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On the assessment of body weight
R. Knussmann M. Toeller H. D. Holler Anthrofiologisches Institut a’er Universitiit, 2 Hamburg 13, Von-Melle-Park 10, Federal Republic of Germany
On the Assessment of Body Weight Body height-weight indices are useful for determining body buIk and of these Rohrer’s body bulk index (weight divided by the cube of the body height) is the only one that has a theoretically acceptable base. The statistical analysis of data on 747 healthy men and women and comparison with empirical ideal weights also showed this index to be the most suitable. A nomogram for its graphical determination is therefore added. Indices are not all necessary for the determination of overweight or underweight; it is preferable to orientate the assessment on heightspecific ideal weights. Broca’s rule for the determination of ideal weights is groundless and supplies unsatisfactory results. The ideal weights based on the criterion of length of life elicited by the Metropolitan Life Insurance Company are preferable. Nomograms for these weight norms are given which permit direct determination of the absolute and percentual deviation from the ideal norm.
1. Body Height-weight
Indices
doubt body weight represents a factor that has considerable importance both from the medical and the human ecological points of view. It is equally true that it is not the absolute body weight but the relationship between weight and size that supplies reIevant information in this respect. The indicator generally used as a guide to body size is the height as the largest linear, i.e. one-dimensional extension of the body. By setting body weight in relation to body height (centimetre-weight, Quetelet-Bouchard) (Table 1) a measure, in this case weight, containing information on the three-dimensional body is compared with a one-dimensional measure. The resulting index shows how much weight per centimetre body height a person has, but completely ignores the fact that a tall individual has a broader girth and consequently must have more weight per centimetre than a small person. There has therefore been a general trend to balance the dimensional differences of body height and body weight by either raising one of the measures to a higher power or by taking the root of one of them. Thus the weight as expressed in the “body build index” (Quetelet, Table 1) is related to the square of the height and thus is compared as a body in its three-dimensional parameter with a two-dimensional one. Only if the cube of the body height is used as a relative basis for the weight (body bulk index, Rohrer, 1908, Table 1) are both parameters raised to the same dimensional level. The same applies to the index ponderis (Livi, see Rohrer, 1908) in which the cube root of the weight is divided by the linear body height, which has the disadvantage, when compared with the Rohrer index, that it is less easy to take a root than it is to raise to a power. Rohrer’s body bulk index leads to exactly comparable inter-individual values if the body weight is proportional to body volume. This premise is adequately fulfilled because the inter-individual differences in the body’s specific gravity are only slight. For the body volume, however, it can be clearly demonstrated that it is only equivalent to the cube of the body height. In this respect one must start with the premise that the index figure for the relation of body volume to body height must be the same in all individuals who represent, in the geometric sense, similar figures, i.e. with completely the same proportions and variability of the three-dimensional size alone. If one simplifies Without
Journal of Human Evolution ( 1975) 4,497-504
498
R.
Table 1
Body height-weight indices. The multiplication by the factor 10 is merely intended to remove the decimal point
KNIJSSMANN,
M.
TOELLER
1. Centimetre-weight
=
2. Body build index (Quetelet)
=
3. Body bulk index (Rohrer)
=
AND
H.
D.
