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On So-called Paresis of 
Divergence 

BY 

GEORGE A. BERRY 

i - 

i . 

■Vr ^ 



Not Published. 



On So-called Paresis of 

Divergence 

\ 

BY • 

GEORGE A. BERRY 




[Read before the Ophthalmological Society of the 
United Kingdom, J anuary 1901 .) 



ON SO-CALLED PARESIS OF 
DIVERGENCE 



Although I have seen a few similar cases, I shall, in 
order to be as brief as possible, base my remarks on the 
subject of this communication on the following case : — 

James Ancrum, aged fourty-four, a previously healthy 
man who neither smokes nor drinks, suddenly developed 
a diplopia on the morning of the i6th September last. He 
is employed on night duty at the Edinburgh Gasworks, 
and principally in regulating pipes, metres, etc. His 
family history is good and unimportant. 

He was first seen by me at the Royal Infirmary three 
days after the occurrence of the diplopia. He stated 
that in the interval he constantly saw double. In the 
mornings, according to his wife’s statement, he had quite 
a marked convergent squint. This passed off in the 
course of the day — after rest. Being always at work at 
night, he slept during part of the day. 

On examination : there was no apparent interference 
with the associated lateral or vertical movements of the 
eyes. On distant fixation there was manifest con- 
vergence. 

In addition to this history of a marked manifest squint, 
which existed in the morning and afterwards diminished 
to such an extent as to be unnoticeable, the further 
examination brought out several points of interest. 



4 ON SO-CALLED PARESIS OF DIVERGENCE 



The convergence on distant fixation, tested with a 
candle flame and red glass in front of one eye, equalled 
about three metre angles {i,e. convergence to a point lying 
about one-third of a metre or thirteen inches from the 
eyes). Any abnormal convergence was not particularly 
apparent on mere inspection. The diplopia was corrected 
by a prism of 22°. 

At the reading distance there was much less excess of 
convergence manifest. Indeed, there did not seem to be 
constantly any diplopia at all. This could always be 
elicited, however, with the flame and red glass. Yet 
there existed a high degree of latent convergence. 
Either eye, if occluded, at once deviated inwards in a 
most marked manner. 

Tested for objects at the distance of six to eight feet, 
the double images were found to be considerably closer 
together on fixation to either side than on looking 
straight forwards. The latter separation was also some- 
what less when the eyes were turned upwards, and 
somewhat greater when they were turned downwards. 

The power of fusion was good. The diplopia could be 
corrected by the same prism at different distances, pro- 
vided the object fixed was not too rapidly moved either 
to vards or away from the patient. This was even found 
to be the case for the fixation of a candle flame with a 
red glass in front of one eye. 

The treatment consisted in complete rest with bromide 
of sodium. After four days all spontaneous diplopia had 
disappeared. There was still some latent convergence, 
though very much less than formerly. Diplopia could 
also be elicited with a red glass, and this was corrected 
by a prism of 12°. After a week only a trace of latent 
convergence could be made out by means of a vertically 






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ON SO-CALLED PARESIS OF DIVERGENCE 



5 



refracting prism. The patient then returned to work, and 
there has since been no recurrence of the symptoms. 

The case was evidently not one of the sudden manifes- 
tation, owing to abolished or restricted fusion power of 
a previously existing latent convergence. This cause, 
though in my experience far from frequent, undoubtedly 
accounts for the sudden appearance of some concomitant 
squints. 1 have only seen this, however, in young people. 
The good fusion existing throughout, and the eventual 
loss of latent convergence, clearly pointed to some other 
cause. The character of the diplopia again showed that 
no paresis of any of the ocular muscles existed. The 
diagnosis was therefore restricted to either convergence 
spasm or divergence paresis. This was in fact an example 
of an affection which has recently received some attention 
and been generally described 2 ,?, paresis of divergence. 

In some respects it might seem immaterial whether 
such cases are regarded as spasm of convergence or as 
paresis of divergence. The effect on convergence might 
well be considered to be the same in either case. Yet it 
is not only of interest, but surely of some clinical import- 
ance, to attempt to make a distinction between a state of 
irritation leading to the stimulation of some nerve centre, 
so that its regulation is withdrawn from normal control, 
and a curtailment of power by which, notwithstanding 
the existence of a normal impulse, the effect falls short of 
what takes place under conditions of health. 

