-equation estimates of long bone length and to underline that the application of such equations to novel populations cannot ig- nore these factors, however significant might be the statistical “fit” of the equations in the original reference population.

One way to minimize the impact of this type of error in future work would be to gen- erate separate sets of regression equations, each derived from and thus appropriate to a more or less internally homogeneous and ex- ternally distinct “type” of human population. The characteristics defining and dis- tinguishing these reference groups would include factors, such as activity pattern and intensity, thought to influence the relative proportions of the bone segments.

The list of logical reference groups is infi- nite, but could include, among others, mounted vs. pedestrian hunger-gatherers, early vs. intensive agriculturalists, and the like. Given ongoing concern regarding the

FMGMENTARY FEMUR AND TIBIA LENGTH ESTIMATION 343

these femoral segments were correlated uni- formly highly with femur length, These and other such possible modifications to Steele’s very sound methodology require further investigation.

extent to which limb size and proportions vary between the major continental groupings of human populations (e.g., Feldesman et al., 1990 and references therein), reference equations for each such techno-ecological “type” ideally should be established for each continent. In brief, something rather like extant collections of model life tables might be produced. A researcher wishing t o estimate bone lengths for a particular sample could choose the most appropriate reference set, testing its accuracy against the intact bones in hisher sample. A less formalized fashion to accomplish the same result is for regression equations on differ- ing samples to be calculated where sample sizes permit, and for these then to be pub- lished. To that end, the regressions derived in this study appear in the Appendix. Equa- tions for male, female, and combined-sexes are given. The calculations are for all single- segments and segment combinations. All possible segment combinations, including those with non-adjacent segments, are given. These latter may be of use in archaeological situations where two or more non- connecting fragments clearly pertain to a single individual. Significance values attached to the equations are found in Tables 7 and 8. While these equations are con- strained by all the limitations discussed here, the Standard Error values are compa- rable in nearly all cases to those given by Steele,

A further way in which extraneous variation in segment proportions might be reduced, at least regarding the tibia, is by re- considering the lengths employed. The role of T5 (largely uncorrelated both here and in Steele’s original study) could be eliminated altogether by measuring tibial length as physiological length. This in itself is a more meaningful variable as regards the functional length of the lower leg. Further, the confounding variability seen here in T1 and T2 lengths might be reduced by making their shared breakpoint the midpoint of the tibial tuberosity, as opposed to the most proximal point. This then would be analogous to the F1P2 breakpoint (the midpoint of the lesser trochanter) which, it should be recalled, did not vary unpredictably. Both of

CONCLUSIONS Steele’s (1970) equations for the estima-

tion of femur and tibia length from fragmentary bones have been shown to lack adequate accuracy when applied to a prehistoric European sample. This apparent failure does not reflect an inherent methodoiogicai flaw, however (cf. Simmons et al., 1990). Rather, this inaccuracy results from a sys- tematically different distribution of maximum bone length among the various bone segments in the study sample. This differential distribution of bone length in turn seems to reflect activity pattern and intensity differences between the reference and the study samples. When regression equations are calculated for the study sample itself, Steele’s methodological premises are shown to be in fact quite sound. The relative proportions of some bone segments differ even within the study sample, however, resulting in a small number of non-significant correlations between bone segment-length and maximum bone-length. These results underscore the need for extreme caution in the derivation and application of such equations. Future work to expand the inventory of reference equation sets appropriate ta populations from particular techno-ecolugi- cal contexts is clearly indicated.

ACKNOWLEDGMENTS I am grateful to two anonymous reviewers

for their very useful suggestions. My special thanks to one of these in particular, whose comments prompted me to rework and then reinsert a part of the Discussion that I earlier had chosen to excise from the manuscript as originally submitted. Thanks to D. G. Steele for reading an earlier version of this paper and, for technical help, to L. Goupil and C . Daoust. The European material used here was measured during research supported by the Deutsche Akade- mische Austauschdienst and by IREX. The hospitality of the many curators of the col-

344 K. JAC

lections used in this study is deeply appreci- ated. Preparation of the manuscript was partially underwritten by le Departement danthropologie, l'universite de Montreal. Finally, my gratitude to Cheryl, Ian, and Kenna for the intangibles.

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LITERATURE CITED Bridges PS (1989) Changes in activities with the shift to

agriculture in the southeastern United States. Curr. Anthropol. 30:385-394.

Brooks S, Steele DG, and Brooks RH (1990) Formulae for stature estimation on incomplete long hones: A survey of their reliability. Adli Tip Dergisi J. Forensic Medicine (Istanbul) 6: 167-1 70.

Brown F, Harris J , Leakey R, and Walker AC (1985) Early Homo erectus skeleton from West Lake Tur- kana. Nature 316:78&792.

