VOL. LXXIII.] PHILOSOPHICAL TRANSACTIONS. 351 



Sir Isaac Newton has shown, in his Lectiones Opticas, in that section De 

 Phaenomenis Lucis per Prisma in Oculum transmissae, that the appearance of 

 olours on the edges of objects, when viewed through a prism, depends on the 

 proportion of the distance between the prism and the object, compared with that 

 between the prism and the eye, that is to say, the nearer the object is brought 

 to the prism, the less will be the bordre of colours on the contours of 

 the object. To apply this to practice, says Mr. R., I placed a piano convex lens 

 a (fig. 1, pi. 6,) with its plane side near an object, or an image in formed by 

 the object-glass of a telescope, and thus magnified the image which, from the 

 position of the lens, was sensibly free from colour; but the respective foci of a 

 lens so placed being very near each other, and on the same side, the emergent 

 pencils diverge on the eye, and give indistinct vision : this was remedied by 

 placing a second lens k a little within the focus of the former, the combined 

 foci of the two lenses being in the place of the image, the rays were thus made 

 to fall parallel on the eye, and to show the object in distinctly. If, by putting 

 the lens a very near the image, any imperfection in it become too visible, that 

 distance may be considerably increased, without producing any bad effect ; for 

 theory, as well as experiment, shows, that a small aberration from the different 

 refrangibility of light is of little consequence, compared with the same quantity 

 of aberration caused by the spherical figure of the lenses ; but even that colour- 

 ing may be corrected in the nearer eye-glass : for let a ray (fig. 2) from an object 

 o, by passing through a lens b, be separated into colours, ac being the direction 

 of the violet rays, and a t that of the red ; if another lens be put at c, the violet 

 rays passing through its centre will suffer no refraction, while those of the red, 

 passing at some distance from thence, are refracted, and the emergent red and 

 violet will be parallel, when the mean refracting angle of the lenses, at the in- 

 cidence of each pencil, are to each other inversely as the diameters of those 

 pencils. If we attend to this position of the eye-glasses, it will be found equally 

 advantageous for obviating the spherical aberration of an oblique pencil as that 

 from colour. In both, where there is a necessity for having a large portion of 

 a sphere, we have only to make the pencil on such lens as small as possible, and 

 we may regulate the direction of the rays in each pencil at pleasure when they 

 approach the axis of the telescope. 



To illustrate this, let us compare the effect of the spherical aberration of a 

 lens on an oblique pencil in this position, with that produced by the same lens, 

 placed as usual at its focal distance from the image. Let ac, fig. 3, represent 

 the semi-object-glass of a telescope, ct its axis, e an eye-glass, and f the 

 common focus of both the object-glass and eye-glass. Let afh be an oblique 

 pencil of homogeneous rays, g and h the points where the axis and the extreme 

 rays pass through the eye-glass : the aberration of this pencil from the spherical 



