of the Eye-pieces of Telescopes. 39. 



Again, suppose 



f u « + 1 ^• 



v= f^ ; . Here e = — — / : 



2(n-l) 2(n-l)'^ 



n- 1 



whence B= F, ?■ = to , s = n- l . F, 



n 



or the lens is plano-convex. This construction is represented in Fig. 9: 

 and for this case an easy geometrical demonstration may be given. If 



f 

 K be < -^ -, there are two positions of the diaphragm equally 



goodj both above the lens. 



These constructions, it will be observed^ are found by making V=0. 

 Now, we have remarked that when V=0, the rays of the pencil converge 

 to a point nearer to the lens than the plane at the distance Z, by the space 



— . — . If, then, the bottom of the camera obscura, instead of being a 

 plane, were a concave spherical surface, whose radius =nF (which would 



make the elevation of every point above the plane nearly = — . — ) , the 



image would be accurately formed upon it. It is remarkable that in all tjje 

 varieties of form of the lens, and position of the diaphragm, which make 

 the above equations possible, the radius of the spherical surface proper to 

 receive the image, continues the same. 



This is the theory of Dr. Wollaston's periscopic camera obscura ; 

 and, supposing the direction of the rays reversed, it applies also to his 

 periscopic spectacles. 



Prop. V. To find the effect of the aberration of the Jenses 

 of an eye-piece on the distinctness of an object seen through a 

 telescope. 



