of the Eye-pieces of Telescopes. 17 



that is, if the first lens be a meniscuSj its convexity toward the object- 

 glass, and the radius of its concavity about double that of its con- 

 vexity, or if the first lens be double-convex, the convexity being 

 somewhat greatest on the side next the second lens. 



6th. A single lens to produce the same effect must have a focal 



length , and, therefore, its smallest value of Q would be 



108 'M*' 



Ex. 5. The eye-piece is the old erecting eye-piece, consisting 

 of three lenses of equal focal length M, placed at intervals of 2M. 



It will easily be seen that B' = F', and, therefore, we must recur to 

 the investigation for that particular case. Now, as F= F' = M, and /= 2 M, 

 I—F—F' will = 0. To calculate b-B\s, therefore, unnecessary : we have 

 merely to add the expressions for Q and Qi : and a = a'=a". Selecting at 

 once the parts belonging to each lens, 



2 In \ 2/ n n "^ 4n •' 4{«-l)) 



2ln\ 2/ •'V2 «•' 



3n + 2 re „„j\) 



Making the substitutions. 



« = «-(5"-n»M"''). 



To/. III. Parti. 



