SNKI.I, S I. WV 



225 



tto sin 0o = /fi sin j3'„ , 

 «i sin /3i = »2 sin (3'i , etc. 



Multiply the first equation by r , the second by n, 

 etc. Then 



Wo sin /3 = Wo sin /3' , 

 /d''i sin |3i = n 2 fi sin /3'i, etc. 



But from the triangle OAB 



sin /3'n sin /3 



''i 



?'o 



- , etc. , 



so that : 



7i r sin f} = mri sin /3i = n 2 '"2 sin /3 2 = ■ • ■ . 



Again introducing the angle a with the horizontal 

 and making the transition to a continuously variable 

 refractive index gives 



nr cos a = n r cos ao , 



which is the generalization of SnelPs law for a curved 

 earth. r may be chosen as any convenient height, 

 say a for the surface of the earth or a + hi for the 

 height of the transmitter, and n is the corresponding 

 value of n. 



