of the Eye-pieces of Telescopes. 43 



2(1. Since, in the common eye-pieces, f,f', &c. are all positive, 

 it is impossible to make k and k vanish at the same time. This 

 appears to be an insuperable obstacle to the improvement of eye- 

 pieces. 



3d. By assuming tor 2(F) different values, we may form 

 a series of ellipses representing the different appearances of a point 

 in a given part of the field of view, and may select that whicli 

 appears least offensive. In this manner. Fig. 10 was constructed*; 

 the values of 2 (F) are placed below. It will be observed that this 

 series of figures is essentially different from that in Figs. 6 and 7 : 

 the latter are sections of the same pencil at different distances from 

 the lens, while those under consideration are sections of different 

 pencils (produced by altering the curvatures of the lenses without 

 altering their focal lengths) at the same distance from the lens which 

 we take as representing the eye. Thus, in Fig. 6, the two straight 

 lines are equal in length; in Fig. 10, the line corresponding to 



2(F) = -2(/), 



is three times as long as that corresponding to 



4th. It appears to me that the confusion least disagreeable is 

 that corresponding to 



2(n = -42({); 

 or, if another is to be preferred, the negative multiple of 2 (~ ) is 



• It must be observed that Fig. 10 represents the appearances of a point seen at the 

 top or bottom of the field of view. If each of the ellipses be turned through an angle of 90", 

 it will represent the appearance of a point seen at the right or left side of the field. 



F 2 