Constandse-Westermann TS, Blok ML, and Newel1 RR (1985) Long bone length and stature in the Western European Mesolithic. I. Methodological problems and solutions. J. Hum. Evol. 14:399-410.

Feldesman MR, Kleckner JG, and Lundy JK (1990) The femurktature ratio and estimates of stature in Mid- and Late-Pleistocene fossil hominids. Am. J. Phys. Anthropol. 83r359-372.

Formicola V (1983) Stature in Italian prehistoric samples, with particular reference to methodological problems. Homo 34t33-47.

Frankel VH (1971) Biomechanics of the knee. Orthop. Clin. North Am. 2:175-190.

Holliday TW, and Trinkaus E (1991) Limbkrunk proportions in Neandertals and early anatomically modern humans. Am. J . Phys. Anthropol. Suppl. 12t93-94 (abstract).

Jacobs K(1985a) Evolution ofthe postcranial skeleton of late glacial and early postglacial European hominids. Z. Morphol. Anthropol. 75t307-326.

Jacobs K (1985b1 Climate and the hominia postcranial skeleton in Wurm and early Holocene Europe. Curr. Anthropol. 26:512-514.

Jacobs K (ad . , a,) Olenostrovskii social organization re- visited: Skeletal biology and social differentiation in the mesolithic cemetery of Olenii Ostrov. J. Anthrop. Arch. (in review).

Jacobs K (n.d., b.) Human skeletal changes during the Ukrainian Mesolithic-Neolithic transition. Unpub- lished manuscript.

Kaufer H (1971) Mechanical functions of the patella. J . Bone Joint Surg. 53A: 1551-1560.

Larsen CS (1981 ) Functional implications of postcranial size reduction on the prehistoric Georgia Coast, USA. J . Hum. Evol. IOt489-502.

Lovejoy CO (1970) Biomechanical methods for the analysis of skeletal variation with an application by comparison of the theoretical diaphyseal strength of platycnemic and euricnemic tibias. Ph.D. Disserta- tion, University of Massachusetts, Amherst.

Lovejoy CO, Heiple KG, and Burstein AH (1973) The gait of Australopithecus. Am. J . Phys. Anthropol. 38:757-780.

Lovejoy CO, and Trinkaus E (1980) Strength and robusticity of the Neandertal tibia. Am. J. Phys. Anthropol. 53:465-470.

Simmons T, Jantz R, and Bass W (1990) Stature estimation from fragmentary femora: A revision of the Steele method. J . Forensic Sci 3513):628-636.

Steele DG (1970) Estimation of stature from fragments of long limb bones. In TD Stewart (ed.): Personal Iden- tification in Mass Disasters. Washington: Smithso- nian, pp. 85-97.

Steele DG, and TW McKern (1969) A method for the assessment of maximum long hone length and stature from fragmentary long bones. Am. J. Phys. Anthropol. 31t215-228.

Steele DG, and Bramblett CA (1988) The Anatomy and Biology of the Human Skeleton. Texas A&M Univer- sity Press.

Trinkaus E (1976) The evolution of the hominid femoral diaphysis during the Upper Pleistocene in Europe and the Near East. Z. Morphol. Anthropol. 67t29l-319.

Trinkaus E (1980) Sexual differences in Neandertal limb bones. J. Hum. Evol. 9:377-397.

Trinkaus E (1981) Neanderthal limb proportions and cold adaptations. In CB Stringer (ed.): Aspects of Hu- man Evolution. London: Taylor & Francis, pp. 187- 224.

Trinkaus E (1983) Neandertal postcrania and the adap- tive shift to modern humans. In E Trinkaus (ed.): The Mousterian Legacy. Brit. Archaeol. Rep., Internat. Ser. No. 164, pp. 165-200.

APPENDIX A. Regression equations and Standard Errors for femoral length: males. All values in mm.

2 65F1+ 258 1 = FLT i 18 4 0 79F2 + 287 9 = FLT t 17 5 003F3 + 456 7 - FLT ? 26 7 2 26F4 + 367 9 = FLT t 24 3 1 78F1 + 56F2 + 202 5 - FLT t 13 3 2 65F1 + 05F3 + 251 8 = FLT t 18 6 2 4iFI i 17F4 - 229 6 = FLT t i 7 8 115F1 - 103F2 - 9LF3 T 31 1 - FLT - 4 6 1 74F1+ 54F2 + 38F4 + 195 4 = FLT rt 13 4 2 39F1 + 17F3 + 1 4F4 + 200 4 = FLT t 17 9 125F2 + 1 IF3 i 49 0 = FLT t 8 6 0 73F2 + 79F4 t 269 2 = FLT + 17 4 118F2 + 116F3 132F4 + 4 2 = F L T i 6 3 0.24F3 + 2.56F4 + 324.6 = FLT i 24.3

APPENDIX B. Regression equations and Standard Errors for femur length,: females. All values in m.m.