A curious feature in these cases is the diminution in 
the distance apart of the double images on lateral fixation. 
Evidently if both external recti were paretic, the images, 
instead of being nearer together on looking to either side, 
would be further apart. The fact that the reverse is the 
case has been considered as diagnostic of paresis of diver- 



6 ON SO-CALLED PARESIS OF DIVERGENCE 



gence. Certainly, on the assumption that there is any 
weakness in the innervation of the external recti, a weak- 
ness in their lateral associated contraction must from this 
symptom be excluded. This fact seems, however, to be 
the only ground for assuming that a weakness in their 
divergence innervation must therefore exist. 

Before offering an explanation for this relation of the 
double images on lateral fixation, it is necessary first to con- 
sider a point which is mainly mechanical. We must inquire 

X 



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what must be the double image relations on the assumption 
that the same degree of over-convergence is maintained as 
the eyes move from side to side. Does the same approxi- 
mation of the images on lateral fixation as characterises the 
affection with which we are now dealing, result as a conse- 
quence merely of concomitance? It is easy to show that 
this is not so. Let O (figs, i and 2 ) be an object in the 
middle line. Let us suppose that in attempting to fix O it 
is impossible to do so binocularly owing to the tendency to 



ON SO-CALLED PARESIS OF DIVERGENCE 



7 



over-convergence. One eye alone is then used for fixation, 
while the other deviates in a degree corresponding to the 
over-convergence. Suppose the left to be the fixing eye. 
The visual axis of the other then cuts the line of fixation 
at c. If the object be moved to O' both eyes must move 
laterally through the same angle <f>, on the assumption 
that the same degree of convergence is maintained 
between their axes. The left being still the fixing eye, 
their axes would now meet at c . 



X 




Fig. 2. 

In the triangles Rmc and Lmc' the["angles 0 and m are 
equal, therefore the angles c and c' are also equal. In the 
triangles LRc and LRc', the angles c and c' being equal, 
it follows that Z, R, c and c' are points on a circle — the 
circle of equal convergence. Now prolong Rc and Rc' 
till they meet the line or circle along which the fixation 
object is moved at to and to'. Then join OR and O'R. 
We have then two angles 6 and 6' which are related to 
each other in the same manner as the angular excen- 



8 ON SO-CALLED PARESIS OF DIVERGENCE 



tricities of the misdirected right eye’s retinal images, for 
fixation in the middle line and laterally, respectively. If, 
therefore, the angles Q and 6' are unequal, the images of 
O and O' will be at different distances from the fovea of 
the right eye and be projected accordingly upon the 
fixation plane or circle, the one further than the other 
from the true image of the left eye. 

The figures enable us to demonstrate geometrically the 
relation ^ in a general way. 

The angle a is less than a, because O' lies outside the 
circle of which LR is a chord and which passes through 
O. In the triangles and the external angles 

c and c' are equal to the two internal and opposite angles 
respectively, a-f^ and a We have then : 

c — a =6 
and c' — a'=6' 

but as c = c' and a is greater than a, it follows that : 

c' — a is greater than c—a 
i.e. 6' is greater than 6. 

The false image in the right eye must therefore be more 
excentric on fixation to the side than when the object 
looked at lies in the middle line in front of the eyes. The 
excentricity, too, will be greater for objects moved along 
a plane at right angles to the face than for those moved 
in a circle, as on the perimeter. Only for objects moved 
along a circle passing through O and the centres of rota- 
tion of the two eyes is the excentricity the same in both 
cases. 

A constant degree of convergence should therefore 
sometimes be associated with a greater and not a less 
degree of separation of the double images to the 
side. 



ON SO-CALLED PARESIS OF DIVERGENCE 



9 



It may easily be shown that this difference between 6' 
and 6 is greater the smaller the angle of convergence at 
c is {i.e. the greater the circle of equal convergence) and 
the nearer the plane along which the fixation object is 
moved is situated to the circle of equal convergence. 

Indeed, only under such circumstances as considerably 
increase the difference could the greater separation of the 
double images on lateral fixation be appreciable. For a 
test made at the distance of ten or twelve feet and 
more, and any marked degree of over-convergence, the 
separation would be practically the same for lateral as 
for central fixation. 

