20 Professor Airy on the Spherical Aberration 



3d. If the second lens be plano-convex, its convex side towards 



2 a* 



the first, /i'=-^,.,0694. If equi-convex, ij'= - ^, . ,0488. 

 If plano-convex, its plane side towards the first lens, 

 /J' =-^,,0329. 

 4th. If the third lens be plano-convex, its convex side towards 

 the second, R' = - ^.,1836. If equi-convex, R" = - j^.,1639. 

 If plano-convex, its plane side towards the second lens, 



R"=-~..Am. 



5th. If the fourth lens be plano-convex, its convex side towards 



2 



the third, ii"'= -^.,0849. If equi-convex, i?'" = -^ . ,1459. 

 If plano-convex in the other position, i?"' = -^.,2885. 



6th. The most favourable combination of these is, if ail the 

 lenses be plano-convex, the first, third, and fourth, having their 

 convexities towards the object-glass, and the second its plane side 

 turned the same way ; they give 



R + R'+R"+R"'=-^.,OOOQ. 



The next is, if the first and second be plano-convex, with their plane 

 sides towards the object-glass, the third equi-convex, and the fourth 

 • plano-convex, with its convexity towards the object-glass : they give 



R + R' + R" + R"= ~ ,0010. 



The next is, if all the lenses be equi-convex, which makes 



U + ii' -h ^" -t- /2"' = - -^ . ,0024. 



