eyes can converge toward, the punctum proximum of relative con

vergence.

7'

The latter, on the other hand, can be reduced to 0.5 m a, which is equivalent to saying that, notwithstanding the effort of accommodation, amounting to four dioptries, the lines of fixation can cross each other This is the punctum remotum of rela

1m. 0.5

at a point situated =2 ma.

tive convergence.

Hence the relative amplitude of convergence, in our example, is

ao1 = 7 −0·5 = 6·5 m a.

The positive portion of the relative range of convergence amounts to 3 ma (to the right of the diagonal), the negative portion to 35 ma (to the left of the diagonal). That is to say that the eyes, while maintaining the same accommodation, can overcome the effect of adducting prisms producing a deviation of 3 m a, and that of abducting prisms requiring a diminution of convergence equal to 3.5 m a.

In Fig. 83 is given a diagram of the relative ranges of accommodation and convergence of another emmetrope. The subject of this examination was Dr. Eperon, who, at the time when it was made,

was my clinical assistant, and twenty-six years of age. The dotted curves mark the results of the first examination; the plain line curves were obtained from an examination made after his eyes had been

trained for some time. The signs used have the same meaning as heretofore: p, is the binocular, and p the absolute punctum proximum. This diagram corresponds very nearly, as will be seen, to that of Donders. But it also shows one very important thing, viz., that the mutual relations of the two functions are easily susceptible of modification.

The relative Amplitudes of Accommodation and Convergence

in Ametropia.

We have already remarked above that the relation between accommodation and convergence must necessarily be different in the ametrope, in case he is to see binocularly and distinctly without the aid of auxiliary glasses. Indeed, myopia represents, even in a state of repose, a certain degree of positive refraction, while convergence under such circumstances, is nil, and any degree of positive convergence requires a convergence effort. Let us take, for instance, the case of a myope of eight dioptries: when the accommodation is totally relaxed, he sees distinctly at a distance of of a metre. Binocular vision at this distance, however, requires convergence amounting to 8 m a. The zero-point of accommodation, therefore, is at i.e., at a distance for which the convergence is not zero, but 8 metre-angles.

1m.

8'

If the object be brought nearer, the accommodation and convergence will increase; but the accommodation will always be eight units below the convergence. Thus, the object being of a metre distant, 10 metre-angles of convergence and 10 dioptries of accommodation will be required. But eight of these ten dioptries are furnished by the static refraction of the eye, leaving only two to be furnished by the dynamic refraction (accommodation).

For 12 metre-angles of convergence, 12-8=4 dioptries of accommodation are necessary.

Let us now carry the object beyond the zero-point of accommodation, the punctum remotum of the eye, to infinity, for instance. It will then be at the zero of convergence. Hence, in order that vision be clear, the accommodation would have to be eight dioptries below zero. But accommodation cannot become negative. The eye can only nullify it. In this case the eye is adapted to its punctum remotum-its zero of accommodation-below which it cannot descend. Our myope will be able to see, binocularly, objects situated between infinity and of a metre from the eyes, if he have a normal range of convergence; but along this whole range he will see indistinctly, because his refraction will always be too strong. For infinity it will

be excessive by eight dioptries; for an object 2 metres distant, by 8-75 D; for an object 1 metre away, by 8-1-7 D; for one at metre, by 8-2-6 D. Hence the myope must abstain from all effort of accommodation while the convergence increases from zero up to the figure which represents the degree of his myopia. From this moment on, the amount of accommodation brought into play will always be below the value of the convergence, by a number of dioptries equal to that of the myopia.

In hyperopia we find a different condition of affairs.

Here the zero of accommodation is below the zero of convergence. When the latter is nil, the lines of fixation being parallel, the eyes must have already made an effort of accommodation in order to correct their defect of refraction, i.e., to adapt themselves to infinity. Let us suppose the hyperopia of each eye to amount to two dioptries; the punctum remotum, the zero of accommodation, is metre to the rear of the eye, in the negative portion of the diagram, 2 D below zero. In order to see at infinity, the accommodation must make good this refractive defect, while the convergence is still at rest.