A geometrical proof of this kind, although it enables one to 
demonstrate the greater excentricity of the deviating eye’s image 
on lateral fixation, does not afford data for the calculation of the 
increase of excentricity under different conditions, and, there- 
fore, of how far the extra excentricity is likely to be appreciable. 
I therefore append a more complete analytical proof for the case 
where the object of fixation is moved along a horizontal line in 
a plane parallel to the vertical plane through the centres of 
rotation of the two eyes. With the same lettering as in the 
figures, and putting D for the perpendicular distance from the 
eyes of the plane along which the object of fixation is moved, 
d for half the intra-ocular distance, and x for the variable dis- 
tance 00' we get — 





x — d 
D 




but B—c—a. 



=r— 2 tan 1 ^ . 

D 

and d'=c—a 




A 2 



lo ON SO-CALLED PARESIS OF DIVERGENCE 

From 2.) it is evident that when x increases {i.e. when the 
fixation object is carried further and further from the middle 
line) O' also increases. For.a;=o (coincidence of (9 and O') O' =6, 

as tan'i =2tan"i ^ . 

j)2_d2 jy 

O' 

I.) and 2.) also show that the proportion ^ is greater the 

smaller c is. The less marked, therefore, the over-convergence 
for fixation in the middle line, the more appreciable should be 
the increased separation of double images on lateral fixation. 

Whilst there can be no doubt, therefore, that the main- 
tenance of a constant degree of convergence would cause 
a greater separation of the double images on lateral 
fixation, we must next determine whether the amount 
of this difference is sufficiently great to be appreciable 
under circumstances which ordinarily present themselves, 
and under conditions in which the test is usually made. 
To get at this we have to calculate the distances along 
the horizontal line cut by lines from the eye, forming 
angles 6 and 0' with RO and RO', but on the opposite 
side from those shown on the figures, as these new lines 
represent the directions of projection. 

I have already referred to the conditions which 
determine whether the difference on medial or lateral 
fixation is likely to be appreciable or not. I add here 
one example. For fixation on a plane about twenty 
inches distant and convergence towards thirteen or four- 
teen inches, the double images in the middle line would 
be rather over an inch apart, and for fixation 30° to the 
side about if inches. This difference would no doubt be 
quite appreciable. 

Under all circumstances, however, retention of a per- 
manent degree of, convergence would at least not cause 
the images on lateral fixation to appear nearer. If 



ON SO-CALLED PARESIS OF DIVERGENCE ii 

there were any appreciable difference they would, on 
the contrary, appear further apart. 

When, therefore, the images are closer on lateral 
fixation, it shows either that the right eye image is 
projected on to a plane nearer to the eyes when a 
lateral object is fixed than when fixing a central object, 
or that converge 7 ice has decreased. The former assump- 
tion is one which there does not seem to be any reason 
for entertaining. We must therefore infer that in 
spasmodic convergence or so-called paretic divergence, 
the tendency to over - convergence is not so firmly 
established, that it is incapable of being lessened under 
conditions in which equally strong convergent move- 
ments are not habitually called for. 

It is interesting to observe that although on the 
assumption of a constant degree of convergence the 
excentricity of the image in the deviating eye, of an 
object fixed by the other eye, may increase, but never 
diminishes, on lateral fixation, this is not the case if 
convergence, while always excessive so far as the require- 
ments of binocular fixation are concerned, is altered, on 
lateral fixation, in a manner which may be looked upon 
as habitual. Let us assume, e.g. that as the eyes move 
to either side, the degree of convergence diminishes to 
the extent necessary to maintain the fixation of objects 
in a plane near to and parallel with the eyes {e.g. the 
page of a book). The relations of the excentricity of the 
deviating eye’s images, when the other fixes an object 
centrally or laterally placed on a plane parallel to this 
one, but at a greater distance from the eyes, may then 
be deduced from the accompanying figures (figs. 3 and 4). 
Here, although there is some difference according to 
which of the two eyes fixes to either side, we have 



ON SO-CALLED PARESIS OF DIVERGENCE 



I 2 



0 = A—aand 6' = A' — a. For anything beyond ten feet 



distance of fixation, at any rate, a and a are so small 
that they may be neglected. Practically, therefore, & 
then = ^ and 6' = A'. And as A is always, on looking 
to the side of the fixing eye, and also, except for small 
lateral displacements on looking to the other side, greater 
than A', 6 is generally greater than 6'. With any ordinary 
degree of over-convergence the diminution of 6' for distant 



fixation (ten feet or more) would be readily appreciable. 
On fixation, 30 ° to either side, the double images would 
appear distinctly closer together than on median fixation. 

