A Method of Estimating Adduction and 
Abduction of the Leg in Hip Disease, 
By ROBERT W. LOVETT, M. D., 
OF BOSTON. 
Reprinted from the Boston Medical and Surgical Journal 
of March 8, 1888. 
BOSTON : 
OUPPLES AND HURD, Publishers, 
94 Boylston Street, 
1888. A METHOD OF ESTIMATING ADDUCTION AND 
ABDUCTION OF THE LEG IN HIP DISEASE. 
KOBEBT W. BOYETT, M.D., OF BOSTOK. 
The presence of adduction or abduction of the dis- 
eased limb in hip-joint disease is one of the commonest 
and most troublesome of the complications of that 
affection, and the estimation of the amount of mal- 
position present is a matter of much importance, both 
during the acute stage of the disease, as an index of 
the progress of the case, and after the arrest of the 
disease, where a return of the adduction and a conse- 
quent increase of the limp and discomfort is always to 
be feared. It has been customary to calculate in 
degrees the amount of malposition present either by a 
rough guess or by the use of the goniometer, an in- 
strument not often at hand, and always clumsy and 
inaccurate. 
The following article is a purely mathematical de- 
duction from certain evident anatomical relations, by 
which it has been possible to construct a simple and 
practical table for working purposes in the estima- 
tion of the amount of this malposition. The method 
is, in a word, the estimation of the angle of malposi- 
tion of the diseased limb by the varying differences 
between what we may call the real and the apparent 
shortening of that leg. Real shortening is the term 
to be applied to the difference in the length of the 
legs, measuring from the anterior superior spines of 
the ilium to the external or internal malleoli the 
common measurement.1 Practical shortening will be 
1 Stimson. Treatise on Fractures, 1883, p. 511. 2 
used to denote the difference in the length of the legs 
when the measurement is taken from the umbilicus to 
the malleoli while the patient lies straight, with the 
legs parallel,2 and represents, of course, the amount of 
shortening which will be present when the patient 
stands or walks, for the legs must then necessarily be 
made parallel, even if the pelvis has to be tilted to 
make them so. Practically, real shortening may be 
the same as apparent shortening; it may be greater, 
or it may be less, and I had noted that it varied in 
Fig. I, 
Fig. 11. 
2 Gibney. Diseases of the Hip, 1884, p. 28. 3 
proportion to the amount of deformity present, but I 
was unable to express this variation as degrees of mal- 
position, and I am wholly indebted to Mr. G. L. 
Kingsley, of the Harvard Medical School, for the 
mathematical assistance which has made it possible to 
work out and prove the practical usefulness of the 
method. 
When the patient lies straight and neither leg is 
adducted, it hardly needs mathematical proof to show 
that the real shortening is equal to the practical short- 
ening (Figure I). Here E and C represent the mal- 
leoli, I) and B the anterior superior spines, and A the 
umbilicus. A glance shows that the difference in the 
length of A E and A C will be the same as the differ- 
ence between D E and B C (both differences in this 
case being zero) so long as the pelvis is square. 
The mathematical proof of this is; Since F Band GO are parallel 
in this case, and PD= 6B (F G being parallel to DB) and P A = 
A G, and ABE and AGO are right angles, 
„ . „ AC 
Sec. G ACrr 
A E 
sec. AFE 
r. ar. GC 
tan. G A C = 
tan. AFEr 
FE = AE:SsineAFElGC-FB=AC-BineGAC-AE-sineAFE 
that is. practically differing only by the difference in the sines of 
the angles A 0 G, and AED and since the angles in the class of 
cases under observation are very nearly equal, the error is not appre- 
ciable, for the maximum error would be 0.03 inches. 
If, however, one leg is held adducted or abducted 
by muscular spasm or anchylosis, the pelvis must 
necessarily be tilted when the legs are made parallel, 
as in standing or walking, and the state of affairs is 
represented by Figure 11. It is obvious that now the 
distances from B to C and D to E are the same as 
before, whereas AC has grown very much longer than 
AE; the practical shortening of the leg D E has, in 
fact, become greater than the real shortening because 4 
the leg is adducted. It is, moreover, evident that 
this must vary in proportion to the amount of adduc- 
tion and consequent pelvic tilting, for, by the latter, 
one leg must be carried up and the other down, while 
the umbilicus remains stationary, so that as the pelvis 
tilts more and more, A E grows shorter and A C 
longer. 