2.27F1 + 267.5 = FLT i: 20.3 .84F2 + 259.8 = FLT i 19.9 .38F3 + 374.2 = FLT t 26.1

1.61F1 + .62F2 + 193.0 = FLT t 16.5

1.33F1 + 3.8OF4 + 195.4 = FLT i 14.8

1.i3FI + .39F2 + 2.94F4 + 164.9 = FLT t 13.3 1.39F1 + .31F3 + 3.64F4 + 158.9 = FLT t 14.2 1.32F2 + 1.22F3 + 15.0 = FLT f 8.9 .47F2 + 3.68F4 + 199.6 = FLT i 15.2 1.07F2 + 1.02F3 + 1.7F4 + 27.2 = FLT t 7.2 .26F3 + 4.82F4 + 216.2 7 FLT 2 17.0

4 .92~4 + 245.7 = Fur t 17.2

2.29F1 + .40F3 -t 215.3 = FLT t 19.6

1.14F1 t 1.12F2 + 1.1F3 - 8.9 = FLT k 3.6

FRAGMENTARY FEMUR AND

APPENDIX C. Regression equations and Standard Errors for estimating femur length: indiuiduals of unknown sex.

All values in mm.

2.97F1 + 228.8 = FLT t 20.6 .95F2 + 247.0 = FLT t 19.7 .25F3 -t 410.8 = FLT t 31.3 3.9734 + 292.8 = FLT t 25.3 1.86F1 + .64F2 + 176.1 = FLT t 15.1 2 97F1 + 26F3 + 195 4 - FLT k 20 3 2 4F1 + 2 16F4 + 188 5 = FLT 2 18 6 116F1 T 107F2 + 101F3 + 11 6 - FLT 2 4 4 1 67F1 + 57F2 + 1 23F4 T 159 2 = FLT i- 14 4 2 36F1+ 33F3 t 2 32F4 + 142 6 = FLT t 17 9 1 31F2 i 1 18F3 T 23 8 = FLT i: 8 7 78F2 + 1 94F4 + 208 8 = FLT i- 18 1 i17F2-112F3 lYOFi 6 1 - F I T + G S 38F3 + 4 13F4 + 238 0 = FLT I 24 7

APPENDIX D. Regression equations and Standard Errors for estimating tibia length: males. All values in mm.

.95T1 + 354.6 = TLT i 23.8

.04T2 i- 376.7 = TLT i 24.4

.64T3 + 278.8 = TLT t 19.5

.88T4 + 293.1 = TLT t 19.4 -1.18T5 + 399.6 = TLT t 24.1 .98T1 - .07T2 + 359.5 = TLT t 24.5 1.14T1 -t .66T3 + 245.0 = TLT t 19.1 1.14T1 + .91T4 i- 260.1 = TLT t 19.0 .99T1 - 1.27T5 + 374.2 = TLT i 24.1

1.29T1 - .4T2 + .95T4 i~ 283.5 = TLT t 19.2 .99T1 -- .01T2 - 1.27T5 + 374.7 = TLT i 24.8

.74T1 + 1.41T2 + .98T3 - .72T5 + 104.0 = TLT 2 16.7 1.29T1 - .43T2 + .98T4 + ,431'5 + 276.2 = TLT t 19.8 1.37T1 + ,741'3 + 1.01T4 + 127.3 = TLT i 8.7 1.16T1 + .65T3 - .52T5 + 255.1 = TLT t 19.6 1.35T1 + .77T3 + 1.09T4 + 1.32T5 + 92.7 = TLT i- 7.9 1.5T2 + 1.01T3 + 101.0 = TLT t 16.4

.72T1 + 1.391'2 + .99T3 + 92.2 = TLT i- 16.4

1.04T1 + 1.05T2 + .98T3 + .93T4 + 20.5 = TLT t 3.3

-.23T2 + .91T4 + 309.5 = TLT t 19.9 .llT2 - 1.23T5 + 391.8 = TLT t 24.7 1221'2 i 1 OT3 + 9T4 + 35 7 = TLT i 6 4 1 R2T2 + 1 OT3 - 681'5 * 112 4 = TT2T i 16 7 117T2 T 102T3 i 9774 102T5 + l % b - TLT ~ 3 8 .71T3 + .98T4 + 171.2 = TLT i 11.2 .63T3 - ,441'5 + 287.5 = TLT t 20.0 .75T3 + 1.06T4 + 1.371'5 + 134.6 = TLT t 10.7 .9T4 + .23T5 + 288.0 = TLT i 20.0

TIBLA LENGTH ESTIMATION 345

APPENDIX E. Regression equations and Standard Errors for estimating tibia length: females. All values in m n .

