SPECTACLES. 839 



to the dioptric value of a lens of 4 inches focus. Conversely, two eyes may have 

 the same range of accommodation, and yet have unequal power of accommoda- 

 tion. Example: One eye may have p = 3, r = 6, the other p = 6, r =9 (both 

 have a range of accommodation of 3 in.). The power of accommodation for the 



first is ] - = \\ orx =6; for the second = ; or x = 18. The general 



x x 



law for these relations is as follows: If the ranges of accommodation of two eyes 

 are equal, their powers of accommodation are equal, provided their near points 

 are the same. If, however, the range of accommodation is the same for each 

 eye, but the near points are unequal, then the powers of accommodation are 

 unequal; and that eye has the greatest power of accommodation that has the 

 shortest near point. The reason for this is "that every difference in distance near a 

 lens has a much greater influence on the image than the same difference in distance 

 far from the lens. The normal eye can, in fact, see distinctly all objects at a 

 distance between 60 or 70 meters and infinity without any accommodation. 



While p and r can be directly determined for the emmetropic and the myopic 

 eye, this is not possible for the far-sighted eye. The resting point (far point) 

 in the latter is negative; in fact in cases of hyperopia of high grade even the 

 near point may be negative. The far point, however, may be determined by 

 means of the convex lens that renders the far-sighted eye emmetropic. The 

 relative near point is then determined by means of the lens. 



From the fifteenth year on the power of accommodation for near vision com- 

 mences to diminish, perhaps because the lens gradually loses its elasticity. 



SPECTACLES. 



Older Measurement in Inches (i Inch = 27 Mm.). The focal length of both 

 concave (diverging) and convex (converging) glasses depends, of course, upon 

 the refractive index of the glass (usually 3:2), and upon the length of the radius 

 of curvature. If the curvature of both sides of the lens is the same (biconcave 

 or biconvex) , then with the ordinary refractive index of glass the focal length is 

 equal to the radius of curvature. If one side of the lens is plane, the focal length 

 is twice the radius of curvature of the spherical surface. The glasses may be 

 designated either in accordance with their focal lengths in inches, none shorter 

 than i inch being usually taken; or in accordance with their refractive power. 

 By this method the unit chosen is the refractive power of a lens with a focal dis- 

 tance of i inch. A lens with a focal distance of 2 inches, refracts the light only 

 one-half as much as a lens with a focal distance of i inch ; a lens of 3 inches focus has 

 a refractive power only one-third as great, etc. This is true for both convex and 

 concave lenses, the latter of course having negative focal distances. For example, 

 the designation "convex " would indicate a convex lens with a refractive power 

 only one-fifth as great as a lens with a focal distance of i inch; or "concave " 

 would indicate a concave lens that caused the rays of light to diverge only one- 

 eighth as much as the concave lens (negative) with a focal distance of i inch. 



If the far point (always too close) of a myopic eye is determined, a concave 

 lens of the same focal distance as the far point will be required in order to make 

 the divergent rays coming from the far point parallel. The emmetropic eye 

 has a far point of infinity. If, for example, a myopic eye has a far point of 6 

 inches, it needs a concave lens with a focus of 6 inches in order to see distinctly 

 at an infinite distance. Therefore in a myopic eye, the readily determined dis- 

 tance of the far point from the eye is directly equal to the focus of the (weakest) 

 concave lens that enables the eye to see distant objects distinctly; this lens 

 is usually the number of the glass to be chosen. Example: A myopic eye with 

 a far point of 8 inches needs, therefore, a concave lens with a focus of 8 inches, 

 that is the concave glass No. 8. For the hyperopic eye the focal distance of the 

 strongest convex lens that still allows the eye to see distant objects clearly is 

 at the same time the distance of the far point from the eye. Example: A hyper- 

 opic eye that sees objects at a distance clearly through a convex lens with a focus 

 of 12 inches has a far point of 12; the proper glass is likewise No. 12. 



Newer Measurement in Diopters. Instead of the older designation of the 

 strength of lenses in inches, the meter has been adopted as a unit, following the 

 suggestion of Bonders, Nagel, Zehender, and others. By this system the lenses 

 are designated according to their refractive power. The unit is a lens of small 

 refractive power (large focus), that is one with a focus of i meter 40 inches. 

 This unit is called a diopter (abbreviated, D). The refractive power of D is 



