^ Professor Airy on the Spherical Aberration 



tI^(U+U'+U" + U"'). 

 In this form the diffusion can be numerically calculated. 



In the same manner, putting 17 for a, and Y for U, we find, for the 

 apparent extent of the diffusion in the paper-plane, 



Pj[^ (^Y + Y' + Y"+Y"'). 



Hence, the appearance presented by a point is an ellipse, the apparent 

 angular extents of whose axes are respectively 



HM. (U+U'+U"+U"'), and ^^ ( Y + Y' + Y" + Y'"), 

 and of which the real angular extents are, therefore, 



^^{U), and:^2(Y). 

 These we shall call k and «. 



1st. Since U = "^ + F, and Y= "i + 3 F, we have 

 n n 



3f/-Y-^, 

 n 



a constant depending only on the focal length of the lens. A similar 

 equation is true for every lens : adding all 



3 2((/)-2(Y) = 2(^). 



TQ3 



Multiplying by — , 



3k - K = i^^ (/). 