HOLLER
10 (body weight in kg) (body height in cm) 1000 (body weight in kg) (body height in cm)z 10 000 (body weight in kg) (body height in cm)”
the human body to a block for which the symbols h, w and d are used for height, width and depth respectively, then the volume is the product hwd. All solids in which the three dimensions are multiplied by the same, but individually arbitrary factor x, must have the same index, as is shown by the following: Weight
---=-= hS
hwd
(xh) (xw) (xd)
h3
(xh)3
x3)$
’
hwd
x3hwd =
7
’
The usefulness of body height-weight indices is sometimes assessed by the degree to which the indices concerned are independent of the body height, i.e. to what extent the effect of body height is excluded (e.g. Traebert, 1947). An empirical check shows that independence of body height is least in the Rohrer index (Table 2). This is, however, only an apparent contradiction to the theoretical basis of the Rohrer index. The requirement of index consistency for, in the geometrical sense, similar bodies, and thus for bodies of the same “bulk” does not include the requirement that the variability of the index should be independent of the body height. These two requirements coincide if both interindividual variability of the body height at the statistical mean and proportional variability of the other two body dimensions exist, i.e. if the tall and the small are on average geometrically similar. This is, however, not the case. It is well known that pyknomorphs, i.e. people with larger than average girth, are in the statistical mean relatively small, while leptomorphs, who have a lesser girth, are relatively tall (see Knussmann, 1961a, 6). In addition, the ratio to one another of the individual sections constituting both height shifts with the mean body height. It has been demonstrated many times, (e.g. Knussmann 19616, Knussmann & Mtiller, 1968) that tall people’s legs account for a greater proportion of their total body height than is the case with small people. Thus the relative leg length, i.e. related to absolute body height, correlates to a highly significant degree positively with body height to an extent that is very remarkable for a correlation between an absolute measure and an index based on that same absolute parameter (men: n = 341, r = O-32; women: n = 323, r = O-39). As, however, the legs, or at least the lower part of them, must weigh less per centimetre than the trunk, to which the arms must also be added, it may be assumed that with increasing height a weight index, that is supposed to represent total body bulk, will diminish. This means that there must be a negative correlation between the weight index and body height. The expectation coincides best with the Rohrer index (see Table 2). The requirement of independence, i.e. non-correlation, between the weight index and body
ASSESSMENT
OF BODY
499
WEIGHT
Table 2
Kmpirical data on body height and body height-weight indices based on au investigation of 741 healthy West German adults of all age groups (Knussmann, 1961a; Oberdisse, Knussnnum, Toeller, Daweke, Gries & Irmscher, 1971). 0 = body height, l-3 = indices according to Table 1. n = number of individuals, g & m = arithmetic mean and standard error of the mean, s = standard deviation, r = coefficient of the product-moment correlation to body height
Character
SeX
?I
0 $
393 354
F
393 354
? f”
1 2 3
s
n+m 171.31 & o-34 159.41 * 0.33
f
6.72 6.16
1.00 1 .oo
4.37 * 0.03 4.09 * 0.04
0.56 0.73
0.28 0.02
393 354
2.55 * 0.02 2.57 * 0.03
O-32 0.47
-0.03 -0.19
393 354
1.49 * 0.01 1.62 -+ 0.02
o-21 0.31
-0.29 -0.38
height is insufficient for the problem concerned, namely the definition of a parameter for body bulk. It follows from the above considerations that small individuals must, on the average, be attributed a greater body bulk than tall people. On the basis of observations by American life insurance societies on almost 5 million people, the Metropolitan Life Insurance Company (MLIC) determined empirical ideal weights for individual height classes on the basis of lifetimes (see N. N., 1960; Diem & Lentner, 1968). According to these ideal weights, the Rohrer indices are markedly higher for smali than for tall people (Figure l), which supports the above contention. In addition, the Rohrer index can be represented with an accuracy, which can be described as satisfactory for empirically obtained data, as a straight line resultant of ideal weight and the cube of body height Figure 1. Rohrer indices for the MLIC body height classes of both sexes. Rohrer Index * \L-
,
s ? *‘ ‘
,
s
,
,
t; .
ll3.
.
,
s
*
d I
.
L
s
*
s
I
*
.
,
I *a
"L. 'L '.
l* .'0
*0 '+s
12
ideal weights for individual
.