With the same notation as before, and putting D' for the 
vertical distance of the nearer plane from the line joining the 
rotation centres of the two eyes, we get as the general value of 
& for varying values of x : — 



X 




Fig. 3. 




ON SO-CALLED PARESIS OF DIVERGENCE 



On differentiating the two angles in 3.) with respect to it is 
found that the rate of change with increase of x is much greater 
in the first {A') than in the second (a). Approximately, 



dx^' _D 
d , ~n 

dx 

The maximum value for & is therefore got for the value of x 
which makes ^ (x±^/)=F^=o, i.e. x=^d (^—1^. This is 

also evident from the figures, as then ^' = tan " = 2 tan " . 

In fixing with the left eye then, for instance^ If -the fixation 




object be carried to the left, 6 ' diminishes constantly as x 
increases, while if the object of fixation be carried to the right 

6 ' first increases until x=d then diminishes, and 

vice versa for fixation with the right eye. 

An. equal change in the angle to either side, and a consequent 
equal change in the degree of separation of the resulting double 
images would only be got when one eye fixes to one side and the 



14 ON SO-CALLED PARESIS OF DIVERGENCE 



other to the other side, while the greatest and continuous 
decrease of separation would take place when the right eye fixed 
objects to the right, and the left eye objects to the left, probably 
a less frequent condition than the opposite, which is the rule 
in ordinary alternating concomitant strabismus. 

It seems not improbable, when we take into eonsideration 
the fact of the approximation of the double images on lateral fixa- 
tion in cases like the one here recorded, that such a retention of 
the habitual association which occurs between convergence and 
lateral fixation is actually, or at all events approximately, what 
takes place. 

This consideration surely too points to spasm of convergence as 
the cause. We can readily understand that the effect of an 
irritation of the converging centre might be to withdraw the 
relaxation of convergence beyond a certain point (a point which 
may, and no doubt does, vary from time to time) from the control 
of the will, and yet to leave the play of convergence, as the eyes 
move from side to side, to be effected in a habitual manner. 
This would be similar, in fact, to the natural convergent move- 
ments which would take place if, on attempting to fix a more 
distant object moved from side to side, the eyes kept converged 
on points in a plane which lay nearer to them. This, while 
consistent with the idea of spasm, appears to me a much less 
likely state of matters to co-exist with anything of the nature of 
paralysis. 

I have already stated that there was no obvious reason why 
the peculiar relations of the double images should to some 
appear in favour of the diagnosis, paresis of divergence. If they 
have any bearing at all on the diagnosis, it seems more reasonable 
to infer that they suggest spasm of convergence. 

In support of such a diagnosis, however, it is perhaps better 
to rely upon arguments afforded by the clinical facts which are 
afterwards referred to. 

The effect of habit indeed often asserts itself more or 
less even where the conditions are peculiarly unfavourable. 
Just as we often see in the case of abduceus paresis that 
the resulting double images are further apart on down- 
ward or upward fixation, because of the habitual associa- 



ON SO-CALLED PARESIS OF DIVERGENCE 15 



tion of convergence with downward rotation and the 
absence of any call for convergence when the eyes are 
directed upwards, so we find a degree of abnormal 
convergence lessen when associated with wide lateral 
movements, as there is not habitually as great a degree 
of convergence associated with marked lateral fixation 
as for central fixation. In the case here referred to, both 
these effects of habit were evidenced. 

It has sometimes been questioned whether the increase 
of convergence on looking downwards, which is common, 
more or less, to all forms of pathological convergence, 
may not be dependent solely upon anatomical conditions. 
That this is not the case I have shown by an examination 
of a number of individuals, as to the influence of downward 
and upward rotation of the eyes on the degree of what 
may be looked upon as physiological latent lateral devia- 
tions. The result of this investigation was communicated 
to this society. The cause is therefore, no doubt, as was 
first maintained by v. Graefe, the influence of habit. 

