ABE 



tSe atrrration is =0,00564 <//i, if the cirtU's di.lAnc: be 

 fii;)pjfeJ I ; anj if this Jillancc bo ri.'p'\-r>.Mt.»i by lO, the 

 aifrniiinn will be =o,0O35i'i4 i/m, \ip;)n wliioh f;ip:)orit;on 

 the folIowiniT table was c<ii.1ruacd. If the diliance be 

 jjreater than 10, e.g. 37, fiiid the valuj for 10, multipr'.y it 

 by 3,anJ add to the prjjiirt th.- value for 7. 



A TABLE 



To Jind the Aberration of a rianet or Co-.net, in i^aUiuJ:, 

 Longiludt, Ri^^ht Afcntjion or Declinalion. 



Suppofe the diftance of a comet to be 43, and its appa- 

 rent motion in 24 liours to be 2° 15' in longitude, and it be 

 required to find the aberrc.lion in longitude. If we enter 

 the table with the diftance 10 and daily motion 2° 15', 

 we thus get 45",68, which multiplied by 4, gives i82",7, 

 and by entering with the diftance 3, we obtain I3",7 ; 

 and therefore the aberration is I96'',4. 



Eor reducing the place of the body computed from the 

 table, to the apparent place, add the aberration, if the lati- 

 tude, longitude, right afeenfion, or declination of the body 

 decnitfe, but JubtraS, if it increafe ; and the contraiy, to 

 reduce the apparent to the true place. See Vince's Aftrono- 

 my, vol. i. p. 332 — 338. See remarks on the effects of 

 aberration on the tranfit of Venus over the fun by Dr. Price 

 in Phil. Tranf. vol. Ix. art. 47. p. 536. 



ABtRRATiON, in Medicine, figniiies a deviation from the 

 ordinary courfe of nature. 



Aberration, in Optics, is ufed to denote that error or 

 deviation of the rays of light, when inflefted by a lens or 

 fpeculum, whereby they are hindered from meeting or unit- 

 ing in the fame point, called the geometrical focus. It is 

 either lateral or longitudinal. The latei-al aberration is mea- 

 fured by a perpendicular to the a.\is of the fpeculum, pro- 



A B E 



d.ic.d from tli': focus, to meet the refleft:d or refrafled 

 ray : the longitudinil ab-rration is the diitar.ce of the focus 

 from the point in which the' fame r.iy interfect;-. the axis. If 

 the focal diftance of any lenfcs be given, their apertures be 

 fmall, and the incident rays homogeneous and parallel, the 

 longitudinal ahe>-ra.'ions will be as the fquaves, and the lateral 

 al.rrartns as the cubes of the linear apertures. 



There arc two fpec: s of aberration, diftinguifiied by their 

 different cav.fes : one anllng from the figure of the glafs or 

 fneculum ; the other from the imequal refraugibility of the 

 niys of lif'ht. The fecond fpccies of alerraiiou is fometimes 

 called the Newtonian, from its having been difcovered by Sir 

 I. Newton. With regard to the former fpecies ot aberration we 

 may obferve, that if rays proceed from a point at a given dif- 

 tance, they will be reflected into the other focus of an ellipfe 

 when the luminous point is in one focus, or directly from the 

 other focus of an hv])erbola ; and if the luminous point be in- 

 finitely dittant, fo that the rays are parallel, they will be re- 

 flefted by a parabola into its focus : but in both cafes they 

 will he difperfed by lenfes of all other figures. Specula of 

 the former kind are made with difFicidty ; and therefore 

 curved fpecula are commonly of a fpherical figure, which 

 have no accurate geometrical focus. Let BVE (Optics 

 PI. i. fig. I-) repre.ent a concave fpherical fpeculum, whofe 

 centre is C ; and let AB, EF be two incident rays parallel 

 to the axis C V. At the angle of refleftion is equal to the 

 angle of incidence, if CB and CF be drawn to the points of 

 incidence, and the lines Bl) and FG be drawn fo as to 

 make the angles CBD and CFG refpet^ively equal to 

 CBA and CFE, BD and FG will be the reflefted rays, and 

 D and G the points in which they meet the axis. Becaufe 

 the triangles CBD and CFG are ifofceles, the angles at the 

 bafe being equal, the fides CD, DB, and CG, GF, are re- 

 fpeiitively equal, and therefore the points of coincidence 

 with the axis are equally diftant from the point of incidence 

 and the centre. Hence it appears, that if B be indefinitely 

 near the vertex V, D will be in the middle of the radius 

 C V ; and the nearer the incident rays are to the axis, fo much 

 the nearer will the reflefted ra}' be to the middle of the 

 radius, and vice ver/a. So that the aberration of any inci- 

 dent ray increafes, as it in farther removed from the axis, 

 till the diftance VI become 60 degrees ; in which cnfe the 

 reflefted ray is equal to the radius, its point of interfeftion 

 coincides with the vertex, and the aberration is equal to the 

 radius. This illuftration ftiews us why fpecula are made of 

 very fmall fegments of fpheres, viz. that aU their reflefted 

 rays may interfeft the axis near the middle point of the 

 radius, and thus fuffer the leall aberration, and render the 

 image more diftinit. The cafe is the fame with regard to 

 rays refratted through lenfes. 



In different fpherical lenfes M. Huygens has demonftrated 

 that the aberration from the figure is as follows: i. In all 

 plano-convex lenfes, having their plane furface expofed to 

 parallel rays, the longitudinal aberration of the extreme ray, 

 or that remoteft from the axis, is equal to | of the thicknefs 

 of the lens. 



2. In all plano-convex lenfes, having their convex fur- 

 face expofed to parallel rays, the longitudinal aberration 

 of the extreme ray is equal to i of the thicknefs of the 

 lens : the aberration in this cafe being about ^th of that in 

 the former, or in proportion to it, as 7 to 27. 



3. In all double convex lenfes of equal fpheres, the 

 aberration of the extreme rays is equal to i of the thicknefs of 

 the lens. 



4. In a double convex lens, the radii of whofe fpheres 

 are as i to 6, if the more convex furface be expofed to 

 parallel rays, the aberration from the figure is lefs than in any- 

 other fpherical lens, being no more than ^1 of its thicknefs. 



M. 