**
‘I
l*
's
‘0
*+
‘*
+c
‘*
‘.+
*+
** ++
‘* ‘*,
101 . 150
65
160
185
l70
175
190
195
190
+**
stature +
195
Figure 2. The ratio of ideal weights to the cube of the body height. +line = Broca ideal weight, x - lines = MLIG ideal weights for men and women. The continuous straight lines were approximate on the basis the x - values according to the method of the sum of least squares. 95
wisht
90-
+
m-
15 -
l
+
+
+
+
+
+
+
+
+
+
stature3 150
155
165
im
175
150
165
190
135
Figure 3. Ratio of ideal weight to linear body height. fline = Broca ideal weights, x - lines = MLIC ideal weights for men and women. The continuous straight lines represent tangents to the curve approximations at the points of the empirical means of the population samples in question (2) and are intended to make the curves as such more conspicuous.
501
ASSESSMENT OF BODY MrEIGHT
(Figure 2, x-lines). This means that the increase in one variable is in-a constant ratio to the increase of the other, so that there is a good inter-individual comparability from the reference values derived from the two variables. In the square of the body height (body build index) or even the linear height (centimetre-weight), is used instead of the cube to produce the index, then the ideal weights lead to index values that describe a curve with a lefthand inflexion and particularly so in the case of the centimetre-weight. (Figure 3 : x -lines). This is only to be expected as the volume, and thus the weight of the body, too, rises to a greater degree than its largest linear extension, and also to a higher degree than the area of any one of its surfaces. In summary, it can be said that Rohrer’s body bulk index is the most suitable combination of body weight and body height, if an inter-individually comparable and premise-free or prejudice-free quantitative measure for the body bulk and thus the weight situation is required. This is important medically and from the point of view of human ecology. As the calculation of the Rohrer index is time consuming because of the cubing of the height, a nomogram is appended for the direct reading off of the index (Figure 4). Figure 4. Nomograms for the reading of the Rohrer index. The values measured for the body height and weight are sought in the respective scales, and the two points found are joined by a straight line (e.g. by laying a ruler between them). The intersection of the straight line with the right-hand scale is the Rohrer index.
statWe
weigm
in cm
:
in kg
Rohrer Index
40
210 300
b 200
= 3.5
250 :
:
200
190
3,O
1 2a 236
= 150 -
160 -
7
-
170
160
120 110 1GO
2>2
90
I>9
2,O
60
1,6
70
I>7
60 50 -
214
150 CO
1,6 1,s CL 1,3 V
-
140
-
30
V CO
-
130
-
20
0‘9 0>6
o;!
502
R. KNUSSMANN, M. TOELLER
AND H. D. HOLLER
2. Overweight and Underweight On the basis of the above-mentioned MLIC ideal weights, an assessment of overweight and underweight can be conducted without the necessity of calculating a body heightweight index. This involves the individual deviation from a norm for which the heightspecific norm may be utilized. It can, however, be disputed whether the MLIC ideal norms represent real norm values. They are undoubtedly more useful for the assessment Figure 5. Nomograms for determining deviations from MLIC ideal weights (desirable weights) for men. The values obtained for height and weight (actual weight in clothes for wear at home) are sought in the appropriate scale and the two points are joined by a straight line (e.g. by means of a ruler). The intersection of this straight line with the two right-hand scales shows the absolute and percentage deviations from the ideal weight, i.e. related to the corresponding desired weight. In addition, the desired weight as such can be read from the right-hand side of the scale on the far left.
d
deviation from ideal weight . in kg -70 -65 -60 -55 actual we’gk %n
:
60
-45
50
-40
40
-35
-50
kg
-30
830 20
E -25
10
-20
loo
-15
90
80 70
5 normal range
o -5
En
10 50
-10 -20
40
30
-15
,
ASSESSMENT
OF BODY
WEIGHT
503
Figure 6. Nomogram for the determination of deviation from MLIC ideal weights (desired weights) for women. For explanation see Figure 5.
