454 
PROFESSOR STOKES ON THE COMMUNICATION OE VIBRATION 
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 2 re 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„ for the functions F n (c) of the first five orders, for each of the values 4, 2, 1, 
and -j- of me. 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 significant 
figures at least are retained. 
me. 
n= 0. 
n= 1. 
n = 2. 
n= 3. 
n= 4. 
4 
17 
16-25 
14-879 
13-848 
20-177 
2 
5 
5 
9-3125 
80 
1495-8 
=tH 
1 
2 
5 
89 
3965 
300137 
<D 
0-5 
1-25 
16-25 
1330-2 
236191 
72086371 
Js 
0-25 
1-0625 
64-062 
20878 
14837899 
18160 x 10 6 
£ 
4 
1 
0-95588 
0-87523 
0-81459 
1-1869 
2 
1 
1 
1-8625 
16 
299-16 
1 
1 
2-5 
44-5 
1982-5 
150068 
0 
0*5 
1 
13 
1064-2 
188953 
57669097 
0*25 
1 
60-294 
19650 
13965 x10 s 
17092 xio 6 
c3 
>■ 
When me = co we get from the analytical expressions I n =l. We see from the Table 
that when me is somewhat large I n is liable to be a little less than 1, and consequently the 
sound to be a little more intense than if lateral motion had been prevented. The pos- 
sibility of this is explained by considering that the waves of condensation spreading from 
those compartments of the sphere which at a given moment are vibrating positively, i. e. 
outwards, after the lapse of a half period may have spread over the neighbouring com- 
partments, which are now in their turn vibrating positively, so that these latter com-, 
partments in their outward motion work against a somewhat greater pressure than if 
each compartment had opposite to it only the vibration of the gas which it had itself 
occasioned ; and the same explanation applies mutatis mutandis to the waves of rare- 
faction. However, the increase of sound thus occasioned by the existence of lateral 
motion is but small in any case, whereas when me is somewhat small I n increases enor- 
mously, and the sound becomes a mere nothing compared with what it would have been 
had lateral motion been prevented. 
The higher be the order of the function, the greater will be the number of com- 
partments, alternately positive and negative as to their mode of vibration at a given 
moment, into which the surface of the sphere will be divided. We see from the Table 
that for a given periodic time as well as radius the value of I n becomes considerable 
when n is somewhat high. However practically vibrations of this kind are produced 
when the elastic sphere executes, not its principal, but one of its subordinate vibra- 
tions, the pitch corresponding to which rises with the order of the vibration, so that to 
increases with that order. It was for this reason that the Table was extended from 
