194 Mr. G. Pierce on Indices of 



The amplitude of the first maximum enables us to determine 

 k. For x ■=■ ~ 



1 = (l + P + 2k).f(a) 

 = (1 + h) 2 ./ (a) = of (a) (experiment). 



Whence (1 + *)»=' 3, 



k = -73. 



The square of this k is the coefficient of reflexion of copper 

 for norma! incidence. 



With this approximation, other maxima are seen to be at 

 <r = 3\/2, 5A./2, ....; and minima at x = \ 2\, 3\, .... 

 Hence the value of x that gives maxima and minima is 

 independent of k, and in the experiments on indices of 

 refraction, if observations are made on nodes and loops whoso 

 double distance from the oscillator can be neglected in com- 

 parison with a, absorption by the medium would not introduce 

 error into the value obtained for the index of refraction. 



Returning to the general case, let us solve equation (1) for 

 maxima and minima, by differentiating I with respect to x 

 and equating to zero. The derivative of f(r) with respect to 

 r is denoted by f'(r). 



D x I = P . 2f(a + x) . f(a + x) 



- 2k. f (a), f (a + x). cos —^ 



A, 



« » >./ \ // \ • 2ttx 2tt 



+ 2k ./(a) ./(a + x) . sin -^~~ . ~r~ 



0. 



Whence 

 sin 



2ttx X f f(a + z) 27Tzr _ f( a + x) \ 

 ~Y~-27r\f(a + x) GOS ~*r ' /(a) J 



which may be written briefly 



sin0 = Acos0-B, 



where 



A= \ , /'(a + .r ) ; 

 2it f (a + x)' 



tir* j\a) 