The question as to whether this curious and rare form 
of strabismus is the result of convergence spasm or of 
divergence paresis, is not, perhaps, one which the con- 
sideration of such cases alone can enable one to decide. 
As the symptoms might be supposed to be the same in 
the one case as in the other, the proper conclusion to 
draw, apart from other considerations, is, as it appears 
to me, that the diagnosis, divergence paresis, is not 
justified. Such a diagnosis involves the admission of 
a divergence innervation which for many reasons is at 
least problematical. I have seen the same condition of 
suddenly arising convergent strabismus followed, after 
a short time, by a persistent associated lateral deviation 
of the eyes of an undoubtedly spasmodic nature, which 



i6 ON SO-CALLED PARESIS OF DIVERGENCE 



has also disappeared after some time. One case of this 
kind I communicated to this society. Such an associa- 
tion is more than suggestive of spasm. In the present 
case, the very curious great excess of latent over manifest 
convergence for near fixation would also seem to point 
to spasm as the cau.se of the symptoms. On accommoda- 
tion for a near object, with one eye occluded, the tendency 
evidently existed to association with an undue degree of 
convergence. This too was presumably the result of an 
abnormally excitable state of the convergence centre. It 
was, however, counteracted by fusion the moment binocular 
fixation. becarrie possible. : i , 

This tendency to over-action is also seen sometimes 
in what is known as spasmodic myopia. In .my experi- 
ence there is no such thing as a constant spasmodic 
myopia. The nature of such cases is this : that whenever 
attempts at accommodation are made, they result in a 
degree which is in excess of the requirements. Often 
the subjects are slightly hypermetropic, and' therefore 
have to accommodate to see smaller objects at a distance. 
This tendency is probably a purely innervational one, 
and seems analagous to the excessive latent convergence 
in the case which I have just described, i 

Apart from the above considerations, which point to 
spasm of convergence instead of paresis of divergence, 
there are, as I have elsewhere pointed out,^ many reasons 
for altogether disbelieving in a real divergent innervation, 
i.e. one starting from what, from analogy, we might call 
a divergence centre. 

The common conception seems to he that if one admits 
the existence of a convergence centre, there must surely 
be a divergence centre as well. There is a centre for 
* Ophthalmic Review., October 1893. 



17 



ON SO-CALLED PARESIS OF DIVERGENCE 

associated eye movements to the right, and one for move- 
ment to the left, and these are antagonistic. And indeed 
all analogy would point to the arrangement of innerva- 
tion centres in antagonistic pairs. I long ago pointed 
out that there were physiological and clinical reasons for 
rejecting the view that the cessation of convergence was 
brought about by active divergence, and therefore for 
concludfng that no diverging centre existed. . . . , 

Divergence would thus constitute an' exception to the 
rule which obtains in the body generally, as well as an 
apparent exception to what takes place in regard to the 
lateral movements of the eyes. I say apparent, because 
the relative divergence which takes place on the cessation 
or relaxing of a converging impulse is no doubt effected 
in the same way as is the return of the eyes to the middle 
line on the cessation of an impulse which causes them to 
rotate to one side. The divergence, on the one hand, is 
due to the passive return of the external recti to the 
length which corresponds to their tonic state of inner- 
vation after the degree of greater stretching to which 
they have been subjected is removed. ’ The return to the 
middle line of eyes laterally displaced, on the other hand, 
is due to the passive return of the associated internus 
of one eye and externus of the other to the physio- 
logical states which they have in virtue of their tonic 
innervation. An active innervation is not called for'until 
rotation beyond the middle line in the opposite direction 
is begun. ' \ 

This view of the matter was also entertained by the 
late Professor Alfred Graefe. In his. admirable mono- 
graph on the anomalies of the ocular muscles in the 
second edition of the Graefe-Saemfsch handbook he 
says: ‘One can only agree with Berry when he rejects 



i8 ON SO-CALLED PARESIS OF DIVERGENCE 



as superfluous the assumption of the existence of a 
special divergence innervation, and consequently of a 
definite centre for this innervation.’ 

