1870.] Hon. J. W. Stratt on the Theory of Resonance. 107 



This supposes the neck a circular cylinder. If the section be an ap- 

 proximate circle of area <r, we may put 



I-IuA A 



When the neck is very long the second term may be neglected, and 

 when L is very small the first term becomes insignificant. In the third 

 part experiments are described which were instituted to compare the 

 general formula with observation, and which gave a satisfactory agreement. 



The value given above for - is only approximate. It is proved, however, 



that the resistance of a finite cylindrical conductor whose plane ends lie in 

 two infinite insulating planes, but join on to conducting masses on the 

 further side, corresponds to a length L + a of the cylinder, where 



. on(fcT , 10-615-e _8 R 

 a< 2-305 R r 



14771 _ e - 8 R 



>1B. 



As a particular case, it appears that the correction to the length of an 

 organ-pipe, supposed, as in Helmholtz's paper, to be surrounded at the 

 mouth by a wide flange, lies between */85 R and "8282 R. 



Approximate formulae are investigated for the resistance of tubes which 

 are not exact circular cylinders. It will be sufficient to particularize here 

 the case of tubes of revolution. The resistance is shown to lie between the 

 two limits 



1 Cdx 



and 



where y denotes the radius of the tube at the point x. 



When there is more than one vessel in the vibrating system, there are 

 several independent periods of vibration corresponding to the degrees of 

 freedom. The theory of these vibrations is also considered. 



In the experimental part of the investigation the object is to determine 

 with sufficient precision the pitch of the resonant note. This is generally 

 done by causing the resonator to speak. For several reasons, which are 

 detailed, I consider this course unsatisfactory, and have availed myself of 

 other indications to fix the pitch, which are not, indeed, capable of so great 

 an apparent precision, but yet are more to be depended on. 