Q
deviation from
deviition from
actualweight in kg
60 50
of overweight or underweight, and thus of a medical parameter, than the average norm which is calculated from the population means. There are, however, other ideal norms. Particularly in the medical profession a rule of the thumb derived from the last century has persisted the present day, and can even be found in scientific papers. This is Broca’s rule, which says that an individual should weigh as many kilogrammes as the number of centimetres by which his body height exceeds one metre. (Broca, 1868; cited by Ries, 1964). Broca’s rule only supplies usable indicativeweights for men over a small range of heights. It can easily be shown by means of an extreme case, that outside this range it leads to absurdities. An individual measuring only one metre, i.e. a dwarf or a child, should, according to the Broca rule, weigh nothing at all. From this it is readily apparent that the height-specific weight norm by Broca’s method is apparently dependent to an unrealistic degree on body height. The too marked, absolutely linear dependence of the Broca norms on body height is seen biometrically in the fact that the norm values plotted on the co-ordinates weight, and body height give a straight line (Figure 3: +-lines),
504
R.
KNUSSMANN,
M.
TOELLER
AND
H.
D.
HOLLER
whereas one ought to expect a curve with a left inflexion as the volume of a body does not increase proportionally to but to a greater degree than its major linear extension. If one uses the cube of the body height, then a straight line should be obtained, whilst for the Broca values a curve with an imlexion to the right (Figure 2 : +-line) is produced, which indicates poor inter-individual comparability of the Broca values. At the same time it can be seen from Figures 2 and 3 that the Broca ideal norms are not even approximately comparable with the empirically obtained ideal norms. As medical experience has also shown that the Broca rule does not lead to a satisfactory assessment of overweight or underweight, various modifications of the rule have been published. All these modifications, however, merely represent an attempt to make a primarily unfounded formula subsequently more useful. Ott (1963), who offers the best and at the same time the most complicated version, based his corrective values for the Broca rule on the MLIC ideal norms. It appears more sensible to assess overweight and underweight purely on the basis of these empirically obtained ideal values. Two nomograms are appended for this purpose (Figures 5 and 6). The MLIC ideal weights are not, of course, based on an error-free investigation, but at the present moment there are no better values. They are in any case preferable to the Broca ideal weights, the irrationality of which has been demonstrated. Adapted from: Knmsmann,
R., Toeller, M. & Holler, H. D. (1972). Zur BeurteilungdesKiirpergewichts.
Die MedizinischeWelt NF 23, 529-535 (where the bibliography is to be found).
On the Assessment of Body Weight Body height-weight indices are useful for determining body buIk and of these Rohrer’s body bulk index (weight divided by the cube of the body height) is the only one that has a theoretically acceptable base. The statistical analysis of data on 747 healthy men and women and comparison with empirical ideal weights also showed this index to be the most suitable. A nomogram for its graphical determination is therefore added. Indices are not all necessary for the determination of overweight or underweight; it is preferable to orientate the assessment on heightspecific ideal weights. Broca’s rule for the determination of ideal weights is groundless and supplies unsatisfactory results. The ideal weights based on the criterion of length of life elicited by the Metropolitan Life Insurance Company are preferable. Nomograms for these weight norms are given which permit direct determination of the absolute and percentual deviation from the ideal norm.
1. Body Height-weight
Indices
doubt body weight represents a factor that has considerable importance both from the medical and the human ecological points of view. It is equally true that it is not the absolute body weight but the relationship between weight and size that supplies reIevant information in this respect. The indicator generally used as a guide to body size is the height as the largest linear, i.e. one-dimensional extension of the body. By setting body weight in relation to body height (centimetre-weight, Quetelet-Bouchard) (Table 1) a measure, in this case weight, containing information on the three-dimensional body is compared with a one-dimensional measure. The resulting index shows how much weight per centimetre body height a person has, but completely ignores the fact that a tall individual has a broader girth and consequently must have more weight per centimetre than a small person. There has therefore been a general trend to balance the dimensional differences of body height and body weight by either raising one of the measures to a higher power or by taking the root of one of them. Thus the weight as expressed in the “body build index” (Quetelet, Table 1) is related to the square of the height and thus is compared as a body in its three-dimensional parameter with a two-dimensional one. Only if the cube of the body height is used as a relative basis for the weight (body bulk index, Rohrer, 1908, Table 1) are both parameters raised to the same dimensional level. The same applies to the index ponderis (Livi, see Rohrer, 1908) in which the cube root of the weight is divided by the linear body height, which has the disadvantage, when compared with the Rohrer index, that it is less easy to take a root than it is to raise to a power. Rohrer’s body bulk index leads to exactly comparable inter-individual values if the body weight is proportional to body volume. This premise is adequately fulfilled because the inter-individual differences in the body’s specific gravity are only slight. For the body volume, however, it can be clearly demonstrated that it is only equivalent to the cube of the body height. In this respect one must start with the premise that the index figure for the relation of body volume to body height must be the same in all individuals who represent, in the geometric sense, similar figures, i.e. with completely the same proportions and variability of the three-dimensional size alone. If one simplifies Without
Journal of Human Evolution ( 1975) 4,497-504
498
R.
