finite distance." This elastic power of the lens is greatest in youth, and gradually grows less with advancing age, so that the range of accommodation decreases from childhood to about seventy years of age, when it becomes nil, and the eye is incapable of adjustment for objects nearer than infinity. The following table gives the range of accommodative power which, as a rule, each age is found to possess. will be explained a few pages further on :

The term D. (Dioptries)

Thus we see that at all ages (except extreme ones to be considered later) the position of the p.r. remains the same, whatever the defect. But the near point* (þ.p.) is, with each year, being set a little further from the eye. The location of the p. p. for any age is theoretically determinable by divid. ing 100 Cm. by the range of accommodation as given in the table. Thus, 100 Cm. at 40 years of age, we should have

4.5

22 Cm. as the distance of

the Emmetrope's p.p. If Am.† preëxists, the amount of the defect must be added to or subtracted from the range, as will be further elucidated under Presbyopia.

Perfect Vision, therefore, demands that all rays proceeding from a point which pass through the pupil, shall be again united in a point in the retinal image. For instance, all the beams from A, Fig. 8, not, as Aw intercepted by the iris, must, after traversing the dioptric system of the eye, be reunited at d of the image Cgd. The same must take place for all the rays from † See page 18.

*See Far and Near Points, p. 18.

B, and so for every intermediate point. Should they not unite except at a point behind the retina, as is shown in Fig. 9, M, then the rays from a point are, in the image, spread over a larger space than a point, circles of dispersion or of diffusion-as they are called-are formed, the image is blurred and its outlines indefinite. If the focus be imagined in front of the retina, the rays will cross and produce similar diffusion circles and indistinctness of outline results as before; see Fig. 9 H.

FIG. 9.

The

Emmetropia and Ametropia. emmetropic eye Fig. 9, E, is the only one having perfect vision; it reunites at the retina, all rays passing through it which proceeded from a point of the object. The ametropic eye is one not having this power, and it may vary from the normal in three principal ways:

1. The retina may be in front of the focus, shown in Fig. 9, H, and this condition is called Hyperopia ;

2. The retina may be behind the focus,

Fig. 9, M, which constitutes Myopia;

3. The retina may be either in front or behind the focus, or both, but

by different amounts for two or more meridians of the eye. This is called Astigmatism-to be explained further on.

One of the authors has planned, and Messrs. Queen & Co. have manufactured, a model designed for class demonstration of the principles of Emmetropia and Ametropia of all kinds. It is shown in Fig. 10. Its consultation will greatly aid the student in gaining an easy comprehension of the principles involved.

Far and Near Points.-When the ciliary muscle is entirely relaxed, i. e., when the accommodative power of the eye is in complete suspension, the eye is then adapted for its far point. In this condition parallel rays of light (that is, from objects at an "infinite distance") are by an emmetropic eye brought to an accurate focus upon the retina. On the other hand, with the total accommodative power of the eye exerted, the distance of an object clearly seen constitutes its near point. This, as we shall see by and by, is, even for the emmetropic eye, dependent upon the age of the person. The distance between the far and near points (punctum remotum and punctum proximum, as they are called) is the Range or Amplitude of Accommodation. To express this we must understand the

System of Measurement.-Lenses were formerly numbered according to the radius of curvature of the surfaces in inches, a lens with a 2-inch radius being taken as the standard. Consequently, a lens of a 5 or a 10inch radius had or the refracting power of the standard. This, as will be seen, necessitated the constant use of fractions to express the power of a lens, especially disadvantageous in the weak glasses most in use. Moreover, the inch was different in every country. In thus numbering lenses it was taken for granted that the refractive index of the glass used was 1.5, but it is found that the index is always greater and were more properly estimated at 1.53. To avoid all these difficulties the Dioptric system has been adopted. A weak glass with an actual focus of one metre is taken as the standard, and called one Dioptry. Two lenses of this power, or one lens with twice the refractive power of the standard, has a focal length of half a metre. The focal length is always easily found by dividing 100 cm. (about 40 inches) by the dioptric number of the glass; thus a lens of 5 dioptrics would have a focal length of eight inches, etc. The table on opposite page, by Landolt, sets forth perspicuously the differences between the systems.

The Expression of the Degree of Ametropia may thus be given in terms of the dioptric system of measurement. We may entirely leave out of view the cause of the defect, giving only its kind in units of quantitative dioptrics. If rays of light are not accurately focalized upon the retina when coming from, the amount of that defect may be expressed in dioptries, estimated by the size of the lens required before the eye in order to bring such parallel rays to the desired focus. Thus we call an eye hyperopic to the extent of 2 D.† when a + Sph. lens of that power is required to bring the p. r. from its false position, beyond infinity, to the normal, as in E. Conversely, an eye with 2 D. of M. requires a Sph. lens to carry the p. r. from its abnormal position, twenty inches away, to 0. Refraction of the Eye.-The term, consequently, means the statement in D. of the location of its p. r. The Errors of Refraction of an eye are the amounts of its Am. deviations from the normal position of the p. r. at ∞. The refraction of an E. eye shows, therefore, no errors of refraction. The problem of refracting an eye is thus simply and solely that of locating

* Not as Morton, Hartridge and others say, according to their focal lengths; so that it becomes curious to know what meanings can be attached to the words when a distinction is made between "focal lengths" and "refracting power." Hartridge, e. g., says: "Each lens is numbered according to its refractive power, and not, as in the old system, according to its focal length."

† For the sake of brevity we shall hereafter use the contractions indicated.

METHODS OF ASCERTAINING THE ERRORS OF REFRACTION.

21

accurately its p. r., and is called Optometry. Instruments for aiding in this endeavor are called optometers.

Of the many ingenious Methods of Ascertaining the Errors of Refraction of an eye many are objectionable, either because of their complicated nature, their requirement of too high a grade of intelligence or of visual acuity in the patient, the expensiveness of the instruments, etc., or for other equally valid reasons. We shall, therefore, limit ourselves to the few methods which in practice are found most easily and reliably carried out. Specialists may have their preferences, some preferring the