124 



cient of aberration. Adding the two equations (L'"), the interme- 

 diate coefficient L' disappears, and we find, 



"— A"* A* U'" Ay ^ A" U' ~/ 



~" (7:4^ ~ 7A') +<'* — ') (75-— 75J' 



in which, by (K'"), 



A' - IJ.A ~ ij.r ' Jr' - A '^ ''^ '\r' ~ r/' 



and therefore, 



N^-#=(^')(^-|)(«+^+^) 



if we put for abridgment 



Mio) = 4 4- _L+^JiiL + li 



— 2/^ + ft» 



•yr 



r' r 



M(2) = H 3 , 



(M'") 



(N'") 



.in 



I (P'") 



It is easy to see that the formula (0'") agrees with the expression 

 for the spherical aberration of an infinitely thin lens, which Mr. 

 Herschel has deduced by reasonings of a different kind, in his Me- 

 moir "On Aberrations of Compound Lenses and Object-glasses," pub- 

 lished in the second part of the Philosophical Transactions for the 

 year 1821 ; and in his excellent " Treatise on Light," published in 

 the Encyclopadia Metropolitana. 



