102 



Mr. E. A. Milne 



Let (fig. 1) be the position of the observer, T (X, Y, Z) 

 the source of sound, and let OT' be the observed direction of 



Fiar. 1. 



the source, i. e. the normal to the wave-fronts as they reach 0. 

 Take horizontal and vertical axes Chi', Oz in the vertical 

 plane through OT'. Let N, T r be the projection of T on y Ox 

 and z Ox. We require to calculate the correction to the 

 observed azimuth, the angle N'ON (S(f>, say), and the cor- 

 rection to the observed elevation, the angle T'OT x (8E, 

 say). Let TT(,e), W(V) be the components of wind velocity 

 at height z, a(z) the velocity of sound. Call- 9 the angle 

 which the normal at any point makes with the horizontal, 

 measured positive downwards. Since the normal at O is in 

 the plane zOx, it is always parallel to this plane by §4 , 

 and so 



?=— cos#, m = 0, n— — sin (9, 



and the equations of the ray which goes from T to are 

 J = -aG~)cos0 + W(4 



!=W<(*), 



dz 



dt 



= — a(z) sin 6, 



(16) 



(17) 

 (18) 



together with the refraction equation 



a(z) sec 6— a sec # = W(V) — TY 

 the suffix referring to the ground values. 



(19) 



