Refraction of Sound by Wind. 



165 



coordinates start down-wind and in the same vertical plane, 

 and with 



(1) its wave-front initially inclined at 60° to the hori- 

 zontal. Then it suffers total reflexion at a point about 

 1547 feet higher than the origin, and at a horizontal distance 

 of about 6195 feet to leeward of it. The intermediate inclina- 

 tions of wave-fronts and rays are given in the accompanying 

 table, and graphically exhibited by curve A A of fig. 3, in which 

 the numerals along the axes denote thousands of feet. 

 Table of Inclinations of Waves and Rays. 



Coordinates. 



Inclination of 



Inclination 



Angle between 







Wave-front to 

 the Horizontal. 



of Bay to 



the Vertical. 



Ray and Normal 

 to Wave-front. 







X. 



y- 



9. 



f. 



0-0. 



ft. 



ft. 







, 











m 



60 34 



34 



1005 



500 



64 51 



66 27 



1 36 



2383 



1000 



71 28 



73 26 



1 58 



3359 



1250 



76 12 



77 56 



1 44 



5059 



1500 



84 27 



85 15 



48 



6195 



1547 



90 



90 







Fig-. 3. — Continuous Refraction of Sound by Wind. 



(2) Let sound start from the origin, with its wave-front 

 horizontal, then the curve BB (fig. 3) represents the parabolic 

 path described by the ray, the wave-front remaining hori- 

 zontal throughout. But although the wave-front is never 

 refracted, the ray at a height of 3000 feet has drifted more 

 than 500 feet to leeward. It would, however, never suffer 

 total reflexion, but would asymptote to the horizontal at an in- 

 finite height, the ray and the wave-front tending to coincide. 

 Rays intermediate between A A and BB would suffer total 

 reflexion at greater heights than 1547 feet, and rays below 

 A A at less heights. 



University College, Nottingham, Aug. 22, 1900. 



