Refraction for Electric Waves. 



197 



of the composition of waves. This integral I have not been 

 able to treat, so I have attempted to obtain empirically the 

 coefficients c with sufficient approximation for the problem 

 under consideration. 



With the oscillator at various distances from the resonator 

 (r, in the following table) relative intensities at the resonator 

 were measured by the relative deflexions of the instrument. 

 These are placed in the second column of the table. The 

 square-roots of the relative intensities give f[r)ff(a) 9 which 

 are placed in the third column of the table. Equations were 

 then formed on the assumption that terms of f(r) after the 

 fourth vanish, and four coefficients obtained. They are 



c 1 =2'75, c 2 =-2-51, c 3 =l-92, c 4 =-*83. 



With these values of the coefficients, f(r)/f(a) is calculated 

 for the several values of r, and placed for comparison in the 

 fourth column of the table. 



r. 



I/I obs. 



f(r)/f(a)obs. 



A r )tf(fl) calc. 

 1-27 



13 



1-93 



1-39 



16-5 



1-23 



1-11 



1-11 



18 



100 



1-00 



101 



20-o 



•86 



•93 



•92 



23 



•69 



•82 



•86 



25-5 



•62 



•79 



•79 



28 



•51 



•71 



•74 



30-5 



•47 



•69 



•66 



33 



•46 



•68 



•65 



It is seen that within the range actually employed in the 

 experiments on indices of refraction (r=18 to r = 30), the 

 agreement between the observed and calculated values of 

 f{r)lf{a) is close enough to show that no large terms in the 

 series occur after the fourth. 



Employing these experimental values of the c's we can 

 form an estimate of the size of A and B for any value of r. 

 For example, when r=18, 



A=- 



X^ J L l-53-l-r)6 + l-00--32 

 2tt , 1o' l'53-*78 + -34--08~ 



4-4 1 ()5 



frli " 18 ' 100* 



Forr = 33, 



A= ^ 1 -83--46 + 1-65--024 

 ~ 27r , 33'83--23 + -055--00b' 



For both these values of r, and for all intermediate 



4-4 1 -511 

 (r28'33'-(5yy 



