110 Sig. Santini on Achromatic Telescopes. 



be ) d = — 0.003230 ; wherefore d = 0.663437. Recalcu- 

 lating the values of k by this corrected value of d, we obtain 

 the following results : — 



Mean rays. Red rays. 



k = 3.060000 A Ui = 0.0590609 k = 3.094550 A Ui = 0.0603006 



A» = 0.999673 A* = 0.1815420 ft = 1.016946 k" = 0.1828973 



A" = 0.1547307 h? = 0.317137 A u = 0.1580190 A* = 0.317921* 



Remaining aberration = 3.000016 



from which it results that the remaining chromatic aberration 

 may be neglected. 



For the purpose of determining the spherical aberration 

 which takes place in this system of lenses, with the superior 

 distance d corrected, we shall denote the angles of incidence 

 of a luminous ray which goes toward the extremity of the first 

 lens in successively refracting surfaces, by i, i\ if* • • i v ; the re- 

 fracted angles respectively by /, l'\ l' 1 ' 1 •• l v ; the inclinations of 

 the directions of the refracted ray to the axis, by o, o\ o u -« o v ; 

 the distances of the point of meeting from the respective re- 

 fracting surfaces by k, k\ & u -«& v . Then retaining the above 

 quantities for the size of the lenses, and in round numbers 

 regarding i = 2° 43', we shall find, 



* .This should be .317121.— Ed. 



