76 THEORY OF THE MICROSCOPE. 







refracting surface A B (Fig. 36), which brings to a focus in F aL 

 rays between p q and r s which are parallel to the axis a c, the rays 

 of the peripheral pencil p q m n will also, of course, be refracted 

 towards this point. This applies equally for every other cone 

 of rays and the pencil parallel to it. Moreover, the distance of 

 the different focal points of the refracting surface, measured upon 

 the axis of the cone passing through the centre of curvature, and 

 consequently also the distance of the centre of curvature itself, 

 is a variable quantity. The focal points, therefore, lie in a 

 spherical surface whose centre coincides with that of the refract- 

 ing surface. 



If we now suppose the cylindrical pencils converted into 

 slightly converging ones, so that the points of convergence of 

 the differently-inclined pencils are equidistant from the centre 

 of curvature of the refracting surface, their real image-points 

 are brought somewhat nearer to the refracting surface ; they 

 form, however, afterwards as before, a curved surface with 

 the same centre of curvature. Applied to the field-lens, this 

 means that if the objective-image, forming the virtual object, 

 has a curvature which is convex above, its centre coinciding 

 with that of the field-lens, then the image produced by the 

 refraction at the spherical surface has a curvature parallel 

 with it. 



It can be further shown that a curvature is produced in the 

 same sense, even if the objective-image is in a plane. Let us 

 assume, for the sake of simplicity, that it lies in the tangential 

 plane M N (Fig. 36) of the focal surface, and let us denote the 

 distance from the refracting surface of the object-point P by p, 

 that of the corresponding image-point by p*, the distance of the 

 object-point by P l and its image-point by p l and pf t the focal 

 length by /, and the radius of the field-lens by r. 



Then -- = --- + , and therefore in the given case 



2 

 and if the refractive index is taken as 1'5, p* = -. The quantity 



p l is determined by the proportion (p l r): (p r) = l: cos </>, 



