﻿434 Lord Rayleigh on ^Eolian Tones. 



between the frequency of vibration (N) and these data was 

 expressible by 



N=-185V/D, (1)* 



the centimetre and the second being units. 



When the speed is such that the seolian tone coincides 

 with one of the proper tones of the wire, supported so as to 

 be capable of free independent vibration, the sound is greatly 

 reinforced, and with this advantage Strouhal found it pos- 

 sible to extend the range of his observations. Under the 

 more extreme conditions then practicable the observed pitch 

 deviated considerably from the value given by (1). He 

 further showed that with a given diameter and a given speed 

 a rise of temperature was attended by a fall in pitch. 



If, as appears probable, the compressibility of the fluid 

 may be left out of account, we may regard N as a function 

 of the relative velocity V, D, and v the kinematic coefficient 

 of viscosity. In this case N is necessarily of the form 



N=V/D./(v/VD), (2) 



where /represents an arbitrary function; and there is dyna- 

 mical similarity, if v oc VD. In observations upon air at one 

 temperature v is constant ; and if D vary inversely as V, 

 ND/V should be constant, a result fairly in harmony with 

 the observations of Strouhal. Again, if the temperature 

 rises, v increases, and in order to accord with observation, 

 we must suppose that the function / diminishes with in- 

 creasing argument. 



"An examination of the actual values in StrouhaPs experi- 

 ments shows that vjVD was always small ; and we are thus 

 led to represent /by a few terms of MacLaurin's series. If 

 we take 



/(#) = a + ox + ex 2 , 

 we get 



V v v 1 



N=a D +& F2 + C — .... (3) 



" If the third term in (3) may be neglected, the relation 

 between N and V is linear. This law was formulated by 

 Strouhal, and his diagrams show that the coefficient b is 

 negative, as is also required to express the observed effect of 

 a rise of temperature. Further, 



B dV =a ~YW W 



* In (1) V is the velocity of the wire relatively to the walls of the 

 laboratorv. 



