122 



IF", for the change of L the first or principal coefficient of aber- 

 ration, 



Iir", for the change of i-i the coefficient of the fourth power of the 

 sine of the angular aberration, in the expresssion of the longitu- 

 dinal, 



u, f2L.—5L , 3Z.« , ,\ , o . H- /— 2i , \ 



z being the ordinate of the point of central incidence. With respect 

 to the present meaning of the sign A, we may remark, that the 

 first of the three equations (C'") (D"'_) (-E'") is equivalent to the 

 following : 



and the two others are to be similarly interpreted. 



Example ; Spheric Refraction ; Mr. HerscheVs Formula for Aberration 



of a thin Lens. 



11. These general equations for refracting surfaces of revolu- 

 tion may be adapted to the case of a refracting spheric surface, by 

 making '. 



