THE FLATNESS OF THE FIELD OF VIEW. 73 



free from aberration in the aplanatic eye-lens. If the eye is 

 adjusted for infinite distance, the two pencils must therefore 

 proceed parallel after their emergence from the eye-piece, which 

 assumes that parallelism is produced by the refraction at the 

 lower lens-surface. We will extend our remarks on this simple 

 case. 



Let us suppose the eye-lens adjusted so that its centre of curva- 

 ture lies centrally between the points p and q ; then both pencils 

 will be refracted towards each other almost without aberration, and 

 with equal deviation, since they are incident at equal and very small 

 angles (about 1 1'5). For parallelism, obviously, the point b, 

 from which the rays proceed, should lie in the focal point of the 

 refracting surface. Since the corresponding point of the field-lens 

 image must be in exactly the same position to be seen in the virtual 

 image at infinite distance, it follows that aplanatism can only be 

 secured on the hypothesis that the eye-lens is at the distance of its 

 focus from the field-lens, and when, accordingly, the real image ap- 

 pears in the plane of the latter. An increase in this distance must, 

 with similar positions of the centre of curvature (that is, with a 

 shallower field-lens or a deeper eye-lens), necessarily involve con- 

 vergence, while a decrease will necessitate divergence of the 

 emergent pencils. In the first case the aberrant pencil would 

 be refracted towards one assumed to be free from aberration, 

 and its prolongation backwards would correspond to a point lying 

 too near the axis, the virtual image would appear to be less 

 magnified towards the margin. In the second case, the contrary 

 effect is produced ; the pencil, produced backwards, meets a point 

 too far distant from the centre, and the image shows an opposite 

 distortion. 



It is otherwise, if the centre of curvature of the eye-lens lies 

 nearer to it than the points p and q. The angle of incidence of 

 the aberrant pencil is, in this case, noticeably greater than in the 

 preceding, consequently, aberration is also traceable in the eye-lens ; 

 and the pencil is refracted more strongly towards the axis than 

 the one assumed to be free from aberration. If the point of 

 emergence I of the two pencils were at the distance of the focus 

 from the spherical surface, they would diverge after their passage 

 through the eye-piece, whilst in the previous case they were 

 parallel. In order to produce parallelism, therefore, the distance 

 must be chosen somewhat greater than the focus, in proportion to 



