the Refraction of Sound by the Atmosphere, 65 



pending on the wave-length of the sound ; but as the sound pro- 

 ceeds further the diverging rays would gradually become fainter 

 and more nearly parallel to the direct rays, until at a sufficient 

 distance they would practically cease to exist, or, at any rate, be 

 no greater than those which cause the diffraction-bands in a pencil 

 of light*. The divergence would introduce bands of diffraction or 

 interference within the direct or geometrical path of the sound, as 

 in the case of light. These effects would also be complicated by 

 the reflection of the diverging waves from the ground, which, cross- 

 ing the others at a small angle, would also cause bands of inter- 

 ference. The results of all these causes would be very complicated, 

 but their general effect would be to cause a rapid weakening of 

 the sound at the ground- from the point at which it was first 

 lifted ; and as the sound became weaker it would be crossed by 

 bands of still fainter sound, after which the diverging rays, as well 

 as the direct rays, would be lifted, and at the ground nothing would 

 be heard. — September 1874.] 



If we leave out of consideration the divergence, then we may 

 form some idea as to the path which the bottom of the sound, or 

 the rays of sound (considered as the rays of light), would follow. 

 If the variation in the speed of the wind were uniform from the 

 surface upwards, then the rays of sound would at first move up- 

 wards, very nearly in circles. The radii of these circles may be 



shown to be 1100 x , where v, and v 9 are the velocities of the 



wind in feet per second at elevations differing by h feet. In fact, 

 however, the variation is greatest at the ground, and diminishes 

 as we proceed upwards, so that the actual path would be more that 

 of a parabola. 



Also, owing to this unequal variation in the velocity, those parts 

 of the waves immediately adjacent to the ground will rise more 

 rapidly than the part immediately above them ; hence there will be 

 a crowding of the waves at a few feet from the ground, and this 

 will lead to an intensifying of the sound at this point. Hence, 

 notwithstanding the divergence, we might expect the waves to 

 windward to preserve their full intensity so long as they were low 

 enough to be heard. And this is in accordance with the fact, 

 often observed, that sounds at short distances are not diminished 

 but rather intensified when proceeding against the wind. 



It will at once be perceived that by this action of the wind the 

 distance to which sounds can be heard to windward must depend 

 on the elevation of the observer and the sound-producing body. 

 This does not appear to be a fact of general observation. It is diffi- 

 cult to conceive how it can have been overlooked, except that, in nine 

 v^ses out of ten, sounds are not continuous, and thus do not afford 

 an opportunity of comparing their distinctness at different places. 

 It has often astonished me, however, when shooting, that a wind 



* Taking sound of 1 foot wave-length, and comparing it with light whose 

 wave-length is the 50,000th part of an inch, then the divergence of the sound at 

 a mile from the point at which it left the ground would be comparatively the 

 same as that of the light at T V of an inch from the aperture at which the pencil 

 was formed. 



Phil. Mag. S. 4, Vol, 50. No. 328. July 1875. F 



