1 66 Mr. Lubbock on the Double Achromatic Object Glass. 



r± _ ±y, j" j kMi - L + _LV 



\A 4 A,j" T \A 2 toAJXAj A, ij 



= x {a;- a;} + {a;-^a;}{a;-a3 + ^}' 



in order that the telescope may be adapted for seeing nearer 

 as well as more remote objects. This condition gives 



The last equation coincides with the equation (A) of Sir 

 John Herschel, p. 258. This equation is to be combined 

 with the equation, p. 165, line 8, which may be put into the 

 form 



/ 2m + l \ f m 



Having foundy^y^/g,^, the radii of curvature may be ob- 

 tained by means of the equations 



- m — 1 - t»— 1 , - 



^fi^t^ ^ 4 " " "I" + Jv 



If ra= 1-524, w' = 1-585, m = '60, (which are the 

 average values,) Sir John Herschel finds, assuming^ = — *1, 

 and with the conditions which he recommends, 



