of the Principle of Reciprocity to Acoustics. 301 



In experiments having for their object the comparison of sounds 

 heard under different circumstances there is one necessary pre- 

 caution to which it may not be superfluous to allude, depending on 

 the fact that the audibility of a particular sound depends not only 

 upon the strength of that sound, but also upon the strength of 

 other sounds which may be heard along with it. For example, a 

 lady seated iu a closed carriage and carrying on a conversation 

 through an open window in a crowded thoroughfare will hear what 

 is said to her far more easily than she can make herself heard in re- 

 turn ; but this is no failure in the law of reciprocity. 



The explanation of his observations given by Henry depends 

 upon the peculiar action of wind, first explained by Prof. Stokes. 

 According to 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 

 velocity of the air is generally greater overhead than at the sur- 

 face, 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 anomalous 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 curvatures 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 would be possible to secure an actual convergence of 

 rays in a vertical plane upon a particular station. The atmo- 

 sphere 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 be- 

 ginning 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 temperature, to which attention has 