If the object be brought nearer, so that the convergence is increased, the accommodation will always be stronger than the convergence, by a number of dioptries equal to the deficit in static refraction, i.e., to the degree of the hyperopia. Thus, the object at a distance of of a metre requires 8 ma of convergence and 8 D of positive refractive power. But, in order to furnish these, the eye must first make good the deficiency in its static refraction, which, in our example, equals 2 D. This the eye does by means of its accommodation. After this, only, is it able to give itself the required 8 D of positive refractive power. It borrows these, also, from its dynamic refraction. The latter, therefore, amounts to 2+8=10 D, while the convergence is one of only 8 ma.

It is apparent, from this, that the relation between accommodation and convergence must be quite different in ametropia from what it is in emmetropia.

In myopia the amount of the accommodation remains lower than that of the convergence, while hyperopia calls for more accommodation than convergence.

Hence distinct and binocular vision requires that the relation between the accommodation and convergence be different in ametropia and emmetropia. Is this actually the case? This question is one of primary importance.

We have seen (Fig. 82) that our emmetrope can still relax his accommodation by two dioptries, although maintaining his convergence at of a metre.

This shows that, if he should become myopic by one, two, or even three dioptries, he would, notwithstanding this, be able to converge for an object of a metre distant, and see distinctly. He would make an effort of accommodation one, two, or three dioptries less than that of the emmetrope under like circumstances. On the other hand, he still has at his disposal, for the same degree of convergence, three dioptries of positive, relative accommodation. Hence he could maintain his convergence and, at the same time, correct a hyperopia amounting to three dioptries.

If, in emmetropia, there exist such a latitude in the relations between the two functions, it is to be hoped that the accommodation regulates itself, more or less, according to the convergence, in cases where an ametropia has existed for centuries, or where it has been. developed or gradually modified, from generation to generation. We see families, and even peoples that must have been hyperopes from time immemorial. We see others in whose cases hyperopia slowly but regularly changes to emmetropia, and emmetropia to myopia. Why should not the relations of the accommodation and convergencewhich depend, it is true, upon the same nerve, though not upon the same muscles-be modified conformably to the exigencies of the case?

According to Iwanoff's investigations, the development of the ciliary muscle appears to be modified in accordance with the refractive condition of the eye. But, even without pronounced anatomical differences, the necessary correspondence between the functions of accommodation and of the motor muscles of the eye might very well exist, provided the innervation were in keeping with the static refraction.

In myopia, for instance, it would be necessary that the innervation of the muscles controlling convergence should not be accompanied, from the first, by an innervation of the muscle of accommodation, and that the former should always be more energetic than the latter.

In hyperopia the nervous impulsion of the ciliary muscle must prevail. Hence the possibility, of an adaptation of the relation between the accommodation and the convergence to the ametropia, must be admitted, especially if the latter be developed slowly enough in the individual, or rather in the race, to give the normal relation of the two functions time to become modified.

However, we shall not be surprised if we occasionally meet with a lack of harmony between the convergence and the accommodation. We shall see, indeed, in the chapter on the causes of ametropia, that an anomaly of refraction may be developed so rapidly that neither the anatomical disposition of the ciliary muscle, nor the innervation of the intrinsic and extrinsic muscles of the eye could be modified in so short a time.

Moreover, ametropia may reach such degrees that convergence becomes insufficient in myopia, and accommodation in hyperopia. But let us return from these speculative considerations to the positive domain of experimental research.

Donders and Nagel have carefully examined the relation between the accommodation and the convergence in the case with which we are concerned. Figure 84, for instance, gives us the diagram for a myope of four dioptries.1

The subject of the examination was a young man twenty-three years of age, a medical student. The figures in this diagram have the same signification as in that for emmetropia. The zero-point of accommodation, which corresponds to the punctum remotum (r), is at the point 4 of the horizontal, because the eye already has 4 D of positive refraction when at rest. The diagonal, which contains the points for which the effort of convergence and that of accommodation are equal, takes its origin at this point 4. It ascends toward the right, at

an angle of 45 degrees, parallelly with that for emmetropia, but displaced four divisions to the right, which corresponds to four dioptries of myopia.

Above the diagonal we find, as before, the values of the positive relative accommodation; below, those of negative relative accommodation; to the left, negative relative convergence; and to the right, positive rela

1 Nagel, loc. cit., p. 497, Fig. 47.