118 



Lord Rayleigli on the Application of 



[June 15_, 



VI. ^^On tlie Application of the Principle o£ Reciprocity to 

 Acoustics/^ Ey Lord Eayleigh^ F.R.S. Eeceived May 27^ 

 1876. 



In a memoir published some years ago by Helmholtz (Crelle, Bd. Ivii.) 

 it was proA^ed that if a uniform frictionless gaseous medium be thrown 

 into vibration by a simple source of sound of given period and intensity, 

 the variation of pressure is the same at any point B when the source of 

 sound is at A as it would have been at A had the source of sound been 

 situated at B, and that this law is not interfered with by the presence 

 of any number of fixed solid obstacles on which the sound may impinge. 



A simple source of sound is a point at which the condition of con- 

 tinuity of the fluid is broken by an alternate introduction and abstrac- 

 tion of fluid, given in amount and periodic according to the harmonic 

 law. 



The reciprocal property is capable of generalization so as to apply to 

 all acoustical systems whatever capable of vibratiug about a configuration 

 of equilibrium, as I proved in the Proceedings of the Mathematical 

 Society for June 1873, and is not lost even when the systems are subject 

 to damping, provided that the frictional forces vary as the first power of 

 the velocity, as must al^^ays be the case when the motion is small enough. 

 Thus Helmholtz's theorem may be extended to the case when the medium 

 is not uniform, and when the obstacles are of such a character that they 

 share the vibration. 



But although the principle of reciprocity appears to be firmly grounded 

 on the theoretical side, instances are not uncommon in which a sound 

 generated in the open air at a point A is heard at a distant point B, 

 when an equal or even more powerful sound at B fails to make itself 

 heard at A ; and some phenomena of this kind are strongly insisted 

 upon by Prof. Henry in opposition to Prof. Tyndall's views as to the 

 importance of "acoustic clouds" in relation, to the audibility of fog- 

 signals. These observations M^ere not, indeed, made with the simple sono- 

 rous sources of theory ; but there is no reason to suppose that the re- 

 sult would have been different if simple sources could have been used. 



In experiments having for their object the comparison of sounds heard 

 under different circumstances there is one necessary precaution to which 

 it may not be superfluous to allude, depending on the fact that the au- 

 dibility 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. Por example, a lady seated iu a closed carriage and carry- 

 rug on a conversation through an open window in a crowded thorough- 

 fare will hear what is said to her far more easily than she can make herself 

 heard in return ; 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 



