50 Professor Airy on the Spherical Aberration 



169 



'/\ 4 224 



■^ 1 = - m = m. 



9 504 



' 16m V 7 / 16m V 7 / 504 



And ^(^^ =^«» = 

 Vn/ 9 



1st. The equation 



2(n + i2({)=0 



becomes here 



loOT V 7 '^ lorn V 7 ^ 108 



This may be satisfied in an infinite number of ways. Indeed, we 

 may give to 2 {F") any value not less than 



_il9„, or-i^2(/). or - ^ 2 (A nearly, 

 504 224 Vm/' 4 Vn/ '' 



and may, therefore, give to the area of diffusion any of the forms 

 represented in Fig. 6, beginning at the fifth, and continued in- 

 definitely. Of these (as before) we prefer that corresponding to 



or to some smaller negative value. Suppose, then, 



^tl^\ 221 



' 1008 



This gives (« + - m) "*" C'"' ~ 7 "0 ~ ~ '""' 



This may be satisfied (for example) by assumin, 



to 



5 3 5 2 



v+-m=-m, v' - -m = - -m: 



