152 Lord Rayleigh's Acoustical Observations. 



be situated at the surface of a sphere whose circumference 

 is moderate in comparison with the wave-length, the phase 

 (which is the element on which the phenomena under con- 

 sideration principally depend) at a distance is approximately 

 the same as if the source were moved outward from the surface 

 through a distance equal to half the radius, and the sphere 

 were removed altogether. By the theorem of reciprocity, 

 § 294, it follows that in the case of reflection of plane waves 

 there is a silence at the point on the surface of the sphere 

 nearest the wall when, not this point itself, but another fur- 

 ther from the centre by half the radius, is distant from the 

 wall by an odd multiple of the quarter wave-length, provided 

 that the distance between the sphere and wall be not too small 

 a multiple of the radius. Instead therefore of adding with 

 Savart 27 mm., or 77 mm., to the observed distances in the 

 expectation of so arriving at even multiples of the quarter 

 wave-length, we ought rather to subtract some such distance 

 as 50 mm. in the expectation of arriving at odd multiples of 

 the same quantity. 



The following are some of Savart's results given in the 

 first paper : — 



Designations des divers Distances des points 

 points. a la paroi. 



Paroi. 

 I 1 ' ventre. 

 I 1 ' noeud. 

 2 e ventre. 

 2 e noeud. 

 3 e ventre. 

 3 e noeud. 

 4 e ventre. 

 4 e noeud. 



metres. 



o-ooo 



•148 

 •373 

 •716 

 1-000 

 1-358 

 1-615 

 1-997 

 2-275 



If we subtract 27 + 50 ( = 77) from Savart's numbers for 

 nodes we get 



•296, -923, 1-538, 2-198, 



corresponding to 



| (-619), J (-619,) i*(-619), |(619), 

 or to 



•309, -927, 1-546, 2-163; 



•619 being the value of the half-wave (onde). The " ventre " 

 between the wall and the first node does not belong to the 

 regular system at all. 



From a theoretical point of view, it appeared to me highly 

 improbable that the silences for the two ears should occur in 

 the same position of the head, except perhaps in the case of a 



