OP ARTS AND SCIENCES. 



189 



ne = thickness of crown-glass lens. 



n'e' = thickness of Hint-jilass lens. 



s = space between the interior surfaces of the crown 



and flint lenses, measured along the optical axis. 

 ()i — 1)/' = radius of first surface of crown lens. N. B. — This 



is the surface nearest the heliostat. 

 ()i — 1)/" = radius of second surface of crown lens. 

 (»i' — l)y" = radius of first surface of flint lens. 

 (n' — l)y^ = raiiius of second surface of flint lens. 





= focal distance of crown-gla>s lens. 

 = focal distance of flint-glass lens. 



Then, from the "Dioptrische Untersuchungen " given ia "Gauss* 

 "Werke," Vol. 5, pp. 262-2G5, we derive the formulce 



^' 



/'/" 



qp' = 



yw fi 



(3) 



And if the objective is an ordinary double achromatic, corrected either 

 for the visual or chemical rays, 



t' = s + '^ + 





(4) 



But if it is a single lens, then 



f 



(5) 



a 



A'V 



To find the value of the correction T, let abed, Fig. 3, be a section 

 of the reticule plate, and let efhe a. ray of light incident upon it in 



the plane of the paper. If this ray 

 suffered no refraction, it would emerge 

 from the plate at g ; but, owing to 

 refraction, it actually does emerge at 

 h, after which its path is parallel to 

 ef produced. At k erect a perpen- 

 dicular to be. It will be intersected 

 at i by ef produced, and the distance 

 hi will be the required value of T. 

 Let t be the thickness of the glass 

 composing the reticule plate ; n its 

 index of refraction ; and i the angle 

 of incidence of the ray ef. 'Then 