Table 1
Body height-weight indices. The multiplication by the factor 10 is merely intended to remove the decimal point
KNIJSSMANN,
M.
TOELLER
1. Centimetre-weight
=
2. Body build index (Quetelet)
=
3. Body bulk index (Rohrer)
=
AND
H.
D.
HOLLER
10 (body weight in kg) (body height in cm) 1000 (body weight in kg) (body height in cm)z 10 000 (body weight in kg) (body height in cm)”
the human body to a block for which the symbols h, w and d are used for height, width and depth respectively, then the volume is the product hwd. All solids in which the three dimensions are multiplied by the same, but individually arbitrary factor x, must have the same index, as is shown by the following: Weight
---=-= hS
hwd
(xh) (xw) (xd)
h3
(xh)3
x3)$
’
hwd
x3hwd =
7
’
The usefulness of body height-weight indices is sometimes assessed by the degree to which the indices concerned are independent of the body height, i.e. to what extent the effect of body height is excluded (e.g. Traebert, 1947). An empirical check shows that independence of body height is least in the Rohrer index (Table 2). This is, however, only an apparent contradiction to the theoretical basis of the Rohrer index. The requirement of index consistency for, in the geometrical sense, similar bodies, and thus for bodies of the same “bulk” does not include the requirement that the variability of the index should be independent of the body height. These two requirements coincide if both interindividual variability of the body height at the statistical mean and proportional variability of the other two body dimensions exist, i.e. if the tall and the small are on average geometrically similar. This is, however, not the case. It is well known that pyknomorphs, i.e. people with larger than average girth, are in the statistical mean relatively small, while leptomorphs, who have a lesser girth, are relatively tall (see Knussmann, 1961a, 6). In addition, the ratio to one another of the individual sections constituting both height shifts with the mean body height. It has been demonstrated many times, (e.g. Knussmann 19616, Knussmann & Mtiller, 1968) that tall people’s legs account for a greater proportion of their total body height than is the case with small people. Thus the relative leg length, i.e. related to absolute body height, correlates to a highly significant degree positively with body height to an extent that is very remarkable for a correlation between an absolute measure and an index based on that same absolute parameter (men: n = 341, r = O-32; women: n = 323, r = O-39). As, however, the legs, or at least the lower part of them, must weigh less per centimetre than the trunk, to which the arms must also be added, it may be assumed that with increasing height a weight index, that is supposed to represent total body bulk, will diminish. This means that there must be a negative correlation between the weight index and body height. The expectation coincides best with the Rohrer index (see Table 2). The requirement of independence, i.e. non-correlation, between the weight index and body
ASSESSMENT
OF BODY
499
WEIGHT
Table 2
Kmpirical data on body height and body height-weight indices based on au investigation of 741 healthy West German adults of all age groups (Knussmann, 1961a; Oberdisse, Knussnnum, Toeller, Daweke, Gries & Irmscher, 1971). 0 = body height, l-3 = indices according to Table 1. n = number of individuals, g & m = arithmetic mean and standard error of the mean, s = standard deviation, r = coefficient of the product-moment correlation to body height
Character
SeX
?I
0 $
393 354
F
393 354
? f”
1 2 3
s
n+m 171.31 & o-34 159.41 * 0.33
f
6.72 6.16
1.00 1 .oo
4.37 * 0.03 4.09 * 0.04
0.56 0.73
0.28 0.02
393 354
2.55 * 0.02 2.57 * 0.03
O-32 0.47
-0.03 -0.19
393 354
1.49 * 0.01 1.62 -+ 0.02
