204 Lord Rayleigh on Achromatic 



Wh6re __ «o-*ti,\). ...... (45) 



The condition for an achromatic band at f , X is 



# = ; (46) 



and, further, the condition for an achromatic system at this 

 place is 



.. &-"■ •. «"> 



If these conditions are both satisfied, n becomes very 

 approximately a function of £ only throughout the region in 

 question. 



In several cases considered in the present paper, the func- 

 tional relation is such that 



n = £.f(\), _. (48) 



ty(X) denoting a function of X only. The expansion may 

 then be written 



^-«o=f{fN+fN^H|fWW 2 + ...}. (49) 



The line f =0 is here of necessity perfectly achromatic. If 

 there be an achromatic system, 



Y(\>) =0; 

 and when this condition is satisfied, the whole field is achro- 

 matic, so long as (S\) 2 can be neglected. 



If the width of the bands be a function of \ only, n is of 



th6fOTm n = t. m+x <S), (50) 



more general than that just considered (48), though of course 

 less general than (43). The condition for an achromatic 

 line is 



~=^'(K)+^(\) = o, . . . (51) 



and for an achromatic system, 

 d 2 n 

 d%d\ 



so that, for an achromatic system, ty and tf must both 

 vanish. 



Curved Interference-Bands. 



If the bands are not straight, n must be regarded as a 

 function of a second coordinate rj, as well as of f and \. 

 In the equation 



n.= 0(ftifc--Xj, ...... (53) 



= ^(\ )=0; (52) 