3.03T1 + 270.0 == TLT t 18.1 1.09T2 + 261.4 = TLT i: 19.4 34T3 + 221.7 == TLT t 17.3 1.17T4 + 234.0 = TLT t 16.3 25T5 -i- 336.1 TLT i 21.2 2.7511 + .92T2 + 210.8 = TLT i 17.2

1.86Tl + .94T4 + 211.9 = TLT i 15.6 3.31T1 + 1.41T5 + 243.8 = TLT t 18.4 1.78Tl + 1.49T2 + .97T3 + 54.4 = TLT t 10.6 1.88T1 + .52T2 + .80T4 i 187.2 = TLT i 15.7 3.07T1 + .96T2 t 1.641'5 4 177.2 = TLT i 17.3

2.44'1'1 + . 7 1 ~ 3 + 182.9 = TLT 2 15.4

.67T1 t 1.06T2 + 1.04T3 -t ,951'4 + 15.1 = TLT t 3.2 1.92T1 + 1.4912 i- .95T3 + .61T5 + 46.0 = TLT i 10.9 2.2T1 + .54T2 t ,871'4 + Z.U4T5 -"i 143.3 = TLT i iS.2 .81T1 + .90T3 i 1.2T4 + 86.4 = TLT t 8.6 2.581'1 + .69T3 + ,561'5 * 175.3 = TLT ir 16.0 1.02T1 + .86T3 + 1.22T4 + 1.05T5 + 70.2 = TLT i 8.5 1.6672 + 1.09T3 + 66.4 = T1,T t 12.1 .50T2 + 1.04T4 + 210.2 = TLT t 16.4 1.121'2 + .63T5 + 250.9 = TLT t 20.0 1.08T2 + 1.09T3 + 1.03T4 + 15.5 = TLT ir 3.8

1.07T2 + 1.07T3 + 1.07T4 + .73T5 + 4.8 = TLT i 3.4 ,951'3 + 1.3T4 + 88.4 = TLT I 8.8 .85T3 -. .47T5 t 226.3 = TLT i 17.9 .93T3 + 1.34'1'4 + .75T5 + 77.2 = TLT t 8.8 1.251'4 i 1.46T5 + 206.4 -= TLT 2 16.4

1.662'2 + 1.09T3 - .13T5 t 68.0 = TLT i- 12.6

APPENDIX F. Regression equations and Standard Errors for estimating tibia length: indiuiduals of unknown sex.

All values in mni. ~~

3.18T1 + 282.9 = TLT i 26.4 1.241'2 + 270.4 = TLT t 29.1 1.03T3 + 208.0 = TLT t 22.5 1.36T4 + 234.4 = TLT t 23.9 2.0T5 + 334.5 = TLT i 30.7 2.8T1 i .81T2 t 231.3 = TLT * 25.7 2.32T1 + .89T3 + 169.9 = TLT f 19.4 2.41T1 + 1.16T4 + 191.9 = TLT t 20.7 3.lT1 + 1.52T5 + 261.7 = TLT -1 26.3 1.34T1 i 1.6T2 1 l lT3 39.6 =- TLT z 13.7 2.281'1 + ,351'2 t l .lT4 -i 174.2 = TLT T 90.7 2.78T1 1.0T1 + 1.15T2 -+ 1.03T3 + .94T4 + 4.5 = TLT i 3.3 1.34T1 + 1.61TZ + l . l lT3 - .09T5 + 40.0 TLT fi 13.9 2.19T1 + .12T2 + 1.22T4 + 2.31'5 + 147.6 = TLT -t 19.8 1.58Tl + 371'3 + 1.13T4 + 83.6 = TLT t 10.2 2.28T1 + 282'3 + 1.05T5 + 157.0 = TLT _f 19.3 1.46T1 + .85T3 + 1.2T4 + 1.9T5 + 55.2 = TLT 5 8.4

.63T + 1.241'4 + 198.1 = TLT i 23.5 1.14T2 + 1.19T5 + 259.4 = TLT t 29.2 1.3212 + 1.1lT3 + .98T4 + 1.4 = TLT t 5.9

.73T2 + 1.06T5 + 221.7 = TLT i 25.8

1 .86~2 + 1 .22~3 4- 37.6 = w r t 15.0

1.871'2 -i- 1.22T3 - .15T5 + 38.2 1.2T2 + 1.08T3 + 1.04T4 + 1.04T5 - - 5.4 = TLT t 5 . 1

TLT i 15.2

.96T3 t 1.251'4 + 98.8 = TLT ? 12.9 1.01T3 + 1.3T5 + 191.1 = TLT i 22.4 .92T3 + 1.32T4 + 2.141'5 + 65.5 = TLT i 11.1 1.44T4 + 2.85T5 -t 183.3 = TLT i 22.4

estimating femur and tibia length from fragmentary bones: an evaluation of steele's (1970)...

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