It is not quite correct practically, to assume that D E = B C in fig- 
ure 11, for Dr. Halstead3 has pointed out that a leg in adduction has 
not the same real length when measured from the anterior superior 
spines to the malleoli, as the same leg in the normal position or ab- 
ducted, hut the difference is to he expressed in milimetres and prac- 
tically does not enter into this method as an error, it is too small to 
he of any account. 
Of course it is not assumed that the anterior superior spines are the 
same distance apart as the acetahula, but the practical centre of 
motion of the leg in adduction and abduction is not at the acetabu- 
lum hut outside of it, as can easily be seen in the skeleton. This is 
of course on account of the angle that the shaft makes with the neck 
of the femur. So far as could be determined, it was well enough 
represented by saying that it was in the lines of the anterior superior 
spines. The only inaccuracy likely to be caused by this, would be 
possibly in the adult female pelvis where the flare was extreme and 
even here the error would be small and of little account. 
The problem was to make this variation express in 
degrees the angular deformity of the adducted or ab- 
ducted leg which caused this pelvic tilting; and for 
working purposes Figure 111 had to be constructed, 
where the original position of the pelvis is represented 
by dotted lines, and the tilted pelvis by heavy lines. 
Of course, a working triangle must be found, and such 
a triangle is L F B, for F L B is the angle to be meas- 
ured, for it is the angle of pelvic tilting which is equal 
to the lateral variation of the diseased leg from the 
normal. 
For, letting DB = pelvis in new position, and GF = pelvis when 
square, D B position of leg, and DM = position leg should have if 
still at right angles to pelvis, andM I) E = adduction angle, 
A L G = 90°, L D M 90°, E D L= D L A (since A N and D E are paral- 
lel and cut by the line D L). 
90° = ALG = ALD + DLG Ip,-,*, at ta tt, p 
90° = L I) M=r L I) E + M D E ] OUI A Xj u ~ 
D LS = M D E= abduction or adduction angle. 
8 New York Medical Journal, 1884, page 317. 5 
Now of this right-angled triangle, LF B, two 
sides are known: LB, which is equal to half the 
distance between the anterior superior spines of the 
ilium ; and BF, which is equal to half the difference 
between the real and apparent shortening. The pelvis 
tilts, and one foot is carried up and the other down, 
and the practical shortening is the sum of these excur- 
sions. 
Fig. 111. 
First, when the legs are of equal length. 
In this case the problem becomes to prove that twice the sine of 
the angle of ad- or abduction is equal (or very nearly so) to the dif- 
ference between the distances from the umbilicus to the internal 
malleoli. 6 
In Figure 4if we suppose D and E to be the positions of the ante- 
rior superior spines of the ilium, A the umbilicus, B and C the inter- 
nal malleoli, then the angle BED' (which equals BE' IV) will be 
equal to the angle of duction (as proven in Figure 3), IV and E' are 
the positions which the anterior superior spines would have if there 
was no ad- or abduction. 
The Figure D' E' C' B' will be a rectangle. Suppose a circle with 
a radius BE'to be described on E'as a centre; then the points B', 
C", C and C' will lie in the circumference of this circle, since they are 
points all equally distant from E'. 
It is to be proved that 
AC A B B C" = BCi'=BT) 
or if there is an error in the equality, to show that the same is so 
small as to he inappreciable in the estimation of the ultimate result. 
Suppose the triangle AE'oto he rotated on AE'as an axis. Then 
C will fall at C" and the are BB' will equal the arc B'C". On A 
as a centre with a radius equal to A B described an arc which shall 
cut Ao"at S and therefore make A B equal to AS. Now C" S will 
equal the difference between A B and AC". 
From observation in a large number of typical cases the angle of 
ah-or adduction is found not to exceed 30°. It has also been ascer- 
tained from observations that the ratio of AE' to B' E' lies within 
the limits of six to one and eight to one. 
It is evident that the smaller the angle of duction and the larger 
the ratio of AE' to IV E' the less will be the error arising from the 
assumption that C" B equals C" S. 
Therefore if it is computed, in the case where the angle of duction 
is greatest (equal to 30°) and the ratio is smallest (equal to 6 :1), the 
value of C" B and C" S, the quantity by which these two lines differ 
in length, should be the largest possible error entering into the com- 
putation. 
