258 0» tht Meckm^/n-y" I'hi Eye. 



y= ^ 5 aad the leaft circle of aberration will be aMbe diftancc 



*ffu — «?; ' - .It . ,('.;!" ■ - {i+uii).[)iiu—-!it) 



dividing the length ol ^berratioVi in the ratio bf'the dlttahce of itis limits from the furface. 



'■■ '> 1.'. 



Iti' the fcafe ofCoi. rb>T=- T"i' '^ T> - 



■ i -.■.Corollary 12.^ This' propofitlon «5fte»d8 a!fo to' tdfle£led rays; and, in that ?alk, the 

 line from the centre palTes through the point of incidence. 



Propo/itiou V. Problem. 



• , \- 



■ To find the place and magnitude of thq image ©f a fmall objeft, after refra^ion at any 

 number of fpherical furfaces. 



ConJlruBion. (Plate XIII. Fig. 3.) From any point (B) in the objefl: (AB),;drawlin«Sto 

 (C)j the centre pfthe ^^rft furface, and to v(.D), the focus of parallel rays coaning in 

 a contrary direction : from the interfedion of the fecond line (BD) with the tangent (EF) 

 at the vertex, draw a line (EH) parallel to the axis, and it will cut the firfl ftne (BC) in 

 (H), the firft image of the point (B). Proceed with this image as a new objcdt, and 

 orgpeat the operltion for ?Bch fuTfacCjiittpd the laft point vvill be in the image required. 

 For calculation, find the place of the image by Cor. 5. Prop. IV, and its magnitude will 

 be to that of the obje£l:, as their refpeilive dtflances from the centre. 



Corollary. If a confufed image be received on any given plane, its magnitude*wiU"be 

 deteirmiried by the liae drawn from the preceding image through the centre of the laft 

 furface. 



Propofitmyi. Problem. 



To determine the law by which the refra^ion at a fpherical furface mull vary, fo as to 

 tolleft parallel rays to a perfeft focus. ,), ., ,/ 



Solution. Let v be the verfed fine to the radius i ; then, at each point without the axis, 



» remaining the fame, m muft become ^ mm ^ t n -u; and all the rays will be collected 

 in the principal focus. 



Corollary. The fame law will ferve for a double convex lens, in the cafe of equidiftant 

 conjugate foci, fubftituting n for fn. 



Prapo/ition VII. Problem, 



To find the principal focus of a fphere, or lens, of which the internal parts arc mo*e 

 denfe than the external. 



Solution. In order that the focal diftance may be finite, the deflCty of a finite portion 

 about the centre muft be equable: call the radius of this portion |, that of the fphere being 



uouj t let the whole refradion out of the furrounding medium into this central part, be ii 

 4, - . . "mto 



