from a Vibrating Body to a surrounding Gas. 409 



alteration of intensity at a distance, produced by the lateral mo- 

 tion which actually exists. 



The intensity will be measured by the vis viva produced in a 

 given time, and consequently will vary as the density multiplied 

 by the velocity of propagation multiplied by the square of the 

 amplitude of vibration. It is the last factor alone that is dif- 

 ferent from what it would have been if there had been no lateral 

 motion. The amplitude is altered in the proportion of /x to fi n ; 

 so that if 



I n is the quantity by which the intensity which would have ex- 

 isted if the fluid had been hindered from lateral motion has to 

 be divided. 



For the first five orders the values of the function F n (c) are as 

 follows : — 



F (c)=«mc+ lj 



~FAc) = imc+ 2 + . > 

 lv ' nnc 



9 9 



F 2 (c) = fmc+ 4+ -r— + 



imc (imc)' 



■o / \ • . » 27 60 60 



imc [imcy [imc) a 



„ , x . _ _ 65 240 525 525 



zmc {imc) z (imc)* [imc)* 



If \ be the length of the sound-wave corresponding to the 



2-7T 



period of the vibration, m— — - ; so that jwc is the ratio of the cir- 



cumference of the sphere to the length of a wave. If we suppose 

 the gas to be air and X to be 2 feet, which would correspond to 

 about 550 vibrations in a second, and the circumference 2ttc to 

 be 1 foot (a size and pitch which would correspond with the case 

 of a common house bell), we shall have mc=^. The following 

 Table gives the values of the square of the modulus and of the 

 ratio I /t for the functions F„(c) of the first five orders, for each of 

 the values 4, 2, 1, ^, and l of mc. It will presently appear why 

 the Table has been extended further in the direction of values 

 greater than ^ than it has in the opposite direction. Five sig- 

 nificant figures at least are retained. 



