Refraction of Sound by the Atmosphere . 535 



the rays of sound would at first move upwards, very nearly in circles. 

 The radii of these circles may be shown to be 1100 x - , where 



v l and v 2 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 dis- 

 tance 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 difficult to conceive how 

 it can have been overlooked, except that, in nine cases 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, how- 

 ever, when shooting, that a wind which did not appear to me to make 

 the least difference to the direction in which I could hear small sounds 

 most distinctly, should yet be sufficient to cover one's approach to par- 

 tridges, and more particularly to rabbits, even until one was within a few 

 feet of them a fact which shows how much more effectively the wind 

 obstructs sound near the ground than even a few feet above it. 



Elevation, however, clearly offered a crucial test whether such an action 

 as that I have described was the cause of the effect of wind upon sound. 

 Having once entertained the idea, it was clearly possible to put it to 

 the test in this way. Also, if the principles hold in sound, something 

 analogous must hold in the case of waves on the surface of a running 

 stream of water for instance, waves made near the bank of a river. 



I had just reached the point of making such tests when I discovered 

 that the same views had been propounded by Professor Stokes so long 

 ago as 1857*. Of course, after such a discovery, it seemed almost un- 

 necessary for me to pursue the matter further ; but as there were one 

 or two points about which I was not then quite certain, and as Prof. 

 Stokes's paper does not appear to be so well known as it might be (I 

 do not know of one writer on sound who has adopted this explanation), 

 it still seemed that it might be well, if possible, to put the subject 

 on an experimental basis. I therefore made the experiments I am 

 * Brit. Assoc. Eeport, 1857, Trans, of Sect. p. 22. 



