VOL. XXX.] PHILOSOPHICAL TRANSACTIONS, 425 



This lemma is also demonstrated by dioptrical writers. 



Lemma 3. — If two pencils of rays, all parallel to the axis, as a, fig. 6, fall 

 on different parts of the cornea, at the greatest distance from each other that 

 can be allowed for those rays to enter the pupil pp ; after entering the aqueous 

 humour, their axes will converge, and meet either in the vitreous or crystalline 

 humour, according to the convexity of the cornea through which they passed, 

 and diverge again before they come to the retina; the rays of each pencil con- 

 verging on their respective axes, to the place where the said axes cross one 

 another. 



Demonstration. — ^The axes aca, aca, falling obliquely on the cornea at c, c, 

 and entering from air into the aqueous humour, will be refracted towards the 

 perpendicular to k; where striking more directly on the crystalline, they will 

 go on to a, a, on the retina rrrr, decassating at v within the vitreous humour. 

 The other rays r, r, ^, ^, after their refraction in the aqueous humour, fall 

 more obliquely on the crystalline, and therefore are refracted again so as to 

 meet at v, where the axes also meet, and thence go on to the retina rrrr. 



Lemma 4. — But if the axes of the above-mentioned pencils are parallel, the 

 rays that accompany them diverging from a point so near the eye, that the 

 divergence maybe proportionable to the too great convexity of the eye; then 

 only the axes will meet in the eye before they come to the retina, by lemma 3; 

 but the other rays will not unite on their respective axes, till they come to the 

 retina, by lemma 1. 



Proposition. — I suppose the eye of the myopes so convex that he can see no 

 farther than a common eye, with the eye-glass of a telescope before it: then 

 the eye of the myopes, being in the place of the eye-glass, will receive the 

 rays diverging from the several points of the image, projected by the object- 

 glass in its focus, iri such a manner, that after their several refractions they will 

 meet in respective points on the retina; and the axes of the pencils which come 

 from the extremities of the object, will, in the eye, make the angle bv^a = to 

 bca, fig. 7, under which the image ab is seen, by lemma 4. The cornea and 

 aqueous humour here supply the place of the eye-glass, and the crystalline and 

 vitreous humours that of a common eye; wherein r is the retina, v the vitreous 

 humour, and kk the crystalline humour; and the image ba is supposed to be 

 brought down from fig. 2, which represents the astronomic telescope; the too 

 great convexity of the eye here being in the place of an eye-glass. 



I have also found out a way for the presbytae to make use of an object-glass, 

 by placing their eye nearer the lens than its focus, by so much as their eye is 

 flatter than a common eye, so as to make, as it were, the telescope of Galilaeo; 



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