o-21 0.31
-0.29 -0.38
height is insufficient for the problem concerned, namely the definition of a parameter for body bulk. It follows from the above considerations that small individuals must, on the average, be attributed a greater body bulk than tall people. On the basis of observations by American life insurance societies on almost 5 million people, the Metropolitan Life Insurance Company (MLIC) determined empirical ideal weights for individual height classes on the basis of lifetimes (see N. N., 1960; Diem & Lentner, 1968). According to these ideal weights, the Rohrer indices are markedly higher for smali than for tall people (Figure l), which supports the above contention. In addition, the Rohrer index can be represented with an accuracy, which can be described as satisfactory for empirically obtained data, as a straight line resultant of ideal weight and the cube of body height Figure 1. Rohrer indices for the MLIC body height classes of both sexes. Rohrer Index * \L-
,
s ? *‘ ‘
,
s
,
,
t; .
ll3.
.
,
s
*
d I
.
L
s
*
s
I
*
.
,
I *a
"L. 'L '.
l* .'0
*0 '+s
12
ideal weights for individual
.
**
‘I
l*
's
‘0
*+
‘*
+c
‘*
‘.+
*+
** ++
‘* ‘*,
101 . 150
65
160
185
l70
175
190
195
190
+**
stature +
195
Figure 2. The ratio of ideal weights to the cube of the body height. +line = Broca ideal weight, x - lines = MLIG ideal weights for men and women. The continuous straight lines were approximate on the basis the x - values according to the method of the sum of least squares. 95
wisht
90-
+
m-
15 -
l
+
+
+
+
+
+
+
+
+
+
stature3 150
155
165
im
175
150
165
190
135
Figure 3. Ratio of ideal weight to linear body height. fline = Broca ideal weights, x - lines = MLIC ideal weights for men and women. The continuous straight lines represent tangents to the curve approximations at the points of the empirical means of the population samples in question (2) and are intended to make the curves as such more conspicuous.
501
ASSESSMENT OF BODY MrEIGHT
(Figure 2, x-lines). This means that the increase in one variable is in-a constant ratio to the increase of the other, so that there is a good inter-individual comparability from the reference values derived from the two variables. In the square of the body height (body build index) or even the linear height (centimetre-weight), is used instead of the cube to produce the index, then the ideal weights lead to index values that describe a curve with a lefthand inflexion and particularly so in the case of the centimetre-weight. (Figure 3 : x -lines). This is only to be expected as the volume, and thus the weight of the body, too, rises to a greater degree than its largest linear extension, and also to a higher degree than the area of any one of its surfaces. In summary, it can be said that Rohrer’s body bulk index is the most suitable combination of body weight and body height, if an inter-individually comparable and premise-free or prejudice-free quantitative measure for the body bulk and thus the weight situation is required. This is important medically and from the point of view of human ecology. As the calculation of the Rohrer index is time consuming because of the cubing of the height, a nomogram is appended for the direct reading off of the index (Figure 4). Figure 4. Nomograms for the reading of the Rohrer index. The values measured for the body height and weight are sought in the respective scales, and the two points found are joined by a straight line (e.g. by laying a ruler between them). The intersection of the straight line with the right-hand scale is the Rohrer index.
statWe
weigm
in cm
:
in kg
Rohrer Index
40
210 300
b 200
= 3.5
250 :
:
200
190
3,O
1 2a 236
= 150 -
160 -
7
-
170
160
120 110 1GO
2>2
90
I>9
2,O
60
1,6
70
I>7
60 50 -
214
150 CO
1,6 1,s CL 1,3 V
-
140
-
30
V CO
-
130
-
20
0‘9 0>6
o;!
