72 ACHROMATISM OF EYE-PIECES 



Again, we have the simply geometrical relation 



or 



The advantage gained by introducing y n is, that we thus have 

 precisely similar equations for the optical and geometrical con- 

 ditions of the problem. Nothing is now easier than by suc- 

 cessive substitutions to determine the value of y n in terms of y 

 and z, and y n is the tangent of the " visual angle," which we 

 are seeking. As an instance, let it be proposed to determine 

 the conditions of achromatism in a system of three lenses. Mr 

 Airy has done this only for rays originally parallel to the axis : 

 the method here proposed applies with equal facility to the 

 general case. 



The equations required are these, 



Hence 



i/> J yi 



Taking the chromatic variations of the two terms in the 

 usual way, and equating each to zero, we find 



S = 



= 0. 



The first of these equations becomes unnecessary in the par- 

 ticular case considered by Mr Airy, viz. that in which y t = 0; 

 the second is identical with that given by him at p. 245, when 

 attention is paid to the signs. Taken together they determine 



