On the Mechanifm tf the Eye. 257 



Corollary 7. For a double convex lens, neglefting the thicknefs, call the firft radius ^, 



^ r , t J " ^ g ^ Tt d e s + h 



the fecond h, and e = -; —-7 j. Hence « — -7- — . - . ; and, for parallel 



fl g h i '^ ^ re r ' tl a d 



rays, e = ■ ■ - ■, and « _ f. ^. Ug = h = aye = ■ — ; and for parallel rays 



*= — : calling this principal focallength b, e =z -, as in Cor. 4; whence we hare 



2 • d-^ b 



d e 

 the joint focus of two lenfes *, alfo, b — 



Corollary 8. 



and b = — . 



d + e 



, d -\- n rt 



In a fphere, s = m a. —r — -, for the diftance from the centre, 



2 a — ^w — " 2) a - ' 



Scholium 2. In all thefe cafes, if the rays converge, d mud be negative. For inftance, 

 to find the joint focus of two convex, or concave lenfes, the expreflioa becomes, 

 bd 



'-TTd' 



Corollary 9. In Cor. 3, the dlvifor becomes ultimately conftant ; and, when the in- 

 clination is fmall, the focus varies as « «. 



Corollary lO. For parallel rays falling obliquely on a double convex, or double conCavc 



lens, of inconfiderable thicknefs, the radius being i,e = — ; which varies ul- 



2 [m u—n t) 



timately as the produd of the cofines, or as t + t^. 



Scholium 3. In the double convex lens, the thicknefs diminifhes the effed of the obliquity 

 near the axis ; in the double concave, it increafes it. 



Scholium 4. No fpherical furface, excepting one particular cafe, (Wood, 155,) can col- 

 left an oblique pencil of rays, even to a phyfical point. The oblique rays which we have 

 hitherto confidered, are only fuch as lie in that fe£tion of the pencil which is made by a 

 plane pafling through the centre and the ladlanc point. They continue in this plane, not- 

 wjthftanding the refra£tion, and therefore will not meet the rays of the collateral feftions, 

 till they arrive at the axis. The remark was made by Sir Ifaac Newton, and extended by 

 Dr. Smith, (Smith r. 493, 494 ;) it appears, however, to have been too little noticed. 

 (Wood, 362.) The geometrical focus thus becomes a line, a circle, an oval, or other, 

 figure, according to the form of the pencil, the nature of the furface, and the place of the 

 plane receiving the image. Some of the varieties of the focal image' of a cylindrical 

 pencil obliquely refradled are fliown in Fig. 28. 



Corollary 11. Hence the line joining the remoter conjugate foci, will always pafs 

 through the centre. The diftance of the remoter focus of parallel rays will be exprefled by 



VoL.V. — October 1801. LI /— 



