RANGE OF ACCOMMODATION. 25
plete an apparatus adjusted for the nearest point upon which the eye could have been adjusted by its own physiological power.
The near point p corresponds always to the optical adjustment of the eye when to its anatomical condition of refraction (deter- mined by the position of the far point r) the result of accommo- dation is added. Expressed in an optical formula we have tH" i = j;, — that is, refraction plus accommodation gives the near point. An immediate deduction from this is the expression ^=j — t, — that is, when we know the positions of the far and near points we can calculate the range of accommodation. The value which we obtain assumes the form of a fraction wdiose numerator is 1 and whose denominator expresses in inches the principal focal length of that convex lens which placed in front of the relaxed eye would have accomplished the same as the accommodation.
The same method of mathematical expression is employed for the relative range of accommodation, which is generally denoted by A'.
We found, for example (page 18), with a convergence upon a point 12 inches distant, that the relative far point lay at 48 inches, and the relative near point at 6 inches ; from this we can calculate the value of the relative range of accommodation, x' = 1 — -lg=-^. The negative part of the relative range of accom- modation is in this case -^q, the positive yj-
PRESBYOPIA.
Having thus obtained a common measure for the range of accommodation in different individuals, Donders further showed that the extent of the range of accommodation depends upon the age of the individual. With the increase of years the near point moves gradually from the eye, and the range of accommodation is thereby reduced. Two possibilities suggested themselves by which to explain this phenomenon: either the power of the muscle of accommodation must weaken, or there must be changes in the elasticity of the lens. The circumstance that the range of accommodation is already noticeably diminished at a time when the strength of all other parts of the muscular system is unimpaired must banish the idea of a premature loss of power in the muscle of accommodation; on the other hand, however, there are all-sufficient proofs of changes in the lens dependent upon age.
