10 Professor Airy on the Spherical Aberration 



whence (since B = F), 



c' = F'-^{b-B)-''^.F"-iP+Pr 



Hence, b" - B" ^y\\\ = ^ {h- B) +^^.F- {P+P'). 

 ^o'ain F'H' = GK- -a= (putting for GK tlie value found before) 



' b > c 



Hence, (as before) 



_ :^^{^+l\^±(L+L')-p]£--Lth-B)a. 



= " ^ IJe Vr + S/ ' A'Vr' ^ s'>' 3 2 F' ^ ^ 



Now, the tangent of the angle made with the axis after refraction at the second 

 lens, is ev"^, : that before incidence, is 



FH g 



AH 



F+b-B + ^ 

 2r 



Dividin"- the former by the latter, the proportion required, after all sub- 



F 



stitutions, is p(l + Q,)> where 



i^F-P' 



p. {b-B). 



