1876.] the Principle of Reciprocity to Acoustics. 



119 



this view a sound is ordinarily heard better with the wind than against 

 it, in consequence of a curvature of the rays. With the wind a ray will 

 generally be bent downwards, since the ^s-elocity of the air is generally 

 greater overhead than at the surface, and therefore the upper part of 

 the wave-front tends to gain on the lower. The ray which ultimately 

 reaches the observer is one which started in some degree upwards from 

 the source, and has the advantage of being out of the way of obstacles 

 for the greater part of its course. Against the wind, on the other hand, 

 the curvature of the rays is upwards, so that a would-be observer at a 

 considerable distance is in danger of being left in a sound-shadow. 



It is very important to remark that this effect depends, not upon the 

 mere existence of a wind, but upon the velocity of the wind being greater 

 overhead than below. A uniform translation of the entire atmosphere 

 would be almost without effect. In particular cases it may happen that 

 the velocity of the wind diminishes with height, and then sound is best 

 transmitted against the wind. Prof. Henry shows that several anoma- 

 lous phenomena relating to the audibility of signals may be explained by 

 various suppositions as to the velocity of the wind at different heights. 

 "When the distances concerned are great, comparatively small cur^ atures 

 of the ray may produce considerable results. 



There is a further possible consequence of the action of wind (or 

 variable temperature), which, so far as I know, has not hitherto been 

 remarked. By making the velocity a suitable function of height it M ould 

 be possible to secure an actual convergence of rays in a vertical plane 

 upon a particular station. The atmosphere would then act like the lens 

 of a lighthouse, and the intensity of sound might be altogether abnormal. 

 This may perhaps be the explanation of the extraordinary distances at 

 which guns have sometimes been heard. 



The difference in the propagation of sound against and with the wind 

 is no exception to the general law referred to at the beginning of this 

 communication, for that law applies only to the vibrations of a system 

 about a configuration of equilibrium. A motion of the medium is thus 

 excluded. But the bending of the sound-ray due to a variable tempera- 

 ture, to which attention has been drawn by Prof. Reynolds, does not 

 interfere with the application of the law. 



An experiment has, however, been brought forward by Prof. Tyndall, 

 m which there is an apparent failure of reciprocity not referable to any 

 motion of the medium*. The source of sound is a very high-pitched 

 reed mounted in a short tube and blown from a small bellows with 

 which it is connected by rubber tubing. The variation of pressure at 

 the second point is made apparent by means of the sensitive flame, which 

 has been used by Prof. Tyndall with so much success on other occasions. 

 Although the flame itself, when unexcited, is 18 to 24 inches high, it was 



* Proceedings of the Royal Institution, January 1875 ; also Prof. TyndaU's work 

 on Sound, 3rd edition. 