Suppose B'E' to be equal to one, AE' equal to 6 (the smallest 
ratio), BE'B'equal to 30° (the largest angle); then A E'B'equals 
90°, BE'B' = B'E'C", AE'C" = 120° and AE'B = 60°. 
Since by trigonometry in oblique angle triangle when two sides 
and the included angle are given the third side is equal to the square 
root of the sums of the squares on the two given sides diminished by 
twice the product of these sides into the cosine of the included angle. 
The formula is 
C" A = y/C" R'2 +R'A2— 2 . C" R'. R' A . cos. AR'C" = = 6.557 
BA= y,BR'J + ATv2-2.BR'.AR'COB.AR'B= = 5.567 
Therefore 0" A BA = .01 when B'R' = 1 
But B T (=: = sine BE'T =|, therefore BC" - 1 
Since the greatest pelvic measurement which wouldhave to be dealt 
with would not exceed 14 inches, and therefore one-half of it not more 
C" S 
than 7, therefore the error arising from considering B T = —(— 
sine duction angle) could not exceed .035 of an inch in any case and 
usually would not exceed .02 of an inch which is a quantity far too 
small to have any influence in the computing of the table where 7 
single degrees only are considered and measurements considered only 
accurate to the nearest one-eighth inch. 
The same relation is easily proved by a similar figure, to exist 
■where the legs are of unequal length. It hardly seems worthwhile 
to add it here. 
Fig. IV. 8 
Having, then, a right-angled triangle with two 
known sides, the angle F L B was calculated by the 
formula, sine FLB = and from the results ob- 
tained, the following table was constructed for all 
breadths of pelvis and all degrees of variation. 
Difference in inches between Eeal and Apparent Shortening. 
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Distance between Anterior Superior Spines in incites. 
The patient lies straight, with the legs parallel. 
Real shortening is measured with the ordinary tape- 
measijre, and then apparent shortening is obtained in 9 
the same way. The difference between the two shorten- 
ings is seen at a glance. The only additional measure- 
ment necessary is the distance between the anterior 
superior spines, which is taken with the tape. Turn- 
ing now to the table, if the line which represents the 
amount of difference in inches between the real and 
apparent shortening is followed until it intersects the 
line which represents the pelvic breadth, the angle of 
deformity will be found in degrees where they meet. 
If the practical shortening is greater than the real short- 
ening, the diseased leg is adducted; if less than the real 
shortening, it is abducted. Take an example : Length 
(from anterior superior spine) of right leg, 23 ; left 
leg, length (from umbilicus) of right leg, 25; 
left leg, 23 ; difference between real and practical 
shortening, inches ; pelvic measurement, 7 inches. 
If we follow the line for inches until it intersects 
the line for pelvic breadth of 7 inches, and we find 
12° to be the angular deformity, as the practical 
shortening is greater than the real, it is 12° of adduc- 
tion of the left leg. 
Certain objections which are likely to he made may 
he formulated and dismissed : 
(1) That inequality in the length of the legs, con- 
genital or acquired, would vitiate the result. Any 
such inequality would appear in both the real and 
the apparent shortening, and not affect the difference 
between the two. 
(2) That the co-existence of flexion of the thigh 
upon the pelvis would render the method inaccurate. 
A moment’s consideration will show that the flexion 
of the thigh upon the pelvis makes no difference, for 
the measurements here considered depend wholly upon 
certain relations in a horizontal plane between the 
iliac spines and the malleoli, and that this relation re- 
mains the same, unaffected by the movement of the 10 
anterior superior spines in another plane so long as 
they move together. 
(3) It may be urged that individual measurers 
vary. But both measurements are taken each time 
by the same man, skilled or not; and in the measure- 
ment for practical shortening he will use the same 
method, and make the same error that he made in 
measuring for real shortening, and it will not appear 
in the difference between the two. It is not unreason- 
able to expect a moderate amount of care to be taken 
in any such measurements. 
Next and last, as to the practical accuracy of the 
method: It has been used by the writer and others 
for some weeks in a large number of cases of hip-joint 
disease in the Surgical Out-patient Department of 
the Children’s Hospital, and afterward a very careful 
measurement has been taken independently with a 
fairly accurate goniometer, and the results have 
always coincided within one or two degrees. THE BOSTON 
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