I shall content myself by repeating here only two 
arguments which can be adduced against the existence 
of a divergence centre. It is evident that divergence 
beyond parallelism of the axes is never a physiological 
requirement, and therefore that the only infaginable 
use for a divergence innervation could be to cause the 
return of the eyes to a position of parallelism from that 
of convergence. Like convergence, divergence must be 
primarily regulated by fusion, and as fusion is not called 
for with diverging axes, no habit of absolute divergence 
can be naturally acquired. Yet it surely ought to be 
possible to induce further divergence in the interests of 
single vision by means of abducting prisms were there an 
active centre for divergence. In the case of convergence, 
one finds that very little practice is required to overcome 
adducting prisms of a strength which cause a very much 
greater degree of convergence than is ever called for 
physiologically. No doubt abducting prisms can also 
be overcome so that it is possible to have an absolute 
divergence. But there is a limit to the degree of this 
absolute divergence even after prolonged exercise with 
prisms. This limit coincides with the degree of divergence 
which is assumed when there is a complete loss of any 
converging power. In other words, the limit of possible 
divergence is the same as the starting-point of convergence. 
This is the physiological reason for disbelieving in a 
divergence centre. 

A more important, more convincing evidence is afforded 
by certain conditions of paralysis. For instance, cases 
occur in which there is a complete loss of power of 



ON SO-CALLED PARESIS OF DIVERGENCE 19 



associated movement to one side, and even (though they 
are extremely rare) to either side, without any inter- 
ference with convergent movements, and with return to 
parallelism on convergence being relaxed. 

It might be argued, however, that just as the interni, 
though not receiving an innervation to lateral associated 
movements, are able to respond to a convergence impulse, 
so the external recti might retain the power of active con- 
traction in response to an unimpaired divergence impulse. 

This loophole of escape for those who cling to a 
divergence centre is surely closed, however, by the not 
unfrequent coexistence of complete paralysis of one ex- 
ternus with the power of bringing the affected eye back 
to the middle line on the cessation of convergence. In 
such cases the same result follows the relaxation of an 
active contraction of the internus in association with the 
externus of the other eye. In neither case would the 
mere removal of the internus innervation effect the return 
of the eye to the middle line, while the absence of any 
power in the externus makes it certain that it responds 
to no active innervation, which is antagonistic to that 
which is supplied to the internus. The return of the eye 
to the middle line must therefore have a purely physical 
cause, or must depend upon the resumption by the muscle 
of that state or that length xvhich corresponds to its tonic 
innervation when opposed by the tonically innervated 
mternus. That the latter and not the former is the 
true cause seems to me evident from the phenomenon 
of so-called secondary contracture of the antagonist in 
cases of ocular paralysis. This phenomenon may either 
slowly develop or be apparent from the outset. It is no 
doubt due to the loss, gradual or sudden, of this tonic 
innervation in the paralysed or paretic muscle. It is not 



20 ON SO-CALLED PARESIS OF DIVERGENCE 



due to, any change which takes place in the innervation 
or -in the physical state of the antagonist. With the 
more or less complete disappearance of tonic innervation 
in an external rectus, for instance, a greater or less pre- 
ponderance of action takes place in the internus'whose 
tonic innervation is unimpaired. Thus is developed the 
position of convergence which in many cases characterises 
the position of rest in paralysis or paresis of- the sixth 
nerve. The term secondary contracture Js therefore, I 
believe, and have always maintained, a mi.snom'er. -It is 
one of the many terms expressive of conceptions borrowed 
from muscular changes in other parts of the body.. It is 
very generally, I think, lost sight of-that the eye muscles 
differ in various ways, both anatomically and physiologi- 
cally from the skeletal muscles. 

In conclusion, I may say that I have brought forward 
this case, a typical example of what, in my- experience, is 
a rather rare affection, firstly to prove that the nature of 
the diplopia is an evidence of the pathological convergence 
being diminished on lateral fixation. Again 1 wished to 
offer an explanation of this symptom. As I have ex- 
plained, it can only be caused by the influence of habit. 
Finally, and more particularly, I wished to make it clear 
that the correct diagnosis is spasm of convergence, and not 
paresis of divergence, any more than a persistent associated 
lateral deviation of both eyes is to be looked upon as an 
expression of paresis of associated movement in the 
opposite direction. Both conditions, moreover, are, in 
my experience, always transitory, whereas both paresis 
of convergence and of associated lateral movement are 
often permanent. 



Printed liy T. and A. Constable, (late) Printers to Her Majesty 
at the Edinburgh University Press 




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