502
R. KNUSSMANN, M. TOELLER
AND H. D. HOLLER
2. Overweight and Underweight On the basis of the above-mentioned MLIC ideal weights, an assessment of overweight and underweight can be conducted without the necessity of calculating a body heightweight index. This involves the individual deviation from a norm for which the heightspecific norm may be utilized. It can, however, be disputed whether the MLIC ideal norms represent real norm values. They are undoubtedly more useful for the assessment Figure 5. Nomograms for determining deviations from MLIC ideal weights (desirable weights) for men. The values obtained for height and weight (actual weight in clothes for wear at home) are sought in the appropriate scale and the two points are joined by a straight line (e.g. by means of a ruler). The intersection of this straight line with the two right-hand scales shows the absolute and percentage deviations from the ideal weight, i.e. related to the corresponding desired weight. In addition, the desired weight as such can be read from the right-hand side of the scale on the far left.
d
deviation from ideal weight . in kg -70 -65 -60 -55 actual we’gk %n
:
60
-45
50
-40
40
-35
-50
kg
-30
830 20
E -25
10
-20
loo
-15
90
80 70
5 normal range
o -5
En
10 50
-10 -20
40
30
-15
,
ASSESSMENT
OF BODY
WEIGHT
503
Figure 6. Nomogram for the determination of deviation from MLIC ideal weights (desired weights) for women. For explanation see Figure 5.
Q
deviation from
deviition from
actualweight in kg
60 50
of overweight or underweight, and thus of a medical parameter, than the average norm which is calculated from the population means. There are, however, other ideal norms. Particularly in the medical profession a rule of the thumb derived from the last century has persisted the present day, and can even be found in scientific papers. This is Broca’s rule, which says that an individual should weigh as many kilogrammes as the number of centimetres by which his body height exceeds one metre. (Broca, 1868; cited by Ries, 1964). Broca’s rule only supplies usable indicativeweights for men over a small range of heights. It can easily be shown by means of an extreme case, that outside this range it leads to absurdities. An individual measuring only one metre, i.e. a dwarf or a child, should, according to the Broca rule, weigh nothing at all. From this it is readily apparent that the height-specific weight norm by Broca’s method is apparently dependent to an unrealistic degree on body height. The too marked, absolutely linear dependence of the Broca norms on body height is seen biometrically in the fact that the norm values plotted on the co-ordinates weight, and body height give a straight line (Figure 3: +-lines),
504
R.
KNUSSMANN,
M.
TOELLER
AND
H.
D.
HOLLER
whereas one ought to expect a curve with a left inflexion as the volume of a body does not increase proportionally to but to a greater degree than its major linear extension. If one uses the cube of the body height, then a straight line should be obtained, whilst for the Broca values a curve with an imlexion to the right (Figure 2 : +-line) is produced, which indicates poor inter-individual comparability of the Broca values. At the same time it can be seen from Figures 2 and 3 that the Broca ideal norms are not even approximately comparable with the empirically obtained ideal norms. As medical experience has also shown that the Broca rule does not lead to a satisfactory assessment of overweight or underweight, various modifications of the rule have been published. All these modifications, however, merely represent an attempt to make a primarily unfounded formula subsequently more useful. Ott (1963), who offers the best and at the same time the most complicated version, based his corrective values for the Broca rule on the MLIC ideal norms. It appears more sensible to assess overweight and underweight purely on the basis of these empirically obtained ideal values. Two nomograms are appended for this purpose (Figures 5 and 6). The MLIC ideal weights are not, of course, based on an error-free investigation, but at the present moment there are no better values. They are in any case preferable to the Broca ideal weights, the irrationality of which has been demonstrated. Adapted from: Knmsmann,
R., Toeller, M. & Holler, H. D. (1972). Zur BeurteilungdesKiirpergewichts.
Die MedizinischeWelt NF 23, 529-535 (where the bibliography is to be found).